R/clases/1_introduccion/2_core_R.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Notas para contenedor de docker:**\n",
    "\n",
    "Comando de docker para ejecución de la nota de forma local:\n",
    "\n",
    "nota: cambiar `dir_montar` por la ruta de directorio que se desea mapear a `/datos` dentro del contenedor de docker.\n",
    "\n",
    "```\n",
    "dir_montar=<ruta completa de mi máquina a mi directorio>#aquí colocar la ruta al directorio a montar, por ejemplo: \n",
    "#dir_montar=/Users/erick/midirectorio.\n",
    "```\n",
    "\n",
    "Ejecutar:\n",
    "\n",
    "```\n",
    "VERSION=<versión imagen de docker>\n",
    "docker run --rm -v $dir_montar:/datos --name jupyterlab_prope_r_kernel_tidyverse -p 8888:8888 -d palmoreck/jupyterlab_prope_r_kernel_tidyverse:$VERSION\n",
    "\n",
    "```\n",
    "\n",
    "Ir a `localhost:8888` y escribir el password para jupyterlab: `qwerty`\n",
    "\n",
    "\n",
    "Detener el contenedor de docker:\n",
    "\n",
    "```\n",
    "docker stop jupyterlab_prope_r_kernel_tidyverse\n",
    "```\n",
    "\n",
    "Documentación de la imagen de docker `palmoreck/jupyterlab_prope_r_kernel_tidyverse:<versión imagen de docker>` en [liga](https://github.com/palmoreck/dockerfiles/tree/master/jupyterlab/prope_r_kernel_tidyverse)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para ejecución de la nota usar:\n",
    "\n",
    "[docker](https://www.docker.com/) (instalación de forma **local** con [Get docker](https://docs.docker.com/install/)) y ejecutar comandos que están al inicio de la nota de forma **local**. \n",
    "\n",
    "O bien dar click en alguno de los botones siguientes:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/palmoreck/dockerfiles-for-binder/jupyterlab_prope_r_kernel_tidyverse?urlpath=lab/tree/Propedeutico/R/clases/1_introduccion/2_core_R.ipynb) esta opción crea una máquina individual en un servidor de Google, clona el repositorio y permite la ejecución de los notebooks de jupyter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Run on Repl.it](https://repl.it/badge/github/palmoreck/dummy)](https://repl.it/languages/Rlang) esta opción no clona el repositorio, no ejecuta los notebooks de jupyter pero permite ejecución de instrucciones de Python de forma colaborativa con [repl.it](https://repl.it/). Al dar click se crearán nuevos ***repl*** debajo de sus users de ***repl.it***.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ejemplos y enunciados de diferentes libros"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## J. Albert & M. Rizzo, \"R by Example\", 2012."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El libro tiene github: https://github.com/mariarizzo/RbyExample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "options(repr.plot.width=7, repr.plot.height=7) #this line is not necessary to execute in R, is just\n",
    "                                               #to have a smaller plot because we're using the kernel of R\n",
    "                                               #in jupyterlab"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Valores, tipos, operadores aritméticos, variables, *print* y *assignment* statements en *R*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ejemplos de valores y tipos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2"
      ],
      "text/latex": [
       "2"
      ],
      "text/markdown": [
       "2"
      ],
      "text/plain": [
       "[1] 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "2L #es un número entero, la L le indica a R que se almacene como entero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'integer'"
      ],
      "text/latex": [
       "'integer'"
      ],
      "text/markdown": [
       "'integer'"
      ],
      "text/plain": [
       "[1] \"integer\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "typeof(2L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3"
      ],
      "text/latex": [
       "3"
      ],
      "text/markdown": [
       "3"
      ],
      "text/plain": [
       "[1] 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "3.0 #es un número en punto flotante "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'double'"
      ],
      "text/latex": [
       "'double'"
      ],
      "text/markdown": [
       "'double'"
      ],
      "text/plain": [
       "[1] \"double\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "typeof(3.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'double'"
      ],
      "text/latex": [
       "'double'"
      ],
      "text/markdown": [
       "'double'"
      ],
      "text/plain": [
       "[1] \"double\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "typeof(3) #observen que por default le asigna double"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'Hola mundo!'"
      ],
      "text/latex": [
       "'Hola mundo!'"
      ],
      "text/markdown": [
       "'Hola mundo!'"
      ],
      "text/plain": [
       "[1] \"Hola mundo!\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"Hola mundo!\" #es un tipo character"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'character'"
      ],
      "text/latex": [
       "'character'"
      ],
      "text/markdown": [
       "'character'"
      ],
      "text/plain": [
       "[1] \"character\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "typeof(\"Hola mundo!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'2'"
      ],
      "text/latex": [
       "'2'"
      ],
      "text/markdown": [
       "'2'"
      ],
      "text/plain": [
       "[1] \"2\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"2\" #es un character, en R no hacemos distinción con '2'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'2'"
      ],
      "text/latex": [
       "'2'"
      ],
      "text/markdown": [
       "'2'"
      ],
      "text/plain": [
       "[1] \"2\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'2'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'character'"
      ],
      "text/latex": [
       "'character'"
      ],
      "text/markdown": [
       "'character'"
      ],
      "text/plain": [
       "[1] \"character\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "typeof(\"2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'character'"
      ],
      "text/latex": [
       "'character'"
      ],
      "text/markdown": [
       "'character'"
      ],
      "text/plain": [
       "[1] \"character\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "typeof('2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ejemplos de operadores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "9"
      ],
      "text/latex": [
       "9"
      ],
      "text/markdown": [
       "9"
      ],
      "text/plain": [
       "[1] 9"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "4 + 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "6"
      ],
      "text/latex": [
       "6"
      ],
      "text/markdown": [
       "6"
      ],
      "text/plain": [
       "[1] 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "-3 + 9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "8"
      ],
      "text/latex": [
       "8"
      ],
      "text/markdown": [
       "8"
      ],
      "text/plain": [
       "[1] 8"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "2*4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.5"
      ],
      "text/latex": [
       "1.5"
      ],
      "text/markdown": [
       "1.5"
      ],
      "text/plain": [
       "[1] 1.5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "3/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "243"
      ],
      "text/latex": [
       "243"
      ],
      "text/markdown": [
       "243"
      ],
      "text/plain": [
       "[1] 243"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "3^5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## *Print statement*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Hola mundo!\"\n"
     ]
    }
   ],
   "source": [
    "print(\"Hola mundo!\") #imprime en pantalla"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 4\n"
     ]
    }
   ],
   "source": [
    "print(4.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.0"
     ]
    }
   ],
   "source": [
    "cat(sprintf(\"4.0\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## *Assignment statement*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creamos una variable y le damos un valor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "m <- \"Este mensaje es un string que almacenamos en la variable m, tal variable hace referencia a un valor de tipo string\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'Este mensaje es un string que almacenamos en la variable m, tal variable hace referencia a un valor de tipo string'"
      ],
      "text/latex": [
       "'Este mensaje es un string que almacenamos en la variable m, tal variable hace referencia a un valor de tipo string'"
      ],
      "text/markdown": [
       "'Este mensaje es un string que almacenamos en la variable m, tal variable hace referencia a un valor de tipo string'"
      ],
      "text/plain": [
       "[1] \"Este mensaje es un string que almacenamos en la variable m, tal variable hace referencia a un valor de tipo string\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 17 #variable que hace referencia a un dato tipo integer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "17"
      ],
      "text/latex": [
       "17"
      ],
      "text/markdown": [
       "17"
      ],
      "text/plain": [
       "[1] 17"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vectores"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[c](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/c) es una función que realiza un *combine*, crea un vector de sus argumentos que se almacena en `x`. Por ejemplo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "x <- c(-2, 109, 1, 0) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1]  -2 109   1   0\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Otras funciones que crean vectores las encontramos en el paquete de [stats](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/00Index.html) como [rpois](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/Poisson.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(2000)\n",
    "y <- rpois(200, lambda = .61)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  [1] 0 1 0 0 1 0 2 1 1 1 0 0 0 0 3 0 1 0 2 0 2 2 1 1 2 1 0 1 1 0 1 0 0 2 1 1 0\n",
      " [38] 2 0 0 1 0 0 0 1 0 1 0 1 2 0 1 0 1 0 0 0 1 2 0 0 1 0 0 0 1 0 1 0 0 0 0 1 1\n",
      " [75] 1 0 0 0 0 1 0 1 0 4 1 0 1 1 2 0 1 1 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0 2 0 0 1\n",
      "[112] 0 1 3 1 1 0 0 1 2 1 0 0 6 0 0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 2 0 0 0 1 0 0\n",
      "[149] 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 2 1 0 1 0 0 1 0 0 2 1 0 2\n",
      "[186] 0 0 0 1 2 1 0 1 0 0 0 0 1 0 0\n"
     ]
    }
   ],
   "source": [
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos hacer operaciones con los vectores, por ejemplo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1]  -6 105  -3  -4\n"
     ]
    }
   ],
   "source": [
    "print(x-4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1]  -8.000000 140.000000  -4.000000  -5.333333\n"
     ]
    }
   ],
   "source": [
    "print(4/3*(x-4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y realizar operaciones entre vectores como:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "x2 <- c(48.2, 11.05, -1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] -50.20  97.95   2.00   0.00\n"
     ]
    }
   ],
   "source": [
    "print(x-x2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Otra función para crear un vector de ceros en memoria es con la función [vector](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/vector):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "vec <- vector(\"double\", 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>0</li><li>0</li><li>0</li><li>0</li><li>0</li><li>0</li><li>0</li><li>0</li><li>0</li><li>0</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0\n",
       "2. 0\n",
       "3. 0\n",
       "4. 0\n",
       "5. 0\n",
       "6. 0\n",
       "7. 0\n",
       "8. 0\n",
       "9. 0\n",
       "10. 0\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 0 0 0 0 0 0 0 0 0 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejemplo: President's heights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An article in [Wikipedia](https://en.wikipedia.org/wiki/Heights_of_presidents_and_presidential_candidates_of_the_United_States) reports data on the heights of Presidents of the United States and the heights of their opponents in the presidential election. It has been observed ([reference](https://www.washingtonpost.com/?noredirect=on), [reference](https://usatoday30.usatoday.com/news/politicselections/nation/president/2004-06-23-bush-kerry-cover_x.htm)) that the taller presidential candidate typically wins the election. In this example, we explore the data corresponding to the elections in the television era. Next values are the heights of the presidents and their opponents in the U.S. presidential elections of 1948 through 2008, extracted from the Wikipedia article."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "winner <- c(185, 182, 182, 188, 188, 188, 185, 185, 177,\n",
    "            182, 182, 193, 183, 179, 179, 175)\n",
    "opponent <- c(175, 193, 185, 187, 188, 173, 180, 177, 183,\n",
    "              185, 180, 180, 182, 178, 178, 173)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "16"
      ],
      "text/latex": [
       "16"
      ],
      "text/markdown": [
       "16"
      ],
      "text/plain": [
       "[1] 16"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(winner)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using [seq](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/seq) function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "year <- seq(from=2008, to=1948, by=-4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to the [Washington Post blog](https://www.washingtonpost.com/?noredirect=on), Wikipedia misstates “Bill Clinton’s height, which was measured during official medical exams at 6 foot 2-1/2, making him just a tad taller than George H.W. Bush.” We can correct the height measurement for Bill Clinton by assigning a height of 189 cm to the fourth and fifth entries of the vector winner"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "winner[4:5] <- 189"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [1] 185 182 182 189 189 188 185 185 177 182 182 193 183 179 179 175\n"
     ]
    }
   ],
   "source": [
    "print(winner)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Are presidents taller than average adult males? According to the National Center for Health Statistics, in 2005 the average height for an adult male in the United States is 5 feet 9.2 inches or 175.768 cm. The sample mean is computed by the [mean](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/mean) function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "183.4375"
