{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Supervised Learning"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"suppressPackageStartupMessages(library(tidyverse))"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"options(repr.plot.width=4, repr.plot.height=4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Regression"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"set.seed(10)\n",
"\n",
"x <- 1:10 \n",
"y = x + rnorm(10, 0.5, 1)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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IUa+FHrYGPBe37PKLSFGniyfTj5Cb9n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\nwOARGDwCg0dg8AgMHoHB+3/x7RbKJKWydAAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(x, y, xlim = c(0, 10), ylim = c(0, 10), pch = 19)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Detour: Image formatting in base graphics\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Linear Regression"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"model.lm <- lm(y ~ x) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Predicting from a fitted model"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- 1
\n",
"\t\t- 1.26208403232277
\n",
"\t- 2
\n",
"\t\t- 2.20591939228898
\n",
"\t- 3
\n",
"\t\t- 3.14975475225518
\n",
"\t- 4
\n",
"\t\t- 4.09359011222138
\n",
"\t- 5
\n",
"\t\t- 5.03742547218758
\n",
"\t- 6
\n",
"\t\t- 5.98126083215378
\n",
"\t- 7
\n",
"\t\t- 6.92509619211998
\n",
"\t- 8
\n",
"\t\t- 7.86893155208618
\n",
"\t- 9
\n",
"\t\t- 8.81276691205238
\n",
"\t- 10
\n",
"\t\t- 9.75660227201858
\n",
"
\n"
],
"text/latex": [
"\\begin{description*}\n",
"\\item[1] 1.26208403232277\n",
"\\item[2] 2.20591939228898\n",
"\\item[3] 3.14975475225518\n",
"\\item[4] 4.09359011222138\n",
"\\item[5] 5.03742547218758\n",
"\\item[6] 5.98126083215378\n",
"\\item[7] 6.92509619211998\n",
"\\item[8] 7.86893155208618\n",
"\\item[9] 8.81276691205238\n",
"\\item[10] 9.75660227201858\n",
"\\end{description*}\n"
],
"text/markdown": [
"1\n",
": 1.262084032322772\n",
": 2.205919392288983\n",
": 3.149754752255184\n",
": 4.093590112221385\n",
": 5.037425472187586\n",
": 5.981260832153787\n",
": 6.925096192119988\n",
": 7.868931552086189\n",
": 8.8127669120523810\n",
": 9.75660227201858\n",
"\n"
],
"text/plain": [
" 1 2 3 4 5 6 7 8 \n",
"1.262084 2.205919 3.149755 4.093590 5.037425 5.981261 6.925096 7.868932 \n",
" 9 10 \n",
"8.812767 9.756602 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"predict(model.lm)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Predicting for new data"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- 1
\n",
"\t\t- 1.73400171230588
\n",
"\t- 2
\n",
"\t\t- 3.62167243223828
\n",
"\t- 3
\n",
"\t\t- 5.50934315217068
\n",
"
\n"
],
"text/latex": [
"\\begin{description*}\n",
"\\item[1] 1.73400171230588\n",
"\\item[2] 3.62167243223828\n",
"\\item[3] 5.50934315217068\n",
"\\end{description*}\n"
],
"text/markdown": [
"1\n",
": 1.734001712305882\n",
": 3.621672432238283\n",
": 5.50934315217068\n",
"\n"
],
"text/plain": [
" 1 2 3 \n",
"1.734002 3.621672 5.509343 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"predict(model.lm, data.frame(x = c(1.5, 3.5, 5.5)))"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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ft3GGtW0IQQTU3N1atXDxjQ+quJVq9e7ezs7Ovr2405q6qqQkJChEJhO2OysrK6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\nrkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(x, y, xlim = c(0, 10), ylim = c(0, 10), pch = 19)\n",
"lines(x, predict(model.lm), col = 3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Alternative\n",
"\n",
"Note that `abline` plots the fitted line throughout the plot limits for the x-axis."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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E4mk/0j9MOZgj16W+0nd4OK1ZcN7QkJCe++++7u3bs5rQ7A+HgT0HFxcTNmzNi5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\nhF4AAAAASUVORK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(x, y, xlim = c(0, 10), ylim = c(0, 10), pch = 19)\n",
"abline(model.lm, col=\"purple\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Detour: Colors in base graphics\n",
"\n",
"\n",
"\n",
"You can also used named colors - run `colors` to get all named colors available."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- 'white'
\n",
"\t- 'aliceblue'
\n",
"\t- 'antiquewhite'
\n",
"\t- 'antiquewhite1'
\n",
"\t- 'antiquewhite2'
\n",
"\t- 'antiquewhite3'
\n",
"\t- 'antiquewhite4'
\n",
"\t- 'aquamarine'
\n",
"\t- 'aquamarine1'
\n",
"\t- 'aquamarine2'
\n",
"\t- 'aquamarine3'
\n",
"\t- 'aquamarine4'
\n",
"\t- 'azure'
\n",
"\t- 'azure1'
\n",
"\t- 'azure2'
\n",
"\t- 'azure3'
\n",
"\t- 'azure4'
\n",
"\t- 'beige'
\n",
"\t- 'bisque'
\n",
"\t- 'bisque1'
\n",
"\t- 'bisque2'
\n",
"\t- 'bisque3'
\n",
"\t- 'bisque4'
\n",
"\t- 'black'
\n",
"\t- 'blanchedalmond'
\n",
"\t- 'blue'
\n",
"\t- 'blue1'
\n",
"\t- 'blue2'
\n",
"\t- 'blue3'
\n",
"\t- 'blue4'
\n",
"\t- 'blueviolet'
\n",
"\t- 'brown'
\n",
"\t- 'brown1'
\n",
"\t- 'brown2'
\n",
"\t- 'brown3'
\n",
"\t- 'brown4'
\n",
"\t- 'burlywood'
\n",
"\t- 'burlywood1'
\n",
"\t- 'burlywood2'
\n",
"\t- 'burlywood3'
\n",
"\t- 'burlywood4'
\n",
"\t- 'cadetblue'
\n",
"\t- 'cadetblue1'
\n",
"\t- 'cadetblue2'
\n",
"\t- 'cadetblue3'
\n",
"\t- 'cadetblue4'
\n",
"\t- 'chartreuse'
\n",
"\t- 'chartreuse1'
\n",
"\t- 'chartreuse2'
\n",
"\t- 'chartreuse3'
\n",
"\t- 'chartreuse4'
\n",
"\t- 'chocolate'
\n",
"\t- 'chocolate1'
\n",
"\t- 'chocolate2'
\n",
"\t- 'chocolate3'
\n",
"\t- 'chocolate4'
\n",
"\t- 'coral'
\n",
"\t- 'coral1'
\n",
"\t- 'coral2'
\n",
"\t- 'coral3'
\n",
"\t- 'coral4'
\n",
"\t- 'cornflowerblue'
\n",
"\t- 'cornsilk'
\n",
"\t- 'cornsilk1'
\n",
"\t- 'cornsilk2'
\n",
"\t- 'cornsilk3'
\n",
"\t- 'cornsilk4'
\n",
"\t- 'cyan'
\n",
"\t- 'cyan1'
\n",
"\t- 'cyan2'
\n",
"\t- 'cyan3'
\n",
"\t- 'cyan4'
\n",
"\t- 'darkblue'
\n",
"\t- 'darkcyan'
\n",
"\t- 'darkgoldenrod'
\n",
"\t- 'darkgoldenrod1'
\n",
"\t- 'darkgoldenrod2'
\n",
"\t- 'darkgoldenrod3'
\n",
"\t- 'darkgoldenrod4'
\n",
"\t- 'darkgray'
\n",
"\t- 'darkgreen'
\n",
"\t- 'darkgrey'
\n",
"\t- 'darkkhaki'
\n",
"\t- 'darkmagenta'
\n",
"\t- 'darkolivegreen'
\n",
"\t- 'darkolivegreen1'
\n",
"\t- 'darkolivegreen2'
\n",
"\t- 'darkolivegreen3'
\n",
"\t- 'darkolivegreen4'
\n",
"\t- 'darkorange'
\n",
"\t- 'darkorange1'
\n",
"\t- 'darkorange2'
\n",
"\t- 'darkorange3'
\n",
"\t- 'darkorange4'
\n",
"\t- 'darkorchid'
\n",
"\t- 'darkorchid1'
\n",
"\t- 'darkorchid2'
\n",
"\t- 'darkorchid3'
\n",
"\t- 'darkorchid4'
\n",
"\t- 'darkred'
\n",
"\t- 'darksalmon'
\n",
"\t- 'darkseagreen'
\n",
"\t- 'darkseagreen1'
\n",
"\t- 'darkseagreen2'
\n",
"\t- 'darkseagreen3'
\n",
"\t- 'darkseagreen4'
\n",
"\t- 'darkslateblue'
\n",
"\t- 'darkslategray'
\n",
"\t- 'darkslategray1'
\n",
"\t- 'darkslategray2'
\n",
"\t- 'darkslategray3'
\n",
"\t- 'darkslategray4'
\n",
"\t- 'darkslategrey'
\n",
"\t- 'darkturquoise'
\n",
"\t- 'darkviolet'
\n",
"\t- 'deeppink'
\n",
"\t- 'deeppink1'
\n",
"\t- 'deeppink2'
\n",
"\t- 'deeppink3'
\n",
"\t- 'deeppink4'
\n",
"\t- 'deepskyblue'
\n",
"\t- 'deepskyblue1'
\n",
"\t- 'deepskyblue2'
\n",
"\t- 'deepskyblue3'
\n",
"\t- 'deepskyblue4'
\n",
"\t- 'dimgray'
\n",
"\t- 'dimgrey'
\n",
"\t- 'dodgerblue'
\n",
"\t- 'dodgerblue1'
\n",
"\t- 'dodgerblue2'
\n",
"\t- 'dodgerblue3'
\n",
"\t- 'dodgerblue4'
\n",
"\t- 'firebrick'
\n",
"\t- 'firebrick1'
\n",
"\t- 'firebrick2'
\n",
"\t- 'firebrick3'
\n",
"\t- 'firebrick4'
\n",
"\t- 'floralwhite'
\n",
"\t- 'forestgreen'
\n",
"\t- 'gainsboro'
\n",
"\t- 'ghostwhite'
\n",
"\t- 'gold'
\n",
"\t- 'gold1'
\n",
"\t- 'gold2'
\n",
"\t- 'gold3'
\n",
"\t- 'gold4'
\n",
"\t- 'goldenrod'
\n",
"\t- 'goldenrod1'
\n",
"\t- 'goldenrod2'
\n",
"\t- 'goldenrod3'
\n",
"\t- 'goldenrod4'
\n",
"\t- 'gray'
\n",
"\t- 'gray0'
\n",
"\t- 'gray1'
\n",
"\t- 'gray2'
\n",
"\t- 'gray3'
\n",
"\t- 'gray4'
\n",
"\t- 'gray5'
\n",
"\t- 'gray6'
\n",
"\t- 'gray7'
\n",
"\t- 'gray8'
\n",
"\t- 'gray9'
\n",
"\t- 'gray10'
\n",
"\t- 'gray11'
\n",
"\t- 'gray12'
\n",
"\t- 'gray13'
\n",
"\t- 'gray14'
\n",
"\t- 'gray15'
\n",
"\t- 'gray16'
\n",
"\t- 'gray17'
\n",
"\t- 'gray18'
\n",
"\t- 'gray19'
\n",
"\t- 'gray20'
\n",
"\t- 'gray21'
\n",
"\t- 'gray22'
\n",
"\t- 'gray23'
\n",
"\t- 'gray24'
\n",
"\t- 'gray25'
\n",
"\t- 'gray26'
\n",
"\t- 'gray27'
\n",
"\t- 'gray28'
\n",
"\t- 'gray29'
\n",
"\t- 'gray30'
\n",
"\t- 'gray31'
\n",
"\t- 'gray32'
\n",
"\t- 'gray33'
\n",
"\t- 'gray34'
\n",
"\t- 'gray35'
\n",
"\t- 'gray36'
\n",
"\t- 'gray37'
\n",
"\t- 'gray38'
\n",
"\t- 'gray39'
\n",
"\t- 'gray40'
\n",
"\t- 'gray41'
\n",
"\t- 'gray42'
\n",
"\t- 'gray43'
\n",
"\t- 'gray44'
\n",
"\t- 'gray45'
\n",
"\t- 'gray46'
\n",
"\t- 'gray47'
\n",
"\t- 'gray48'
\n",
"\t- 'gray49'
\n",
"\t- 'gray50'
\n",
"\t- 'gray51'
\n",
"\t- 'gray52'
\n",
"\t- 'gray53'
\n",
"\t- 'gray54'
\n",
"\t- 'gray55'
\n",
"\t- 'gray56'
\n",
"\t- 'gray57'
\n",
"\t- 'gray58'
\n",
"\t- 'gray59'
\n",
"\t- 'gray60'
\n",
"\t- 'gray61'
\n",
"\t- 'gray62'
\n",
"\t- 'gray63'
\n",
"\t- 'gray64'
\n",
"\t- 'gray65'
\n",
"\t- 'gray66'
\n",
"\t- 'gray67'
\n",
"\t- 'gray68'
\n",
"\t- 'gray69'
\n",
"\t- 'gray70'
\n",
"\t- 'gray71'
\n",
"\t- 'gray72'
\n",
"\t- 'gray73'
\n",
"\t- 'gray74'
\n",
"\t- 'gray75'
\n",
"\t- 'gray76'
\n",
"\t- 'gray77'
\n",
"\t- 'gray78'
\n",
"\t- 'gray79'
\n",
"\t- 'gray80'
\n",
"\t- 'gray81'
\n",
"\t- 'gray82'
\n",
"\t- 'gray83'
\n",
"\t- 'gray84'
\n",
"\t- 'gray85'
\n",
"\t- 'gray86'
\n",
"\t- 'gray87'
\n",
"\t- 'gray88'
\n",
"\t- 'gray89'
\n",
"\t- 'gray90'
\n",
"\t- 'gray91'
\n",
"\t- 'gray92'
\n",
"\t- 'gray93'
\n",
"\t- 'gray94'
\n",
"\t- 'gray95'
\n",
"\t- 'gray96'
\n",
"\t- 'gray97'
\n",
"\t- 'gray98'
\n",
"\t- 'gray99'
\n",
"\t- 'gray100'
\n",
"\t- 'green'
\n",
"\t- 'green1'
\n",
"\t- 'green2'
\n",
"\t- 'green3'
\n",
"\t- 'green4'
\n",
"\t- 'greenyellow'