      ],
      "text/latex": [
       "183.4375"
      ],
      "text/markdown": [
       "183.4375"
      ],
      "text/plain": [
       "[1] 183.4375"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(winner)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "181.0625"
      ],
      "text/latex": [
       "181.0625"
      ],
      "text/markdown": [
       "181.0625"
      ],
      "text/plain": [
       "[1] 181.0625"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(opponent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "difference <- winner - opponent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [1]  10 -11  -3   2   1  15   5   8  -6  -3   2  13   1   1   1   2\n"
     ]
    }
   ],
   "source": [
    "print(difference)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An easy way to display our data is as a *data frame*, see [data.frame](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/data.frame):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 16 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>year</th><th scope=col>winner</th><th scope=col>opponent</th><th scope=col>difference</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>2008</td><td>185</td><td>175</td><td> 10</td></tr>\n",
       "\t<tr><td>2004</td><td>182</td><td>193</td><td>-11</td></tr>\n",
       "\t<tr><td>2000</td><td>182</td><td>185</td><td> -3</td></tr>\n",
       "\t<tr><td>1996</td><td>189</td><td>187</td><td>  2</td></tr>\n",
       "\t<tr><td>1992</td><td>189</td><td>188</td><td>  1</td></tr>\n",
       "\t<tr><td>1988</td><td>188</td><td>173</td><td> 15</td></tr>\n",
       "\t<tr><td>1984</td><td>185</td><td>180</td><td>  5</td></tr>\n",
       "\t<tr><td>1980</td><td>185</td><td>177</td><td>  8</td></tr>\n",
       "\t<tr><td>1976</td><td>177</td><td>183</td><td> -6</td></tr>\n",
       "\t<tr><td>1972</td><td>182</td><td>185</td><td> -3</td></tr>\n",
       "\t<tr><td>1968</td><td>182</td><td>180</td><td>  2</td></tr>\n",
       "\t<tr><td>1964</td><td>193</td><td>180</td><td> 13</td></tr>\n",
       "\t<tr><td>1960</td><td>183</td><td>182</td><td>  1</td></tr>\n",
       "\t<tr><td>1956</td><td>179</td><td>178</td><td>  1</td></tr>\n",
       "\t<tr><td>1952</td><td>179</td><td>178</td><td>  1</td></tr>\n",
       "\t<tr><td>1948</td><td>175</td><td>173</td><td>  2</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 16 × 4\n",
       "\\begin{tabular}{llll}\n",
       " year & winner & opponent & difference\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 2008 & 185 & 175 &  10\\\\\n",
       "\t 2004 & 182 & 193 & -11\\\\\n",
       "\t 2000 & 182 & 185 &  -3\\\\\n",
       "\t 1996 & 189 & 187 &   2\\\\\n",
       "\t 1992 & 189 & 188 &   1\\\\\n",
       "\t 1988 & 188 & 173 &  15\\\\\n",
       "\t 1984 & 185 & 180 &   5\\\\\n",
       "\t 1980 & 185 & 177 &   8\\\\\n",
       "\t 1976 & 177 & 183 &  -6\\\\\n",
       "\t 1972 & 182 & 185 &  -3\\\\\n",
       "\t 1968 & 182 & 180 &   2\\\\\n",
       "\t 1964 & 193 & 180 &  13\\\\\n",
       "\t 1960 & 183 & 182 &   1\\\\\n",
       "\t 1956 & 179 & 178 &   1\\\\\n",
       "\t 1952 & 179 & 178 &   1\\\\\n",
       "\t 1948 & 175 & 173 &   2\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 16 × 4\n",
       "\n",
       "| year &lt;dbl&gt; | winner &lt;dbl&gt; | opponent &lt;dbl&gt; | difference &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| 2008 | 185 | 175 |  10 |\n",
       "| 2004 | 182 | 193 | -11 |\n",
       "| 2000 | 182 | 185 |  -3 |\n",
       "| 1996 | 189 | 187 |   2 |\n",
       "| 1992 | 189 | 188 |   1 |\n",
       "| 1988 | 188 | 173 |  15 |\n",
       "| 1984 | 185 | 180 |   5 |\n",
       "| 1980 | 185 | 177 |   8 |\n",
       "| 1976 | 177 | 183 |  -6 |\n",
       "| 1972 | 182 | 185 |  -3 |\n",
       "| 1968 | 182 | 180 |   2 |\n",
       "| 1964 | 193 | 180 |  13 |\n",
       "| 1960 | 183 | 182 |   1 |\n",
       "| 1956 | 179 | 178 |   1 |\n",
       "| 1952 | 179 | 178 |   1 |\n",
       "| 1948 | 175 | 173 |   2 |\n",
       "\n"
      ],
      "text/plain": [
       "   year winner opponent difference\n",
       "1  2008 185    175       10       \n",
       "2  2004 182    193      -11       \n",
       "3  2000 182    185       -3       \n",
       "4  1996 189    187        2       \n",
       "5  1992 189    188        1       \n",
       "6  1988 188    173       15       \n",
       "7  1984 185    180        5       \n",
       "8  1980 185    177        8       \n",
       "9  1976 177    183       -6       \n",
       "10 1972 182    185       -3       \n",
       "11 1968 182    180        2       \n",
       "12 1964 193    180       13       \n",
       "13 1960 183    182        1       \n",
       "14 1956 179    178        1       \n",
       "15 1952 179    178        1       \n",
       "16 1948 175    173        2       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.frame(year, winner, opponent, difference)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... We see that most, but not all, of the differences in height are positive, indicating that the taller candidate won the election. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "taller.won <- winner > opponent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [1]  TRUE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE  TRUE  TRUE\n",
      "[13]  TRUE  TRUE  TRUE  TRUE\n"
     ]
    }
   ],
   "source": [
    "print(taller.won)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [table](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/table) function summarizes discrete data such as the result in the vector `taller.won`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "taller.won\n",
       "FALSE  TRUE \n",
       "    4    12 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "table(taller.won)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the result of table to display percentages if we divide the result by 16 and multiply that result by 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "taller.won\n",
       "FALSE  TRUE \n",
       "   25    75 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "table(taller.won) / 16 * 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, in the last 16 elections, the odds in favor of the taller candidate winning the election are 3 to 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Several types of graphs of this data may be interesting to help visualize any pattern. For example, we could display a barplot of differences using the [barplot](https://www.rdocumentation.org/packages/graphics/versions/3.6.2/topics/barplot) function. For the plot we use the [rev](https://www.rdocumentation.org/packages/DescTools/versions/0.99.36/topics/Rev) function to reverse the order of the differences so that the election year is increasing from left to right. We also provide a descriptive label for both axes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EHQBAIIQdAEAghB0AQCCE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\ntvV1G0kAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "barplot(rev(difference), \n",
    "        xlab=\"Election years 1948 to 2008\",\n",
    "        ylab=\"Height difference in cm\", \n",
    "        col=\"steelblue\") #see colors() for built-in colors in R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Barplot of the difference in height of the election winner in the Electoral College over the height of the main opponent in the U.S. Presidential elections. Height differences in centimeters for election years 1948 through 2008 are shown from left to right. The electoral vote determines the outcome of the election. In 12 out of these 16 elections, the taller candidate won the electoral vote. In 2000, the taller candidate (Al Gore) did not win the electoral vote, but received more popular votes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It would also be interesting to display a *scatterplot* of the data. A *scatterplot* of loser’s heights vs winner’s height..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cmpa9euBw4cYNVZIRuj0Si6oUFOnz49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\ngg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(winner, opponent, pch=3, col=\"red\") #pch argument defines type of symbol, see ?points\n",
    "abline(0,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are some overlappings, we can use [jitter](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/jitter) to add some noise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uPomKWlZGkpOgQgSRQ7AIDWXbhwQSaTVVZWZmRk9OvXT3QcoAlhFAsA0KbExEQH\nB4fOnTtnZWXR6gA9o9gBALRGoVCMHz/ex8cnPj7e1tZWdBygyWEUCwDQgsrKyoCAgLi4uHXr\n1s2ePVt0HKCJotgBAF5UYWGhl5fXtWvXjh49am9vLzoO0HQxigUAvJC0tDR7e/uWLVuqVCpa\nHSAWxQ4A8PwUCoW7u7unp2dycnL79u1FxwGaOkaxAIDnUVVV9cEHH2zatOkf//jH3LlzRccB\nIEkUOwDAc7h58+bkyZPPnTt35MgRZ2dn0XEA/AujWABA4+Tk5Njb21dXV6tUKlodYFAodgCA\nRoiOjnZ1dR05cmRycnLHjh1FxwHwGIodAKBBampqgoKC/Pz8QkJCNm3a1KpVK9GJANTFNXYA\nAM1KSkqmTp164sSJxMRENzc30XEA1I9iBwDQ4MSJE3K53NraOjs7287OTnQcAE/FKBYA8Cxx\ncXEuLi5OTk5KpZJWBxg4ih0AoH5qtXr58uWzZs36+OOPt2zZYmVlJToRAA0YxQIA6lFWVubj\n43PkyJGdO3dOmDBBdBwADUKxAwDUlZ+fL5PJ7t+/n5mZ+cYbb4iOA6ChGMUCAB6zb98+R0fH\n7t270+oAo0OxAwD8i1qtDg8PnzhxYkBAwI8//mhtbS06EYDGYRQLAJAkSaqoqPDz80tMTNy6\ndauXl5foOACeB8UOACBduHBBJpNVVlZmZGT069dPdBwAz4lRLAA0dQcOHHBwcHjttdeysrJo\ndYBRo9gBQJOmUCjGjRvn4+Ozd+9eW1tb0XEAvBBGsQDQRFVWVgYEBMTFxa1bt2727Nmi4wDQ\nAoodADRFhYWFXl5e165dO3r0qL29veg4ALSDUSwANDlpaWn29vYtW7ZUqVS0OsCUUOwAoGlR\nKBTu7u6enp7Jycnt27cXHQeANjGKBYCmoqqq6oMPPti0adM//vGPuXPnio4DQPsodgDQJNy8\neXPy5Mnnzp07cuSIs7Oz6DgAdKJxo9iKioqamhodRQEA6EhOTo69vX15eXl6ejqtDjBhGopd\nZWVlXFzcvHnzXn/99ZYtW/7pT39q0aLFyy+/7O7uHhoaeubMGf2krNfRo0f/4z/+45VXXvnT\nn/40aNCgyMhISicAPCk6OtrV1XXkyJFpaWldunQRHQeADj212BUXF//1r3/t3LnztGnT1q1b\nd/nyZVtb2759+9rZ2dXU1Bw6dOjjjz/u16/fqFGj4uPj9RC0Q4cOixcvfvhjTF4uPrEAACAA\nSURBVEzM6NGjExISSkpKKioqTpw4ERgYOGnSJLVarYcwAGAUampqgoKC/Pz8QkJCNm3a1KpV\nK9GJAOhW/cXuq6++6tmz55dfftmrV69vv/02Ozv7zp07165dO3369MWLF0tLS69du7Zz586A\ngIC8vLwJEyZ4eHj88ssvOg16/fr10tLSB69LSkrmz5+vVquXLVt28eLFW7du7dy5s2PHjrt3\n796yZYtOYwCAsSgpKRk7duzatWsTExOXLl0qOg4Afai/2AUFBcnl8l9++SU9PX3x4sX29vYW\nFhaPntChQwe5XP7Pf/7z2rVr33//fUFBQWxsrF4CS5Ikbd++vaKi4sMPP/z000+7detma2sr\nl8t/+OEHSZI2btyotxgAYLDy8vIcHByKi4tVKpWbm5voOAD0pP67Yn/++edevXo15N9bWlr6\n+PhMnz79ypUrWg32LHl5eZIkvfvuu48uOjk5DRo06Pjx43qLAQCGaevWrXPmzBk/fvx3331n\nZWUlOg4A/an/G7sGtrqHzM3Nu3Xrpo08DfLHH39IkvTkJ3bv3v327dt6iwEAhkatVi9fvnzm\nzJkff/xxTEwMrQ5oajRvd7J58+ZLly7Ve+jUqVObN2/WdiTNevbsKUlSWVlZnfXff//d2tpa\n/3kAwBCUlZXJ5fJvvvlm586dS5cuNTMzE50IgL5pLnY+Pj5KpbLeQ7t27fLx8dF2pKfatGlT\ny5YtW7ZsuXz5ckmSTp06VeeES5cu/fnPf9ZbHgAwHPn5+c7Ozr/88ktmZuaECRNExwEgxgs9\neaK2tlZvfxH27t27zkpWVpa7u/vDH3Nyci5fvjx27Fj95AEAw7Fv374ZM2a4urpGR0czuACa\nshcqdmfOnHnppZe0FeXZNG6nUltb++WXXz5a9QDA5KnV6oiIiODg4MDAwLCwsGbNGvc8IQAm\n5qnFbtq0aQ9fr1q1qs4uxLW1tb/++mtWVtbEiRN1mK4xHBwcHBwcRKcAAP2pqKjw8/NLTEzc\nunWrl5eX6DgAxHtqsYuLi3v4OiMjIyMj48lznJ2dv/nmG53kAgA804ULF2QyWWVlZUZGRr9+\n/UTHAWAQnlrszp079+BFr169vvrqK09Pz0ePNm/e/OWXX27btq1u0zVAQUHB8ePHLS0thw0b\nxpUlAJqIlJSUyZMnDxkyJCYmxtbWVnQcAIbiqVdj9Pz/ff7552PHju35uG7duum/1W3cuLFL\nly5WVlZyuby4uFiSpKVLl/bo0UMmk73zzjudOnVavXq1niMBgP4pFAoPD4/p06fv3buXVgfg\nUZpvnggKCtJDDo3S09P9/f3VarW5ufmuXbvu3bs3ffr0iIiIP//5z87OztevXz969OjChQt7\n9+49evRo0WEBNMznn0sLFkj6ugfLBFRWVi5cuDA2NnbdunWzZ88WHQeAwTGa+6e+/vrrZs2a\n/fjjj1VVVXv27ElMTPzb3/42duzYs2fPbt26NSUlZefOnZIkffvtt6KTAmiw4GDpxAnRIYxG\nUVHRyJEjk5KSUlNTaXUA6tWg7U5SUlIiIyOzsrJ+//332traOkdramp0EKwulUo1duzYB7tu\njh8//u233967d29cXFyrVq0enCCTydzd3TMzMxv7zleuXLl3794zTngw9gWgHatXS+fPS199\nJTqHkVEqlZMmTerZs6dKpWrfvr3oOAAMlOZiFx8f7+npef/+fWtr6169epmbv9DWd8/t2rVr\nMpns4Y8PnipWZ9fivn37pqSkNOptL1y48OCtNFKr1Y16ZwD1O39eys8XHcLIKBSKRYsW+fn5\nrVy50sLCQnQcAIZLc0tbvny5mZlZdHT09OnTBT558OWXXy4pKXn444PXN27c6Nq168PFGzdu\nNPaJ1z169CgqKqqsrHzGOTExMcuWLeOpiwD0r7q6+v3339+0adM//vGPuXPnio4DwNBpLnan\nTp2Sy+UzZszQQ5pn6N279549e3777bcOHTr89ttv8fHxbdu2jYqKCgsLe3BCYWFhfHx8//79\nG/vOnTp1evYJr7zyyvMkBoAXc/PmzcmTJ587d+7IkSPOzs6i4wAwApqLXevWrdu1a6eHKM+2\ncOHCKVOmDBw40MHBITs7+/bt21u2bJk5c2ZBQcGoUaNu3LixcuXKO3fuCC+gAOpXUyPl5Ulq\ntXT9ulRaKv3007/W8/OlOnsn9egh2djoP6ChycnJkcvlr7zySnp6epcuXUTHAWAcNBc7Dw+P\n57gjQesmTZoUEBCwevXqffv2mZubf/7559OnT//5558//fTTLVu2PDjHw8Nj4cKFYnMCqF9K\nijRmjPTwWlV7+3+9CAioe+ayZdKnn+ovmEGKjo5+9913vb29FQrFw1vEAEAjM433BBQUFDg5\nOS1cuHDZsmXNmzfXT6ynuXjx4qVLl954443XXnvtwUpiYuK+ffuqq6tHjhw5ZcoUXSSMiooK\nCAgoLy9v06aN1t8cMHFRUdKlS4+tHD4s3boleXtLkiSFh0vTp0tdukht20r/8z8SV7JKUk1N\nzbJlyyIjI0NDQ5cuXSo6DoB6VFdXW1paKpXK4cOHi85Sl+Zv7EJCQvr167d8+fL169cPGjTI\n5okRyYYNG3QSrT7du3fv3r37oytvv/3222+/rbcAABrn0iXp4sXHVm7flu7e/ffi1atSTY3U\npo10/74k+k9H4UpKSqZOnXr8+PHExEQ3NzfRcQAYH83FbuPGjQ9eFBQUFBQUPHmCPosdACPz\nxRd1VwIDpfx8aetWSZKkZs2kkBCJp8VIkiRJeXl5Mpmsbdu22dnZ3bp1Ex0HgFHSXOxyc3P1\nkAMAmrKtW7fOmTNn/Pjx3333XWO3bQKAhzQXu0GDBukhh1YEBgZu37798uXLooMAQEOp1eqI\niIhly5aFhob+9a9/ZctMAC+iEY+RKCgouHr1at++fa2trXUX6EUUFxfXOywGYKCaNZOaGc0T\nq3WhvLzcx8fn8OHDO3bsmDhxoug4AIxeg36lZmRkvPnmm3Z2dsOHD8/Ozn6wGBsb279//8Y+\nwgsA/i0+XmrC++7m5+c7OTn9/PPPmZmZtDoAWqH5G7uff/7Zw8PDzMzM09Nz9+7dD9fHjx8/\nb968bdu2vfXWW7pM+C/Tpk3TeI4h7LcHQAMbm3/vPzx2rNAoIu3bt2/mzJkuLi7R0dEGOwYB\nYHQ0F7vQ0NB79+6pVKqOHTs+WuzatGkzevTotLQ0Xcb7t7i4OP18EADdCg6W7t8XHUKkBxfV\nBQcHBwYGhoWFNWvaw2gA2qW52CUnJ8vl8gEDBhQXF9c59MYbb6Snp+smWF2tW7d+7bXXIiMj\nn3HOt99+m5ycrJ88AJ6TmVlT3q+uoqLCz88vMTFx69atXl5eouMAMDWai11JSYmdnV29h5o3\nb15eXq7lRE8xcODA06dPjxs37hm3jG3fvl0/YQDgOVy4cEEmk1VWVqanp/fv3190HAAmSPMI\nwNbW9ubNm/Ueys3N7dixo7Yj1W/IkCFlZWUX62xhDwBGIiUlZdiwYa+99lpWVhatDoCOaC52\nLi4ue/furaqqqrN+6NChgwcPjho1Sie5nuDm5jZ06NDCwsJnnDNx4sTg4GD95AGAhlMoFB4e\nHnK5PD4+3tbWVnQcACZLc7ELDAy8efOmXC4/c+aMJEl//PFHdnb2kiVLxo4da25u/t///d+6\nDylJkuTl5aVSqZ59B66Xl1doaKh+8gBAQ1RWVvr7+y9evHjdunVRUVHm5o3YPRQAGkvzrxgX\nF5dVq1YtWrQoISFBkqSHmy1ZWFisXbt24MCBug0IAEarqKhILpdfu3YtNTXVwcFBdBwApq9B\nfzsGBASMGDFi9erV6enpJSUl1tbWzs7OixYt6tevn67zAYCRUiqVkyZN6tmzp0qlat++veg4\nAJqEhg4F+vXrt2LFCp1GAQCToVAoFi1a5Ofnt3LlSgsLC9FxADQVXO0BANpUXV39wQcffP/9\n96tWrZo3b57oOACaFoodAGjNzZs3p0yZcvbs2SNHjjg34cfgAhClQY+ySUlJmThxYocOHSwt\nLc2foOuIAGAUcnNz7e3ty8rKMjIyaHUAhNBcy+Lj4z09Pe/fv29tbd2rVy+aHAA8acuWLfPm\nzfPy8lqzZk2rVq1ExwHQRGluacuXLzczM4uOjp4+ffozHucFAE1TbW1tcHBwZGRkaGjo0qVL\nRccB0KRpLnanTp2Sy+UzZszQQxoAMC4lJSXTpk3Lzc3dv3+/u7u76DgAmjrNxa5169bt2rXT\nQxQAMC55eXkymaxt27bZ2dndunUTHQcAGnDzhIeHR2Zmph6iAIAR2bp16/Dhwx0dHY8dO0ar\nA2AgNBe7iIiIwsLC//u//6utrdVDIAAwcGq1Ojw8fMaMGYGBgTExMVZWVqITAcC/aB7FhoSE\n9OvXb/ny5evXrx80aJCNjU2dEzZs2KCTaABgeMrLy318fA4fPrxz586Hz84GAAOhudht3Ljx\nwYuCgoKCgoInT6DYAWgizp075+npWVtbm5GR0adPH9FxAKAuzcUuNzdXDzkAwMDt27dv5syZ\nLi4u0dHR1tbWouMAQD00F7tBgwbpIQcAGCy1Wh0REREcHBwYGBgWFtasWYOe2QMA+te4x0jc\nvn27tLTU2tr6ySvtAMAkVVRU+Pv779+/Py4uztvbW3QcAHiWBv3dWV1d/dlnn3Xv3t3W1tbO\nzs7W1rZ79+5hYWH37t3TdT4AEOjChQvDhw/Pzc1NT0+n1QEwfJqLXWVlpYeHx7Jlyy5fvtyp\nU6ehQ4d26tTp8uXLwcHBY8aMqaqq0kNKANC/lJSUYcOGderUKTs7u3///qLjAIBmmotdZGTk\n0aNH33nnndOnTxcVFalUqqKiojNnzrzzzjspKSnffPONHlICgJ4pFIoxY8bI5fL4+HhbW1vR\ncQCgQTQXu5iYmL59+/7444+P3tv/