\n",
"\t- 'grey'
\n",
"\t- 'grey0'
\n",
"\t- 'grey1'
\n",
"\t- 'grey2'
\n",
"\t- 'grey3'
\n",
"\t- 'grey4'
\n",
"\t- 'grey5'
\n",
"\t- 'grey6'
\n",
"\t- 'grey7'
\n",
"\t- 'grey8'
\n",
"\t- 'grey9'
\n",
"\t- 'grey10'
\n",
"\t- 'grey11'
\n",
"\t- 'grey12'
\n",
"\t- 'grey13'
\n",
"\t- 'grey14'
\n",
"\t- 'grey15'
\n",
"\t- 'grey16'
\n",
"\t- 'grey17'
\n",
"\t- 'grey18'
\n",
"\t- 'grey19'
\n",
"\t- 'grey20'
\n",
"\t- 'grey21'
\n",
"\t- 'grey22'
\n",
"\t- 'grey23'
\n",
"\t- 'grey24'
\n",
"\t- 'grey25'
\n",
"\t- 'grey26'
\n",
"\t- 'grey27'
\n",
"\t- 'grey28'
\n",
"\t- 'grey29'
\n",
"\t- 'grey30'
\n",
"\t- 'grey31'
\n",
"\t- 'grey32'
\n",
"\t- 'grey33'
\n",
"\t- 'grey34'
\n",
"\t- 'grey35'
\n",
"\t- 'grey36'
\n",
"\t- 'grey37'
\n",
"\t- 'grey38'
\n",
"\t- 'grey39'
\n",
"\t- 'grey40'
\n",
"\t- 'grey41'
\n",
"\t- 'grey42'
\n",
"\t- 'grey43'
\n",
"\t- 'grey44'
\n",
"\t- 'grey45'
\n",
"\t- 'grey46'
\n",
"\t- 'grey47'
\n",
"\t- 'grey48'
\n",
"\t- 'grey49'
\n",
"\t- 'grey50'
\n",
"\t- 'grey51'
\n",
"\t- 'grey52'
\n",
"\t- 'grey53'
\n",
"\t- 'grey54'
\n",
"\t- 'grey55'
\n",
"\t- 'grey56'
\n",
"\t- 'grey57'
\n",
"\t- 'grey58'
\n",
"\t- 'grey59'
\n",
"\t- 'grey60'
\n",
"\t- 'grey61'
\n",
"\t- 'grey62'
\n",
"\t- 'grey63'
\n",
"\t- 'grey64'
\n",
"\t- 'grey65'
\n",
"\t- 'grey66'
\n",
"\t- 'grey67'
\n",
"\t- 'grey68'
\n",
"\t- 'grey69'
\n",
"\t- 'grey70'
\n",
"\t- 'grey71'
\n",
"\t- 'grey72'
\n",
"\t- 'grey73'
\n",
"\t- 'grey74'
\n",
"\t- 'grey75'
\n",
"\t- 'grey76'
\n",
"\t- 'grey77'
\n",
"\t- 'grey78'
\n",
"\t- 'grey79'
\n",
"\t- 'grey80'
\n",
"\t- 'grey81'
\n",
"\t- 'grey82'
\n",
"\t- 'grey83'
\n",
"\t- 'grey84'
\n",
"\t- 'grey85'
\n",
"\t- 'grey86'
\n",
"\t- 'grey87'
\n",
"\t- 'grey88'
\n",
"\t- 'grey89'
\n",
"\t- 'grey90'
\n",
"\t- 'grey91'
\n",
"\t- 'grey92'
\n",
"\t- 'grey93'
\n",
"\t- 'grey94'
\n",
"\t- 'grey95'
\n",
"\t- 'grey96'
\n",
"\t- 'grey97'
\n",
"\t- 'grey98'
\n",
"\t- 'grey99'
\n",
"\t- 'grey100'
\n",
"\t- 'honeydew'
\n",
"\t- 'honeydew1'
\n",
"\t- 'honeydew2'
\n",
"\t- 'honeydew3'
\n",
"\t- 'honeydew4'
\n",
"\t- 'hotpink'
\n",
"\t- 'hotpink1'
\n",
"\t- 'hotpink2'
\n",
"\t- 'hotpink3'
\n",
"\t- 'hotpink4'
\n",
"\t- 'indianred'
\n",
"\t- 'indianred1'
\n",
"\t- 'indianred2'
\n",
"\t- 'indianred3'
\n",
"\t- 'indianred4'
\n",
"\t- 'ivory'
\n",
"\t- 'ivory1'
\n",
"\t- 'ivory2'
\n",
"\t- 'ivory3'
\n",
"\t- 'ivory4'
\n",
"\t- 'khaki'
\n",
"\t- 'khaki1'
\n",
"\t- 'khaki2'
\n",
"\t- 'khaki3'
\n",
"\t- 'khaki4'
\n",
"\t- 'lavender'
\n",
"\t- 'lavenderblush'
\n",
"\t- 'lavenderblush1'
\n",
"\t- 'lavenderblush2'
\n",
"\t- 'lavenderblush3'
\n",
"\t- 'lavenderblush4'
\n",
"\t- 'lawngreen'
\n",
"\t- 'lemonchiffon'
\n",
"\t- 'lemonchiffon1'
\n",
"\t- 'lemonchiffon2'
\n",
"\t- 'lemonchiffon3'
\n",
"\t- 'lemonchiffon4'
\n",
"\t- 'lightblue'
\n",
"\t- 'lightblue1'
\n",
"\t- 'lightblue2'
\n",
"\t- 'lightblue3'
\n",
"\t- 'lightblue4'
\n",
"\t- 'lightcoral'
\n",
"\t- 'lightcyan'
\n",
"\t- 'lightcyan1'
\n",
"\t- 'lightcyan2'
\n",
"\t- 'lightcyan3'
\n",
"\t- 'lightcyan4'
\n",
"\t- 'lightgoldenrod'
\n",
"\t- 'lightgoldenrod1'
\n",
"\t- 'lightgoldenrod2'
\n",
"\t- 'lightgoldenrod3'
\n",
"\t- 'lightgoldenrod4'
\n",
"\t- 'lightgoldenrodyellow'
\n",
"\t- 'lightgray'
\n",
"\t- 'lightgreen'
\n",
"\t- 'lightgrey'
\n",
"\t- 'lightpink'
\n",
"\t- 'lightpink1'
\n",
"\t- 'lightpink2'
\n",
"\t- 'lightpink3'
\n",
"\t- 'lightpink4'
\n",
"\t- 'lightsalmon'
\n",
"\t- 'lightsalmon1'
\n",
"\t- 'lightsalmon2'
\n",
"\t- 'lightsalmon3'
\n",
"\t- 'lightsalmon4'
\n",
"\t- 'lightseagreen'
\n",
"\t- 'lightskyblue'
\n",
"\t- 'lightskyblue1'
\n",
"\t- 'lightskyblue2'
\n",
"\t- 'lightskyblue3'
\n",
"\t- 'lightskyblue4'
\n",
"\t- 'lightslateblue'
\n",
"\t- 'lightslategray'
\n",
"\t- 'lightslategrey'
\n",
"\t- 'lightsteelblue'
\n",
"\t- 'lightsteelblue1'
\n",
"\t- 'lightsteelblue2'
\n",
"\t- 'lightsteelblue3'
\n",
"\t- 'lightsteelblue4'
\n",
"\t- 'lightyellow'
\n",
"\t- 'lightyellow1'
\n",
"\t- 'lightyellow2'
\n",
"\t- 'lightyellow3'
\n",
"\t- 'lightyellow4'
\n",
"\t- 'limegreen'
\n",
"\t- 'linen'
\n",
"\t- 'magenta'
\n",
"\t- 'magenta1'
\n",
"\t- 'magenta2'
\n",
"\t- 'magenta3'
\n",
"\t- 'magenta4'
\n",
"\t- 'maroon'
\n",
"\t- 'maroon1'
\n",
"\t- 'maroon2'
\n",
"\t- 'maroon3'
\n",
"\t- 'maroon4'
\n",
"\t- 'mediumaquamarine'
\n",
"\t- 'mediumblue'
\n",
"\t- 'mediumorchid'
\n",
"\t- 'mediumorchid1'
\n",
"\t- 'mediumorchid2'
\n",
"\t- 'mediumorchid3'
\n",
"\t- 'mediumorchid4'
\n",
"\t- 'mediumpurple'
\n",
"\t- 'mediumpurple1'
\n",
"\t- 'mediumpurple2'
\n",
"\t- 'mediumpurple3'
\n",
"\t- 'mediumpurple4'
\n",
"\t- 'mediumseagreen'
\n",
"\t- 'mediumslateblue'
\n",
"\t- 'mediumspringgreen'
\n",
"\t- 'mediumturquoise'
\n",
"\t- 'mediumvioletred'
\n",
"\t- 'midnightblue'
\n",
"\t- 'mintcream'
\n",
"\t- 'mistyrose'
\n",
"\t- 'mistyrose1'
\n",
"\t- 'mistyrose2'
\n",
"\t- 'mistyrose3'
\n",
"\t- 'mistyrose4'
\n",
"\t- 'moccasin'
\n",
"\t- 'navajowhite'
\n",
"\t- 'navajowhite1'
\n",
"\t- 'navajowhite2'
\n",
"\t- 'navajowhite3'
\n",
"\t- 'navajowhite4'
\n",
"\t- 'navy'
\n",
"\t- 'navyblue'
\n",
"\t- 'oldlace'
\n",
"\t- 'olivedrab'
\n",
"\t- 'olivedrab1'
\n",
"\t- 'olivedrab2'
\n",
"\t- 'olivedrab3'
\n",
"\t- 'olivedrab4'
\n",
"\t- 'orange'
\n",
"\t- 'orange1'
\n",
"\t- 'orange2'
\n",
"\t- 'orange3'
\n",
"\t- 'orange4'
\n",
"\t- 'orangered'
\n",
"\t- 'orangered1'
\n",
"\t- 'orangered2'
\n",
"\t- 'orangered3'
\n",
"\t- 'orangered4'
\n",
"\t- 'orchid'
\n",
"\t- 'orchid1'
\n",
"\t- 'orchid2'
\n",
"\t- 'orchid3'
\n",
"\t- 'orchid4'
\n",
"\t- 'palegoldenrod'
\n",
"\t- 'palegreen'
\n",
"\t- 'palegreen1'
\n",
"\t- 'palegreen2'
\n",
"\t- 'palegreen3'
\n",
"\t- 'palegreen4'
\n",
"\t- 'paleturquoise'
\n",
"\t- 'paleturquoise1'
\n",
"\t- 'paleturquoise2'
\n",
"\t- 'paleturquoise3'
\n",
"\t- 'paleturquoise4'
\n",
"\t- 'palevioletred'
\n",
"\t- 'palevioletred1'
\n",
"\t- 'palevioletred2'
\n",
"\t- 'palevioletred3'
\n",
"\t- 'palevioletred4'
\n",
"\t- 'papayawhip'
\n",
"\t- 'peachpuff'
\n",
"\t- 'peachpuff1'
\n",
"\t- 'peachpuff2'
\n",
"\t- 'peachpuff3'
\n",
"\t- 'peachpuff4'
\n",
"\t- 'peru'
\n",
"\t- 'pink'
\n",
"\t- 'pink1'
\n",
"\t- 'pink2'
\n",
"\t- 'pink3'
\n",
"\t- 'pink4'
\n",
"\t- 'plum'
\n",
"\t- 'plum1'
\n",
"\t- 'plum2'
\n",
"\t- 'plum3'
\n",
"\t- 'plum4'
\n",
"\t- 'powderblue'
\n",
"\t- 'purple'
\n",
"\t- 'purple1'
\n",
"\t- 'purple2'
\n",
"\t- 'purple3'
\n",
"\t- 'purple4'
\n",
"\t- 'red'
\n",
"\t- 'red1'
\n",
"\t- 'red2'
\n",
"\t- 'red3'
\n",
"\t- 'red4'
\n",
"\t- 'rosybrown'
\n",
"\t- 'rosybrown1'
\n",
"\t- 'rosybrown2'
\n",
"\t- 'rosybrown3'
\n",
"\t- 'rosybrown4'
\n",
"\t- 'royalblue'
\n",
"\t- 'royalblue1'
\n",
"\t- 'royalblue2'
\n",
"\t- 'royalblue3'
\n",
"\t- 'royalblue4'
\n",
"\t- 'saddlebrown'
\n",
"\t- 'salmon'
\n",
"\t- 'salmon1'
\n",
"\t- 'salmon2'
\n",
"\t- 'salmon3'
\n",
"\t- 'salmon4'
\n",
"\t- 'sandybrown'
\n",
"\t- 'seagreen'
\n",
"\t- 'seagreen1'
\n",
"\t- 'seagreen2'
\n",
"\t- 'seagreen3'
\n",
"\t- 'seagreen4'
\n",
"\t- 'seashell'
\n",
"\t- 'seashell1'
\n",
"\t- 'seashell2'
\n",
"\t- 'seashell3'
\n",
"\t- 'seashell4'
\n",
"\t- 'sienna'
\n",
"\t- 'sienna1'
\n",
"\t- 'sienna2'
\n",
"\t- 'sienna3'
\n",
"\t- 'sienna4'
\n",
"\t- 'skyblue'
\n",
"\t- 'skyblue1'
\n",
"\t- 'skyblue2'
\n",
"\t- 'skyblue3'
\n",
"\t- 'skyblue4'
\n",
"\t- 'slateblue'
\n",
"\t- 'slateblue1'
\n",
"\t- 'slateblue2'
\n",
"\t- 'slateblue3'
\n",
"\t- 'slateblue4'
\n",
"\t- 'slategray'
\n",
"\t- 'slategray1'
\n",
"\t- 'slategray2'
\n",
"\t- 'slategray3'
\n",
"\t- 'slategray4'
\n",
"\t- 'slategrey'
\n",
"\t- 'snow'
\n",
"\t- 'snow1'
\n",
"\t- 'snow2'
\n",
"\t- 'snow3'
\n",
"\t- 'snow4'
\n",
"\t- 'springgreen'
\n",
"\t- 'springgreen1'
\n",
"\t- 'springgreen2'
\n",
"\t- 'springgreen3'
\n",
"\t- 'springgreen4'
\n",
"\t- 'steelblue'
\n",
"\t- 'steelblue1'
\n",
"\t- 'steelblue2'
\n",
"\t- 'steelblue3'
\n",
"\t- 'steelblue4'
\n",
"\t- 'tan'
\n",
"\t- 'tan1'
\n",
"\t- 'tan2'
\n",
"\t- 'tan3'
\n",
"\t- 'tan4'
\n",
"\t- 'thistle'
\n",
"\t- 'thistle1'
\n",
"\t- 'thistle2'
\n",
"\t- 'thistle3'
\n",
"\t- 'thistle4'
\n",
"\t- 'tomato'
\n",
"\t- 'tomato1'
\n",
"\t- 'tomato2'
\n",
"\t- 'tomato3'
\n",
"\t- 'tomato4'
\n",
"\t- 'turquoise'
\n",
"\t- 'turquoise1'
\n",
"\t- 'turquoise2'
\n",
"\t- 'turquoise3'
\n",
"\t- 'turquoise4'
\n",
"\t- 'violet'
\n",
"\t- 'violetred'
\n",
"\t- 'violetred1'
\n",
"\t- 'violetred2'
\n",
"\t- 'violetred3'
\n",
"\t- 'violetred4'
\n",
"\t- 'wheat'
\n",
"\t- 'wheat1'
\n",
"\t- 'wheat2'
\n",
"\t- 'wheat3'
\n",
"\t- 'wheat4'
\n",
"\t- 'whitesmoke'
\n",
"\t- 'yellow'
\n",
"\t- 'yellow1'
\n",
"\t- 'yellow2'
\n",
"\t- 'yellow3'
\n",
"\t- 'yellow4'
\n",
"\t- 'yellowgreen'
\n",
"
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 'white'\n",
"\\item 'aliceblue'\n",
"\\item 'antiquewhite'\n",
"\\item 'antiquewhite1'\n",
"\\item 'antiquewhite2'\n",
"\\item 'antiquewhite3'\n",
"\\item 'antiquewhite4'\n",
"\\item 'aquamarine'\n",
"\\item 'aquamarine1'\n",
"\\item 'aquamarine2'\n",
"\\item 'aquamarine3'\n",
"\\item 'aquamarine4'\n",
"\\item 'azure'\n",
"\\item 'azure1'\n",
"\\item 'azure2'\n",
"\\item 'azure3'\n",
"\\item 'azure4'\n",
"\\item 'beige'\n",
"\\item 'bisque'\n",
"\\item 'bisque1'\n",
"\\item 'bisque2'\n",
"\\item 'bisque3'\n",
"\\item 'bisque4'\n",
"\\item 'black'\n",
"\\item 'blanchedalmond'\n",
"\\item 'blue'\n",
"\\item 'blue1'\n",
"\\item 'blue2'\n",
"\\item 'blue3'\n",
"\\item 'blue4'\n",
"\\item 'blueviolet'\n",
"\\item 'brown'\n",
"\\item 'brown1'\n",
"\\item 'brown2'\n",
"\\item 'brown3'\n",
"\\item 'brown4'\n",
"\\item 'burlywood'\n",
"\\item 'burlywood1'\n",
"\\item 'burlywood2'\n",
"\\item 'burlywood3'\n",
"\\item 'burlywood4'\n",
"\\item 'cadetblue'\n",
"\\item 'cadetblue1'\n",
"\\item 'cadetblue2'\n",
"\\item 'cadetblue3'\n",
"\\item 'cadetblue4'\n",
"\\item 'chartreuse'\n",
"\\item 'chartreuse1'\n",
"\\item 'chartreuse2'\n",
"\\item 'chartreuse3'\n",
"\\item 'chartreuse4'\n",
"\\item 'chocolate'\n",
"\\item 'chocolate1'\n",
"\\item 'chocolate2'\n",
"\\item 'chocolate3'\n",
"\\item 'chocolate4'\n",
"\\item 'coral'\n",
"\\item 'coral1'\n",
"\\item 'coral2'\n",
"\\item 'coral3'\n",
"\\item 'coral4'\n",
"\\item 'cornflowerblue'\n",
"\\item 'cornsilk'\n",
"\\item 'cornsilk1'\n",
"\\item 'cornsilk2'\n",
"\\item 'cornsilk3'\n",
"\\item 'cornsilk4'\n",
"\\item 'cyan'\n",
"\\item 'cyan1'\n",
"\\item 'cyan2'\n",
"\\item 'cyan3'\n",
"\\item 'cyan4'\n",
"\\item 'darkblue'\n",
"\\item 'darkcyan'\n",
"\\item 'darkgoldenrod'\n",
"\\item 'darkgoldenrod1'\n",
"\\item 'darkgoldenrod2'\n",
"\\item 'darkgoldenrod3'\n",
"\\item 'darkgoldenrod4'\n",
"\\item 'darkgray'\n",
"\\item 'darkgreen'\n",
"\\item 'darkgrey'\n",
"\\item 'darkkhaki'\n",
"\\item 'darkmagenta'\n",
"\\item 'darkolivegreen'\n",
"\\item 'darkolivegreen1'\n",
"\\item 'darkolivegreen2'\n",
"\\item 'darkolivegreen3'\n",
"\\item 'darkolivegreen4'\n",
"\\item 'darkorange'\n",
"\\item 'darkorange1'\n",
"\\item 'darkorange2'\n",
"\\item 'darkorange3'\n",
"\\item 'darkorange4'\n",
"\\item 'darkorchid'\n",
"\\item 'darkorchid1'\n",
"\\item 'darkorchid2'\n",
"\\item 'darkorchid3'\n",
"\\item 'darkorchid4'\n",
"\\item 'darkred'\n",
"\\item 'darksalmon'\n",
"\\item 'darkseagreen'\n",
"\\item 'darkseagreen1'\n",
"\\item 'darkseagreen2'\n",
"\\item 'darkseagreen3'\n",
"\\item 'darkseagreen4'\n",
"\\item 'darkslateblue'\n",
"\\item 'darkslategray'\n",
"\\item 'darkslategray1'\n",
"\\item 'darkslategray2'\n",
"\\item 'darkslategray3'\n",
"\\item 'darkslategray4'\n",
"\\item 'darkslategrey'\n",
"\\item 'darkturquoise'\n",
"\\item 'darkviolet'\n",
"\\item 'deeppink'\n",
"\\item 'deeppink1'\n",
"\\item 'deeppink2'\n",
"\\item 'deeppink3'\n",
"\\item 'deeppink4'\n",
"\\item 'deepskyblue'\n",
"\\item 'deepskyblue1'\n",
"\\item 'deepskyblue2'\n",
"\\item 'deepskyblue3'\n",
"\\item 'deepskyblue4'\n",
"\\item 'dimgray'\n",
"\\item 'dimgrey'\n",
"\\item 'dodgerblue'\n",
"\\item 'dodgerblue1'\n",
"\\item 'dodgerblue2'\n",
"\\item 'dodgerblue3'\n",
"\\item 'dodgerblue4'\n",
"\\item 'firebrick'\n",
"\\item 'firebrick1'\n",
"\\item 'firebrick2'\n",
"\\item 'firebrick3'\n",
"\\item 'firebrick4'\n",
"\\item 'floralwhite'\n",
"\\item 'forestgreen'\n",
"\\item 'gainsboro'\n",
"\\item 'ghostwhite'\n",
"\\item 'gold'\n",
"\\item 'gold1'\n",
"\\item 'gold2'\n",
"\\item 'gold3'\n",
"\\item 'gold4'\n",
"\\item 'goldenrod'\n",
"\\item 'goldenrod1'\n",
"\\item 'goldenrod2'\n",
"\\item 'goldenrod3'\n",
"\\item 'goldenrod4'\n",
"\\item 'gray'\n",
"\\item 'gray0'\n",
"\\item 'gray1'\n",
"\\item 'gray2'\n",
"\\item 'gray3'\n",
"\\item 'gray4'\n",
"\\item 'gray5'\n",
"\\item 'gray6'\n",
"\\item 'gray7'\n",
"\\item 'gray8'\n",
"\\item 'gray9'\n",
"\\item 'gray10'\n",
"\\item 'gray11'\n",
"\\item 'gray12'\n",
"\\item 'gray13'\n",
"\\item 'gray14'\n",
"\\item 'gray15'\n",
"\\item 'gray16'\n",
"\\item 'gray17'\n",
"\\item 'gray18'\n",
"\\item 'gray19'\n",
"\\item 'gray20'\n",
"\\item 'gray21'\n",
"\\item 'gray22'\n",
"\\item 'gray23'\n",
"\\item 'gray24'\n",
"\\item 'gray25'\n",
"\\item 'gray26'\n",
"\\item 'gray27'\n",
"\\item 'gray28'\n",
"\\item 'gray29'\n",
"\\item 'gray30'\n",
"\\item 'gray31'\n",
"\\item 'gray32'\n",
"\\item 'gray33'\n",
"\\item 'gray34'\n",
"\\item 'gray35'\n",
"\\item 'gray36'\n",
"\\item 'gray37'\n",
"\\item 'gray38'\n",
"\\item 'gray39'\n",
"\\item 'gray40'\n",
"\\item 'gray41'\n",
"\\item 'gray42'\n",
"\\item 'gray43'\n",
"\\item 'gray44'\n",
"\\item 'gray45'\n",
"\\item 'gray46'\n",
"\\item 'gray47'\n",
"\\item 'gray48'\n",
"\\item 'gray49'\n",
"\\item 'gray50'\n",
"\\item 'gray51'\n",
"\\item 'gray52'\n",
"\\item 'gray53'\n",
"\\item 'gray54'\n",
"\\item 'gray55'\n",
"\\item 'gray56'\n",
"\\item 'gray57'\n",
"\\item 'gray58'\n",
"\\item 'gray59'\n",
"\\item 'gray60'\n",
"\\item 'gray61'\n",
"\\item 'gray62'\n",
"\\item 'gray63'\n",
"\\item 'gray64'\n",
"\\item 'gray65'\n",
"\\item 'gray66'\n",
"\\item 'gray67'\n",
"\\item 'gray68'\n",
"\\item 'gray69'\n",
"\\item 'gray70'\n",
"\\item 'gray71'\n",
"\\item 'gray72'\n",
"\\item 'gray73'\n",
"\\item 'gray74'\n",
"\\item 'gray75'\n",
"\\item 'gray76'\n",
"\\item 'gray77'\n",
"\\item 'gray78'\n",
"\\item 'gray79'\n",
"\\item 'gray80'\n",
"\\item 'gray81'\n",
"\\item 'gray82'\n",
"\\item 'gray83'\n",
"\\item 'gray84'\n",
"\\item 'gray85'\n",
"\\item 'gray86'\n",
"\\item 'gray87'\n",
"\\item 'gray88'\n",
"\\item 'gray89'\n",
"\\item 'gray90'\n",
"\\item 'gray91'\n",
"\\item 'gray92'\n",
"\\item 'gray93'\n",
"\\item 'gray94'\n",
"\\item 'gray95'\n",
"\\item 'gray96'\n",
"\\item 'gray97'\n",
"\\item 'gray98'\n",
"\\item 'gray99'\n",
"\\item 'gray100'\n",
"\\item 'green'\n",
"\\item 'green1'\n",
"\\item 'green2'\n",
"\\item 'green3'\n",
"\\item 'green4'\n",
"\\item 'greenyellow'\n",
"\\item 'grey'\n",
"\\item 'grey0'\n",
"\\item 'grey1'\n",
"\\item 'grey2'\n",
"\\item 'grey3'\n",
"\\item 'grey4'\n",
"\\item 'grey5'\n",
"\\item 'grey6'\n",
"\\item 'grey7'\n",
"\\item 'grey8'\n",
"\\item 'grey9'\n",
"\\item 'grey10'\n",
"\\item 'grey11'\n",
"\\item 'grey12'\n",
"\\item 'grey13'\n",
"\\item 'grey14'\n",
"\\item 'grey15'\n",
"\\item 'grey16'\n",
"\\item 'grey17'\n",
"\\item 'grey18'\n",
"\\item 'grey19'\n",
"\\item 'grey20'\n",
"\\item 'grey21'\n",
"\\item 'grey22'\n",
"\\item 'grey23'\n",
"\\item 'grey24'\n",
"\\item 'grey25'\n",
"\\item 'grey26'\n",
"\\item 'grey27'\n",
"\\item 'grey28'\n",
"\\item 'grey29'\n",
"\\item 'grey30'\n",
"\\item 'grey31'\n",
"\\item 'grey32'\n",
"\\item 'grey33'\n",
"\\item 'grey34'\n",
"\\item 'grey35'\n",
"\\item 'grey36'\n",
"\\item 'grey37'\n",
"\\item 'grey38'\n",
"\\item 'grey39'\n",
"\\item 'grey40'\n",
"\\item 'grey41'\n",
"\\item 'grey42'\n",
"\\item 'grey43'\n",
"\\item 'grey44'\n",
"\\item 'grey45'\n",
"\\item 'grey46'\n",
"\\item 'grey47'\n",
"\\item 'grey48'\n",
"\\item 'grey49'\n",
"\\item 'grey50'\n",
"\\item 'grey51'\n",
"\\item 'grey52'\n",
"\\item 'grey53'\n",
"\\item 'grey54'\n",
"\\item 'grey55'\n",
"\\item 'grey56'\n",
"\\item 'grey57'\n",
"\\item 'grey58'\n",
"\\item 'grey59'\n",
"\\item 'grey60'\n",
"\\item 'grey61'\n",
"\\item 'grey62'\n",
"\\item 'grey63'\n",
"\\item 'grey64'\n",
"\\item 'grey65'\n",
"\\item 'grey66'\n",
"\\item 'grey67'\n",
"\\item 'grey68'\n",
"\\item 'grey69'\n",
"\\item 'grey70'\n",
"\\item 'grey71'\n",
"\\item 'grey72'\n",
"\\item 'grey73'\n",
"\\item 'grey74'\n",
"\\item 'grey75'\n",
"\\item 'grey76'\n",
"\\item 'grey77'\n",
"\\item 'grey78'\n",
"\\item 'grey79'\n",
"\\item 'grey80'\n",
"\\item 'grey81'\n",
"\\item 'grey82'\n",
"\\item 'grey83'\n",
"\\item 'grey84'\n",
"\\item 'grey85'\n",
"\\item 'grey86'\n",
"\\item 'grey87'\n",
"\\item 'grey88'\n",
"\\item 'grey89'\n",
"\\item 'grey90'\n",
"\\item 'grey91'\n",
"\\item 'grey92'\n",
"\\item 'grey93'\n",
"\\item 'grey94'\n",
"\\item 'grey95'\n",
"\\item 'grey96'\n",
"\\item 'grey97'\n",
"\\item 'grey98'\n",
"\\item 'grey99'\n",
"\\item 'grey100'\n",
"\\item 'honeydew'\n",
"\\item 'honeydew1'\n",
"\\item 'honeydew2'\n",
"\\item 'honeydew3'\n",
"\\item 'honeydew4'\n",
"\\item 'hotpink'\n",
"\\item 'hotpink1'\n",
"\\item 'hotpink2'\n",
"\\item 'hotpink3'\n",
"\\item 'hotpink4'\n",
"\\item 'indianred'\n",
"\\item 'indianred1'\n",
"\\item 'indianred2'\n",
"\\item 'indianred3'\n",
"\\item 'indianred4'\n",
"\\item 'ivory'\n",
"\\item 'ivory1'\n",
"\\item 'ivory2'\n",
"\\item 'ivory3'\n",
"\\item 'ivory4'\n",
"\\item 'khaki'\n",
"\\item 'khaki1'\n",
"\\item 'khaki2'\n",
"\\item 'khaki3'\n",
"\\item 'khaki4'\n",
"\\item 'lavender'\n",
"\\item 'lavenderblush'\n",
"\\item 'lavenderblush1'\n",
"\\item 'lavenderblush2'\n",
"\\item 'lavenderblush3'\n",
"\\item 'lavenderblush4'\n",
"\\item 'lawngreen'\n",
"\\item 'lemonchiffon'\n",
"\\item 'lemonchiffon1'\n",
"\\item 'lemonchiffon2'\n",
"\\item 'lemonchiffon3'\n",
"\\item 'lemonchiffon4'\n",
"\\item 'lightblue'\n",
"\\item 'lightblue1'\n",
"\\item 'lightblue2'\n",
"\\item 'lightblue3'\n",
"\\item 'lightblue4'\n",
"\\item 'lightcoral'\n",
"\\item 'lightcyan'\n",
"\\item 'lightcyan1'\n",
"\\item 'lightcyan2'\n",
"\\item 'lightcyan3'\n",
"\\item 'lightcyan4'\n",
"\\item 'lightgoldenrod'\n",
"\\item 'lightgoldenrod1'\n",
"\\item 'lightgoldenrod2'\n",
"\\item 'lightgoldenrod3'\n",
"\\item 'lightgoldenrod4'\n",
"\\item 'lightgoldenrodyellow'\n",
"\\item 'lightgray'\n",
"\\item 'lightgreen'\n",
"\\item 'lightgrey'\n",
"\\item 'lightpink'\n",
"\\item 'lightpink1'\n",
"\\item 'lightpink2'\n",
"\\item 'lightpink3'\n",
"\\item 'lightpink4'\n",
"\\item 'lightsalmon'\n",
"\\item 'lightsalmon1'\n",
"\\item 'lightsalmon2'\n",
"\\item 'lightsalmon3'\n",
"\\item 'lightsalmon4'\n",
"\\item 'lightseagreen'\n",
"\\item 'lightskyblue'\n",
"\\item 'lightskyblue1'\n",
"\\item 'lightskyblue2'\n",
"\\item 'lightskyblue3'\n",
"\\item 'lightskyblue4'\n",
"\\item 'lightslateblue'\n",
"\\item 'lightslategray'\n",
"\\item 'lightslategrey'\n",
"\\item 'lightsteelblue'\n",
"\\item 'lightsteelblue1'\n",
"\\item 'lightsteelblue2'\n",
"\\item 'lightsteelblue3'\n",
"\\item 'lightsteelblue4'\n",
"\\item 'lightyellow'\n",
"\\item 'lightyellow1'\n",
"\\item 'lightyellow2'\n",
"\\item 'lightyellow3'\n",
"\\item 'lightyellow4'\n",
"\\item 'limegreen'\n",
"\\item 'linen'\n",
"\\item 'magenta'\n",
"\\item 'magenta1'\n",
"\\item 'magenta2'\n",
"\\item 'magenta3'\n",
"\\item 'magenta4'\n",
"\\item 'maroon'\n",
"\\item 'maroon1'\n",
"\\item 'maroon2'\n",
"\\item 'maroon3'\n",
"\\item 'maroon4'\n",
"\\item 'mediumaquamarine'\n",
"\\item 'mediumblue'\n",
"\\item 'mediumorchid'\n",
"\\item 'mediumorchid1'\n",
"\\item 'mediumorchid2'\n",
"\\item 'mediumorchid3'\n",
"\\item 'mediumorchid4'\n",
"\\item 'mediumpurple'\n",
"\\item 'mediumpurple1'\n",
"\\item 'mediumpurple2'\n",
"\\item 'mediumpurple3'\n",
"\\item 'mediumpurple4'\n",