xhtvPFiJjo7WZTwA0LfKykp/f//FixevWbMmKirK3Lxx\n1yIDgECai9358+fHjRv35K82c3PzcePGnT9/XjfBAECAoqKit956KykpKTU11dfXV3QcAGgc\nzcXOwsLi7t279R66c+eOhYWFtiMBgBhKpdLe3r5FixYqlcrBwUF0HABoNM3FbuDAgdu3by8p\nKamzfvPmzR07drz55pu6CQYAeqVQKNzc3CZOnHjo0KH27duLjgMAz0NzsXvvvfeuX7/u5OS0\ncePGgoKCqqqqgoKCDRs2ODk53bhx4/3339dDSgDQnZqamg8//PDDDz9ctWpVVFQUgwgAxkvz\nRcEzZ87Mycn5+uuv/fz86hz66KOPpk2bppNcAKAXN2/enDJlytmzZ48cOeLs7Cw6DgC8kAbd\n7RUZGenp6fndd9/l5uY+ePLEkCFD5syZM2LECF3nAwDdyc3NlcvlL7/8ckZGRpcuXUTHAYAX\n1dDb+EeOHDly5EidRoGpuXxZmjtXSkqSzMxERwHqsWXLlnnz5nl5ea1Zs6ZVq1ai4wCAFvAo\na+hMYaF06JBUWys6B1BXbW1tUFCQr69vSEjI5s2baXUATEZDv7G7e/funj17Ho5iBw8ePGHC\nBCsrK52GAwCtKykpmTZtWm5u7v79+93d3UXHAQBtalCx++GHH+bPn19cXPzo4iuvvLJmzRqZ\nTKabYACgfXl5eTKZrG3bttnZ2d26dRMdBwC0TPMo9tChQ5MnTy4tLfX19V27du2ePXvWrl3r\n6+tbWlo6adKkw4cP6yElALy4bdu2DR8+3NHRUalU0uoAmCTN39iFhIS0aNFCqVQOHjz44eLc\nuXMXL17s4uISEhIyevRoXSYEgBelVqsjIiKCg4OXLVsWEhJixg09AEyU5mL3008/zZgx49FW\n98DgwYNnzJgRExOjm2AwNjk50sGDj61cvixJkvTll1KzR74YNjOTfHykjh31GQ1NXHl5uY+P\nz+HDh3fu3Dlx4kTRcQBAhzQXO0tLy45P+d9wx44dLS0ttR0JxunMGSkp6bGV27clSZKSk+tu\nd+LhQbGD3pw7d87T07O2tjYjI6NPnz6i4wCAbmkudiNGjFAqlfUeUiqVrq6u2o4E4zRrljRr\n1mMraWnSiBHS/v2SeUNvvga0a9++fTNnznRxcYmOjra2thYdBwB0TvPNE1988UVOTk5QUFBF\nRcXDxYqKiqCgoJycnC+++EKX8QDgeajV6vDw8IkTJy5YsODHH3+k1QFoIjR/lRIRETFgwIDw\n8PCoqKjBgwe3b9/++vXrubm5t2/fdnV1jYiIePTkDRs26CopADRMRUWFv7///v374+LivL29\nRccBAP3RXOw2btz44MXt27frbG6SlpaWlpb26ArFDoBYFy9elMlkd+/eTU9P79+/v+g4AKBX\nmotdbm6uHnIAwItLTU2dPHnyoEGDYmNjbW1tRccBAH3TXOwGDRqkhxwwQW3aSK1aPbbXCaBL\nCoXigw8+8Pf3X7VqlTm37ABokvjdB50ZNEi6do1iBz2oqqoKCAiIjY1ds2aNr6+v6DgAIExD\ni93du3f37NmTm5tbWlpqbW09ePDgCRMmWFlZ6TQcjB63IkL3ioqKvLy8rl69mpqa6uDgIDoO\nAIjUoGL3ww8/zJ8/v7i4+NHFV155Zc2aNTKZTDfBAEAzpVI5adKknj17qlSq9u3bi44DAIJp\nHpMdOnRo8uTJpaWlvr6+a9eu3bNnz9q1a319fUtLSydNmlTnPlkA0BuFQuHm5jZx4sTk5GRa\nHQBIDfnGLiQkpEWLFkql8tHHxc6dO3fx4sUuLi4hISGjR4/WZUIAqKumpmbJkiVRUVGrVq2a\nN2+e6DgAYCg0F7uffvppxowZj7a6BwYPHjxjxoyYmBjdBAOA+t28eXPKlCmnT59OTEx86623\nRMcBAAOieRRraWnZ8SmPbO/YsaOlpaW2IwHAU+Xm5jo4OJSVlalUKlodANShudiNGDFCqVTW\ne0ipVLq6umo7EgDUb8uWLS4uLq6urmlpaV26dBEdBwAMjuZi98UXX+Tk5AQFBVVUVDxcrKio\nCAoKysnJ+eKLL3QZDwAkSZJqa2uDgoJ8fX1DQkI2b97cqlUr0YkAwBBpvsYuIiJiwIAB4eHh\nUVFRgwcPbt++/fXr13Nzc2/fvu3q6hoREfHoyTwrFoDW3bp1a+rUqbm5ufv373d3dxcdBwAM\nl5lardZwhplZw99O47sZo6ioqICAgPLy8jZt2ojOAjQ5eXl5crm8TZs2u3bt6tatm+g4ACBV\nV1dbWloqlcrhw4eLzlKX5m/scnNz9ZADAJ60bds2f3//cePGfffdd61btxYdBwAMneZiN2jQ\nID3kAIBHqdXqiIiI4ODgZcuWhYSENGp0AABNVkOfFfvA7du3Hzwr1sbGRkeBAKC8vHz27NmH\nDh3asWOHp6en6DgAYDQ03xUrSVJ1dfVnn33WvXt3W1tbOzs7W1vb7t27h4WF3bt3T9f5ADQ1\n586dc3Z2PnPmTEZGBq0OABpFc7GrrKz08PBYtmzZ5cuXO3XqNHTo0E6dOl2+fDk4OHjMmDFV\nVVV6SAmgiUhISHB0dLSzs8vKyurTp4/oOABgZDQXu8jIyKNHj77zzjunT58uKipSqVRFRUVn\nzpx55513UlJSvvnmGz2kBGDy1Gp1eHj4hAkTFixYsGfPHmtra9GJAMD4aN7upH///mq1+sSJ\nE+bmj12QV1NTM3DgwObNm588eVKXCcVjuxNA1yoqKvz9/ffv379hwwZvb2/RcQDgWQx5uxPN\n39idP39+3LhxdVqdJEnm5ubjxo07f/68boIBaCquXLkyatSo3Nzc9PR07bS6sDApKkoL7wMA\nxkZzsbOwsLh79269h+7cuWNhYaHtSACakNTUVHt7+zZt2qSnp/fv3187b3r8uGTqkwQAqJfm\nYjdw4MDt27eXlJTUWb958+aOHTvefPNN3QQDYPoUCoWHh4dMJktKSnr11VdFxwEAo6e52L33\n3nvXr193cnLauHFjQUFBVVVVQUHBhg0bnJycbty48f777+shJQATU1VV5e/vv3jx4jVr1kRF\nRT15sQcA4Dlo/mU6c+bMnJycr7/+2s/Pr86hjz76aNq0aTrJBcB0FRUVeXl5FRUVpaamOjg4\niI4DAKajQX8lR0ZGenp6fvfdd7m5uQ+ePDFkyJA5c+aMGDFC1/kAmBilUjlp0qQePXqoVKoO\nHTqIjgMAJqWh44+RI0eOHDlSp1EAmDyFQrFo0SI/P78VK1a0aNFCO28aFSXdvv3Yyi+/SIWF\nUnj4Y4udOkk+Ptr5RAAwVFzXAkAfampqlixZsnr16lWrVs2bN09r76tWS8nJ0u+/P7Z444Z0\n+7aUlPTYop0dxQ6Ayau/2N29e9fKyqpRb/Qc/wRAE1FcXDx58uTTp08fOHDgrbfe0uZbm5lJ\nW7fWXZwyRWrXTlq5UpsfBADGoP67Ynv06LFy5crq6uqGvMXJkyflcvmXX36p1WAATERubq69\nvX1ZWZlKpdJyqwMAPK7+Yufm5rZo0aJOnTotWrRIqVRWVVU9ec7ly5ejoqJcXFwGDhyYnZ3N\n72sAT4qJiXF1dXV1dU1LS+vSpYvoOABg4uofxUZHR3/wwQf/+7//u3LlypUrV7Zo0aJfv34d\nOnSwtbWtrKwsKSn55Zdfrl+/LknSSy+9FBIS8te//pU5LIBH1dbWBgcHR0ZGhoaGLl26VHQc\nAGgSnnrzxLBhww4fPnzq1Km1a9cmJSUdP35crVY/PGptbT1u3Dhvb+/p06e3bNlSL1EBGI1b\nt25NnTo1Nzd3//797u7uouMAQFOh4a7Y/v37f/vtt5Ik/f7771euXCkpKWnVqlW7du26du3a\nvHlzvSQEYGTy8vLkcnmbNm2ys7O7desmIEGbNlKbNgI+FwBE07zdSUZGRsuWLQcNGmRra6uH\nQACM2p49e2bNmjV27NjvvvuudevWYkL84x8Sf3kCaJI0Pyt2+PDhoaGheogCwKip1erw8HC5\nXP5f//VfsbGxwlqdJEktW0oWFsI+HQDE0fyN3csvv8yNEQCerby8fPbs2cnJyTt27PD09BQd\nBwCaKM3FbtSoUVlZWbW1tVxUB6Be586dk8lkNTU1mZmZffr0ER0HAJouzaPYsLCw4uLi//zP\n/7x7964eAgEwLgkJCY6OjnZ2drQ6ABBO8zd2n3322cCBA1euXBkbGzto0KBOnTqZmZk9esKG\nDRt0lQ6AAVOr1REREcHBwYGBgWFhYc2aaf5DEQCgU5qL3caNGx+8KC4uTqrzUG1Jkih2QJN0\n584dPz+//fv3x8XFeXt7i44DAJCkhhS73NxcPeQAYESuXLkil8tv376dnp7ev39/0XEAAP+i\nudgNGjRIDzkAGIvU1NTJkyf36dMnISHh1VdfFR0HAPBvjbgmpqCgID09vbS0VHdpABg4hULh\n4eEhk8mSkpJodQBgaBpU7DIyMt588007O7vhw4dnZ2c/WIyNje3fv39KSoou4wEwFFVVVXPm\nzFm8eLFCoYiKijI31/x9PwBAzzQXu59//tnDw+PixYt1Nh0dP3785cuXt23bprNsAAxFUVHR\nyJEjDxw4kJqa6ufnJzoOAKB+motdaGjovXv3jh07tnbt2kfX27RpM3r06LS0NJ1lA2AQlEql\nvb29hYWFSqVycHAQHQcA8FSai11ycrJcLh8wYMCTh954443CwkIdpAJgKBQKhZub28SJEw8d\nOtShQwfRcQAAz6L5KpmSkhI7O7t6DzVv3ry8vFzLiQAYhpqamiVLlqxevXrVqlXz5s0THQcA\noJnmYmdra3vz5s16D+Xm5nbs2FHbkQCIV1xcPHny5NOnTx84cOCtt94SHQcA0CCaR7EuLi57\n9+6tqqqqs37o0KGDBw+OGjVKJ7kAiJObm2tvb19aWqpSqWh1AGBENBe7wMDAmzdvyuXyM2fO\nSJL0xx9/ZGdnL1myZOzYsebm5v/93/+t+5AA9CcmJsbV1dXFxUWpVHbp0kV0HABAI2gexbq4\nuKxatWrRokUJCQmSJE2cOPHBuoWFxdq1awcOHKjbgAD0pba2Njg4ODIyMjQ0dOnSpaLjAAAa\nrUFbjAYEBIwYMWL16tXp6eklJSXW1tbOzs6LFi3q16+frvMB0I9bt25NmzYtJycnISHBw8ND\ndBwAwPNo6N7x/fr1W7FihU6jABDl5MmTMpmsTZs22dnZ3bp1Ex0HAPCcNF9jt3nz5kuXLtV7\n6NSpU5s3b9Z2JAB6tWfPHldXV3t7+2PHjtHqAMCoaS52Pj4+SqWy3kO7du3y8fHRdiQAeqJW\nq8PDw+Vy+cKFC2NjY1u3bi06EQDghbzQY7xra2vNzMy0FQWAPpWXl8+ePTs5OXnHjh11ngQN\nADBSL1Tszpw589JLL2krCgC9OXfunEwmq6mpyczM7NOnj+g4AADteGqxmzZt2sPXq1atio+P\nf/RobW3tr7/+mpWV9XD3EwDGIiEhYcaMGcOHD4+OjraxsREdBwCgNU8tdnFxcQ9fZ2RkZGRk\nPHmOs7PzN998o5NcAHRArVZHREQEBwcHBgaGhYU1a6b5KlsAgBF5arE7d+7cgxe9evX66quv\n6lyC07x585dffrlt27a6TQdAe+7cuePn57d///64uDhvb2/RcQAA2vfUYtezZ88HLz7//POx\nY8c+/BGAMbpy5YpcLr99+/axY8cGDBggOg4AQCc0D2I6d+5sZWVV7yH2sQOMQmpqqr29fZs2\nbdLT02l1AGDC2McOMHEKhcLDw0Mmkx08ePDVV18VHQcAoEPsYweYrKqqqoULF8bExCgUCj8/\nP9FxAAA6xz52gGkqKiry9vYuLCxMSUlxdHQUHQcAoA/sYweYoGPHjnl7e/fo0UOlUnXo0EF0\nHACAnhjfPnZqtTo/Pz8/P7+0tFStVtvY2Lz++uuvv/46Q2HgAYVCsWjRIj8/vxUrVrRo0UJ0\nHACA/hjTPnZ//PFHZGTk6tWri4qK6hzq3LnzggULlixZ0qpVK31GAgxK09vNxAAAIABJREFU\nTU3NsmXLIiMjv/7660WLFomOAwDQN6PZx+7OnTvu7u6ZmZnNmjUbPHhwr169rK2tzczMbt++\nnZ+fn5eX9/HHH+/duzc5Oflpm7MApq24uHjKlCmnTp06ePDgqFGjRMcBAAig+eaJoKAgPeTQ\nKCwsLDMzc+bMmREREZ06dapztKio6KOPPoqJiQkLCwsNDRWSEBAoNzdXLpe/9NJLKpWqS5cu\nouMAAMQwmidFxsbGDh069Pvvv3+y1UmS9Nprr23evHnIkCGPXhoINBExMTGurq4uLi5KpZJW\nBwBNWf3f2MlkMkmSPv/88z59+jx4/Qy7du3Sfq4nFBYWTpw48RnPLG/WrNmIESNWr16thzCA\ngaitrQ0ODo6MjAwNDV26dKnoOAAAweovdrt375YkKTAw8OFr4aytrS9duvTscy5evGhjY6Of\nPIBwt27dmjZtWk5OTkJCgoeHh+g4AADx6i92V65ckSSpXbt2D18L5+HhERcX9/3338+ePbve\nEzZs2BAfHz99+nQ9BwOEOHnypEwma9OmTXZ2drdu3UTHAQAYhPqLXefOnet9LdCnn366b98+\nX1/fb7/9duzYsb1797a2tpYkqbS09OzZswkJCcePH7exsfnb3/4mOimgc3v27Jk1a9bbb7+9\nfv361q1bi44DADAUL/RIMX3q0aNHWlra3Llzs7KycnNznzzB0dFx3bp1PXr00H82QG/UanVE\nRERwcHBgYODnn3/OvtwAgEcZTbGTJKl///6ZmZk5OTmHDh06e/ZsaWmpJEnW1ta9e/d2c3Mb\nMmSI6ICAbpWXl8+ePTs5OXnHjh119gw3StXV0rFjElvuAYD2aOGuWEtLy86dO3t7ew8fPlz7\nAZ8wZMgQOhyaoHPnzslksnv37mVmZvbp00d0HG3IzJTc3aXaWtE5jMGVK9LLL0vsvg5AE63d\nFfv1119v3bp18uTJWgwH4IGEhIQZM2YMHz48OjradG79rq2V7t8XHcJITJ0qTZsmffih6BwA\nDJ0W7oqtqak5d+6cv7//Z599pv9iV1BQcPz4cUtLy2HDhj24nQIwJY9eVBcWFvaMrRxhyu7d\nk6qrRYcAYAS0c1esnZ3dzJkzV6xYobVc9dm4cePHH39cXFz89ttvr1mz5pVXXlm6dGlkZGRt\nba0kSVZWVpGRkQEBATrNAOhTZWXlu+++u2vXrtjY2EmTJomOAwDGLCpKkiRpwQLROXRLazdP\n+Pj4DBgwQFvv9qT09HR/f3+1Wm1ubr5r16579+5Nnz49IiLiz3/+s7Oz8/Xr148e/f/au/u4\nqMqE/+PX8KSioagRKgniY2quCYKGrSKa7QoxgCGmqHinYLb7u9u1YtPswbKw9KUv2wzatE1E\nTEJNNJEnERGDUdF0S0VNIVQWrHxAQIb5/TF7s4CKoMxcM2c+79f+ARcXZ76nTme/nOvMmZz5\n8+cPHDjQ19fXcDEAoykuLg4KCvr1118PHDhg0P+4AMAiHDwohPKLXZst6wwdOnTGjBlttbXb\nrVy50srK6ptvvqmurt6xY0dqauo777zzzDPPnDx58quvvsrOzk5OThZCrFq1ynAZAKPZt2+f\np6dnp06d8vLyaHUAgBYym8edaDSaZ555JiAgQAjh7+8/adKknTt3bt68uUOHDvoJarXaz8/v\nu+++a9Vmf/311zfeeKOm2ZtXfvjhh/uODdyHuLi4l156KSIi4uOPP7a1tZUdp428/bZ46607\njDd5FJ+VlUhLE+PHGyUTACiN2RS7ixcvNnzwSr9+/YQQAwcObDhn8ODB2dnZrdqsVqv99ddf\nq6urm5lTWVnZqm0C9626unr+/PkJCQlxcXGzZ8+WHadNLVggfHwajRw9KhYuFGlpjQatrZtO\nszQVFeL3vxdVVY0Gf/5ZnDsn1q5tNOjrK/7xD2NGA2D6zKbYdevWraKiov5b/ddlZWWurq71\ng2VlZfatfM5Tt27dNmzY0Pyc2NjYQ4cOtWqzwH0oLS0NDg4uKSnZt2+fl5eX7DhtrXt3MWFC\noxEbGyFE00E4Ooo33hBXrzYaXLZMeHqKp59uNPi73xkzFwCzYDbFbuDAgTt27Lh06ZKzs/Ol\nS5dSUlIcHBxiY2OXLVumn1BSUpKSkjJ06FC5OYH7c+DAgSlTpri7u2s0GmdnZ9lxII+VlQgL\nazr42Wdi1Cgxb56MQIB52rRJXLjQaOT774UQIiam0WDv3mLaNOOlMjyzKXbz588PDQ0dNmzY\nyJEjCwoKfv3114SEhOnTp58/f37cuHFlZWUff/zxjRs3nn/+edlJgVaLi4v705/+NHv27DVr\n1tjZ2cmOAwDmb9MmUVraaOSnn4QQYsuWRoM9e1Ls5JgyZUpUVNSnn366a9cuGxub999/f9q0\naT/88MPSpUsTEhL0cyZMmDB//ny5OYFWqa2tXbx48YoVK1asWPFnPlcAANrKN980HYmIEEKI\n9euNn8WYzKbYqVSqtWvXvvLKK+fOnRs0aFCvXr2EEO+8846Pj8+uXbtqamp+//vfh4aGWltb\ny04KtFR5eXloaOjx48fT0tLGjRsnOw4AwOyZTbHTc3d3d3d3bzgyadKkSZMmycoD3LfCwkK1\nWt21a9eCgoKG7wGyIEOH3vkBKACA+8XnTgISbNq0ycfHx8fHJzc310JbnRCie3fx5puyQ5iJ\nwEDh7S07BAAzQLEDjEqr1UZHR8+cOXPJkiUbN26sf8I20JzFi8VTT8kOAcAMmNlSbPMWLlyY\nlJT0k/5tL4DpuXLlSlhY2OHDh7/99tsJPL8NAIypfXvZCYxBUcWuvLz8/PnzslMAd/b999+r\n1epOnToVFBT06dNHdhwAsDAffig7gTGwFAsYw44dO8aMGePh4XHgwAFaHQBI0KmT6NRJdgiD\nM5srdmG3P4r9Nt99950RkgCtotPpli9fvmjRooULF77//vuqJp95DwBA2zGbYrd582bZEYBW\nu3bt2syZMzMyMr7++uvAwEDZcQAACmc2xa5jx469evVasWJFM3NWrVqVkZFhtEhA84qKigID\nA2/dunXw4MHBgwfLjgMAUD6zKXbDhg07ceLE5MmTm1nJSkpKMmYkoBm7d++eNm3a6NGjExIS\nunTpIjsOAMAimM2bJ0aMGHH16tWzZ8/KDgLcg06ni4mJ8ff3j4yMTElJodUBAIzGbK7YjR8/\n/uDBgyUlJX379r3bnGeffdbFxcWYqYAmqqqq5s2bt3Xr1sTExClTpsiOAwCwLGZT7IKDg4OD\ngx98DmA4xcXFQUFBZWVle/fu9fDwkB0HAGBxzGYpFjBx+/bt8/T07Nixo0ajodUBAKSg2AFt\nIC4ubsKECWq1Oj093cnJSXYcAICFMpulWMA0VVdXv/jiixs3boyLi5s9e7bsOAAAi0axA+5f\naWlpcHBwSUnJvn37vLy8ZMcBAFg6lmKB+3TgwAFPT08bGxuNRkOrAwCYAoodcD/i4uJ8fX0D\nAgIyMzOdnZ1lxwEAQAiKHdBatbW10dHRCxYs+PDDD2NjY+3s7GQnAgDgP7jHDmiF8vLy0NDQ\n77//Pi0tbdy4cbLjAADQCMUOaKnCwsKgoCBHR0eNRuPq6io7DgAATbEUC7RIYmKij4/P6NGj\n9+/fT6sDAJgmih1wD1qtNjo6Ojw8fMmSJQkJCfb29rITAQBwZyzFAs25cuVKWFjYoUOHvv32\n2wkTJsiOAwBAcyh2wF2dPHkyMDCwXbt2BQUF7u7usuMAAHAPLMUCd5aSkuLl5TVs2LADBw7Q\n6gAAZoFiBzSl0+liYmLUavX8+fMTExM7duwoOxEAAC3CUizQyLVr12bNmpWenp6UlKRWq2XH\nAQCgFSh2wH8VFRUFBgbeunXr4MGDgwcPlh0HAIDWYSkW+I/du3ePHDnS1dU1Pz+fVgcAMEcU\nO+A/N9X5+/tHRkampKR06dJFdiIAAO4HS7GwdFVVVfPmzUtOTk5MTJwyZYrsOAAA3D+KHSxa\ncXFxcHDw5cuXs7OzPTw8ZMcBAOCBsBQLy5WTk+Pp6Wlvb6/RaGh1AAAFoNjBQsXFxfn5+anV\n6vT0dCcnJ9lxAABoAyzFwuJUV1e/+OKLGzdujI2NjYiIkB0HAIA2Q7GDZSktLQ0ODi4pKdm3\nb5+Xl5fsOAAAtCWWYmFBDhw44OnpaWNjo9FoaHUAAOWh2MFSbNiwwc/PLyAgIDMz09nZWXYc\nAADaHsUOyldbWxsdHT1nzpyYmJjY2Fg7OzvZiQAAMAjusYPClZeXh4aGfv/992lpaePGjZMd\nBwAAA6LYQckKCwuDgoIcHR01Go2rq6vsOAAAGBZLsVCsxMREHx+f0aNH79+/n1YHALAEFDso\nkFarjY6ODg8PX7JkSUJCgr29vexEAAAYA0uxUJorV66EhYUdOnRo165dEydOlB0HAADj4Yod\nFOXkyZM+Pj6XLl0qKCgweKtbu1YEBRn2JQAAaA2KHZQjJSXF29u7f//++/fvd3d3b8tNb9sm\nPvus6WB5uaioaMtXAQDgwVDsoAQ6nS4mJkatVkdFRW3bts3BwaGNXyArS+ze3cbbBACgrXGP\nHczetWvXZs2alZ6enpSUpFarZccBAEAaih3MW1FRkVqtrqmpOXjw4ODBg2XHAQBAJpZiYcZ2\n797t5eXVu3fv/Px8Wh0AAFyxg1nS6XTLly9ftGjRwoULly1bZmVl+D9RTp4UoaGNRv71L3H5\nctPBjh3F2rWifXuD5wEA4DYUO5ifqqqqefPmJScnJyYmTpkype1fICdHXLrUaOT0aVFZKX75\npdHgrVvCxkY4OjYadHAQ1tZtHwkAgBag2MHMFBcXBwcHX758OTs728PDwyCv8d574vTpRiMV\nFaK2VqhUjQZv3hT9+4vYWINkAACg9Sh2MCc5OTlTpkwZNGiQRqNxcnIy1Mvc/mST//f/REmJ\n+PrrRoNLl4q0NENlAACg9XjzBMxGXFycn5+fWq1OT083YKsDAMBsccUOZqC6uvrFF1/cuHFj\nbGxsRESE7DgAAJgoih1MXWlpaUhISHFxcXZ2tre3t+w4AACYLpZiYdLy8vI8PT2trKw0Go3J\ntTpXV9G3r+wQAAD8F8UOpis+Pn78+PEBAQFZWVnOzs4yo9jYCFvbpoMzZ4r162WkAQDgzliK\nhSmqra1dvHjxihUr3n333ddee012HCEWLxZVVbJDAABwDxQ7mJzy8vKpU6ceO3Zsz549vr6+\nsuMIIUTTpxADAGCSKHYwLYWFhUFBQY6OjhqNxtXVVXYcAADMCffYwYQkJib6+PiMHj16//79\ntDoAAFqLYgeToNVqo6Ojw8PDlyxZkpCQYG9vLzsRAADmh6VYyHflypVp06ZpNJpdu3ZNnDhR\ndhwAAMwVxQ6SnTx5Uq1W29raFhQUuLu7y44DAIAZYykWMqWkpHh7e/fv33///v20OgAAHhDF\nDnLodLqYmBi1Wh0VFbVt2zYHBwfZiQAAMHssxUKC69evz5w5Mz09PSkpSa1Wy44DAIBCUOxg\nbEVFRWq1uqam5uDBg4MHD5YdBwAA5WApFka1e/duLy+v3r175+fn0+oAAGhbFDsYz+rVq/39\n/efNm5eSktKlSxfZcQDTdu6cOHtWdggAZoalWBhDVVVVZGTk119/vWnTpueee052HMAcLFsm\namvF+vWycwAwJxQ7GFxJSUlQUNDly5ezs7M9PDxkxwHMRF2dqKuTHQKAmWEpFoaVk5Pj6elp\nb2+v0WhodQAAGBTFDgYUFxfn5+cXGBiYnp7u5OQkOw4AAArHUiwMorq6+sUXX9y4cWNsbGxE\nRITsOAAAWASKHdpeaWlpSEhIcXFxdna2t7e37DgAAFgKlmLRxvLy8jw9Pa2srDQaDa0OaKkB\nA4RK1eh/69aJL79sOshHKgNoFlfs0Jbi4+Pnzp07c+bMNWvW2NnZyY4DmI8tW8S//91oZMUK\nodWKV19tNNi9uzFDATA7FDu0jdra2sWLF69YseLdd9997bXXZMcBzM3vftd0ZNMmUVsrJkyQ\nkQaAuaLYoQ2Ul5dPnTr12LFje/bs8fX1lR0HAAALRbHDgyosLAwKCurSpYtGo3F1dZUdBwAA\ny8WbJ/BAEhMTfXx8Ro8enZubS6sDAEAuih3uk1arjY6ODg8PX7JkSUJCgr29vexEAABYOpZi\ncT+uXr06Y8aM3NzcXbt2TZw4UXYcQImCg/msWACtRbFDq508eVKtVtva2hYUFLjzVC3AQCZP\nlp0AgPlhKRatk5KS4u3t3b9///3799PqAAAwKRQ7tJROp4uJiVGr1VFRUdu2bXNwcJCdCAAA\nNMJSLFrk+vXrM2fOTE9PT0pKUqvVsuMAAIA7oNjh3oqKitRqdU1NzcGDBwcPHiw7DgAAuDOW\nYnEPu3fv9vLy6t27d35+Pq0OAABTRrFDc1avXu3v7z9v3ryUlJQuXbrIjgMAAJrDUizurKqq\nKjIy8quvvvriiy9mzJghOw4AALg3ih3uoKSkJCgo6PLly/v37/fw8JAdBwAAtAhLsWgqJyfH\n09PT3t5eo9HQ6gAAMCMUOzQSFxfn5+cXGBiYnp7u5OQkOw4AAGgFlmLxH9XV1QsWLIiPj//0\n00/nzJkjOw4AAGg1ih2EEKK0tDQkJOTChQvZ2dne3t6y4wAAgPvBUixEXl6ep6enlZWVRqOh\n1QEAYL4odpYuPj7ez88vICAgKyurR48esuMAAID7R7GzXLW1tdHR0REREW+++WZsbKydnZ3s\nRAAA4IFwj52FKi8vnzp16rFjx/bs2ePr6ys7DgAAaAMUO0tUWFgYFBTUpUsXjUbj6uoqOw4A\nAGgbLMVanMTERB8fn9GjR+fm5tLqAABQEoqdBdFqtdHR0eHh4UuWLElISLC3t5edCAAAtCWW\nYi3F1atXZ8yYkZubu2vXrokTJ8qOAwAA2h7FziKcPHlSrVbrdLoDBw4MHDhQdhwAAGAQLMUq\n386dO729vfv165efn0+rAwBAwSh2SqbT6WJiYgIDA6OiorZv3+7g4CA7EQAAMCCWYhXr+vXr\ns2bNSktL27JlS1BQkOw4AADA4Ch2ylRUVKRWq6urq/Py8oYMGSI7DgAAMAaWYhUoNTXVy8vr\n0UcfLSgooNUBAGA5KHZKs3r16smTJ8+bNy8lJaVLly6y4wAAAONhKVY5qqqqIiMjv/rqq/Xr\n14eHh8uOAwAAjI1ipxAlJSVBQUGXL1/ev3+/h4eH7DgAAEAClmKVICcnx9PT097eXqPR0OoA\nALBYFDuzFxcX5+fnFxgYmJ6e7uTkJDsOAACQxoyLXU5Ozh//+Mfu3bs/9NBDw4cPX7FiRW1t\nrexQRlVdXf3CCy/8+c9//vTTT2NjY21tbWUnAgAAMpnNPXbOzs5Tp05dvXq1/ttNmzaFh4dr\ntVr9t0ePHj169GhOTs7WrVtVKpW8mMZTWloaEhJy4cKF7Oxsb29v2XEAAIB8ZnPF7vLly7/9\n9pv+64qKinnz5ul0usWLF589e/bKlSvJyck9evTYvn17QkKC3JzGcfjw4dGjR1tZWWk0Glod\nAADQM5ti11BSUtL169f//Oc/L126tE+fPo6OjkFBQVu3bhVC/POf/5SdzuDi4+PHjBkzadKk\nrKysHj16yI4DAABMhVkWu2PHjgkh5s6d23DQ29t7+PDhhYWFkkIZQ21tbXR0dERExJtvvhkX\nF2dnZyc7EQAAMCFmc49dQzdv3hRC9OnTp8m4u7v7iRMnZCQyhoqKitDQ0GPHju3Zs8fX11d2\nHAAAYHLM8opdv379hBBXr15tMv7LL7907txZRiKDO3r0qKen55UrVwoKCmh1AADgjsyp2G3Y\nsKF9+/bt27d/6623hBDHjx9vMuHcuXOPPvqohGQGtnnz5ieffHLUqFG5ublubm6y4wAAABNl\nNsVu4MCB/fv3d3Nzc3Nzc3d3HzhwYH5+fsMJhw8f/umnnxT2FlGtVhsdHT1jxowlS5Zs2rTJ\n3t5ediIApuHLL0VwsOwQAEyO2dxj9+OPPzY/QavVfvjhh35+fsbJYwRXr16dMWNGbm7url27\nJk6cKDsOAFNy8aIoLZUdAoDJMZtid08jR44cOXKk7BRt5uTJk2q1WqfTHThwYODAgbLjAAAA\nM2A2S7EWZefOnd7e3v369cvPz6fVAQCAFjKbYlf/6WHKptPpYmJiAgMDo6Kitm/f7uDgIDsR\nAAAwG2ZT7GxsbMaPH7958+aamhrZWQzl+vXrU6ZMee+997Zs2fLBBx9YWZnNvx0AAGAKzOke\nu6ysrKysrIcffjgiImLu3Ln6p9kpRlFRUVBQUFVVVV5e3pAhQ2THAWBK/v53cexYo5HCQvHT\nTyIystFgu3YiJkZ06GDMaABMijldE/Ly8vrDH/5QUVGxfPnyAQMGTJw4MSkp6datW7JztYHU\n1FQvLy8XF5f8/HxaHYCmWnj9XqUycA4Aps6crtg99thjX3zxxfnz5+Pi4tatW5eenp6env7I\nI4/MmTNn7ty5t3/CWAvduHGj+eXdysrK+9tyC61evXrhwoV//etf33vvPWtra4O+FgCzNH9+\n05GYGLF1q4iNlZEGgOkypyt2eq6uru+9915xcXFSUtLEiRPLysref//9vn37PvPMM1u3bq2t\nrW3V1s6cOePg4NC1WX/5y1+EECoD/ClcVVU1a9as6OjodevWffDBB7Q6AADwIMzpil1DNjY2\nISEhISEhZ8+ejYuLW79+fWpqampqao8ePUpb89DOvn37FhYWNn/F7tixY3PmzLG1tX3g1I2U\nlJQEBwdfunQpJyfH09OzbTcOAAAskLkWu3ru7u4ffPDB0qVLt27dGhsbm5WV1dotPP74481P\nqK6uvt90d7V///4pU6YMGDBAo9E4OTm1+fYBAIAFMr+l2DuytbUNDQ3NyMi45yePmYK4uLjx\n48cHBgZmZGTQ6gAAQFsx+yt2TQwYMEB2hOZUV1cvWLAgPj7+008/nTNnjuw4AMxWz57i0Udl\nhwBgcsym2G3YsKFv376yUzyQ0tLSkJCQCxcuZGdne3t7y44DwJyFh4vwcNkhAJgcsyl2M2bM\nkB3hgRw+fDgoKMjFxUWj0fTo0UN2HAAAoEAKucfOxMXHx48ZM2bs2LEZGRm0OgAAYCAUO8Oq\nra2Njo6OiIh48803v/zyy/bt28tOBAAAFMtslmJbYuHChUlJST/99JPsIP9RUVExderUo0eP\npqamjh8/XnYcAACgcIoqduXl5efPn5ed4j+OHj0aFBTUuXPngoICNzc32XEAAIDysRRrEJs3\nb37yySe9vb1zc3NpdQAAwDjM5opdWFjYPed89913RkjSPK1Wu2jRohUrVrz77ruvvfaa7DgA\nAMCCmE2x27x5s+wI93b16tXw8PD9+/fv3Lnz6aeflh0HAABYFrMpdh07duzVq9eKFSuambNq\n1aqMjAyjRWri1KlTgYGBOp0uNzd30KBBsmIAAACLZTbFbtiwYSdOnJg8ebJKpbrbnKSkJGNG\namjnzp3Tp09/6qmn4uPjO3fuLCsGAACwZGbz5okRI0ZcvXr17NmzsoM0pdPpYmJiAgMDo6Ki\ntm/fTqsDAACymM0Vu/Hjxx88eLCkpKSZT4x99tlnXVxcjJnq+vXrs2bNSktL27JlS1BQkDFf\nGgAAoAmVTqeTncHUHThwwMfHp7q62s7OruF4UVFRUFBQVVXVtm3bhgwZIiseAAAwppqamnbt\n2uXm5j755JOyszRlNkuxpiY1NdXLy8vFxSU/P59WBwAATAHF7n7ExcX5+/uHh4enpKQ4OjrK\njgMAACCEGd1jZyKqqqoiIyO/+uqrzz//fObMmbLjAAAA/BfFrhVKSkqCg4MvXryYk5Pj6ekp\nOw4AAEAjLMW2VG5urqenZ/v27TUaDa0OAACYIIpdS02aNCk0NDQzM/ORRx6RnQUAAOAOWIpt\nqU8++eSFF16QnQIAAOCuuGLXUrxVAgAAmDiKHQAAgEJQ7AAAABSCYgcAAKAQFDsAAACFoNgB\nAAAoBMUOAABAISh2AAAACkGxAwAAUAiKHQAAgEJQ7AAAABSCYgcAAKAQFDsAAACFoNgBAAAo\nBMUOAABAISh2AAAACkGxAwAAUAiKHQAAgEJQ7AAAABSCYgcAAKAQFDsAAACFoNgBAJTohRfE\njh2yQwDGRrEDACjRkSPi9GnZIQBjo9gBAAAoBMUOAABAISh2AAAACkGxAwAAUAgb2QEsz4UL\nQgjRu7fsHACgFNXVIiZGVFY2Gvz5Z7FzpygrazTo4SGee86Y0QAjo9gZ3TvvCCHEP/4hOwcA\nKEVVldBoxM2bjQYrK0VJibBqvDBlb2/MXIDxUeyMTquVnQAAlKVzZ/HNN00HPTzE9OniL3+R\nEQiQhnvsAAAAFIJiBwAAoBAUOwAAAIWg2AEAACgEb54wsMcfFz//3Gjkxg0hhNi+vdFgr17i\n+++NlwoAFM/BQXTuLDsEYGwUOwP75z/FlSuNRj78UAghXnml0WDXrsaLBACWYPduYWcnOwRg\nbBQ7AxsxounIxo1CCDFhgvGzAIAFaddOdgJAAu6xAwAAUAiKHQAAgEJQ7AAAABSCYgcAAKAQ\nvHnC6AIDZScAAADKRLEzOrVadgIAAKBMLMUCAAAoBMUOAABAISh2AAAACkGxAwAAUAiKHQAA\ngEJQ7AAAABSCYgcAAKAQFDsAAACFoNgBAAAoBMUOAABAISh2AAAACkGxAwAAUAiKHQAAgEJQ\n7AAAABTCRnYAM2BnZyeEaNeunewgAADAVOjrgalR6XQ62RnMwNGjR2traw2x5cTExE2bNn3w\nwQeG2DjM1EcffeTi4hIWFiY7CEyFTqebOXPmokWLBg0aJDsLTMWRI0fWrl2bk5MjO4iFsrGx\n+d3vfic7xR1Q7CT75JNP/v73v584cUJ2EJiQyZMnDx06NCYmRnYQmAqdTmdlZbV3796xY8fK\nzgJTsWPHjunTp1+9elV2EJgW7rEDAABQCIodAACAQlDsAAAAFIK0a/pUAAARQklEQVRiBwAA\noBAUOwAAAIWg2AEAACgExQ4AAEAhKHYAAAAKQbEDAABQCIqdZHZ2dqb5YXOQiKMCt+OoQBMc\nErgjPlJMspqamrKyMhcXF9lBYEL+/e9/t2/f/qGHHpIdBCbk3Llzbm5uKpVKdhCYirq6ugsX\nLri5uckOAtNCsQMAAFAIlmIBAAAUgmIHAACgEBQ7AAAAhaDYAQAAKATFDgAAQCEodgAAAApB\nsQMAAFAIih0AAIBCUOwAAAAUgmIHAACgEBQ7AAAAhaDYAQAAKATFDgAAQCEodgAAAApBsQMA\nAFAIil0bS05O/tOf/uTj49OpUyeVShUWFnb7nPj4eNXdabXa+pmDBg26fYKzs7MRdwgPqiWH\nhBBCp9Nt3brVz8/PxcWlQ4cO7u7uzz33XF5e3u0zz5w5M336dGdn5/bt2/fv33/x4sWVlZUG\n3gm0sbY9KjhRKEMLjwohxBdffDF69OiHHnrI3t5++PDhq1atqq2tvX0a5wrLZCM7gNIsW7bs\n0KFDDg4OvXr1OnXq1B3n9O3bd9asWU0Gf/jhh/z8fF9fX2tr64bjVlZW4eHhDUc6d+7ctplh\nUC05JIQQL7300ieffNK5c+eAgIBu3bqdOnUqOTn566+/Xr9+fcOj5fjx40899dRvv/3m7+/v\n7u6ek5Pz3nvvZWRkZGZmdujQwSg7hDbQtkeF4EShCC08KiIiIr744ouuXbsGBgZ27NgxMzPz\n5Zdfzs7O/vrrr62s/nuxhnOF5dKhTWVlZZ0+fbqurm7Hjh1CiKlTp7bwF//whz8IIRITExsO\nDhw4sF27dgaICeNpySFx5swZIUT37t1//vnn+sFt27YJIR599NGGM728vIQQ69ev13+r1Wqn\nTZsmhFi6dKkhdwJtrG2PCk4UytCSo0L/I1dX14sXL+pHqqqq/vjHPwohPv/884YzOVdYLJZi\n29i4ceP69eunUqla9Vvnz59PTU19+OGHg4KCDBQMsrTkkDh37pwQwsvLq2fPnvWDAQEBNjY2\n5eXl9SOHDx/Oz88fPnz47Nmz9SNWVlYffvihlZVVbGysTqczyA7AANrwqIBitOSoSE5OFkIs\nXLiwfqm9Xbt277//vhDi448/rp/GucKSsRRrEuLi4urq6iIiIuzs7Jr8qK6ubtmyZWfOnOnQ\nocOwYcOmTJnStWtXKSFhOIMGDbK2ti4oKLh06VL9+XrXrl21tbX+/v710zIzM4UQ+ou79Xr1\n6jVs2LDCwsJTp04NHDjQmLFhUC08KvQ4UViIS5cuCSH69u3bcLBfv35CiCNHjvzyyy+Ojo6C\nc4Vlo9jJV1tbu27dOpVKNXfu3Nt/euvWrUWLFtV/+9e//jUuLk5/RR2K0atXr7fffnvx4sWP\nPfaY/m6q06dPp6amTp48+bPPPqufdvLkSSHE7WfkAQMGcLJWnhYeFXqcKCxE9+7dxf9dza1X\n/+3JkydHjRolOFdYNpZi5du+ffulS5f8/Pz0f3U1NGvWrLS0tIsXL1ZWVh4/fvyll16qrKwM\nDw/PycmREhWGs2jRooSEhLq6ug0bNqxatWrnzp19+/adPn26/jyu99tvv4k73RTfpUsXIcSv\nv/5qzMAwgpYcFYIThSXRX6xduXLllStX9CO1tbVLlizRf/3LL7/ov+BcYckodvLFxsYKISIj\nI2//0d/+9rcJEyY4Ozt36NBhyJAha9as+dvf/qbVavV3VEBJ3n777enTp0dFRZ07d+7GjRuH\nDh1ydXV9/vnnX3/99Xv+rv6Omdbe2QnT18KjghOF5ZgyZUpAQMCZM2cGDx48b968//3f/x0+\nfPiuXbv01wWaPFThdpwrLAHFTrKzZ8+mp6c/8sgjgYGBLZn/P//zP0KI/Px8A+eCUe3Zs+et\nt94KCwuLiYlxc3Ozt7cfMWLEtm3bHn300eXLl58/f14/Tf/3t/5v8Ybu9tc5zFoLj4o74kSh\nVFZWVsnJyStXruzRo8eGDRs+//xzFxeXffv26W+pdHJy0k/jXGHJKHaSxcXF6XS6OXPm2Nra\ntmS+/kJ6dXW1gXPBqHbu3CmE8PX1bTjYoUOHUaNGabXawsJC/Yj+thj93TMNnT59WggxYMAA\nY2SFsbTwqLgjThQKZmNj8/LLLx85cuTmzZvXrl3bvXv3oEGDCgsL9ddr9XM4V1gyip1Mt27d\nWr9+/d3eNnFH2dnZ4ra3RMHc1dTUCCHKysqajF++fFkI0a5dO/2348ePF0Ls3r274ZzS0tKj\nR4/26tWLk7XCtPCouCNOFBYlLi6upqYmNDS0/gIB5wpLRrGTaevWrWVlZU8//XSfPn1u/2lB\nQcGxY8cajmg0mgULFgghmjxiHubuqaeeEkJ8/PHHJSUl9YM7duzIycmxt7cfPXq0fmTEiBFe\nXl5Hjhz58ssv9SN1dXWvvvpqXV1dVFQU980oTAuPCk4UlubUqVMNH0S3bdu2N954o1OnTvVv\noRCcKyybigcVtq3k5ORvvvlGCFFSUpKRkeHm5jZ27FghRPfu3T/66KMmk/38/DIzM5OTk+/4\nXOKPPvrolVde6du3b58+fRwcHM6dO1dYWKjT6Z599tmkpKQWLt1CupYcElqtduLEiVlZWR07\ndvT393/kkUd++OGHtLQ0IcTatWujoqLqt3b8+PExY8Zcu3YtICCgT58+OTk5hw4d8vb2zsrK\n4mOCzEgbHhWcKBSjhf/34enpefny5SFDhjz00EM//PDDiRMn7O3tk5OTJ02a1HBrnCssl7TP\nvFCoho+SasjV1bXJzFOnTqlUqh49ety6deuOmzp8+PDcuXMff/zxrl272tjYdO/efeLEiRs2\nbKirqzP4bqDttPCQqK6uXrlypZeXV6dOnaytrR9++OGAgICMjIzbN1hUVDRt2rSHH37Yzs7O\n3d399ddfv379upF2Bm2kDY8KThSK0cKjYs2aNaNGjXJ0dLSzs3Nzc4uMjDx37twdN8i5wjJx\nxQ4AAEAhuMcOAABAISh2AAAACkGxAwAAUAiKHQAAgEJQ7AAAABSCYgcAAKAQFDsAAACFoNgB\nAAAoBMUOAABAISh2AAAACkGxAwAAUAiKHQAAgEJQ7AAAABSCYgcAAKAQFDsAAACFoNgBAAAo\nBMUOAABAISh2AAAACkGxAwAAUAiKHQAAgEJQ7AAAABSCYgcAAKAQFDsAAACFoNgBAAAoBMUO\nAABAISh2AAAACkGxAwAAUAiKHQAAgEJQ7AAAABSCYgcAAKAQFDsAAACFoNgBAAAoBMUOgPGU\nlJSoVCq1Wt3MiBTPP/98jx49Kisr7+/XTWQv7ujUqVM2NjYrVqyQHQSAMVDsAJiWoqIilUoV\nFhbWwvEHl5eXl5iYuGjRInt7+zbfuHQDBgwIDw9funRpeXm57CwADM5GdgAAFsTJySknJ6db\nt27NjBjf66+/3rVr13nz5t33FkxhL5oRHR39xRdfLF++fPny5bKzADAsrtgBMB47O7sxY8Y8\n9thjzYwY2fHjx/fu3Ttt2jQ7O7v73oj0vWjewIEDR40atW7duqqqKtlZABgWxQ6A8dzzHrsP\nPvigf//+QojNmzer/k98fPzdxuu3k5eXFxIS4uzsbGdn17NnzxkzZvz444/1Py0sLFSpVLNn\nzz5z5kxYWJiTk5OVldXBgweFEP/4xz+EEA1XeK9fv25nZ+fj41M/cvPmzfbt26tUqg0bNtQP\nfvLJJyqVat26dXfcr/pXLC4ufv7557t3796hQ4eRI0fu2rWr4T+QFk57wH3U72BFRcX27dtb\n8G8JgBljKRaACQkICLC1tV24cOGoUaMWLFigH/Tx8amsrLzjuP6Lzz77LCoqqlu3bv7+/k5O\nTufOnduyZcu2bdsyMjK8vb3rN15cXOzt7d29e/dnnnnmxo0b7du3F0Kkp6fb2dl5enrWT+vU\nqZOXl9d333137dq1hx56SAiRm5tbXV0thMjIyAgPD9dPy8zMFEL4+fk1szvFxcUjR47s1atX\naGhoWVnZtm3bAgIC9u7d+9RTT7V22oPsY/0/q7S0tKlTp7b8XwcA86MDAGMpLi4WQgQGBjYz\ncvr0aSHE1KlTm/zu3cb/9a9/2draTpo0qbKysn7w6NGjnTp1GjZsmP7bI0eO6M94L730Um1t\nbf20K1euqFSqJ554osk233jjDSFESkqK/tvo6Ghra2tfX18XFxf9iFar7datm7u7+932ov4V\nFy9eXFdXpx/UX/ALCAho7bQH2Ue9mpoaW1vb/v376wAoGkuxAMzbJ598cuvWrddff/3GjRvl\n/6dnz55+fn7Hjh07f/58/czu3bvHxMRYW1vXjxQXF+t0Omdn5ybb1F+Hy8jI0H+bkZHh4eER\nEhJSUlJy6tQpIURhYWFFRUXzl+uEEL17937zzTdVKpX+2+nTp3fu3Dk/P7+10x5kH/VsbW27\ndet24cKF5gMDMHcsxQIwb3l5eUKIsWPH3vGnFy9edHV11X89fPjwJg80qaioEEI4Ojo2+a3R\no0d36NBBX+x+++23w4cPv/rqq+PHjxdCZGRkDBgwQL8Oqx9pxhNPPGFj89/TrEqlcnFx0V96\nbNW0B9nHel27dr106dL169c7derUfGwA5otiB8C86cvZN99806FDh9t/2vCdqj179mzyU/2v\n3P5eUf27XNPT08vKyvLy8rRarZ+f32OPPdazZ8+MjIz58+dnZGSoVKp7FrsuXbo0GbGxsdFq\nta2d9iD7WO/mzZsqlar+rjsAikSxA2DeOnfuLIRwdnYeOXJk8zPr1zrrOTk5if+rTU2MHz8+\nLS0tMzPzwIED7dq107/5wNfX99tvv62urs7JyRkyZIj+143gQfaxXkVFhaOjY8NLgwCUh3vs\nAJgW/f1ht1/Wutv4qFGjhBCJiYn38Vqurq6dO3du+NCQevW32WVmZvr4+OgvdPn5+V25cmXt\n2rU3bty45w12behB9lHv0qVLV69eHT58eNuFAmCKKHYATIv+8xtuv83/buMvvfSSjY3NmjVr\n9Pe91bt+/frmzZubfy1ra+sxY8Zcvnz5p59+avIjDw+PLl26bN++/cSJE/UdTv/F+++/L1pw\ng10bepB91NPfpefr62uQfABMBtfkAZgWBwcHb2/v7777btq0aYMGDbK2tlar1UOHDr3b+NCh\nQ2NjYyMjIydMmPD0008/8cQTWq32xx9/zMzMdHNzu+dj20JCQnbu3JmamhoZGdlw3MrKauzY\nsfon+tYXu969e/ft2/fMmTPW1tZ3eyuDITzgPgoh9uzZI4QIDg42fFgAMlHsAJic+Pj4l19+\nOTU1dfPmzTqdzs3NbejQoc2Mz5kzZ8SIEStXrty7d29WVlbHjh179uwZHh7eksYTFha2cOHC\nL7/8skmxE0L4+flt377dwcGh4eOL/fz8zpw54+Hhob/vzWgeZB+rq6s3b948duzYwYMHGyEq\nAIlUOp1OdgYAlqKoqKh///6hoaEtXEA0jrfeeuvtt98+duzY448/LjuLQWzYsGHmzJk7duzw\n9/eXnQWAYXGPHQDj0T/d18XFRXaQRl599dVevXotWbJEdhCDqK2tfeedd/z8/Gh1gCVgKRaA\nMRw/fnzDhg0JCQlCiJCQENlxGrG3t4+Pj8/Ozq6srLzb033NV3Fx8fTp08PCwmQHAWAMLMUC\nMIb4+Pi5c+cOGDBg0aJFoaGhsuMAgDJR7AAAABSCe+wAAAAUgmIHAACgEBQ7AAAAhaDYAQAA\nKATFDgAAQCEodgAAAApBsQMAAFAIih0AAIBCUOwAAAAUgmIHAACgEBQ7AAAAhaDYAQAAKATF\nDgAAQCEodgAAAApBsQMAAFAIih0AAIBCUOwAAAAUgmIHAACgEBQ7AAAAhaDYAQAAKATFDgAA\nQCEodgAAAApBsQMAAFAIih0AAIBCUOwAAAAUgmIHAACgEP8fAi2y7DBdlT8AAAAASUVORK5C\nYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(jitter(winner), jitter(opponent), pch=3, col='red')\n",
    "abline(0,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**Comentario**\n",
    "\n",
    "El ejemplo anterior lo podemos escribir en un sólo *script* el cual contiene las líneas de código de arriba.\n",
    "\n",
    "Archivo con extensión `.R`:\n",
    "\n",
    "```r\n",
    "winner <- c(185, 182, 182, 188, 188, 188, 185, 185, 177,\n",
    "182, 182, 193, 183, 179, 179, 175)\n",
    "\n",
    "opponent <- c(175, 193, 185, 187, 188, 173, 180, 177, 183,\n",
    "185, 180, 180, 182, 178, 178, 173)\n",
    "\n",
    "year <- seq(from=2008, to=1948, by=-4)\n",
    "\n",
    "winner[4:5] <- 189\n",
    "\n",
    "difference <- winner - opponent\n",
    "\n",
    "data.frame(year, winner, opponent, difference)\n",
    "\n",
    "taller.won <- winner > opponent\n",
    "\n",
    "if (sum(taller.won) > sum(!taller.won)) print('its true that the taller presidential candidate typically wins the election')\n",
    "```\n",
    "\n",
    "Y lo ejecutamos guardándolo con nombre `example_script_presidents_heights.R` en el directorio de trabajo, el cual se obtiene con: `getwd()`\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'/datos/ramas_repo/prope-main/R/clases/1_introduccion'"
      ],
      "text/latex": [
       "'/datos/ramas\\_repo/prope-main/R/clases/1\\_introduccion'"
      ],
      "text/markdown": [
       "'/datos/ramas_repo/prope-main/R/clases/1_introduccion'"
      ],
      "text/plain": [
       "[1] \"/datos/ramas_repo/prope-main/R/clases/1_introduccion\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "getwd()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hacemos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"its true that the taller presidential candidate typically wins the election\"\n"
     ]
    }
   ],
   "source": [
    "source(\"example_script_presidents_heights.R\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ¿Cómo ejecutamos algunos comandos de R desde bash?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una forma sencilla es con la opción de `-e`\n",
    "\n",
    "```\n",
    " R -e 'print(\"Hola Mundo!\")' -e 'library(prob)' \n",
    " ```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ¿Cómo ejecutamos un script de R desde bash?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una opción es con [Rscript](https://www.rdocumentation.org/packages/utils/versions/3.6.2/topics/Rscript)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "Rscript example_script_presidents_heights.R\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Output:*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "   year winner opponent difference\n",
    "1  2008    185      175         10\n",
    "2  2004    182      193        -11\n",
    "3  2000    182      185         -3\n",
    "4  1996    189      187          2\n",
    "5  1992    189      188          1\n",
    "6  1988    188      173         15\n",
    "7  1984    185      180          5\n",
    "8  1980    185      177          8\n",
    "9  1976    177      183         -6\n",
    "10 1972    182      185         -3\n",
    "11 1968    182      180          2\n",
    "12 1964    193      180         13\n",
    "13 1960    183      182          1\n",
    "14 1956    179      178          1\n",
    "15 1952    179      178          1\n",
    "16 1948    175      173          2\n",
    "[1] \"its true that the taller presidential candidate typically wins the election\"\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Otra opción es con [R CMD batch](https://stat.ethz.ch/R-manual/R-devel/library/utils/html/BATCH.html) la cual generará un archivo con extensión `.out`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "R CMD BATCH example_script_presidents_heights.R\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Resultado:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "cat example_script_presidents_heights.Rout \n",
    "\n",
    "R version 3.6.3 (2020-02-29) -- \"Holding the Windsock\"\n",
    "Copyright (C) 2020 The R Foundation for Statistical Computing\n",
    "Platform: x86_64-pc-linux-gnu (64-bit)\n",
    "\n",
    "R is free software and comes with ABSOLUTELY NO WARRANTY.\n",
    "You are welcome to redistribute it under certain conditions.\n",
    "Type 'license()' or 'licence()' for distribution details.\n",
    "\n",
    "R is a collaborative project with many contributors.\n",
    "Type 'contributors()' for more information and\n",
    "'citation()' on how to cite R or R packages in publications.\n",
    "\n",
    "Type 'demo()' for some demos, 'help()' for on-line help, or\n",
    "'help.start()' for an HTML browser interface to help.\n",
    "Type 'q()' to quit R.\n",
    "\n",
    "> #Archivo con extensión .R:\n",
    "> winner <- c(185, 182, 182, 188, 188, 188, 185, 185, 177,\n",
    "+ 182, 182, 193, 183, 179, 179, 175)\n",
    "> opponent <- c(175, 193, 185, 187, 188, 173, 180, 177, 183,\n",
    "+ 185, 180, 180, 182, 178, 178, 173)\n",
    "> year = seq(from=2008, to=1948, by=-4)\n",
    "> winner[4:5] = 189\n",
    "> difference = winner - opponent\n",
    "> data.frame(year, winner, opponent, difference)\n",
    "   year winner opponent difference\n",
    "1  2008    185      175         10\n",
    "2  2004    182      193        -11\n",
    "3  2000    182      185         -3\n",
    "4  1996    189      187          2\n",
    "5  1992    189      188          1\n",
    "6  1988    188      173         15\n",
    "7  1984    185      180          5\n",
    "8  1980    185      177          8\n",
    "9  1976    177      183         -6\n",
    "10 1972    182      185         -3\n",
    "11 1968    182      180          2\n",
    "12 1964    193      180         13\n",
    "13 1960    183      182          1\n",
    "14 1956    179      178          1\n",
    "15 1952    179      178          1\n",
    "16 1948    175      173          2\n",
    "> taller.won = winner > opponent\n",
    "> if (sum(taller.won) > sum(!taller.won))\n",
    "+     print('its true that the taller presidential candidate typically wins the election')\n",
    "[1] \"its true that the taller presidential candidate typically wins the election\"\n",
    "> \n",
    "> proc.time()\n",
    "   user  system elapsed \n",
    "  0.140   0.020   0.193 \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Funciones"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sintaxis de una función:\n",
    "\n",
    "```r\n",
    "f <- function(x, ...){\n",
    "\n",