"\\item 'mediumseagreen'\n",
"\\item 'mediumslateblue'\n",
"\\item 'mediumspringgreen'\n",
"\\item 'mediumturquoise'\n",
"\\item 'mediumvioletred'\n",
"\\item 'midnightblue'\n",
"\\item 'mintcream'\n",
"\\item 'mistyrose'\n",
"\\item 'mistyrose1'\n",
"\\item 'mistyrose2'\n",
"\\item 'mistyrose3'\n",
"\\item 'mistyrose4'\n",
"\\item 'moccasin'\n",
"\\item 'navajowhite'\n",
"\\item 'navajowhite1'\n",
"\\item 'navajowhite2'\n",
"\\item 'navajowhite3'\n",
"\\item 'navajowhite4'\n",
"\\item 'navy'\n",
"\\item 'navyblue'\n",
"\\item 'oldlace'\n",
"\\item 'olivedrab'\n",
"\\item 'olivedrab1'\n",
"\\item 'olivedrab2'\n",
"\\item 'olivedrab3'\n",
"\\item 'olivedrab4'\n",
"\\item 'orange'\n",
"\\item 'orange1'\n",
"\\item 'orange2'\n",
"\\item 'orange3'\n",
"\\item 'orange4'\n",
"\\item 'orangered'\n",
"\\item 'orangered1'\n",
"\\item 'orangered2'\n",
"\\item 'orangered3'\n",
"\\item 'orangered4'\n",
"\\item 'orchid'\n",
"\\item 'orchid1'\n",
"\\item 'orchid2'\n",
"\\item 'orchid3'\n",
"\\item 'orchid4'\n",
"\\item 'palegoldenrod'\n",
"\\item 'palegreen'\n",
"\\item 'palegreen1'\n",
"\\item 'palegreen2'\n",
"\\item 'palegreen3'\n",
"\\item 'palegreen4'\n",
"\\item 'paleturquoise'\n",
"\\item 'paleturquoise1'\n",
"\\item 'paleturquoise2'\n",
"\\item 'paleturquoise3'\n",
"\\item 'paleturquoise4'\n",
"\\item 'palevioletred'\n",
"\\item 'palevioletred1'\n",
"\\item 'palevioletred2'\n",
"\\item 'palevioletred3'\n",
"\\item 'palevioletred4'\n",
"\\item 'papayawhip'\n",
"\\item 'peachpuff'\n",
"\\item 'peachpuff1'\n",
"\\item 'peachpuff2'\n",
"\\item 'peachpuff3'\n",
"\\item 'peachpuff4'\n",
"\\item 'peru'\n",
"\\item 'pink'\n",
"\\item 'pink1'\n",
"\\item 'pink2'\n",
"\\item 'pink3'\n",
"\\item 'pink4'\n",
"\\item 'plum'\n",
"\\item 'plum1'\n",
"\\item 'plum2'\n",
"\\item 'plum3'\n",
"\\item 'plum4'\n",
"\\item 'powderblue'\n",
"\\item 'purple'\n",
"\\item 'purple1'\n",
"\\item 'purple2'\n",
"\\item 'purple3'\n",
"\\item 'purple4'\n",
"\\item 'red'\n",
"\\item 'red1'\n",
"\\item 'red2'\n",
"\\item 'red3'\n",
"\\item 'red4'\n",
"\\item 'rosybrown'\n",
"\\item 'rosybrown1'\n",
"\\item 'rosybrown2'\n",
"\\item 'rosybrown3'\n",
"\\item 'rosybrown4'\n",
"\\item 'royalblue'\n",
"\\item 'royalblue1'\n",
"\\item 'royalblue2'\n",
"\\item 'royalblue3'\n",
"\\item 'royalblue4'\n",
"\\item 'saddlebrown'\n",
"\\item 'salmon'\n",
"\\item 'salmon1'\n",
"\\item 'salmon2'\n",
"\\item 'salmon3'\n",
"\\item 'salmon4'\n",
"\\item 'sandybrown'\n",
"\\item 'seagreen'\n",
"\\item 'seagreen1'\n",
"\\item 'seagreen2'\n",
"\\item 'seagreen3'\n",
"\\item 'seagreen4'\n",
"\\item 'seashell'\n",
"\\item 'seashell1'\n",
"\\item 'seashell2'\n",
"\\item 'seashell3'\n",
"\\item 'seashell4'\n",
"\\item 'sienna'\n",
"\\item 'sienna1'\n",
"\\item 'sienna2'\n",
"\\item 'sienna3'\n",
"\\item 'sienna4'\n",
"\\item 'skyblue'\n",
"\\item 'skyblue1'\n",
"\\item 'skyblue2'\n",
"\\item 'skyblue3'\n",
"\\item 'skyblue4'\n",
"\\item 'slateblue'\n",
"\\item 'slateblue1'\n",
"\\item 'slateblue2'\n",
"\\item 'slateblue3'\n",
"\\item 'slateblue4'\n",
"\\item 'slategray'\n",
"\\item 'slategray1'\n",
"\\item 'slategray2'\n",
"\\item 'slategray3'\n",
"\\item 'slategray4'\n",
"\\item 'slategrey'\n",
"\\item 'snow'\n",
"\\item 'snow1'\n",
"\\item 'snow2'\n",
"\\item 'snow3'\n",
"\\item 'snow4'\n",
"\\item 'springgreen'\n",
"\\item 'springgreen1'\n",
"\\item 'springgreen2'\n",
"\\item 'springgreen3'\n",
"\\item 'springgreen4'\n",
"\\item 'steelblue'\n",
"\\item 'steelblue1'\n",
"\\item 'steelblue2'\n",
"\\item 'steelblue3'\n",
"\\item 'steelblue4'\n",
"\\item 'tan'\n",
"\\item 'tan1'\n",
"\\item 'tan2'\n",
"\\item 'tan3'\n",
"\\item 'tan4'\n",
"\\item 'thistle'\n",
"\\item 'thistle1'\n",
"\\item 'thistle2'\n",
"\\item 'thistle3'\n",
"\\item 'thistle4'\n",
"\\item 'tomato'\n",
"\\item 'tomato1'\n",
"\\item 'tomato2'\n",
"\\item 'tomato3'\n",
"\\item 'tomato4'\n",
"\\item 'turquoise'\n",
"\\item 'turquoise1'\n",
"\\item 'turquoise2'\n",
"\\item 'turquoise3'\n",
"\\item 'turquoise4'\n",
"\\item 'violet'\n",
"\\item 'violetred'\n",
"\\item 'violetred1'\n",
"\\item 'violetred2'\n",
"\\item 'violetred3'\n",
"\\item 'violetred4'\n",
"\\item 'wheat'\n",
"\\item 'wheat1'\n",
"\\item 'wheat2'\n",
"\\item 'wheat3'\n",
"\\item 'wheat4'\n",
"\\item 'whitesmoke'\n",
"\\item 'yellow'\n",
"\\item 'yellow1'\n",
"\\item 'yellow2'\n",
"\\item 'yellow3'\n",
"\\item 'yellow4'\n",
"\\item 'yellowgreen'\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 'white'\n",
"2. 'aliceblue'\n",
"3. 'antiquewhite'\n",
"4. 'antiquewhite1'\n",
"5. 'antiquewhite2'\n",
"6. 'antiquewhite3'\n",
"7. 'antiquewhite4'\n",
"8. 'aquamarine'\n",
"9. 'aquamarine1'\n",
"10. 'aquamarine2'\n",
"11. 'aquamarine3'\n",
"12. 'aquamarine4'\n",
"13. 'azure'\n",
"14. 'azure1'\n",
"15. 'azure2'\n",
"16. 'azure3'\n",
"17. 'azure4'\n",
"18. 'beige'\n",
"19. 'bisque'\n",
"20. 'bisque1'\n",
"21. 'bisque2'\n",
"22. 'bisque3'\n",
"23. 'bisque4'\n",
"24. 'black'\n",
"25. 'blanchedalmond'\n",
"26. 'blue'\n",
"27. 'blue1'\n",
"28. 'blue2'\n",
"29. 'blue3'\n",
"30. 'blue4'\n",
"31. 'blueviolet'\n",
"32. 'brown'\n",
"33. 'brown1'\n",
"34. 'brown2'\n",
"35. 'brown3'\n",
"36. 'brown4'\n",
"37. 'burlywood'\n",
"38. 'burlywood1'\n",
"39. 'burlywood2'\n",
"40. 'burlywood3'\n",
"41. 'burlywood4'\n",
"42. 'cadetblue'\n",
"43. 'cadetblue1'\n",
"44. 'cadetblue2'\n",
"45. 'cadetblue3'\n",
"46. 'cadetblue4'\n",
"47. 'chartreuse'\n",
"48. 'chartreuse1'\n",
"49. 'chartreuse2'\n",
"50. 'chartreuse3'\n",
"51. 'chartreuse4'\n",
"52. 'chocolate'\n",
"53. 'chocolate1'\n",
"54. 'chocolate2'\n",
"55. 'chocolate3'\n",
"56. 'chocolate4'\n",
"57. 'coral'\n",
"58. 'coral1'\n",
"59. 'coral2'\n",
"60. 'coral3'\n",
"61. 'coral4'\n",
"62. 'cornflowerblue'\n",
"63. 'cornsilk'\n",
"64. 'cornsilk1'\n",
"65. 'cornsilk2'\n",
"66. 'cornsilk3'\n",
"67. 'cornsilk4'\n",
"68. 'cyan'\n",
"69. 'cyan1'\n",
"70. 'cyan2'\n",
"71. 'cyan3'\n",
"72. 'cyan4'\n",
"73. 'darkblue'\n",
"74. 'darkcyan'\n",
"75. 'darkgoldenrod'\n",
"76. 'darkgoldenrod1'\n",
"77. 'darkgoldenrod2'\n",
"78. 'darkgoldenrod3'\n",
"79. 'darkgoldenrod4'\n",
"80. 'darkgray'\n",
"81. 'darkgreen'\n",
"82. 'darkgrey'\n",
"83. 'darkkhaki'\n",
"84. 'darkmagenta'\n",
"85. 'darkolivegreen'\n",
"86. 'darkolivegreen1'\n",
"87. 'darkolivegreen2'\n",
"88. 'darkolivegreen3'\n",
"89. 'darkolivegreen4'\n",
"90. 'darkorange'\n",
"91. 'darkorange1'\n",
"92. 'darkorange2'\n",
"93. 'darkorange3'\n",
"94. 'darkorange4'\n",
"95. 'darkorchid'\n",
"96. 'darkorchid1'\n",
"97. 'darkorchid2'\n",
"98. 'darkorchid3'\n",
"99. 'darkorchid4'\n",
"100. 'darkred'\n",
"101. 'darksalmon'\n",
"102. 'darkseagreen'\n",
"103. 'darkseagreen1'\n",
"104. 'darkseagreen2'\n",
"105. 'darkseagreen3'\n",
"106. 'darkseagreen4'\n",
"107. 'darkslateblue'\n",
"108. 'darkslategray'\n",
"109. 'darkslategray1'\n",
"110. 'darkslategray2'\n",
"111. 'darkslategray3'\n",
"112. 'darkslategray4'\n",
"113. 'darkslategrey'\n",
"114. 'darkturquoise'\n",
"115. 'darkviolet'\n",
"116. 'deeppink'\n",
"117. 'deeppink1'\n",
"118. 'deeppink2'\n",
"119. 'deeppink3'\n",
"120. 'deeppink4'\n",
"121. 'deepskyblue'\n",
"122. 'deepskyblue1'\n",
"123. 'deepskyblue2'\n",
"124. 'deepskyblue3'\n",
"125. 'deepskyblue4'\n",
"126. 'dimgray'\n",
"127. 'dimgrey'\n",
"128. 'dodgerblue'\n",
"129. 'dodgerblue1'\n",
"130. 'dodgerblue2'\n",
"131. 'dodgerblue3'\n",
"132. 'dodgerblue4'\n",
"133. 'firebrick'\n",
"134. 'firebrick1'\n",
"135. 'firebrick2'\n",
"136. 'firebrick3'\n",
"137. 'firebrick4'\n",
"138. 'floralwhite'\n",
"139. 'forestgreen'\n",
"140. 'gainsboro'\n",
"141. 'ghostwhite'\n",
"142. 'gold'\n",
"143. 'gold1'\n",
"144. 'gold2'\n",
"145. 'gold3'\n",
"146. 'gold4'\n",
"147. 'goldenrod'\n",
"148. 'goldenrod1'\n",
"149. 'goldenrod2'\n",
"150. 'goldenrod3'\n",
"151. 'goldenrod4'\n",
"152. 'gray'\n",
"153. 'gray0'\n",
"154. 'gray1'\n",
"155. 'gray2'\n",
"156. 'gray3'\n",
"157. 'gray4'\n",
"158. 'gray5'\n",
"159. 'gray6'\n",
"160. 'gray7'\n",
"161. 'gray8'\n",
"162. 'gray9'\n",
"163. 'gray10'\n",
"164. 'gray11'\n",
"165. 'gray12'\n",
"166. 'gray13'\n",
"167. 'gray14'\n",
"168. 'gray15'\n",
"169. 'gray16'\n",
"170. 'gray17'\n",
"171. 'gray18'\n",
"172. 'gray19'\n",
"173. 'gray20'\n",
"174. 'gray21'\n",
"175. 'gray22'\n",
"176. 'gray23'\n",
"177. 'gray24'\n",
"178. 'gray25'\n",
"179. 'gray26'\n",
"180. 'gray27'\n",
"181. 'gray28'\n",
"182. 'gray29'\n",
"183. 'gray30'\n",
"184. 'gray31'\n",
"185. 'gray32'\n",
"186. 'gray33'\n",
"187. 'gray34'\n",
"188. 'gray35'\n",
"189. 'gray36'\n",
"190. 'gray37'\n",
"191. 'gray38'\n",
"192. 'gray39'\n",
"193. 'gray40'\n",
"194. 'gray41'\n",
"195. 'gray42'\n",
"196. 'gray43'\n",
"197. 'gray44'\n",
"198. 'gray45'\n",
"199. 'gray46'\n",
"200. 'gray47'\n",
"201. 'gray48'\n",
"202. 'gray49'\n",
"203. 'gray50'\n",
"204. 'gray51'\n",
"205. 'gray52'\n",
"206. 'gray53'\n",
"207. 'gray54'\n",
"208. 'gray55'\n",
"209. 'gray56'\n",
"210. 'gray57'\n",
"211. 'gray58'\n",
"212. 'gray59'\n",
"213. 'gray60'\n",
"214. 'gray61'\n",
"215. 'gray62'\n",
"216. 'gray63'\n",
"217. 'gray64'\n",
"218. 'gray65'\n",
"219. 'gray66'\n",
"220. 'gray67'\n",
"221. 'gray68'\n",
"222. 'gray69'\n",
"223. 'gray70'\n",
"224. 'gray71'\n",
"225. 'gray72'\n",
"226. 'gray73'\n",
"227. 'gray74'\n",
"228. 'gray75'\n",
"229. 'gray76'\n",
"230. 'gray77'\n",
"231. 'gray78'\n",
"232. 'gray79'\n",
"233. 'gray80'\n",
"234. 'gray81'\n",
"235. 'gray82'\n",
"236. 'gray83'\n",
"237. 'gray84'\n",
"238. 'gray85'\n",
"239. 'gray86'\n",
"240. 'gray87'\n",
"241. 'gray88'\n",
"242. 'gray89'\n",
"243. 'gray90'\n",
"244. 'gray91'\n",
"245. 'gray92'\n",
"246. 'gray93'\n",
"247. 'gray94'\n",
"248. 'gray95'\n",
"249. 'gray96'\n",
"250. 'gray97'\n",
"251. 'gray98'\n",
"252. 'gray99'\n",
"253. 'gray100'\n",
"254. 'green'\n",
"255. 'green1'\n",
"256. 'green2'\n",
"257. 'green3'\n",