    "}\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aquí `f` es el nombre de la función, `x` es el nombre del primer parámetro, `...` indica parámetros posibles (las funciones pueden definirse sin parámetros). Los `{}` encierran el cuerpo de la función. El valor que regresa la función es el valor de la última expresión evaluada."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejemplo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "variance_simple_computation <- \n",
    "function(x){\n",
    "    v <- var(x)\n",
    "    n <- NROW(x) #number of observations in x\n",
    "    v*(n-1)/n\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La cual calcula: $$ \\hat{\\sigma}^2 = \\frac{1}{n}\\displaystyle \\sum_{i=1}^n(x_i - \\bar{x})^2 = \\frac{n-1}{n}s^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "vec <- c(51.9, 51.8, 51.9, 53)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.242500000000001"
      ],
      "text/latex": [
       "0.242500000000001"
      ],
      "text/markdown": [
       "0.242500000000001"
      ],
      "text/plain": [
       "[1] 0.2425"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "variance_simple_computation(vec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**Observación** \n",
    "\n",
    "Antes del último `}` anterior, el *statement* `return v*(n-1)/n` también es utilizado.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Argumentos de funciones"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Supóngase que se desea aproximar la integral $$B(a,b) = \\displaystyle \\int_0^1x^{a-1}(1-x)^{b-1}dx,$$ para constantes $a >0, b > 0$ conocidas. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se utiliza la función [integrate](https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/integrate) y la definición del integrando dada por:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "f <- function(x, a=1, b=1)\n",
    "    x^(a-1)*(1-x)^(b-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**Observación**\n",
    "\n",
    "Para el cuerpo de una función que sólo tiene una línea, no son necesarios `{}`. También obsérvese que se definieron valores por *default* \n",
    "para los parámetros `a` y `b`.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "x <- seq(0,1,.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 0.00 0.16 0.24 0.24 0.16 0.00\n"
     ]
    }
   ],
   "source": [
    "print(f(x,a=2,b=2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**Observación** \n",
    "\n",
    "Se definió `x` como un vector y se le pasó a la `f`. Entonces la `f` realiza las operaciones de una forma vectorizada y devuelve un vector del mismo tamaño que `x`.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1666667 with absolute error < 1.9e-15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "integrate(f, lower = 0, upper = 1, a=2, b=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**Observación** \n",
    "\n",
    "La función `integrate` es un ejemplo de una función con *extra arguments*.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre class=language-r><code>function (f, lower, upper, ..., subdivisions = 100L, rel.tol = .Machine$double.eps^0.25, \n",
       "<span style=white-space:pre-wrap>    abs.tol = rel.tol, stop.on.error = TRUE, keep.xy = FALSE, </span>\n",
       "<span style=white-space:pre-wrap>    aux = NULL) </span>\n",
       "NULL</code></pre>"
      ],
      "text/latex": [
       "\\begin{minted}{r}\n",
       "function (f, lower, upper, ..., subdivisions = 100L, rel.tol = .Machine\\$double.eps\\textasciicircum{}0.25, \n",
       "    abs.tol = rel.tol, stop.on.error = TRUE, keep.xy = FALSE, \n",
       "    aux = NULL) \n",
       "NULL\n",
       "\\end{minted}"
      ],
      "text/markdown": [
       "```r\n",
       "function (f, lower, upper, ..., subdivisions = 100L, rel.tol = .Machine$double.eps^0.25, \n",
       "    abs.tol = rel.tol, stop.on.error = TRUE, keep.xy = FALSE, \n",
       "    aux = NULL) \n",
       "NULL\n",
       "```"
      ],
      "text/plain": [
       "function (f, lower, upper, ..., subdivisions = 100L, rel.tol = .Machine$double.eps^0.25, \n",
       "    abs.tol = rel.tol, stop.on.error = TRUE, keep.xy = FALSE, \n",
       "    aux = NULL) \n",
       "NULL"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "args(integrate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "los tres puntos que se observan son los *extra arguments* y en el ejemplo son $a$ y $b$ que se le pasan a la función `f` y la función `integrate` no los utiliza ni los tiene definidos."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se puede realizar la gráfica de una función con la función [curve](https://www.rdocumentation.org/packages/graphics/versions/3.6.2/topics/curve). En el caso anterior si deseamos graficar el integrando: $x^{a-1}*(1-x)^{b-1}$ para $x$ de $0$ a $1$ y $a=b=.5$ se ejecuta:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ht7H/4e2pNkGrCxHveQTEMXJMq1lImCdLb6uxTTgJ3NjztDMY3ZIN1zqvjB1qso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\nBEAAQQIggCABEECQAAj8P/a6xBZQ0df7AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "curve(x^.5*(1-x)^.5, from = 0, to=1, ylab=\"f(x)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vectores y Matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ejemplo: class mobility"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following model of class mobility is discussed in Ross [Introduction to Probability Models, Example 4.19, p. 207]. Assume that the class of a child (lower, middle, or upper class) depends only on the class of his/her parents. The class of the parents is indicated by the row label. The entries in the table below correspond to the chance that the child will transition to the class indicated by the column label."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|-----| lower | middle | upper |\n",
    "|-----|:-----:|:------:|:-----:|\n",
    "|lower| 0.45  | 0.48   | 0.07  | \n",
    "|middle| 0.05 | 0.70   | 0.25  |\n",
    "|upper|0.01   |0.5|0.49|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To create a matrix with these transition probabilities, we use the matrix function. First, the vector of probabilities probs is constructed to supply the entries of the matrix. Then the matrix is defined by its entries, number of rows, and number of columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "probs <- c(.45, .05, .01, .48, .70, .50, .07, .25, .49)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [matrix](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "P <- matrix(probs, nrow=3, ncol=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 3 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>0.45</td><td>0.48</td><td>0.07</td></tr>\n",
       "\t<tr><td>0.05</td><td>0.70</td><td>0.25</td></tr>\n",
       "\t<tr><td>0.01</td><td>0.50</td><td>0.49</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       "\t 0.45 & 0.48 & 0.07\\\\\n",
       "\t 0.05 & 0.70 & 0.25\\\\\n",
       "\t 0.01 & 0.50 & 0.49\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type dbl\n",
       "\n",
       "| 0.45 | 0.48 | 0.07 |\n",
       "| 0.05 | 0.70 | 0.25 |\n",
       "| 0.01 | 0.50 | 0.49 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 0.45 0.48 0.07\n",
       "[2,] 0.05 0.70 0.25\n",
       "[3,] 0.01 0.50 0.49"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the values are entered by column; to enter the data by row, use the optional argument byrow=TRUE in the matrix function. Matrices can optionally have row names and column names. In this case, row names and column names are identical, so we can assign both using"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "rownames(P) <- colnames(P) <- c(\"lower\", \"middle\", \"upper\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the updated value of P is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 3 × 3 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>lower</th><th scope=col>middle</th><th scope=col>upper</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>lower</th><td>0.45</td><td>0.48</td><td>0.07</td></tr>\n",
       "\t<tr><th scope=row>middle</th><td>0.05</td><td>0.70</td><td>0.25</td></tr>\n",
       "\t<tr><th scope=row>upper</th><td>0.01</td><td>0.50</td><td>0.49</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type dbl\n",
       "\\begin{tabular}{r|lll}\n",
       "  & lower & middle & upper\\\\\n",
       "\\hline\n",
       "\tlower & 0.45 & 0.48 & 0.07\\\\\n",
       "\tmiddle & 0.05 & 0.70 & 0.25\\\\\n",
       "\tupper & 0.01 & 0.50 & 0.49\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type dbl\n",
       "\n",
       "| <!--/--> | lower | middle | upper |\n",
       "|---|---|---|---|\n",
       "| lower | 0.45 | 0.48 | 0.07 |\n",
       "| middle | 0.05 | 0.70 | 0.25 |\n",
       "| upper | 0.01 | 0.50 | 0.49 |\n",
       "\n"
      ],
      "text/plain": [
       "       lower middle upper\n",
       "lower  0.45  0.48   0.07 \n",
       "middle 0.05  0.70   0.25 \n",
       "upper  0.01  0.50   0.49 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See: [rownames](https://www.rdocumentation.org/packages/tibble/versions/3.0.1/topics/rownames), [colnames](https://www.rdocumentation.org/packages/gpuR/versions/2.0.3/topics/colnames)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the matrix $P = (p_{ij})$, the probability $p_{ij}$ in the $i$-th row and $j$-th column is the probability of a transition from class $i$ to class $j$ in one generation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This type of matrix has rows that sum to 1 (because each row is a probability distribution on the three classes). This fact can be verified by the [rowSums](https://www.rdocumentation.org/packages/raster/versions/3.1-5/topics/rowSums) function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>lower</dt><dd>1</dd><dt>middle</dt><dd>1</dd><dt>upper</dt><dd>1</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[lower] 1\n",
       "\\item[middle] 1\n",
       "\\item[upper] 1\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "lower\n",
       ":   1middle\n",
       ":   1upper\n",
       ":   1\n",
       "\n"
      ],
      "text/plain": [
       " lower middle  upper \n",
       "     1      1      1 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rowSums(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another approach uses the [apply](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/apply) function. It requires specifying the name of the matrix, MARGIN (row=1, column=2), and FUN (function) as its arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>lower</dt><dd>1</dd><dt>middle</dt><dd>1</dd><dt>upper</dt><dd>1</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[lower] 1\n",
       "\\item[middle] 1\n",
       "\\item[upper] 1\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "lower\n",
       ":   1middle\n",
       ":   1upper\n",
       ":   1\n",
       "\n"
      ],
      "text/plain": [
       " lower middle  upper \n",
       "     1      1      1 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "apply(P, MARGIN=1, FUN=sum)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be shown that the transition probabilities for two generations are given by the product $P^2 =PP$, which can be computed by the matrix multiplication operator [%*%](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/matmult)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 3 × 3 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>lower</th><th scope=col>middle</th><th scope=col>upper</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>lower</th><td>0.2272</td><td>0.5870</td><td>0.1858</td></tr>\n",
       "\t<tr><th scope=row>middle</th><td>0.0600</td><td>0.6390</td><td>0.3010</td></tr>\n",
       "\t<tr><th scope=row>upper</th><td>0.0344</td><td>0.5998</td><td>0.3658</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type dbl\n",
       "\\begin{tabular}{r|lll}\n",
       "  & lower & middle & upper\\\\\n",
       "\\hline\n",
       "\tlower & 0.2272 & 0.5870 & 0.1858\\\\\n",
       "\tmiddle & 0.0600 & 0.6390 & 0.3010\\\\\n",
       "\tupper & 0.0344 & 0.5998 & 0.3658\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type dbl\n",
       "\n",
       "| <!--/--> | lower | middle | upper |\n",
       "|---|---|---|---|\n",
       "| lower | 0.2272 | 0.5870 | 0.1858 |\n",
       "| middle | 0.0600 | 0.6390 | 0.3010 |\n",
       "| upper | 0.0344 | 0.5998 | 0.3658 |\n",
       "\n"
      ],
      "text/plain": [
       "       lower  middle upper \n",
       "lower  0.2272 0.5870 0.1858\n",
       "middle 0.0600 0.6390 0.3010\n",
       "upper  0.0344 0.5998 0.3658"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P2 <- P %*% P\n",
    "P2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$P^2$ squares every element of the matrix and the result is the matrix $(p^2_{ij})$, not the matrix product.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 3 × 3 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>lower</th><th scope=col>middle</th><th scope=col>upper</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>lower</th><td>0.2025</td><td>0.2304</td><td>0.0049</td></tr>\n",
       "\t<tr><th scope=row>middle</th><td>0.0025</td><td>0.4900</td><td>0.0625</td></tr>\n",
       "\t<tr><th scope=row>upper</th><td>0.0001</td><td>0.2500</td><td>0.2401</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type dbl\n",
       "\\begin{tabular}{r|lll}\n",
       "  & lower & middle & upper\\\\\n",
       "\\hline\n",
       "\tlower & 0.2025 & 0.2304 & 0.0049\\\\\n",
       "\tmiddle & 0.0025 & 0.4900 & 0.0625\\\\\n",
       "\tupper & 0.0001 & 0.2500 & 0.2401\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type dbl\n",
       "\n",
       "| <!--/--> | lower | middle | upper |\n",
       "|---|---|---|---|\n",
       "| lower | 0.2025 | 0.2304 | 0.0049 |\n",
       "| middle | 0.0025 | 0.4900 | 0.0625 |\n",
       "| upper | 0.0001 | 0.2500 | 0.2401 |\n",
       "\n"
      ],
      "text/plain": [
       "       lower  middle upper \n",
       "lower  0.2025 0.2304 0.0049\n",
       "middle 0.0025 0.4900 0.0625\n",
       "upper  0.0001 0.2500 0.2401"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P^2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To extract elements from the matrix, the [row, column] syntax is used. If the row or column is omitted, this specifies all rows (columns). In two generations, the probability that descendants of lower class parents can transition to upper class is in row 1, column 3:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.1858"
      ],
      "text/latex": [
       "0.1858"
      ],
      "text/markdown": [
       "0.1858"
      ],
      "text/plain": [
       "[1] 0.1858"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P2[1,3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the probability distribution for lower class to (lower, middle, upper) is given by row 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>lower</dt><dd>0.2272</dd><dt>middle</dt><dd>0.587</dd><dt>upper</dt><dd>0.1858</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[lower] 0.2272\n",
       "\\item[middle] 0.587\n",
       "\\item[upper] 0.1858\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "lower\n",
       ":   0.2272middle\n",
       ":   0.587upper\n",
       ":   0.1858\n",
       "\n"
      ],
      "text/plain": [
       " lower middle  upper \n",
       "0.2272 0.5870 0.1858 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P2[1,]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After several generations, each row of the transition matrix will be approximately equal, with probabilities $p = (l,m,u)$ corresponding to the percentages of lower, middle, and upper class occupations. After eight transitions, the probabilities are $P8$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 3 × 3 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>lower</th><th scope=col>middle</th><th scope=col>upper</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>lower</th><td>0.06350395</td><td>0.6233444</td><td>0.3131516</td></tr>\n",
       "\t<tr><th scope=row>middle</th><td>0.06239010</td><td>0.6234412</td><td>0.3141687</td></tr>\n",
       "\t<tr><th scope=row>upper</th><td>0.06216410</td><td>0.6234574</td><td>0.3143785</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type dbl\n",
       "\\begin{tabular}{r|lll}\n",
       "  & lower & middle & upper\\\\\n",
       "\\hline\n",
       "\tlower & 0.06350395 & 0.6233444 & 0.3131516\\\\\n",
       "\tmiddle & 0.06239010 & 0.6234412 & 0.3141687\\\\\n",
       "\tupper & 0.06216410 & 0.6234574 & 0.3143785\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type dbl\n",
       "\n",
       "| <!--/--> | lower | middle | upper |\n",
       "|---|---|---|---|\n",
       "| lower | 0.06350395 | 0.6233444 | 0.3131516 |\n",
       "| middle | 0.06239010 | 0.6234412 | 0.3141687 |\n",
       "| upper | 0.06216410 | 0.6234574 | 0.3143785 |\n",
       "\n"
      ],
      "text/plain": [
       "       lower      middle    upper    \n",
       "lower  0.06350395 0.6233444 0.3131516\n",
       "middle 0.06239010 0.6234412 0.3141687\n",
       "upper  0.06216410 0.6234574 0.3143785"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P4 <- P2 %*% P2\n",
    "P8 <- P4 %*% P4\n",
    "P8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be shown that the limiting probabilities are 0.07, 0.62, and 0.31. For the solution $p = (l,m,u)$, see Ross [Introduction to Probability Models, p. 207]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To enter a matrix of constants, as in this example, it is usually easier to enter data by rows using byrow=TRUE in the matrix function. The `by row` format makes it easier to see (visually) the data vector as a matrix in the code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q <- matrix(c( 0.45, 0.48, 0.07,\n",
    "               0.05, 0.70, 0.25, \n",
    "               0.01, 0.50, 0.49), nrow=3, ncol=3, byrow=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 3 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>0.45</td><td>0.48</td><td>0.07</td></tr>\n",
       "\t<tr><td>0.05</td><td>0.70</td><td>0.25</td></tr>\n",
       "\t<tr><td>0.01</td><td>0.50</td><td>0.49</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       "\t 0.45 & 0.48 & 0.07\\\\\n",
       "\t 0.05 & 0.70 & 0.25\\\\\n",
       "\t 0.01 & 0.50 & 0.49\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type dbl\n",
       "\n",
       "| 0.45 | 0.48 | 0.07 |\n",
       "| 0.05 | 0.70 | 0.25 |\n",
       "| 0.01 | 0.50 | 0.49 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 0.45 0.48 0.07\n",
       "[2,] 0.05 0.70 0.25\n",
       "[3,] 0.01 0.50 0.49"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix operations for numeric matrices in R:\n",
    "\n",
    "* Elementwise multiplication: $*$\n",
    "  \n",
    "  If matrices $A = (a_{ij})$ and $B = (b_{ij})$ have the same dimension, then $A*B$ is evaluated as the matrix with entries $(a_{ij}b_{ij})$.\n",
    "  \n",
    "* If $A = (a_{ij})$ is a matrix then $A^r$ is evaluated as the matrix with entries $(a_{rij})$.\n",
    "\n",
    "* Matrix multiplication: $\\%*\\%$\n",
    "\n",
    "  If $A = (a_{ij})$ is an $n x k$ matrix and $B = (b_{ij})$ is a $k x m$ matrix, then $A \\%*\\% B$ is evaluated as the $n x m$ matrix product $AB$.\n",
    "\n",
    "* Matrix inverse:\n",
    "\n",
    "  If A is a nonsingular matrix, the inverse of A is returned by *solve(A)*. See [solve](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/solve).\n",
    "  \n",
    "  For eigenvalues and matrix factorization see [eigen](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/eigen), [qr](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/qr), [chol](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/chol), [svd](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/svd)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Frames"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Un *data frame* tiene renglones y columnas. Las variables corresponden a las columnas y las observaciones a los renglones. Las variables pueden ser numéricas (números) o categóricas (caracteres o factores)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ejemplo: USArrests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<table width=\"100%\" summary=\"page for datasets-package {datasets}\"><tr><td>datasets-package {datasets}</td><td style=\"text-align: right;\">R Documentation</td></tr></table>\n",
       "\n",
       "<h2>\n",
       "The R Datasets Package\n",
       "</h2>\n",
       "\n",
       "<h3>Description</h3>\n",
       "\n",
       "<p>Base R datasets\n",
       "</p>\n",
       "\n",
       "\n",
       "<h3>Details</h3>\n",
       "\n",
       "<p>This package contains a variety of datasets.  For a complete\n",
       "list, use <code>library(help = \"datasets\")</code>.\n",
       "</p>\n",
       "\n",
       "\n",
       "<h3>Author(s)</h3>\n",
       "\n",
       "<p>R Core Team and contributors worldwide\n",
       "</p>\n",
       "<p>Maintainer: R Core Team <a href=\"mailto:R-core@r-project.org\">R-core@r-project.org</a>\n",
       "</p>\n",
       "\n",
       "<hr /><div style=\"text-align: center;\">[Package <em>datasets</em> version 4.1.0 ]</div>"
      ],
      "text/latex": [
       "\\inputencoding{utf8}\n",
       "\\HeaderA{datasets-package}{The R Datasets Package}{datasets.Rdash.package}\n",
       "\\aliasA{datasets}{datasets-package}{datasets}\n",
       "\\keyword{package}{datasets-package}\n",
       "%\n",
       "\\begin{Description}\\relax\n",
       "Base R datasets\n",
       "\\end{Description}\n",
       "%\n",
       "\\begin{Details}\\relax\n",
       "This package contains a variety of datasets.  For a complete\n",
       "list, use \\code{library(help = \"datasets\")}.\n",
       "\\end{Details}\n",
       "%\n",
       "\\begin{Author}\\relax\n",
       "R Core Team and contributors worldwide\n",
       "\n",
       "Maintainer: R Core Team \\email{R-core@r-project.org}\n",
       "\\end{Author}"
      ],
      "text/plain": [
       "datasets-package           package:datasets            R Documentation\n",
       "\n",
       "_\bT_\bh_\be _\bR _\bD_\ba_\bt_\ba_\bs_\be_\bt_\bs _\bP_\ba_\bc_\bk_\ba_\bg_\be\n",
       "\n",
       "_\bD_\be_\bs_\bc_\br_\bi_\bp_\bt_\bi_\bo_\bn:\n",
       "\n",
       "     Base R datasets\n",
       "\n",
       "_\bD_\be_\bt_\ba_\bi_\bl_\bs:\n",
       "\n",
       "     This package contains a variety of datasets.  For a complete list,\n",
       "     use ‘library(help = \"datasets\")’.\n",
       "\n",
       "_\bA_\bu_\bt_\bh_\bo_\br(_\bs):\n",
       "\n",
       "     R Core Team and contributors worldwide\n",
       "\n",
       "     Maintainer: R Core Team <email: R-core@r-project.org>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "?datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<table width=\"100%\" summary=\"page for USArrests {datasets}\"><tr><td>USArrests {datasets}</td><td style=\"text-align: right;\">R Documentation</td></tr></table>\n",
       "\n",
       "<h2>Violent Crime Rates by US State</h2>\n",
       "\n",
       "<h3>Description</h3>\n",
       "\n",
       "<p>This data set contains statistics, in arrests per 100,000 residents\n",
       "for assault, murder, and rape in each of the 50 US states in 1973.\n",
       "Also given is the percent of the population living in urban areas.\n",
       "</p>\n",
       "\n",
       "\n",
       "<h3>Usage</h3>\n",
       "\n",
       "<pre>USArrests</pre>\n",
       "\n",
       "\n",
       "<h3>Format</h3>\n",
       "\n",
       "<p>A data frame with 50 observations on 4 variables.\n",
       "</p>\n",
       "\n",
       "<table summary=\"Rd table\">\n",
       "<tr>\n",
       " <td style=\"text-align: right;\">\n",
       "    [,1]  </td><td style=\"text-align: left;\"> Murder    </td><td style=\"text-align: left;\"> numeric </td><td style=\"text-align: left;\"> Murder arrests (per 100,000)</td>\n",
       "</tr>\n",
       "<tr>\n",
       " <td style=\"text-align: right;\">\n",
       "    [,2]  </td><td style=\"text-align: left;\"> Assault   </td><td style=\"text-align: left;\"> numeric </td><td style=\"text-align: left;\"> Assault arrests (per 100,000)</td>\n",
       "</tr>\n",
       "<tr>\n",
       " <td style=\"text-align: right;\">\n",
       "    [,3]  </td><td style=\"text-align: left;\"> UrbanPop  </td><td style=\"text-align: left;\"> numeric </td><td style=\"text-align: left;\"> Percent urban population</td>\n",
       "</tr>\n",
       "<tr>\n",
       " <td style=\"text-align: right;\">\n",
       "    [,4]  </td><td style=\"text-align: left;\"> Rape      </td><td style=\"text-align: left;\"> numeric </td><td style=\"text-align: left;\"> Rape arrests (per 100,000)\n",
       "  </td>\n",
       "</tr>\n",
       "\n",
       "</table>\n",
       "\n",
       "\n",
       "\n",
       "<h3>Note</h3>\n",
       "\n",
       "<p><code>USArrests</code> contains the data as in McNeil's monograph.  For the\n",
       "<code>UrbanPop</code> percentages, a review of the table (No. 21) in the\n",
       "Statistical Abstracts 1975 reveals a transcription error for Maryland\n",
       "(and that McNeil used the same &ldquo;round to even&rdquo; rule that <span style=\"font-family: Courier New, Courier; color: #666666;\"><b>R</b></span>'s\n",
       "<code>round()</code> uses), as found by Daniel S Coven (Arizona).\n",
       "</p>\n",
       "<p>See the example below on how to correct the error and improve accuracy\n",
       "for the &lsquo;&lt;n&gt;.5&rsquo; percentages.\n",
       "</p>\n",
       "\n",
       "\n",
       "<h3>Source</h3>\n",
       "\n",
       "<p>World Almanac and Book of facts 1975.  (Crime rates).\n",
       "</p>\n",
       "<p>Statistical Abstracts of the United States 1975, p.20, (Urban rates),\n",
       "possibly available as\n",
       "<a href=\"https://books.google.ch/books?id=zl9qAAAAMAAJ&amp;pg=PA20\">https://books.google.ch/books?id=zl9qAAAAMAAJ&amp;pg=PA20</a>.\n",
       "</p>\n",
       "\n",
       "\n",
       "<h3>References</h3>\n",
       "\n",
       "<p>McNeil, D. R. (1977)\n",
       "<em>Interactive Data Analysis</em>.\n",
       "New York: Wiley.\n",
       "</p>\n",
       "\n",
       "\n",
       "<h3>See Also</h3>\n",
       "\n",
       "<p>The <code>state</code> data sets.</p>\n",
       "\n",
       "\n",
       "<h3>Examples</h3>\n",
       "\n",
       "<pre>\n",
       "summary(USArrests)\n",
       "\n",
       "require(graphics)\n",
       "pairs(USArrests, panel = panel.smooth, main = \"USArrests data\")\n",
       "\n",
       "## Difference between 'USArrests' and its correction\n",
       "USArrests[\"Maryland\", \"UrbanPop\"] # 67 -- the transcription error\n",
       "UA.C &lt;- USArrests\n",
       "UA.C[\"Maryland\", \"UrbanPop\"] &lt;- 76.6\n",
       "\n",
       "## also +/- 0.5 to restore the original  &lt;n&gt;.5  percentages\n",
       "s5u &lt;- c(\"Colorado\", \"Florida\", \"Mississippi\", \"Wyoming\")\n",
       "s5d &lt;- c(\"Nebraska\", \"Pennsylvania\")\n",
       "UA.C[s5u, \"UrbanPop\"] &lt;- UA.C[s5u, \"UrbanPop\"] + 0.5\n",
       "UA.C[s5d, \"UrbanPop\"] &lt;- UA.C[s5d, \"UrbanPop\"] - 0.5\n",
       "\n",
       "## ==&gt; UA.C  is now a *C*orrected version of  USArrests\n",
       "</pre>\n",
       "\n",
       "<hr /><div style=\"text-align: center;\">[Package <em>datasets</em> version 3.6.3 ]</div>"
      ],
      "text/latex": [
       "\\inputencoding{utf8}\n",
       "\\HeaderA{USArrests}{Violent Crime Rates by US State}{USArrests}\n",
       "\\keyword{datasets}{USArrests}\n",
       "%\n",
       "\\begin{Description}\\relax\n",
       "This data set contains statistics, in arrests per 100,000 residents\n",
       "for assault, murder, and rape in each of the 50 US states in 1973.\n",
       "Also given is the percent of the population living in urban areas.\n",
       "\\end{Description}\n",
       "%\n",
       "\\begin{Usage}\n",
       "\\begin{verbatim}\n",
       "USArrests\n",
       "\\end{verbatim}\n",
       "\\end{Usage}\n",
       "%\n",
       "\\begin{Format}\n",
       "A data frame with 50 observations on 4 variables.\n",
       "\n",
       "\n",
       "\\Tabular{rlll}{\n",
       "[,1]  & Murder    & numeric & Murder arrests (per 100,000)\\\\{}\n",
       "[,2]  & Assault   & numeric & Assault arrests (per 100,000)\\\\{}\n",
       "[,3]  & UrbanPop  & numeric & Percent urban population\\\\{}\n",
       "[,4]  & Rape      & numeric & Rape arrests (per 100,000)\n",
       "}\n",
       "\\end{Format}\n",
       "%\n",
       "\\begin{Note}\\relax\n",
       "\\code{USArrests} contains the data as in McNeil's monograph.  For the\n",
       "\\code{UrbanPop} percentages, a review of the table (No. 21) in the\n",
       "Statistical Abstracts 1975 reveals a transcription error for Maryland\n",
       "(and that McNeil used the same ``round to even'' rule that \\R{}'s\n",
       "\\code{\\LinkA{round}{round}()} uses), as found by Daniel S Coven (Arizona).\n",
       "\n",
       "See the example below on how to correct the error and improve accuracy\n",
       "for the `<n>.5' percentages.\n",
       "\\end{Note}\n",
       "%\n",
       "\\begin{Source}\\relax\n",
       "World Almanac and Book of facts 1975.  (Crime rates).\n",
       "\n",
       "Statistical Abstracts of the United States 1975, p.20, (Urban rates),\n",
       "possibly available as\n",
       "\\url{https://books.google.ch/books?id=zl9qAAAAMAAJ&pg=PA20}.\n",
       "\\end{Source}\n",
       "%\n",
       "\\begin{References}\\relax\n",
       "McNeil, D. R. (1977)\n",
       "\\emph{Interactive Data Analysis}.\n",
       "New York: Wiley.\n",
       "\\end{References}\n",
       "%\n",
       "\\begin{SeeAlso}\\relax\n",
       "The \\code{\\LinkA{state}{state}} data sets.\n",
       "\\end{SeeAlso}\n",
       "%\n",
       "\\begin{Examples}\n",
       "\\begin{ExampleCode}\n",
       "summary(USArrests)\n",