"258. 'green4'\n",
"259. 'greenyellow'\n",
"260. 'grey'\n",
"261. 'grey0'\n",
"262. 'grey1'\n",
"263. 'grey2'\n",
"264. 'grey3'\n",
"265. 'grey4'\n",
"266. 'grey5'\n",
"267. 'grey6'\n",
"268. 'grey7'\n",
"269. 'grey8'\n",
"270. 'grey9'\n",
"271. 'grey10'\n",
"272. 'grey11'\n",
"273. 'grey12'\n",
"274. 'grey13'\n",
"275. 'grey14'\n",
"276. 'grey15'\n",
"277. 'grey16'\n",
"278. 'grey17'\n",
"279. 'grey18'\n",
"280. 'grey19'\n",
"281. 'grey20'\n",
"282. 'grey21'\n",
"283. 'grey22'\n",
"284. 'grey23'\n",
"285. 'grey24'\n",
"286. 'grey25'\n",
"287. 'grey26'\n",
"288. 'grey27'\n",
"289. 'grey28'\n",
"290. 'grey29'\n",
"291. 'grey30'\n",
"292. 'grey31'\n",
"293. 'grey32'\n",
"294. 'grey33'\n",
"295. 'grey34'\n",
"296. 'grey35'\n",
"297. 'grey36'\n",
"298. 'grey37'\n",
"299. 'grey38'\n",
"300. 'grey39'\n",
"301. 'grey40'\n",
"302. 'grey41'\n",
"303. 'grey42'\n",
"304. 'grey43'\n",
"305. 'grey44'\n",
"306. 'grey45'\n",
"307. 'grey46'\n",
"308. 'grey47'\n",
"309. 'grey48'\n",
"310. 'grey49'\n",
"311. 'grey50'\n",
"312. 'grey51'\n",
"313. 'grey52'\n",
"314. 'grey53'\n",
"315. 'grey54'\n",
"316. 'grey55'\n",
"317. 'grey56'\n",
"318. 'grey57'\n",
"319. 'grey58'\n",
"320. 'grey59'\n",
"321. 'grey60'\n",
"322. 'grey61'\n",
"323. 'grey62'\n",
"324. 'grey63'\n",
"325. 'grey64'\n",
"326. 'grey65'\n",
"327. 'grey66'\n",
"328. 'grey67'\n",
"329. 'grey68'\n",
"330. 'grey69'\n",
"331. 'grey70'\n",
"332. 'grey71'\n",
"333. 'grey72'\n",
"334. 'grey73'\n",
"335. 'grey74'\n",
"336. 'grey75'\n",
"337. 'grey76'\n",
"338. 'grey77'\n",
"339. 'grey78'\n",
"340. 'grey79'\n",
"341. 'grey80'\n",
"342. 'grey81'\n",
"343. 'grey82'\n",
"344. 'grey83'\n",
"345. 'grey84'\n",
"346. 'grey85'\n",
"347. 'grey86'\n",
"348. 'grey87'\n",
"349. 'grey88'\n",
"350. 'grey89'\n",
"351. 'grey90'\n",
"352. 'grey91'\n",
"353. 'grey92'\n",
"354. 'grey93'\n",
"355. 'grey94'\n",
"356. 'grey95'\n",
"357. 'grey96'\n",
"358. 'grey97'\n",
"359. 'grey98'\n",
"360. 'grey99'\n",
"361. 'grey100'\n",
"362. 'honeydew'\n",
"363. 'honeydew1'\n",
"364. 'honeydew2'\n",
"365. 'honeydew3'\n",
"366. 'honeydew4'\n",
"367. 'hotpink'\n",
"368. 'hotpink1'\n",
"369. 'hotpink2'\n",
"370. 'hotpink3'\n",
"371. 'hotpink4'\n",
"372. 'indianred'\n",
"373. 'indianred1'\n",
"374. 'indianred2'\n",
"375. 'indianred3'\n",
"376. 'indianred4'\n",
"377. 'ivory'\n",
"378. 'ivory1'\n",
"379. 'ivory2'\n",
"380. 'ivory3'\n",
"381. 'ivory4'\n",
"382. 'khaki'\n",
"383. 'khaki1'\n",
"384. 'khaki2'\n",
"385. 'khaki3'\n",
"386. 'khaki4'\n",
"387. 'lavender'\n",
"388. 'lavenderblush'\n",
"389. 'lavenderblush1'\n",
"390. 'lavenderblush2'\n",
"391. 'lavenderblush3'\n",
"392. 'lavenderblush4'\n",
"393. 'lawngreen'\n",
"394. 'lemonchiffon'\n",
"395. 'lemonchiffon1'\n",
"396. 'lemonchiffon2'\n",
"397. 'lemonchiffon3'\n",
"398. 'lemonchiffon4'\n",
"399. 'lightblue'\n",
"400. 'lightblue1'\n",
"401. 'lightblue2'\n",
"402. 'lightblue3'\n",
"403. 'lightblue4'\n",
"404. 'lightcoral'\n",
"405. 'lightcyan'\n",
"406. 'lightcyan1'\n",
"407. 'lightcyan2'\n",
"408. 'lightcyan3'\n",
"409. 'lightcyan4'\n",
"410. 'lightgoldenrod'\n",
"411. 'lightgoldenrod1'\n",
"412. 'lightgoldenrod2'\n",
"413. 'lightgoldenrod3'\n",
"414. 'lightgoldenrod4'\n",
"415. 'lightgoldenrodyellow'\n",
"416. 'lightgray'\n",
"417. 'lightgreen'\n",
"418. 'lightgrey'\n",
"419. 'lightpink'\n",
"420. 'lightpink1'\n",
"421. 'lightpink2'\n",
"422. 'lightpink3'\n",
"423. 'lightpink4'\n",
"424. 'lightsalmon'\n",
"425. 'lightsalmon1'\n",
"426. 'lightsalmon2'\n",
"427. 'lightsalmon3'\n",
"428. 'lightsalmon4'\n",
"429. 'lightseagreen'\n",
"430. 'lightskyblue'\n",
"431. 'lightskyblue1'\n",
"432. 'lightskyblue2'\n",
"433. 'lightskyblue3'\n",
"434. 'lightskyblue4'\n",
"435. 'lightslateblue'\n",
"436. 'lightslategray'\n",
"437. 'lightslategrey'\n",
"438. 'lightsteelblue'\n",
"439. 'lightsteelblue1'\n",
"440. 'lightsteelblue2'\n",
"441. 'lightsteelblue3'\n",
"442. 'lightsteelblue4'\n",
"443. 'lightyellow'\n",
"444. 'lightyellow1'\n",
"445. 'lightyellow2'\n",
"446. 'lightyellow3'\n",
"447. 'lightyellow4'\n",
"448. 'limegreen'\n",
"449. 'linen'\n",
"450. 'magenta'\n",
"451. 'magenta1'\n",
"452. 'magenta2'\n",
"453. 'magenta3'\n",
"454. 'magenta4'\n",
"455. 'maroon'\n",
"456. 'maroon1'\n",
"457. 'maroon2'\n",
"458. 'maroon3'\n",
"459. 'maroon4'\n",
"460. 'mediumaquamarine'\n",
"461. 'mediumblue'\n",
"462. 'mediumorchid'\n",
"463. 'mediumorchid1'\n",
"464. 'mediumorchid2'\n",
"465. 'mediumorchid3'\n",
"466. 'mediumorchid4'\n",
"467. 'mediumpurple'\n",
"468. 'mediumpurple1'\n",
"469. 'mediumpurple2'\n",
"470. 'mediumpurple3'\n",
"471. 'mediumpurple4'\n",
"472. 'mediumseagreen'\n",
"473. 'mediumslateblue'\n",
"474. 'mediumspringgreen'\n",
"475. 'mediumturquoise'\n",
"476. 'mediumvioletred'\n",
"477. 'midnightblue'\n",
"478. 'mintcream'\n",
"479. 'mistyrose'\n",
"480. 'mistyrose1'\n",
"481. 'mistyrose2'\n",
"482. 'mistyrose3'\n",
"483. 'mistyrose4'\n",
"484. 'moccasin'\n",
"485. 'navajowhite'\n",
"486. 'navajowhite1'\n",
"487. 'navajowhite2'\n",
"488. 'navajowhite3'\n",
"489. 'navajowhite4'\n",
"490. 'navy'\n",
"491. 'navyblue'\n",
"492. 'oldlace'\n",
"493. 'olivedrab'\n",
"494. 'olivedrab1'\n",
"495. 'olivedrab2'\n",
"496. 'olivedrab3'\n",
"497. 'olivedrab4'\n",
"498. 'orange'\n",
"499. 'orange1'\n",
"500. 'orange2'\n",
"501. 'orange3'\n",
"502. 'orange4'\n",
"503. 'orangered'\n",
"504. 'orangered1'\n",
"505. 'orangered2'\n",
"506. 'orangered3'\n",
"507. 'orangered4'\n",
"508. 'orchid'\n",
"509. 'orchid1'\n",
"510. 'orchid2'\n",
"511. 'orchid3'\n",
"512. 'orchid4'\n",
"513. 'palegoldenrod'\n",
"514. 'palegreen'\n",
"515. 'palegreen1'\n",
"516. 'palegreen2'\n",
"517. 'palegreen3'\n",
"518. 'palegreen4'\n",
"519. 'paleturquoise'\n",
"520. 'paleturquoise1'\n",
"521. 'paleturquoise2'\n",
"522. 'paleturquoise3'\n",
"523. 'paleturquoise4'\n",
"524. 'palevioletred'\n",
"525. 'palevioletred1'\n",
"526. 'palevioletred2'\n",
"527. 'palevioletred3'\n",
"528. 'palevioletred4'\n",
"529. 'papayawhip'\n",
"530. 'peachpuff'\n",
"531. 'peachpuff1'\n",
"532. 'peachpuff2'\n",
"533. 'peachpuff3'\n",
"534. 'peachpuff4'\n",
"535. 'peru'\n",
"536. 'pink'\n",
"537. 'pink1'\n",
"538. 'pink2'\n",
"539. 'pink3'\n",
"540. 'pink4'\n",
"541. 'plum'\n",
"542. 'plum1'\n",
"543. 'plum2'\n",
"544. 'plum3'\n",
"545. 'plum4'\n",
"546. 'powderblue'\n",
"547. 'purple'\n",
"548. 'purple1'\n",
"549. 'purple2'\n",
"550. 'purple3'\n",
"551. 'purple4'\n",
"552. 'red'\n",
"553. 'red1'\n",
"554. 'red2'\n",
"555. 'red3'\n",
"556. 'red4'\n",
"557. 'rosybrown'\n",
"558. 'rosybrown1'\n",
"559. 'rosybrown2'\n",
"560. 'rosybrown3'\n",
"561. 'rosybrown4'\n",
"562. 'royalblue'\n",
"563. 'royalblue1'\n",
"564. 'royalblue2'\n",
"565. 'royalblue3'\n",
"566. 'royalblue4'\n",
"567. 'saddlebrown'\n",
"568. 'salmon'\n",
"569. 'salmon1'\n",
"570. 'salmon2'\n",
"571. 'salmon3'\n",
"572. 'salmon4'\n",
"573. 'sandybrown'\n",
"574. 'seagreen'\n",
"575. 'seagreen1'\n",
"576. 'seagreen2'\n",
"577. 'seagreen3'\n",
"578. 'seagreen4'\n",
"579. 'seashell'\n",
"580. 'seashell1'\n",
"581. 'seashell2'\n",
"582. 'seashell3'\n",
"583. 'seashell4'\n",
"584. 'sienna'\n",
"585. 'sienna1'\n",
"586. 'sienna2'\n",
"587. 'sienna3'\n",
"588. 'sienna4'\n",
"589. 'skyblue'\n",
"590. 'skyblue1'\n",
"591. 'skyblue2'\n",
"592. 'skyblue3'\n",
"593. 'skyblue4'\n",
"594. 'slateblue'\n",
"595. 'slateblue1'\n",
"596. 'slateblue2'\n",
"597. 'slateblue3'\n",
"598. 'slateblue4'\n",
"599. 'slategray'\n",
"600. 'slategray1'\n",
"601. 'slategray2'\n",
"602. 'slategray3'\n",
"603. 'slategray4'\n",
"604. 'slategrey'\n",
"605. 'snow'\n",
"606. 'snow1'\n",
"607. 'snow2'\n",
"608. 'snow3'\n",
"609. 'snow4'\n",
"610. 'springgreen'\n",
"611. 'springgreen1'\n",
"612. 'springgreen2'\n",
"613. 'springgreen3'\n",
"614. 'springgreen4'\n",
"615. 'steelblue'\n",
"616. 'steelblue1'\n",
"617. 'steelblue2'\n",
"618. 'steelblue3'\n",
"619. 'steelblue4'\n",
"620. 'tan'\n",
"621. 'tan1'\n",
"622. 'tan2'\n",
"623. 'tan3'\n",
"624. 'tan4'\n",
"625. 'thistle'\n",
"626. 'thistle1'\n",
"627. 'thistle2'\n",
"628. 'thistle3'\n",
"629. 'thistle4'\n",
"630. 'tomato'\n",
"631. 'tomato1'\n",
"632. 'tomato2'\n",
"633. 'tomato3'\n",
"634. 'tomato4'\n",
"635. 'turquoise'\n",
"636. 'turquoise1'\n",
"637. 'turquoise2'\n",
"638. 'turquoise3'\n",
"639. 'turquoise4'\n",
"640. 'violet'\n",
"641. 'violetred'\n",
"642. 'violetred1'\n",
"643. 'violetred2'\n",
"644. 'violetred3'\n",
"645. 'violetred4'\n",
"646. 'wheat'\n",
"647. 'wheat1'\n",
"648. 'wheat2'\n",
"649. 'wheat3'\n",
"650. 'wheat4'\n",
"651. 'whitesmoke'\n",
"652. 'yellow'\n",
"653. 'yellow1'\n",
"654. 'yellow2'\n",
"655. 'yellow3'\n",
"656. 'yellow4'\n",
"657. 'yellowgreen'\n",
"\n",
"\n"
],
"text/plain": [
" [1] \"white\" \"aliceblue\" \"antiquewhite\" \n",
" [4] \"antiquewhite1\" \"antiquewhite2\" \"antiquewhite3\" \n",
" [7] \"antiquewhite4\" \"aquamarine\" \"aquamarine1\" \n",
" [10] \"aquamarine2\" \"aquamarine3\" \"aquamarine4\" \n",
" [13] \"azure\" \"azure1\" \"azure2\" \n",
" [16] \"azure3\" \"azure4\" \"beige\" \n",
" [19] \"bisque\" \"bisque1\" \"bisque2\" \n",
" [22] \"bisque3\" \"bisque4\" \"black\" \n",
" [25] \"blanchedalmond\" \"blue\" \"blue1\" \n",
" [28] \"blue2\" \"blue3\" \"blue4\" \n",
" [31] \"blueviolet\" \"brown\" \"brown1\" \n",
" [34] \"brown2\" \"brown3\" \"brown4\" \n",
" [37] \"burlywood\" \"burlywood1\" \"burlywood2\" \n",
" [40] \"burlywood3\" \"burlywood4\" \"cadetblue\" \n",
" [43] \"cadetblue1\" \"cadetblue2\" \"cadetblue3\" \n",
" [46] \"cadetblue4\" \"chartreuse\" \"chartreuse1\" \n",
" [49] \"chartreuse2\" \"chartreuse3\" \"chartreuse4\" \n",
" [52] \"chocolate\" \"chocolate1\" \"chocolate2\" \n",
" [55] \"chocolate3\" \"chocolate4\" \"coral\" \n",
" [58] \"coral1\" \"coral2\" \"coral3\" \n",
" [61] \"coral4\" \"cornflowerblue\" \"cornsilk\" \n",
" [64] \"cornsilk1\" \"cornsilk2\" \"cornsilk3\" \n",