       "\n",
       "require(graphics)\n",
       "pairs(USArrests, panel = panel.smooth, main = \"USArrests data\")\n",
       "\n",
       "## Difference between 'USArrests' and its correction\n",
       "USArrests[\"Maryland\", \"UrbanPop\"] # 67 -- the transcription error\n",
       "UA.C <- USArrests\n",
       "UA.C[\"Maryland\", \"UrbanPop\"] <- 76.6\n",
       "\n",
       "## also +/- 0.5 to restore the original  <n>.5  percentages\n",
       "s5u <- c(\"Colorado\", \"Florida\", \"Mississippi\", \"Wyoming\")\n",
       "s5d <- c(\"Nebraska\", \"Pennsylvania\")\n",
       "UA.C[s5u, \"UrbanPop\"] <- UA.C[s5u, \"UrbanPop\"] + 0.5\n",
       "UA.C[s5d, \"UrbanPop\"] <- UA.C[s5d, \"UrbanPop\"] - 0.5\n",
       "\n",
       "## ==> UA.C  is now a *C*orrected version of  USArrests\n",
       "\\end{ExampleCode}\n",
       "\\end{Examples}"
      ],
      "text/plain": [
       "USArrests               package:datasets               R Documentation\n",
       "\n",
       "_\bV_\bi_\bo_\bl_\be_\bn_\bt _\bC_\br_\bi_\bm_\be _\bR_\ba_\bt_\be_\bs _\bb_\by _\bU_\bS _\bS_\bt_\ba_\bt_\be\n",
       "\n",
       "_\bD_\be_\bs_\bc_\br_\bi_\bp_\bt_\bi_\bo_\bn:\n",
       "\n",
       "     This data set contains statistics, in arrests per 100,000\n",
       "     residents for assault, murder, and rape in each of the 50 US\n",
       "     states in 1973.  Also given is the percent of the population\n",
       "     living in urban areas.\n",
       "\n",
       "_\bU_\bs_\ba_\bg_\be:\n",
       "\n",
       "     USArrests\n",
       "     \n",
       "_\bF_\bo_\br_\bm_\ba_\bt:\n",
       "\n",
       "     A data frame with 50 observations on 4 variables.\n",
       "\n",
       "       [,1]  Murder    numeric  Murder arrests (per 100,000)  \n",
       "       [,2]  Assault   numeric  Assault arrests (per 100,000) \n",
       "       [,3]  UrbanPop  numeric  Percent urban population      \n",
       "       [,4]  Rape      numeric  Rape arrests (per 100,000)    \n",
       "      \n",
       "_\bN_\bo_\bt_\be:\n",
       "\n",
       "     ‘USArrests’ contains the data as in McNeil's monograph.  For the\n",
       "     ‘UrbanPop’ percentages, a review of the table (No. 21) in the\n",
       "     Statistical Abstracts 1975 reveals a transcription error for\n",
       "     Maryland (and that McNeil used the same “round to even” rule that\n",
       "     R's ‘round()’ uses), as found by Daniel S Coven (Arizona).\n",
       "\n",
       "     See the example below on how to correct the error and improve\n",
       "     accuracy for the ‘<n>.5’ percentages.\n",
       "\n",
       "_\bS_\bo_\bu_\br_\bc_\be:\n",
       "\n",
       "     World Almanac and Book of facts 1975.  (Crime rates).\n",
       "\n",
       "     Statistical Abstracts of the United States 1975, p.20, (Urban\n",
       "     rates), possibly available as <URL:\n",
       "     https://books.google.ch/books?id=zl9qAAAAMAAJ&pg=PA20>.\n",
       "\n",
       "_\bR_\be_\bf_\be_\br_\be_\bn_\bc_\be_\bs:\n",
       "\n",
       "     McNeil, D. R. (1977) _Interactive Data Analysis_.  New York:\n",
       "     Wiley.\n",
       "\n",
       "_\bS_\be_\be _\bA_\bl_\bs_\bo:\n",
       "\n",
       "     The ‘state’ data sets.\n",
       "\n",
       "_\bE_\bx_\ba_\bm_\bp_\bl_\be_\bs:\n",
       "\n",
       "     summary(USArrests)\n",
       "     \n",
       "     require(graphics)\n",
       "     pairs(USArrests, panel = panel.smooth, main = \"USArrests data\")\n",
       "     \n",
       "     ## Difference between 'USArrests' and its correction\n",
       "     USArrests[\"Maryland\", \"UrbanPop\"] # 67 -- the transcription error\n",
       "     UA.C <- USArrests\n",
       "     UA.C[\"Maryland\", \"UrbanPop\"] <- 76.6\n",
       "     \n",
       "     ## also +/- 0.5 to restore the original  <n>.5  percentages\n",
       "     s5u <- c(\"Colorado\", \"Florida\", \"Mississippi\", \"Wyoming\")\n",
       "     s5d <- c(\"Nebraska\", \"Pennsylvania\")\n",
       "     UA.C[s5u, \"UrbanPop\"] <- UA.C[s5u, \"UrbanPop\"] + 0.5\n",
       "     UA.C[s5d, \"UrbanPop\"] <- UA.C[s5d, \"UrbanPop\"] - 0.5\n",
       "     \n",
       "     ## ==> UA.C  is now a *C*orrected version of  USArrests\n",
       "     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "?USArrests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The USArrests data records rates of violent crimes in the US. The statistics are given as arrests per 100,000 residents for assault, murder, and rape in each of the 50 US states in 1973. The percentage of the population living in urban areas is also given. Some basic functions to get started with a data frame are illustrated with this data set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To display the first few lines of data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Murder Assault UrbanPop Rape\n",
      "Alabama      13.2     236       58 21.2\n",
      "Alaska       10.0     263       48 44.5\n",
      "Arizona       8.1     294       80 31.0\n",
      "Arkansas      8.8     190       50 19.5\n",
      "California    9.0     276       91 40.6\n",
      "Colorado      7.9     204       78 38.7\n"
     ]
    }
   ],
   "source": [
    "print(head(USArrests))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [head](https://www.rdocumentation.org/packages/utils/versions/3.6.2/topics/head)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result shows that we have four variables named Murder, Assault, UrbanPop, and Rape, and that the observations (rows) are labeled by the name of the state. We also see that the states appear to be listed in alphabetical order. All of the variables appear to be quantitative, which we expected from the description above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Sample size and dimension**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How many observations are in this data set? (NROW, nrow, or dim). See [nrow](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/nrow), [dim](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/dim)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "50"
      ],
      "text/latex": [
       "50"
      ],
      "text/markdown": [
       "50"
      ],
      "text/plain": [
       "[1] 50"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "NROW(USArrests)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "50"
      ],
      "text/latex": [
       "50"
      ],
      "text/markdown": [
       "50"
      ],
      "text/plain": [
       "[1] 50"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nrow(USArrests)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 50  4\n"
     ]
    }
   ],
   "source": [
    "print(dim(USArrests))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dimension (dim) of a data frame or a matrix returns a vector with the number of rows and number of columns. NROW returns the number of observations. We have 50 observations corresponding to the 50 states in the U.S."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Names of variables**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get (or set) names of variables in the data frame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Murder\"   \"Assault\"  \"UrbanPop\" \"Rape\"    \n"
     ]
    }
   ],
   "source": [
    "print(names(USArrests))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [names](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/names)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Structure of the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display information about the structure of the data frame (str):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t50 obs. of  4 variables:\n",
      " $ Murder  : num  13.2 10 8.1 8.8 9 7.9 3.3 5.9 15.4 17.4 ...\n",
      " $ Assault : int  236 263 294 190 276 204 110 238 335 211 ...\n",
      " $ UrbanPop: int  58 48 80 50 91 78 77 72 80 60 ...\n",
      " $ Rape    : num  21.2 44.5 31 19.5 40.6 38.7 11.1 15.8 31.9 25.8 ...\n"
     ]
    }
   ],
   "source": [
    "str(USArrests)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [str](https://www.rdocumentation.org/packages/utils/versions/3.6.2/topics/str)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result of str gives the dimension as well as the name and type of each variable. We have two numeric type and two integer type variables. Although we can think of integer as a special case of numeric, they are stored differently in R."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For many data sets, like USArrests, all of the data are numbers and in this case the data can be converted to a matrix using as.matrix. But in order to store the data in a matrix, all variables must be of the same type so R will convert the integers to numeric. Compare the result in matrix form:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "arrests <- as.matrix(USArrests)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " num [1:50, 1:4] 13.2 10 8.1 8.8 9 7.9 3.3 5.9 15.4 17.4 ...\n",
      " - attr(*, \"dimnames\")=List of 2\n",
      "  ..$ : chr [1:50] \"Alabama\" \"Alaska\" \"Arizona\" \"Arkansas\" ...\n",
      "  ..$ : chr [1:4] \"Murder\" \"Assault\" \"UrbanPop\" \"Rape\"\n"
     ]
    }
   ],
   "source": [
    "str(arrests)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [as.matrix](https://www.rdocumentation.org/packages/raster/versions/3.1-5/topics/as.matrix)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This output shows that all of the data was converted to numeric, listed on the first line as num. The attributes (attr) are the row and column names (dimnames). The conversion preserved the row labels and converted the variable names to column labels. We used names to get the names of the variables in the data frame, but we would use rownames, colnames or dimnames (to get both) to get the row and/or column names. These last three functions can also be used on data frames."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Missing values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [is.na](https://www.rdocumentation.org/packages/ursa/versions/3.8.20/topics/is.na) function returns TRUE for a missing value and otherwise FALSE. The expression is.na(USArrests) will return a data frame the same size as USArrests where every entry is TRUE or FALSE. To quickly check if any of the results are TRUE we use the any function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "FALSE"
      ],
      "text/latex": [
       "FALSE"
      ],
      "text/markdown": [
       "FALSE"
      ],
      "text/plain": [
       "[1] FALSE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "any(is.na(USArrests))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Working with a data frame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section we illustrate some operations on data frames, and some basic statistics and plots."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Compute summary statistics**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Obtain appropriate summary statistics for each variable using summary. For numeric data, the summary function computes a five-number summary and sample mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     Murder          Assault         UrbanPop          Rape      \n",
       " Min.   : 0.800   Min.   : 45.0   Min.   :32.00   Min.   : 7.30  \n",
       " 1st Qu.: 4.075   1st Qu.:109.0   1st Qu.:54.50   1st Qu.:15.07  \n",
       " Median : 7.250   Median :159.0   Median :66.00   Median :20.10  \n",
       " Mean   : 7.788   Mean   :170.8   Mean   :65.54   Mean   :21.23  \n",
       " 3rd Qu.:11.250   3rd Qu.:249.0   3rd Qu.:77.75   3rd Qu.:26.18  \n",
       " Max.   :17.400   Max.   :337.0   Max.   :91.00   Max.   :46.00  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(USArrests)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [summary](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/summary)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If there were any missing values, the number of missing values would be included in the summaries. If any of our variables were categorical, summary would tabulate the values for those variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the summary it appears that the mean and median are approximately equal for all variables except Assault. The mean for Assault is larger than the median, indicating that the assault data is positively skewed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Extract data from a data frame**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simplest way to extract data from a data frame uses the matrix-style [row, column] indexing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "9"
      ],
      "text/latex": [
       "9"
      ],
      "text/markdown": [
       "9"
      ],
      "text/plain": [
       "[1] 9"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "USArrests[\"California\", \"Murder\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 1 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Murder</th><th scope=col>Assault</th><th scope=col>UrbanPop</th><th scope=col>Rape</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>California</th><td>9</td><td>276</td><td>91</td><td>40.6</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & Murder & Assault & UrbanPop & Rape\\\\\n",
       "  & <dbl> & <int> & <int> & <dbl>\\\\\n",
       "\\hline\n",
       "\tCalifornia & 9 & 276 & 91 & 40.6\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 4\n",
       "\n",
       "| <!--/--> | Murder &lt;dbl&gt; | Assault &lt;int&gt; | UrbanPop &lt;int&gt; | Rape &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| California | 9 | 276 | 91 | 40.6 |\n",
       "\n"
      ],
      "text/plain": [
       "           Murder Assault UrbanPop Rape\n",
       "California 9      276     91       40.6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "USArrests[\"California\", ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Extract a variable using \\\\$**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variables can be extracted using the $ operator followed by the name of the\n",
    "variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [1] 236 263 294 190 276 204 110 238 335 211  46 120 249 113  56 115 109 249  83\n",
      "[20] 300 149 255  72 259 178 109 102 252  57 159 285 254 337  45 120 151 159 106\n",
      "[39] 174 279  86 188 201 120  48 156 145  81  53 161\n"
     ]
    }
   ],
   "source": [
    "print(USArrests$Assault)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Histograms**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the summary of the USArrests data frame, we observed that the distribution of assaults may be positively skewed because the sample mean is larger than the sample median. A histogram of the data helps to visualize the shape of the distribution. We show two versions of the histogram of Assault. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XMdO6BFEHYADXMdO6BFEHYAjeI6dkDm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\nRK5CYII=",