" [67] \"cornsilk4\" \"cyan\" \"cyan1\" \n",
" [70] \"cyan2\" \"cyan3\" \"cyan4\" \n",
" [73] \"darkblue\" \"darkcyan\" \"darkgoldenrod\" \n",
" [76] \"darkgoldenrod1\" \"darkgoldenrod2\" \"darkgoldenrod3\" \n",
" [79] \"darkgoldenrod4\" \"darkgray\" \"darkgreen\" \n",
" [82] \"darkgrey\" \"darkkhaki\" \"darkmagenta\" \n",
" [85] \"darkolivegreen\" \"darkolivegreen1\" \"darkolivegreen2\" \n",
" [88] \"darkolivegreen3\" \"darkolivegreen4\" \"darkorange\" \n",
" [91] \"darkorange1\" \"darkorange2\" \"darkorange3\" \n",
" [94] \"darkorange4\" \"darkorchid\" \"darkorchid1\" \n",
" [97] \"darkorchid2\" \"darkorchid3\" \"darkorchid4\" \n",
"[100] \"darkred\" \"darksalmon\" \"darkseagreen\" \n",
"[103] \"darkseagreen1\" \"darkseagreen2\" \"darkseagreen3\" \n",
"[106] \"darkseagreen4\" \"darkslateblue\" \"darkslategray\" \n",
"[109] \"darkslategray1\" \"darkslategray2\" \"darkslategray3\" \n",
"[112] \"darkslategray4\" \"darkslategrey\" \"darkturquoise\" \n",
"[115] \"darkviolet\" \"deeppink\" \"deeppink1\" \n",
"[118] \"deeppink2\" \"deeppink3\" \"deeppink4\" \n",
"[121] \"deepskyblue\" \"deepskyblue1\" \"deepskyblue2\" \n",
"[124] \"deepskyblue3\" \"deepskyblue4\" \"dimgray\" \n",
"[127] \"dimgrey\" \"dodgerblue\" \"dodgerblue1\" \n",
"[130] \"dodgerblue2\" \"dodgerblue3\" \"dodgerblue4\" \n",
"[133] \"firebrick\" \"firebrick1\" \"firebrick2\" \n",
"[136] \"firebrick3\" \"firebrick4\" \"floralwhite\" \n",
"[139] \"forestgreen\" \"gainsboro\" \"ghostwhite\" \n",
"[142] \"gold\" \"gold1\" \"gold2\" \n",
"[145] \"gold3\" \"gold4\" \"goldenrod\" \n",
"[148] \"goldenrod1\" \"goldenrod2\" \"goldenrod3\" \n",
"[151] \"goldenrod4\" \"gray\" \"gray0\" \n",
"[154] \"gray1\" \"gray2\" \"gray3\" \n",
"[157] \"gray4\" \"gray5\" \"gray6\" \n",
"[160] \"gray7\" \"gray8\" \"gray9\" \n",
"[163] \"gray10\" \"gray11\" \"gray12\" \n",
"[166] \"gray13\" \"gray14\" \"gray15\" \n",
"[169] \"gray16\" \"gray17\" \"gray18\" \n",
"[172] \"gray19\" \"gray20\" \"gray21\" \n",
"[175] \"gray22\" \"gray23\" \"gray24\" \n",
"[178] \"gray25\" \"gray26\" \"gray27\" \n",
"[181] \"gray28\" \"gray29\" \"gray30\" \n",
"[184] \"gray31\" \"gray32\" \"gray33\" \n",
"[187] \"gray34\" \"gray35\" \"gray36\" \n",
"[190] \"gray37\" \"gray38\" \"gray39\" \n",
"[193] \"gray40\" \"gray41\" \"gray42\" \n",
"[196] \"gray43\" \"gray44\" \"gray45\" \n",
"[199] \"gray46\" \"gray47\" \"gray48\" \n",
"[202] \"gray49\" \"gray50\" \"gray51\" \n",
"[205] \"gray52\" \"gray53\" \"gray54\" \n",
"[208] \"gray55\" \"gray56\" \"gray57\" \n",
"[211] \"gray58\" \"gray59\" \"gray60\" \n",
"[214] \"gray61\" \"gray62\" \"gray63\" \n",
"[217] \"gray64\" \"gray65\" \"gray66\" \n",
"[220] \"gray67\" \"gray68\" \"gray69\" \n",
"[223] \"gray70\" \"gray71\" \"gray72\" \n",
"[226] \"gray73\" \"gray74\" \"gray75\" \n",
"[229] \"gray76\" \"gray77\" \"gray78\" \n",
"[232] \"gray79\" \"gray80\" \"gray81\" \n",
"[235] \"gray82\" \"gray83\" \"gray84\" \n",
"[238] \"gray85\" \"gray86\" \"gray87\" \n",
"[241] \"gray88\" \"gray89\" \"gray90\" \n",
"[244] \"gray91\" \"gray92\" \"gray93\" \n",
"[247] \"gray94\" \"gray95\" \"gray96\" \n",
"[250] \"gray97\" \"gray98\" \"gray99\" \n",
"[253] \"gray100\" \"green\" \"green1\" \n",
"[256] \"green2\" \"green3\" \"green4\" \n",
"[259] \"greenyellow\" \"grey\" \"grey0\" \n",
"[262] \"grey1\" \"grey2\" \"grey3\" \n",
"[265] \"grey4\" \"grey5\" \"grey6\" \n",
"[268] \"grey7\" \"grey8\" \"grey9\" \n",
"[271] \"grey10\" \"grey11\" \"grey12\" \n",
"[274] \"grey13\" \"grey14\" \"grey15\" \n",
"[277] \"grey16\" \"grey17\" \"grey18\" \n",
"[280] \"grey19\" \"grey20\" \"grey21\" \n",
"[283] \"grey22\" \"grey23\" \"grey24\" \n",
"[286] \"grey25\" \"grey26\" \"grey27\" \n",
"[289] \"grey28\" \"grey29\" \"grey30\" \n",
"[292] \"grey31\" \"grey32\" \"grey33\" \n",
"[295] \"grey34\" \"grey35\" \"grey36\" \n",
"[298] \"grey37\" \"grey38\" \"grey39\" \n",
"[301] \"grey40\" \"grey41\" \"grey42\" \n",
"[304] \"grey43\" \"grey44\" \"grey45\" \n",
"[307] \"grey46\" \"grey47\" \"grey48\" \n",
"[310] \"grey49\" \"grey50\" \"grey51\" \n",
"[313] \"grey52\" \"grey53\" \"grey54\" \n",
"[316] \"grey55\" \"grey56\" \"grey57\" \n",
"[319] \"grey58\" \"grey59\" \"grey60\" \n",
"[322] \"grey61\" \"grey62\" \"grey63\" \n",
"[325] \"grey64\" \"grey65\" \"grey66\" \n",
"[328] \"grey67\" \"grey68\" \"grey69\" \n",
"[331] \"grey70\" \"grey71\" \"grey72\" \n",
"[334] \"grey73\" \"grey74\" \"grey75\" \n",
"[337] \"grey76\" \"grey77\" \"grey78\" \n",
"[340] \"grey79\" \"grey80\" \"grey81\" \n",
"[343] \"grey82\" \"grey83\" \"grey84\" \n",
"[346] \"grey85\" \"grey86\" \"grey87\" \n",
"[349] \"grey88\" \"grey89\" \"grey90\" \n",
"[352] \"grey91\" \"grey92\" \"grey93\" \n",
"[355] \"grey94\" \"grey95\" \"grey96\" \n",
"[358] \"grey97\" \"grey98\" \"grey99\" \n",
"[361] \"grey100\" \"honeydew\" \"honeydew1\" \n",
"[364] \"honeydew2\" \"honeydew3\" \"honeydew4\" \n",
"[367] \"hotpink\" \"hotpink1\" \"hotpink2\" \n",
"[370] \"hotpink3\" \"hotpink4\" \"indianred\" \n",
"[373] \"indianred1\" \"indianred2\" \"indianred3\" \n",
"[376] \"indianred4\" \"ivory\" \"ivory1\" \n",
"[379] \"ivory2\" \"ivory3\" \"ivory4\" \n",
"[382] \"khaki\" \"khaki1\" \"khaki2\" \n",
"[385] \"khaki3\" \"khaki4\" \"lavender\" \n",
"[388] \"lavenderblush\" \"lavenderblush1\" \"lavenderblush2\" \n",
"[391] \"lavenderblush3\" \"lavenderblush4\" \"lawngreen\" \n",
"[394] \"lemonchiffon\" \"lemonchiffon1\" \"lemonchiffon2\" \n",
"[397] \"lemonchiffon3\" \"lemonchiffon4\" \"lightblue\" \n",
"[400] \"lightblue1\" \"lightblue2\" \"lightblue3\" \n",
"[403] \"lightblue4\" \"lightcoral\" \"lightcyan\" \n",
"[406] \"lightcyan1\" \"lightcyan2\" \"lightcyan3\" \n",
"[409] \"lightcyan4\" \"lightgoldenrod\" \"lightgoldenrod1\" \n",
"[412] \"lightgoldenrod2\" \"lightgoldenrod3\" \"lightgoldenrod4\" \n",
"[415] \"lightgoldenrodyellow\" \"lightgray\" \"lightgreen\" \n",
"[418] \"lightgrey\" \"lightpink\" \"lightpink1\" \n",
"[421] \"lightpink2\" \"lightpink3\" \"lightpink4\" \n",
"[424] \"lightsalmon\" \"lightsalmon1\" \"lightsalmon2\" \n",
"[427] \"lightsalmon3\" \"lightsalmon4\" \"lightseagreen\" \n",
"[430] \"lightskyblue\" \"lightskyblue1\" \"lightskyblue2\" \n",
"[433] \"lightskyblue3\" \"lightskyblue4\" \"lightslateblue\" \n",
"[436] \"lightslategray\" \"lightslategrey\" \"lightsteelblue\" \n",
"[439] \"lightsteelblue1\" \"lightsteelblue2\" \"lightsteelblue3\" \n",
"[442] \"lightsteelblue4\" \"lightyellow\" \"lightyellow1\" \n",
"[445] \"lightyellow2\" \"lightyellow3\" \"lightyellow4\" \n",
"[448] \"limegreen\" \"linen\" \"magenta\" \n",
"[451] \"magenta1\" \"magenta2\" \"magenta3\" \n",
"[454] \"magenta4\" \"maroon\" \"maroon1\" \n",
"[457] \"maroon2\" \"maroon3\" \"maroon4\" \n",
"[460] \"mediumaquamarine\" \"mediumblue\" \"mediumorchid\" \n",
"[463] \"mediumorchid1\" \"mediumorchid2\" \"mediumorchid3\" \n",
"[466] \"mediumorchid4\" \"mediumpurple\" \"mediumpurple1\" \n",
"[469] \"mediumpurple2\" \"mediumpurple3\" \"mediumpurple4\" \n",
"[472] \"mediumseagreen\" \"mediumslateblue\" \"mediumspringgreen\" \n",
"[475] \"mediumturquoise\" \"mediumvioletred\" \"midnightblue\" \n",
"[478] \"mintcream\" \"mistyrose\" \"mistyrose1\" \n",
"[481] \"mistyrose2\" \"mistyrose3\" \"mistyrose4\" \n",
"[484] \"moccasin\" \"navajowhite\" \"navajowhite1\" \n",
"[487] \"navajowhite2\" \"navajowhite3\" \"navajowhite4\" \n",
"[490] \"navy\" \"navyblue\" \"oldlace\" \n",
"[493] \"olivedrab\" \"olivedrab1\" \"olivedrab2\" \n",
"[496] \"olivedrab3\" \"olivedrab4\" \"orange\" \n",
"[499] \"orange1\" \"orange2\" \"orange3\" \n",
"[502] \"orange4\" \"orangered\" \"orangered1\" \n",
"[505] \"orangered2\" \"orangered3\" \"orangered4\" \n",
"[508] \"orchid\" \"orchid1\" \"orchid2\" \n",
"[511] \"orchid3\" \"orchid4\" \"palegoldenrod\" \n",
"[514] \"palegreen\" \"palegreen1\" \"palegreen2\" \n",
"[517] \"palegreen3\" \"palegreen4\" \"paleturquoise\" \n",
"[520] \"paleturquoise1\" \"paleturquoise2\" \"paleturquoise3\" \n",
"[523] \"paleturquoise4\" \"palevioletred\" \"palevioletred1\" \n",
"[526] \"palevioletred2\" \"palevioletred3\" \"palevioletred4\" \n",
"[529] \"papayawhip\" \"peachpuff\" \"peachpuff1\" \n",
"[532] \"peachpuff2\" \"peachpuff3\" \"peachpuff4\" \n",
"[535] \"peru\" \"pink\" \"pink1\" \n",
"[538] \"pink2\" \"pink3\" \"pink4\" \n",
"[541] \"plum\" \"plum1\" \"plum2\" \n",
"[544] \"plum3\" \"plum4\" \"powderblue\" \n",
"[547] \"purple\" \"purple1\" \"purple2\" \n",
"[550] \"purple3\" \"purple4\" \"red\" \n",
"[553] \"red1\" \"red2\" \"red3\" \n",
"[556] \"red4\" \"rosybrown\" \"rosybrown1\" \n",
"[559] \"rosybrown2\" \"rosybrown3\" \"rosybrown4\" \n",
"[562] \"royalblue\" \"royalblue1\" \"royalblue2\" \n",
"[565] \"royalblue3\" \"royalblue4\" \"saddlebrown\" \n",
"[568] \"salmon\" \"salmon1\" \"salmon2\" \n",
"[571] \"salmon3\" \"salmon4\" \"sandybrown\" \n",
"[574] \"seagreen\" \"seagreen1\" \"seagreen2\" \n",
"[577] \"seagreen3\" \"seagreen4\" \"seashell\" \n",
"[580] \"seashell1\" \"seashell2\" \"seashell3\" \n",
"[583] \"seashell4\" \"sienna\" \"sienna1\" \n",
"[586] \"sienna2\" \"sienna3\" \"sienna4\" \n",
"[589] \"skyblue\" \"skyblue1\" \"skyblue2\" \n",
"[592] \"skyblue3\" \"skyblue4\" \"slateblue\" \n",
"[595] \"slateblue1\" \"slateblue2\" \"slateblue3\" \n",
"[598] \"slateblue4\" \"slategray\" \"slategray1\" \n",
"[601] \"slategray2\" \"slategray3\" \"slategray4\" \n",
"[604] \"slategrey\" \"snow\" \"snow1\" \n",
"[607] \"snow2\" \"snow3\" \"snow4\" \n",
"[610] \"springgreen\" \"springgreen1\" \"springgreen2\" \n",
"[613] \"springgreen3\" \"springgreen4\" \"steelblue\" \n",
"[616] \"steelblue1\" \"steelblue2\" \"steelblue3\" \n",
"[619] \"steelblue4\" \"tan\" \"tan1\" \n",
"[622] \"tan2\" \"tan3\" \"tan4\" \n",
"[625] \"thistle\" \"thistle1\" \"thistle2\" \n",
"[628] \"thistle3\" \"thistle4\" \"tomato\" \n",