      "text/plain": [
       "Plot with title “Histogram of USArrests$Assault”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "par(mfrow=c(1,2)) #subplots\n",
    "par(cex=0.4) #control size of labels\n",
    "hist(USArrests$Assault)\n",
    "library(MASS)#need for truehist function\n",
    "truehist(USArrests$Assault, col='lightcyan') #see colors() for built-in colors in R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [hist](https://www.rdocumentation.org/packages/graphics/versions/3.6.2/topics/hist)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The skewness is easier to observe in the right histogram. There are obvious differences in the histograms; one is that the vertical scales differ. Another is that there are a different number of bins. First figure is a frequency histogram, and second figure is a probability histogram."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Try the following command and compare the result with histogram which is on the right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HjIzKdj3TL5QauElIz1+ao4pNZJetAqISVjfb4qDumlvz/1svQeCEmL9fmqNaQ3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\nX8LPaeHjRzE+AAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “Histogram of USArrests$Assault”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(USArrests$Assault, prob=TRUE, breaks=\"scott\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two histogram functions hist and truehist have different default methods for determining the bin width, and the truehist function by default produces a probability histogram. The optional arguments of hist above match the defaults of truehist."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Attaching a data frame**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we attach the data frame, the variables can be referenced directly by name, without the dollar sign operator. For example, computing the percent of crimes that are murders using vectorized operations can be done as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "attach(USArrests)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [attach](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/attach)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 4.881657 3.149606 2.431702 4.031150 2.764128 3.152434\n"
     ]
    }
   ],
   "source": [
    "murder.pct <- 100 * Murder / (Murder + Assault + Rape)\n",
    "print(head(murder.pct))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If a data frame is attached, it can be detached when it is no longer needed using the detach function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "detach(USArrests)\n",
    "rm(murder.pct) #remove variable from memory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [detach](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/detach)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An alternative to attaching a data frame is (sometimes) to use the with function. It is useful for displaying plots or summary statistics. However, variables created using with are local to it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "with(USArrests, expr={murder.pct = 100 * Murder / (Murder + Assault + Rape)})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [with](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/with)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in print(murder.pct): object 'murder.pct' not found\n",
     "output_type": "error",
     "traceback": [
      "Error in print(murder.pct): object 'murder.pct' not found\nTraceback:\n",
      "1. print(murder.pct)"
     ]
    }
   ],
   "source": [
    "print(murder.pct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The documentation for with states that “assignments within expr take place in the constructed environment and not in the user’s workspace.” So all computations involving the variable murder.pct created in the expr block of the with function would have to be completed within the scope of the expr block. This can sometimes lead to unexpected errors in an analysis that can easily go undetected."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is it good programming practice to attach a data frame? A disadvantage is that there can be conflicts with names of variables already in the workspace. Many functions in R have a data argument, which allows the variables to be referenced by name within the list of arguments, without attaching the data frame. Unfortunately, some R functions (such as plot) do not have a data argument. The use of with could lead to unexpected programming errors, especially for novices. Overall, we find that attaching a data frame is sometimes helpful to make code more readable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Scatterplots and correlations**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the USArrests data all of the variables are numbers, so it is interesting to display scatterplots of different pairs of data to look for possible relations between the variables. We can display a single scatterplot using the plot function.... To obtain a plot of murders vs percent urban population we use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "attach(USArrests)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BASIICQAAGEBAggJEAAIQECCAkyMuY/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\n+H+7IXlgbsbwdwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(UrbanPop, Murder)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [plot](https://www.rdocumentation.org/packages/graphics/versions/3.6.2/topics/plot)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot does not reveal a very strong relation between murders and percent population. The pairs function can be used to display an array of scatterplots for each pair of variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EG2X68ymKBpteMEFskUxHWykJQ5w5RL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\n8WNKIj17AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pairs(USArrests, cex.labels=1.1) #control size of diagonal labels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [pairs](https://www.rdocumentation.org/packages/graphics/versions/3.6.2/topics/pairs)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There appears to be a positive association between murder and assault rates, but weak or no association between murder and percent urban population. There is a positive association between rape and percent urban population."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correlation statistic measures the degree of linear association between two variables. One can obtain correlation for a pair of variables or a table of correlation statistics for a group of variables using the cor function. By default it computes the Pearson correlation coefficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0695726217359934"
      ],
      "text/latex": [
       "0.0695726217359934"
      ],
      "text/markdown": [
       "0.0695726217359934"
      ],
      "text/plain": [
       "[1] 0.06957262"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cor(UrbanPop, Murder)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 4 × 4 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Murder</th><th scope=col>Assault</th><th scope=col>UrbanPop</th><th scope=col>Rape</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Murder</th><td>1.00000000</td><td>0.8018733</td><td>0.06957262</td><td>0.5635788</td></tr>\n",
       "\t<tr><th scope=row>Assault</th><td>0.80187331</td><td>1.0000000</td><td>0.25887170</td><td>0.6652412</td></tr>\n",
       "\t<tr><th scope=row>UrbanPop</th><td>0.06957262</td><td>0.2588717</td><td>1.00000000</td><td>0.4113412</td></tr>\n",
       "\t<tr><th scope=row>Rape</th><td>0.56357883</td><td>0.6652412</td><td>0.41134124</td><td>1.0000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 4 × 4 of type dbl\n",
       "\\begin{tabular}{r|llll}\n",
       "  & Murder & Assault & UrbanPop & Rape\\\\\n",
       "\\hline\n",
       "\tMurder & 1.00000000 & 0.8018733 & 0.06957262 & 0.5635788\\\\\n",
       "\tAssault & 0.80187331 & 1.0000000 & 0.25887170 & 0.6652412\\\\\n",
       "\tUrbanPop & 0.06957262 & 0.2588717 & 1.00000000 & 0.4113412\\\\\n",
       "\tRape & 0.56357883 & 0.6652412 & 0.41134124 & 1.0000000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 4 × 4 of type dbl\n",
       "\n",
       "| <!--/--> | Murder | Assault | UrbanPop | Rape |\n",
       "|---|---|---|---|---|\n",
       "| Murder | 1.00000000 | 0.8018733 | 0.06957262 | 0.5635788 |\n",
       "| Assault | 0.80187331 | 1.0000000 | 0.25887170 | 0.6652412 |\n",
       "| UrbanPop | 0.06957262 | 0.2588717 | 1.00000000 | 0.4113412 |\n",
       "| Rape | 0.56357883 | 0.6652412 | 0.41134124 | 1.0000000 |\n",
       "\n"
      ],
      "text/plain": [
       "         Murder     Assault   UrbanPop   Rape     \n",
       "Murder   1.00000000 0.8018733 0.06957262 0.5635788\n",
       "Assault  0.80187331 1.0000000 0.25887170 0.6652412\n",
       "UrbanPop 0.06957262 0.2588717 1.00000000 0.4113412\n",
       "Rape     0.56357883 0.6652412 0.41134124 1.0000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cor(USArrests)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [cor](https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/cor)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All of the correlations are positive in sign. The small correlation of r =. 0.07 between Murder and UrbanPop is consistent with our interpretation of the scatterplot. There is a strong positive correlation (r = 0.80) between Murder and Assault, also consistent with the pairs-plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Secciones 1.3, 1.4, 1.7, 1.8, 1.9, 1.10, 1.16, 1.17 del libro de texto \"Probability and Statistics with R\" de M.D. Ugarte, A. F. Militino, A. T. Arnholt, **2ed**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El libro tiene github para sus scripts [alanarnholt/PASWR2E-Rscripts](https://github.com/alanarnholt/PASWR2E-Rscripts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Temas importantes a revisar:\n",
    "\n",
    "* Vectors (1.3)\n",
    "* Mode & Class of an Object (1.4)\n",
    "* Rstudio (1.7)\n",
    "* Packages (1.8)\n",
    "* R Data Structures (1.9)\n",
    "    * Arrays & Matrices\n",
    "    * Lists\n",
    "    * Data frames\n",
    "* Reading and Saving Data in R (1.10)\n",
    "* Flow Control (1.16)\n",
    "* Creating functions (1.17)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Algunos enunciados relevantes en el libro:\n",
    "\n",
    "**sección 1.3**\n",
    "\n",
    "* \"... All of the elements of a **vector** must have the same mode, that is, data type...\". Para más sobre el *mode* de un objeto ver [3.1 Intrinsic attributes: mode and length](https://cran.r-project.org/doc/manuals/R-intro.html#The-intrinsic-attributes-mode-and-length).\n",
    "\n",
    "* \"..., how do vectors with more than one element interact with vectors containing a single element (scalars)? Mathematical operations may be applied to two vectors provided the vectors are of the same length. **When the two vectors are not of the same length, R recycles the values of the shorter vector until the length of the shorter vector matches that of the longer vector**... **\"...Objects of different modes stored together are automatically converted to the simplest mode to represent the information...\"**.\n",
    "\n",
    "* \"**Indices** for R vectors start at 1, unlike indices in C and C++, which start at 0. Individual elements of a vector are accessed with [] (square brackets)...\" (sección 1.3.2)\n",
    "\n",
    "**sección 1.4**\n",
    "\n",
    "* \"...Many functions in R will behave differently depending on the class of their arguments. **Functions** that behave in this fashion are known as generic functions. Two common generic functions are print() and summary()...\"\n",
    "\n",
    "* \"... Although the only type of data structure discussed thus far has been the vector, which was described as a variable and subsequently called an object, **everything in R is actually an object**. Stored results from analyses, matrices, arrays, vectors, and so on, are all considered objects in R...\" \n",
    "\n",
    "* \"...It is not always the case that the mode and class of an object coincide. The mode of a linear model object is stored as a list; however, the class of a linear model object is lm...\"\n",
    "\n",
    "**sección 1.9**\n",
    "\n",
    "* \"...The concept of a vector is crucial as other data structures are defined in terms of vectors... an array is a vector with a dimension attribute... a matrix is also a vector...most R lists are generic vectors...data frames are data structures similar to matrices that allow the columns (vectors) to be of different types... **Data frames are the fundamental data structure used for most R's modeling software**...\"\n",
    "\n",
    "* \"**Arrays** are multidimensional arrangements of elements. A very common example of an array is a **matrix**, which is a two-dimensional array\"\n",
    "\n",
    "* \"Although two-dimensional arrays are matrices and the array() function can be used to create a matrix, the matrix() function allows the user to create matrices by using row-major order as well as column-major order.\" Para ver más sobre arrays y matrices y operaciones, factorizaciones matriciales y concatenación: [5 Arrays and matrices](https://cran.r-project.org/doc/manuals/R-intro.html#Arrays-and-matrices)\n",
    "\n",
    "* \"A **factor** is a vector with additional information indicating the distinct values or levels of the vector. Many statistical problems use categorical variables to classify subjects or to subdivide the data. Examples include variables such as socioeconomic status, gender, and marriage status. When using R, one should store categorical data in factors. To create a factor from a vector, one can use the factor() function.\" (sección 1.9.3)\n",
    "\n",
    "* \"A **list** is an object whose elements can be of different modes\" (sección 1.9.4). Para ver más sobre listas ver: [6 Lists and data frames](https://cran.r-project.org/doc/manuals/R-intro.html#Lists-and-data-frames).\n",
    "\n",
    "* \"A **data frame** is similar to a matrix in the sense that it is a rectangular structure used to store information. **It is different in that all elements of a matrix must be of the same mode (numeric, character, etc.), but this restriction does not apply to data frames**...\" (sección 1.9.5).\n",
    "\n",
    "* Leer con atención el uso de la función `attach` y `detach` en la sección 1.9.5.2 \"Accessing Data Frames\" y sección 1.9.5.3 \"Accessing Data from Packages\"."
   ]
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    "## Otras referencias utilizadas en esta nota:\n",
    "\n",
    "* https://cran.r-project.org/doc/manuals/R-intro.html"
   ]
  }
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