"[631] \"tomato1\" \"tomato2\" \"tomato3\" \n",
"[634] \"tomato4\" \"turquoise\" \"turquoise1\" \n",
"[637] \"turquoise2\" \"turquoise3\" \"turquoise4\" \n",
"[640] \"violet\" \"violetred\" \"violetred1\" \n",
"[643] \"violetred2\" \"violetred3\" \"violetred4\" \n",
"[646] \"wheat\" \"wheat1\" \"wheat2\" \n",
"[649] \"wheat3\" \"wheat4\" \"whitesmoke\" \n",
"[652] \"yellow\" \"yellow1\" \"yellow2\" \n",
"[655] \"yellow3\" \"yellow4\" \"yellowgreen\" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"colors()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Polynomial Regression"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"model.poly5 <- lm(y ~ poly(x, 5))"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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VM1I6ezOOrWrbt+/frvv//+999/b9269Y4dO6RORAaVm5sLwLsptk3B9hSMWg6N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\nRK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(x, y, xlim = c(0, 10), ylim = c(0, 10), pch = 19)\n",
"lines(x, predict(model.poly5), col = \"orange\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Spline Regression\n",
"\n",
"Splines are essentially piecewise polynomial fits. There are two parameters\n",
"\n",
"- degree determines the type of piecewise polynomials used (e.g. degree=3 uses cubic polynomials)\n",
"- knots are where the piecewise polynomials meet (determine number of pieces)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"library(splines)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"model.spl <- lm(y ~ bs(x, degree=3, knots=4))"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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QP/HH1+9EDBgb+6/IV2htYNbxICz9wqvbUofdFe473D2w/nOguAfLWGgl6wYMGx\nY8e4TgGKkF6RPiV5ynzd+Xi4M7QFraGgfXx8wsLCuE4Bcvda8vrD5A+tVKz2GO3hOguAIvBm\nDtrT07OB0ZiYmOoVtm7dqpBEoFAsYeelzcuvyr9mfO3IoSMxMTE5OTm2trZOTk7Ozs4Mw3Ad\nEED2GJZluc7QJE0/AmX+Ex08eHDRokXFxcUaGhqy3TI03dbcrTtzd/qwPmsnrU1PT685NH78\neD8/PzU1Na6yAa9VVFSoqKiEh4cPGjSI6yy18eYMmhCioaGxcuXKjh071lq+cuVKBweHadOm\ntWCbhYWFnp6eVVVVDawTHx/fgi2DDJ0vOr8pZ9MvnX9Z8f6K3NzcWqNBQUFLliw5evQoF9EA\n5Ig3BR0QELBgwYJffvnl8OHD48aNqzm0cuXK7t27f/bZZ1xlA7l6/Obx3NS5X+l/lX8i/+12\nlvL19d20aZOZmZliowHIF28K2tXVNS4ubuHChePHj3d3d/f29pbJZ9Rqa2vv37+/4XUOHjyI\nNyG58qLqhetT15HtR258b6Prddf6VmNZ9saNGyhoaGX4dBVHp06dzp079+uvv/7xxx89evS4\ncuUK14lAvsSseFbqLHWB+nGz4wxhXr582cDKDY8C8BGfClrK3d39wYMH5ubmH3zwweLFi0tK\nSrhOBPKyMnNldFn0WYuz6gJ1QoiBQUMfktLwKAAf8a+gCSFmZmahoaG7du06cuRI7969uY4D\ncnHs+bEDBQfOmJ+xULGQLnF1rXeKQ01NzcnJSVHRABSElwVNCBEIBGvXro2Ojsalb63SrdJb\nHukePxr/OKL9iOqFM2fOdHBwqHN9Ly8vbW1tRaUDUBC+FrRUz5497927V1lZeejQIa6zgMxk\nV2a7JbvN0523SHdRzeVKSkpBQUETJ06suVBNTW3nzp1r1qxRbEYAReDNVRz1YRhGWZn3PwVU\ney15PenpJAsVC28j77dHdXR0/P394+PjY2Ji8vLyrKysHB0ddXR0FJ8TQAFQbUARlrDz0+Y/\nq3oWbRstYkT1rda1a9euXbsqMhgAJ1DQQJHtudsDiwLDbcI7KXfiOgsA91DQQIs/X/25KWfT\nb2a/9VLtxXUWACrw+01CaDUev3k8PWW6p77nVO2pXGcBoAUKGrhX835urrMAUAQFDRwTs+LZ\nqbNFjOio6VEBXpAANWAOGji2KmtVVFlUpE1kByUZPP0KoDVBQQOXjj0/9nP+z4eXQgAAABaq\nSURBVJe7XLZUseQ6CwB18BclcCaiNOLt+7kBoBoKGriRXZn9n+T/zOw4s9b93ABQDQUNHKi+\nn/uAyQGuswDQC3PQoGjV93NH2UY1cD83AKCgQdG+yf3Gv8g/zDqss3JnrrMAUA0FDQr156s/\nv875+oTZCXs1e66zANAOc9CgONL7uTfob5imPY3rLAA8gIIGBSkUF054OmFE+xFfvfcV11kA\n+AEFDYogZsWzUmYJGeEx02O4nxugiTAHDYqwOmt1ZFlklE0U7ucGaDoUNMid7wvfn/J/wv3c\nAM2FPzZBviJKIxamLfzB6Afczw3QXChokKOcyhy3ZLeZHWcu7rSY6ywA/IOCBnkpFBeOfzoe\n93MDtBgKGuQipzJnWOKwKrbqrMVZ3M8N0DIoaJC91IrUYYnD2jHtQqxCdJV1uY4DwFcoaJCx\n+DfxQxKGGIuMg62CdZR1uI4DwGMoaJClO2V3hiYOfV/9/QuWF9ortec6DgC/oaBBZq4VXxuZ\nNHJsh7FnzM+0E7TjOg4A7+FGlbYrMzPz9OnTjx49IoR079596tSpRkZGLd5aQFHAtJRpC3UX\neht5M4SRXUyAtgsF3Ub5+Ph8+umnb968qV6yYcOGffv2zZ8/vwVbO/HihHua++rOq3cY7pBd\nRoC2DlMcbdFff/21YMGCmu1MCHnz5s2iRYuuXLnS3K3ty9/nnua+33g/2hlAtlDQbdGmTZvq\nXF5VVVXfUH125u1cnbn6hNmJhboL3z0YANSEgm5zysrKIiMj6xu9ffv269evm7IdlrArM1du\nztnsb+lf5wP4y8vL4+LiXrx40fKsAG0bCrrNefnypUQiqW9UIpEUFhY2upEqtmpe2ryjz49e\n7nJ5TIcxtUZjYmKGDx+uoaHRs2dPHR0dc3PzQ4cOsSz7rtEB2hi8Sdjm6OjoCIXCysrKOkeF\nQqGubiP3/pWz5TNSZtwqvRVqHdpHtU+t0dDQ0DFjxpSXl1cvSU1N9fDwiI+P37NnzzuGB2hT\ncAbd5qioqIwaNaq+0VGjRolEDT06o0RSMu7JuNiy2BvWN95u58rKynnz5tVs52re3t7h4eEt\nywzQNqGg26Jt27apqqq+vVxVVXXbtm0NfOOLqhejkkZlV2aHWYdZq1i/vcL169dTU1Pr+3Zf\nX9/mhwVou/hU0BKJ5NSpU4sWLVqxYsXVq1ffXmH37t0uLi6KD8Y7ffv2DQoKMjQ0rLnQ0NAw\nKCiob9++9X1XekX6oMRBVWzVdevrxiLjOtdJSEhoYL8NjwJALbyZgxaLxRMnTrxw4YL0yx9/\n/HHKlClHjhzp0OHfz7h7+PDh5cuXOQrIMyNHjnz69GlwcHBcXBwhpEePHk5OTioqKvWtn/Am\n4YMnH5iLzAMsAxr4XEGhUNjATpWVefN6A6ABbw6Yw4cPX7hwQU9Pb+XKlR06dDh69OjZs2fT\n0tKuXr2qpaXFdTpeUlFRGTt27NixYxtdM7YsdsyTMQPUB/iZ+6kK6pgbqda7d+8GRvv0qT1n\nDQAN4E1B+/r6KisrX79+3cbGhhDi4eHh5eW1efNmZ2fnK1eu1DyPbpbCwkJPT8+qqqoG1omP\nj2/ZxluHGyU3JjydMF5z/BHTI0KmoRNkQkj//v3t7e1jYmLeHhIKhQsWLJBPRoDWiTdz0HFx\ncY6OjtJ2JoQIBAIvL6+9e/dGRUWNHTu2tLSU23it1YWiCy5PXGZ3nO1r5ttoOxNCGIb57bff\n9PX1ay1XUlLau3evra2tfGICtFIsT6ioqLi5ub29/NtvvyWEjBgxoqysbO7cufL4iQ4cOEAI\nKS4ulvmWKffb89+EscJ1meua+425ubnLly/v1q2bUCg0NDScMGFCeHi4PBICvDvpVaF0vkR5\nM8VhbGycmZn59vI1a9aUlJR4eXlNmTJFW1tb8cFaq5/zf16WuWyX4a5VnVc193v19PR++OEH\neaQCaFN4U9B9+vQJCAgoKirS1NSsNbRp06ZXr17t2bNHSUmJk2ytz868nZ7ZnodMDs3Tmcd1\nFoC2izdz0JMnT66oqDh16lSdo99///0nn3wiFosVnKr1YQm7Nmvt19lf+5n7oZ0BuMWbM2hX\nV9c9e/Z07ty5vhUOHDhgZWX1/PlzRaZqZcSs2CPdw6/QL9AycHSH0VzHAWjreFPQ7du3/+yz\nzxpYQSAQrF27VmF5FCY8PPxi/EUfCx89Jb0euj2663Q3EZmYicyMRcaGQkNlRmb/B6WPQAor\nCQu1Dn1f7X1ZbRYAWow3Bd0GZWdnz5gx48aNG0SVkPEkzyjvof7D9/q+x+qzuZW5LGGVGCUD\noYGpyNRUZGosMjYRmpiITMxUzEyEJs39RO0SScmkp5MS3iTcsL7RtV1XOf1EANAsKGhKVVRU\nuLi4PHz4kBBCXhNyhhBCWMJmk+yvvvpqw6YNBVUFOZU5yeXJyRXJyeXJca/jrry6klieWCwu\nJoS0E7QzEBpYiCwsVCzeE75nIDSwULGwEFmYikyVmNpvpRaKC8c9GZdXlXfN+pqliqWif1QA\nqAcKmlK+vr7/tPNbdu7c+emnnxp0MjAQGtir2dcazavMS69Mz6jISK9IT61ITa9IjymLyajI\neFb1jBAiYkRGIiNjobGpyNRUxdREaKIn1Psy60shI7xlfUtPqCf3HwwAmgwFTalLly7VN1Re\nXh4SEjJtWh2fMkUI0RPq6Qn1+qn1q7X8teR1WkVaekV6ekV6RmVGanlqWElYekV6ZkXmAPUB\ngZaBmkq1r18EAG6hoCmVl5fX4tE6qQpUbdvZ2rarfbO1hEgE/LnaEqBNwZFJKR0dnRaPNgva\nGYBaODgp5eTkVN+QkpLS8OHDFZgFALiBgqbU/PnzzczM6hxatGhRrQ9DAYBWCQVNKXV19T//\n/LNr19qXJH/00Ufff/89J5EAQMHwJiG9bGxs7t+/7+/vHxMTk5OTY2tr6+Tk1L9/f65zAYCC\noKCpJhQK3dzc3NzcuA4CABzAFAcAAKVQ0AAAlEJBAwBQCgUNAEApFDQAAKVQ0AAAlEJBAwBQ\nCgUNAEApFDQAAKVQ0AAAlEJBAwBQCgUNAEApFDQAAKVQ0AAAlEJBAwBQCgUNAEApFDQAAKVQ\n0AAAlEJBAwBQCgUNAEApFDQAAKVQ0AAAlEJBAwBQCgUNAEApFDQAAKWUuQ7QbCzLJiYmJiYm\nFhUVsSyrpaVlbW1tbW3NMAzX0QAAZIlPBf369evdu3cfOHAgKyur1pCRkZGHh8fq1atVVVU5\nyQYAIHO8KejS0lInJ6fIyEiBQNC3b18rKytNTU2GYV6+fJmYmPjgwYONGzdeuHAhODhYTU2N\n67AAADLAm4Levn17ZGTkrFmzdu3aZWBgUGs0Kytr7dq1p06d2r59+9atWzlJCAAgWwzLslxn\naBJLS0ttbe2oqCiBoO43NiUSSb9+/V69epWUlNT0zRYWFnp6elZVVTWwTnx8fFhYWHFxsYaG\nRvNCAwD1KioqVFRUwsPDBw0axHWW2nhzFUdmZuaQIUPqa2dCiEAgGDJkSEZGhsx3Le1lkUgk\n8y0DADSAN1McmpqaKSkpDa+TnJyspaXVrM1qa2vv37+/4XVu3bp16dKlZm0WAODd8eYMetSo\nUYGBgb6+vvWtcPTo0aCgICcnJ0WmAgCQH97MQT99+tTe3r6oqKhv374uLi42NjaampqEkKKi\nooSEhEuXLt27d09LS+vOnTuWlpay3fWtW7ccHR3Ly8sxywHQ+tA8B82bKQ5LS8ubN2/Onz8/\nKirq7t27b6/Qv39/Hx8fmbczAABXeFPQhJAePXpERkbGxsaGhIQkJCQUFRURQjQ1NW1sbEaO\nHGlnZ8d1QAAAWeJTQUvZ2dmhiwGgLeDNm4QAAG0NChoAgFL8m+JQPOnFGyoqKlwHAQB5ofMa\nLd5cZset+/fvN3w7OCFk8ODBS5cu7dOnj2Iiycrhw4cJIZ988gnXQZrn3r17+/bt++WXX7gO\n0mwLFiz49NNP8TpRjHv37u3fv//mzZsNr6asrNy7d2/FRGoWFLTMaGho+Pn5jRs3jusgzePu\n7k4IOXLkCNdBmufChQvTpk0rKSnhOkiz4XWiSPx9nUhhDhoAgFIoaAAASqGgAQAohYIGAKAU\nChoAgFIoaAAASqGgAQAohYIGAKAUChoAgFJ4FofMiEQiOm/nbxgfMxPe/tcmvE3Ox8yEt/+1\nq+FWb5lJTU01MTFp4HPH6VRYWEgI0dbW5jpI80gkkvT0dDMzM66DNBteJ4rE39eJFAoaAIBS\nPPs1DgDQdqCgAQAohYIGAKAUChoAgFIoaAAASqGgAQAohYIGAKAUChoAgFIoaAAASqGgAQAo\nhYIGAKAUChoAgFIoaAAASqGgAQAohYIGAKAUCvpdPX36dNasWfr6+u3atbOysvL09CwrK+M6\nVCNKSkr8/PxmzJjRtWtXNTU1TU3NwYMH//LLLxKJhOtozRAYGMgwDMMwnp6eXGdpkuDg4EmT\nJunp6amoqBgbG0+cOPHatWtch2oEy7Lnzp1zcnIyMjJSVVW1sLBwc3OLiIjgOte/zp49u2zZ\nMkdHRw0NDYZhpk+fXt+afDxUCQvv4OHDh1paWgzDuLq6rlixws7OjhDi4OBQVlbGdbSG7Nmz\nhxAiEokcHBzc3NyGDh2qrKxMCJkwYYJYLOY6XZM8e/ZMT09PQ0ODELJhwwau4zTuiy++IISo\nqKgMGzZs6tSpI0aM0NHRoT/5kiVLCCGampqzZ89esWLFmDFjBAIBwzBHjx7lOto/7O3tCSEd\nOnSwtrYmhEybNq3O1Xh6qKKg30n//v0JIUeOHJF+KRaLZ8yYQQjZsmULp7ka8ccff/z0008v\nX76sXvLo0aPOnTsTQk6ePMlhsKabNGnSe++9t3HjRl4U9K+//koIGThwYGZmZvVCsVhcUFDA\nYapGPX36lBCiq6ublZVVvdDf358QYmxszGGwmkJDQ5OSkiQSSWBgYAMFzdNDFQXdcjExMYSQ\nPn361FyYmZkpEAiMjIwkEglXwVrmm2++IYR4eHhwHaRx0r4LCgqS/ilAeUGXl5fr6+urq6vn\n5uZynaV5rl69SggZO3ZszYVisVhZWVlVVZWrVPVpoKD5e6hiDrrlQkJCCCFjxoypudDQ0LBX\nr16ZmZmJiYkc5WohTU1NQoiKigrXQRqRmpq6YsUKd3f3cePGcZ2lSUJCQnJzcydNmqSpqenn\n57dx48bt27cHBwez1H8cqK2trZKSUnR0dG5ubvXCixcvVlVVOTs7cxisufh7qCpzHYDHEhIS\nCCE2Nja1lltbW9+7dy8xMfHtIWqxLOvr60sIcXV15TpLQyQSydy5c7W0tKTnzrwQHR1NCNHR\n0enVq1dSUlL18oEDB547d05PT4+7aI0wNDT08vLy9PTs2rWrq6urjo5OUlLS5cuXx40bd/jw\nYa7TNQN/D1WcQbdcUVER+f8Tz5q0tLQIIS9fvuQgU0t5eXndvn17ypQpo0aN4jpLQ3bv3n3j\nxg0fH5+3/7NT69mzZ4SQ/fv3CwSC0NDQ4uLiBw8ejB49OiIiooFLDiixYcOGkydPSiSS48eP\ne3t7X7hwwdLSctasWbq6ulxHawb+HqooaNmT/unKMAzXQZpq3759Xl5ednZ2R44c4TpLQx4+\nfLhx48ZFixaNHj2a6yzNIBaLCSEMw/j7+w8fPlxDQ6Nnz57nzp0zMDC4du3anTt3uA7YEC8v\nr1mzZi1atCglJaW0tDQmJsbU1HTmzJnr16/nOpoM0H+ooqBbTvoLWfrLuab6fl3Taffu3cuW\nLbO3t7969WqHDh24jlMvlmXnzJljYGDw7bffcp2lebS1tQkhtra2tra21QvV1dWlv2ZoLui/\n/vpr06ZN06dP37lzp5mZmZqamp2dnb+/v7Gx8a5du9LS0rgO2FT8PVRR0C0nnbeSTm/VJJ1n\nlF6VSblNmzatWbNm4MCBwcHB0h6hllgsvn//fkpKSvv27Zn/t3LlSkLItm3bGIZZsGAB1xnr\nJn2dSP+arkm65M2bNxxkapoLFy4QQkaMGFFzoaqqqoODg1gsvnfvHke5mo2/hyreJGy5kSNH\nEkL+/PPP7du3Vy/Mzs6+f/++oaEhzf/XpVatWrVnz57hw4cHBgZK7/igmUAgmD9/fq2Fjx49\nun37dp8+fezt7YcMGcJJsEY5OTkxDPP48ePKykqhUFi9/OHDh4QQc3Nz7qI1oqKigvz/HHpN\neXl5hA8X/FTj8aHK6UV+vCe9+v3YsWPSL8Vi8axZswj1V7+LxeJPPvmEEOLs7Ez5nVQN48V1\n0CzLTpkyhRDy9ddfVy+RXrSrq6tbUlLCXa5G/Pbbb4QQfX39jIyM6oUBAQEMw6ipqdW80YkG\nTblRhXeHKsNSfzEmzeLi4gYPHlxcXOzq6mpubh4WFhYTEzNgwIDQ0FBVVVWu09Xr22+//fzz\nzwUCwbRp00QiUc2hnj17rl69mqtgzeXt7b1y5coNGzZs3bqV6ywNyc7OdnR0TE1NHThwoJ2d\nXVpa2sWLF5WUlM6cOTNx4kSu09VLLBaPHj06NDRUXV19/Pjxenp68fHxV65cIYT8/PPPixYt\n4jogIYScPXs2ICCAEJKZmRkcHGxmZjZs2DBCiK6u7nfffVe9Gk8PVZxBv6snT57MmDGjU6dO\nIpHIwsJi/fr1NJ8TSa1bt66+14OzszPX6ZqBL2fQLMvm5+cvW7bM1NRUKBTq6OhMnjw5Ojqa\n61CNKy8v//777/v376+hoaGkpNSpUydXV1fpXTaU2LBhQ52vZFNT01pr8vFQxRk0AAClcBUH\nAAClUNAAAJRCQQMAUAoFDQBAKRQ0AAClUNAAAJRCQQMAUAoFDQBAKRQ0AAClUNAAAJRCQQMA\nUAoFDQBAKRQ0AAClUNAAAJRCQQMAUAoFDQBAKRQ0AAClUNAAAJRCQQMAUAoFDQBAKRQ0AACl\nUNAAAJRCQQMAUAoFDQBAKRQ0AAClUNAAAJRCQQMAUAoFDQBAKRQ0AAClUNAAAJRCQQMAUAoF\nDQBAKRQ0AAClUNAAAJRCQQMAUAoFDQBAKRQ0ACGETJo0iWGYvXv31ly4ceNGhmEWLFjAVSpo\n4xiWZbnOAMC9Fy9e9O3bNy8vLyIiom/fvoSQ4ODgDz74wNbWNjo6Wk1NjeuA0BahoAH+cevW\nrWHDhpmbm8fGxpaVlfXu3buoqCg6Orp79+5cR4M2ClMcAP8YNGjQli1bkpKSPDw8Zs+enZub\n++OPP6KdgUM4gwb4F8uyY8aMuXz5MiFkxowZJ0+e5DoRtGk4gwb4F8MwkydPlv77s88+4zYM\nAM6gAf6VlJRkZ2cnFAqLioq6d+8eFRXVrl07rkNB24UzaIB/lJeXT5s2rbS09Pfff//yyy8f\nPnyIk2jgFgoa4B9r1qy5e/fu559//sEHH3h5eTk6Oh48ePD06dNc54K2C1McAIQQ4u/vP3ny\n5AEDBty8eVNZWZkQkpGR0adPn6qqqrt371pYWHAdENoiFDQASU9P79Onj0QiuXv3rrm5efXy\n8+fPT5o0qV+/fjdv3hSJRBwmhLYJBQ0AQCnMQQMAUAoFDQBAKRQ0AAClUNAAAJRCQQMAUAoF\nDQBAKRQ0AAClUNAAAJRCQQMAUAoFDQBAKRQ0AAClUNAAAJRCQQMAUAoFDQBAKRQ0AAClUNAA\nAJRCQQMAUAoFDQBAKRQ0AAClUNAAAJRCQQMAUAoFDQBAKRQ0AAClUNAAAJRCQQMAUAoFDQBA\nKRQ0AAClUNAAAJRCQQMAUAoFDQBAqf8DLNp4L696RUUAAAAASUVORK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(x, y, xlim = c(0, 10), ylim = c(0, 10), pch = 19)\n",
"lines(x, predict(model.spl), col = 3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Connect the dots"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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5uFCxcWvE14ePi+ffte/1j0mvbs2ZN32wSIBLYDPwIANBrN3r17WdBUzCjpNLs3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",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(x, y, xlim = c(0, 10), ylim = c(0, 10), pch = 19)\n",
"lines(x, y, col=\"red\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Classification"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- 'setosa'
\n",
"\t- 'versicolor'
\n",
"\t- 'virginica'
\n",
"
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 'setosa'\n",
"\\item 'versicolor'\n",
"\\item 'virginica'\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 'setosa'\n",
"2. 'versicolor'\n",
"3. 'virginica'\n",
"\n",
"\n"
],
"text/plain": [
"[1] \"setosa\" \"versicolor\" \"virginica\" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"levels(iris$Species)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Can we separate two species of iris?"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"df <- iris %>% filter(Species != \"setosa\")\n",
"df$Species <- droplevels(df$Species)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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qqhdHWxYwdmzMD69ejQAW5u+OYb+Pjg3Lkij3JesLXFhQvw9sbXX8PVFV26YNs2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\nAAAgBxTQAAAAAABy+H93a/rjf6R9JgAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"options(repr.plot.width=8, repr.plot.height=4)\n",
"par(mfrow=c(1,2))\n",
"plot(df[,1], df[,2], col=as.integer(df$Species))\n",
"plot(df[,3], df[,4], col=as.integer(df$Species))"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- 9
\n",
"\t- 6
\n",
"\t- 7
\n",
"\t- 3
\n",
"\t- 8
\n",
"
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 9\n",
"\\item 6\n",
"\\item 7\n",
"\\item 3\n",
"\\item 8\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 9\n",
"2. 6\n",
"3. 7\n",
"4. 3\n",
"5. 8\n",
"\n",
"\n"
],
"text/plain": [
"[1] 9 6 7 3 8"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sample.int(10, 5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Split into 50% training and 50% test sets"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"library(class)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"set.seed(10) \n",
"sample <- sample.int(n = nrow(df), size = floor(.5*nrow(df)), replace = F)\n",
"train <- df[sample, 1:4]\n",
"test <- df[-sample, 1:4]\n",
"train.cls = df$Species[sample]\n",
"test.cls = df$Species[-sample]"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"test.pred <- knn(train, test, train.cls, k = 3)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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AAjhnzWbWigAYxVSwvFxdE//0lLl1L3\n7n8ODhhA//sfVVTQ1q1aLQ4AwIghn3UeGmgAY5WeTg8f0oIFsuO2thQdTUeOaKMmAABAPusB\nPW6gz549O378eCcnJ2tr64CAgA0bNjQ3N2u7KAD9kZ9Pdnbk5CRnkY8P5edrvCAwHMhnAKUg\nn3We3jTQbm5ucXFxkpd79+59+umnExMTS0tLhULh1atX33vvvalTpzLGtFgkgD6xsSGhkJqa\n5CwqLSUbG40XBPoK+QygYshnnac3DfSjR48qKyvFP5eWlr711luMsWXLluXm5paVlcXHx/P5\n/KNHj+7Zs0e7dQLojZAQ4nDo2DE5iw4fphEjNF4Q6CvkM4CKIZ91nt400NIOHjwoFAoXLFiw\nevXq3r1729vbT5o06fDhw0S0e/dubVcHoCdsbGj+fJo/n7Ky/h5kjJYvp/R0evdd7VUGegz5\nDKACyGedp5fzQGdmZhLRm2++KT04ZMiQgICAjIwMLRUFoIfWrqW8PAoKouefp4EDqbSUkpIo\nP58OHCAvL20XB3oJ+QygGshn3aaXZ6Dr6uqIqHfv3jLjffr0qaio0EZFAPrJzIx+/JGOHiUP\nD0pNpaIiioqiP/6giAhtVwb6CvkMoBrIZ92ml2egvb29iaiqqsrS0lJ6vLy83NbWVktFAeit\nceNo3DhtFwEGAvkMoErIZ12lTw30999/v2/fPiISiURElJWV5erqKr3CnTt3PDw8tFMcAIAR\nQz4DgFHRmwa6X79+MiNpaWljxoyRvLx8+fLdu3fH4Rc1AADNQj4DgLHRmwb6jz/+aH+FlpaW\n9evXS0c2AABoAPIZAIyN3jTQHRo8ePDgwYO1XQUAAMhCPgOAgdHLWTgAAAAAALTFcM5AFxUV\n3b9/n4iCg4O1XQsAAPwN+QwABsZwGug9e/YsXLiQiBhjnd+qvLx82bJlzc3N7ayTl5enbHEA\nAEYM+QwABsZwGmg7Ozsv9TybRygUElFjY6O5ubk69g8AYNiQzwBgYDgKnQ8wTtu3b4+Jiamu\nrraystJ2LQCgYo2NjTweLyUlJTQ0VNu1gMKQzwAGTJfzGTcRAgAAAAAoAA00AAAAAIACDKGB\nLi8vr66u1nYVAAAgC/kMAAZJnxrou3fvvvXWW08//fTChQtLSkqI6NKlSwMHDnRwcLC1tR01\natTNmze1XSMAgDFCPgOAUdGbWThKSkqGDRtWWFhIRElJSWfOnElMTHzhhRcePXrE5/OLioqS\nk5NHjx597do1Ozs7bRcLAGBEkM8AYGz05gz0559/XlhY+NprryUlJc2fP//KlSvR0dGWlpZZ\nWVkPHz4sLy+fOHHiw4cPN2/erO1KAQCMC/IZAIyN3kxjFxAQUFBQ8ODBAy6Xyxjz9vbOzc39\n8ccfX3rpJfEKpaWlHh4eAwcOPH/+vGoPjWmSNOz27du7d+8WCAQ1NTX+/v5Tp05V5fw1P/9M\nCQl04wbZ21NAAM2aRXy+ynYOekiXp0nSF8hn44F8Bk3S5XzWmzPQ9+7dCw4O5nK5RMThcMTP\ngx01apRkBUdHx6CgIFxmp+927tzp5+eXmJjo6ekZHBx8/fr1sLCwuLg4Ffym19RE06dTZCTl\n5VFoKLm40J491L8/JSSoonAA44V8NhLIZwAJvbkGur6+vnv37pKX9vb2ROTq6iq9jpubm8pP\nb4AmpaamvvXWW5s3b46JiZEMnj17NiIiok+fPnFxcUrt/Z//pLNnKT2d/P3/HGGM/vUvmjaN\nBAJSz2PSAIwB8tkYIJ8BpOnNGWgXF5fS0lLJSwsLC+m8FisrK3N0dNRsXaBK69atmzZtmnQ6\nE1FYWNjq1avXrVsnEom6vuvKStqyhbZs+TudiYjDodWrKSiIPv2063sGMHrIZ2OAfAaQpjcN\ntK+v761btyQvN23aJBQKZda5e/eup6enRssClTp79uzkyZNbj0+ePLmwsDA7O7vru754kRij\nF1+Us2jSJPr9967vGcDoIZ+NAfIZQJreNNDDhg3Lz8/Py8tra4WMjIzc3Fzpq+5AvzDGqqur\nHRwcWi8SD1ZVVXV971VVZGVFZmZyFjk6kjJ7BjB6yGeDh3wGkKE3DfSyZcvq6urc3d3bWqG+\nvn7t2rXR0dEaLApUicPhuLu75+TktF4kHmznX79j7u5UUUFSf2X+W3Y2KbNnAKOHfDZ4yGcA\nGXrTQJuamlpYWHA4nLZWGDp06JIlS3x9fTVZFajWxIkTt27d2tjYKDO+adOmIUOG8JWZzygo\niHr2pM8+kx2vrKRdu2jixK7vGcDoIZ+NAfIZQJreNNBgDP75z3+WlJRERkbeuXNHPFJeXh4X\nF7d3795PlbyPxNSUNm2itWvp3/+mmpo/BwUCevZZsrOjefOUKxwAwMAhnwGkoYEGHeLq6pqU\nlFRVVdWnT5+ePXt6e3s7OTn99NNPJ06cUMEk6pMn05499PnnZGdH/fuTiwsNHEjOzvTrr2Rp\nqYryAQAMFvIZQJrezAMNRsLb2zslJUUgEAgEgtraWn9/f8kDGlRg2jR68UW6eJGuXycHBwoI\nIB8f1ewZAMDQIZ8BJNBAgy4aMGDAgAED1LJrCwsKC6OwMLXsHADA0CGfAQiXcAAAAAAAKAQN\nNAAAAACAAtBAAwAAAAAoAA00AAAAAIAC0EADAAAAACgADTQAAAAAgALQQAMAAAAAKAANNAAA\nAACAAtBAAwAAAAAoAA00AAAAAIAC0EADAAAAACgADTQAAAAAgALQQAMAAAAAKAANNAAAAACA\nAtBAg9ZUVlbW19druwo5ah49qnn0SNtVAABoT2UlIZ8B2oYGGjStsrJy4cKFvXr1srOzs7Ky\n8vX13bRpU0tLi7brovqKiqTw8Dxz825ubt3c3PLMzZPCw+srKrRdFwCAplRW0sKF1KsX2dmR\nlRX5+tKmTYR8BmiFq+0CwLgUFxePHDmSMbZixYrAwMC6urrff/999erVSUlJhw4dMjU11VZh\ntSUlt/v06Vdbmz1pUvULLxBRyfHj/Q8fzu7Vyys3t5uTk7YKAwDQkOJiGjmSGKMVKygwkOrq\n6PffafVqSkqiQ4cI+QwgBQ00aNTixYt5PN7Zs2etra3FI6GhoRMnThwyZMjXX38dExOjrcLS\nJk7sW1fHzcgY6e//59DMmUWZmY6BgWkTJ4b//ru2CgMA0JDFi4nHo7Nn6a98ptBQmjiRhgyh\nr78m5DOAFFzCAZojFAr37dv30UcfSbpnsb59+8bGxn7zzTfaKoyJRE+eO3f75ZedJelMREQu\nAwfefvnlJ8+dYyKRtmoDANAEoZD27aOPPqLH85n69qXYWEI+AzwODTRoTk5OTkNDQ2hoaOtF\noaGh169f13xJYuU5OS4iEX/KlNaL+FOnuohE5Tk5mq8KAEBzcnKooYHk5TOFhhLyGeBxaKAB\nAAAAABSAa6BBc7y9vS0sLFJTU8ePHy+zKDU19cknn9RKVURk7+1dZGJScOiQ98SJMosKDh2y\nNjFx8fbWSmEArZWUlCi6ia2trZmZmTqKAcPh7U0WFpSaSq3ymVJTCfkM8Dj5DTQCGtTByspq\n+vTpH3zwQVhYmPRl0Ldu3dq8efPatWu1VRjHxOT6sGF99+0rfv996cvsijIzvfbuvTFsmKsJ\n/lYDusLZ2VnRTRITE8eNG6eOYsBwWFnR9On0wQcUFvbYZdC3btHmzYR8Bnic/AYaAQ1qsn79\n+pEjRw4ePHjx4sWSaew+/vjjUaNGvfnmm1osLOTIkdt9+jgFBCRPnuwUEUFEJceP9z18uLRb\nt5AjR7RYGEBr/v7+PXv27MyajY2Np0+fVnc9YCDWr6eRI2nwYFq8+O9p7D7+mEaNIuQzwOPa\nvIQDAQ3q4OzsfP78+ZUrV65atSovL8/U1NTHx2f58uWxsbFanASaiLo5Ofncv39+4kSvI0fc\nDxwgonwzsz9GjBh65IiFnZ0WCwNobdGiRdHR0Z1Zs7CwkM/nq7kcMBTOznT+PK1cSatWUV4e\nmZqSjw8tX06xsVqcBJqQz6CT2mygEdCgJra2ths3bty4cWNlZSWPx7OwsNB2RX+ysLMLT0oi\nIvFzYj1cXT20XBEAgGbZ2tLGjbRxI1VWEo9HyGeANuAmQtAaW1tbbZcgX3dXV22XANCm8vLy\nbt26dXJlV1fX8vJyKysrtZYEBgj5DNAu+Q00AhoAQDfZKfI3aw6Ho9D6AADQGfIbaAQ0GKnM\nTNqzhwQCIqIBAygqigYOVMmORc3NaUuWNCUmWhcU1FpbNwUEDNq0ya53705ufv/06dwVKyxz\ncswaG6ufeMLhrbcGzJmjksIAAPQD8hl0CSZ/AfjLunUUGEjnzpGfH/n50blzFBhI69Ypv2Nh\nQcFVF5eBGzZwq6srBg5s6d69z4kTTd7eWZ17Ou7vb7zhOnq06+XL9W5uVX37Wt2/7xcTcyYg\nAA+wBQBjgXwGXcOgI9u2bSOi6upqbRcC6nTgADM3Z/Hxjw3GxzNzc3bwoJL7Tu3V67a5+YNz\n5yQjjTU1yf36lZqYlOXktL9t5rZtTURnXnlFevDqli3VHE7SpElKFgaMsYaGBiJKSUnRdiGK\naWlp2bNnz5w5cxYsWHDy5MnWK3zyySfPPfec5gvTMOSzUUA+Gytdzuf2GmgEtBgC2ig89RR7\n7z054++9xwIDldnx3V9/ZURZ334rM95YU3PXzOz0s8+2v/kFV9eUJ55oPZ40adIjE5OWpiZl\nagOm2wHdlubm5oiICOlTIZMnT66srJReZ+bMmcZwigT5bBSQz8ZKl/O5zVk4WlpaIiMjExIS\nxC8///zzyZMn79y508bGRrKOQCD45ZdfVHtGvEOMsVu3bt26dUv8fws7O7u+ffv27duXw+Fo\nuBIwHEIhXblCW7fKWTR5Mm3YQDU11L171/adt3evmamp3+uvy4ybdet2d+DA7leutL95v6Ki\nG+++23rc5/33XQ4fvvPrr73xACPj8/XXXyckJLi6ui5cuNDGxmbXrl3x8fH37t379ddftXtH\nCvIZVA/5DDqpzQZaBwO6rq5uw4YN27Zte/Dggcwid3f3OXPmLFq0yNLSUiu1gX6rriYicnCQ\ns8jBgRijqqouB3RLebmwjafcM3t7XnZ2O9sykciKMZ68edZte/cmorpHj7pWFei17777jsvl\nnjlzpl+/fkQ0Z86cVatWffjhh88999zJkyelT3NoDPIZ1AX5DDqpzQZa1wK6pqZmzJgxFy5c\nMDExeeqpp3x8fGxtbTkcTkVFxa1btzIzM5cvX56QkPDbb791fgI+gD85OZGFBeXkUN++soty\ncsjCgpycurxvnpeXW0NDU22tWatvJvfOHWG7v45yTEwKuVxhRkbrRQ/OnOlL5DhoUJcLA/2V\nlZU1fPhwcTgTkYmJyapVq5ydnWNjY8ePH//LL79072o/0TXIZ1Aj5DPoprau7bC2th41apTM\n4ObNm4lo+PDhQqGQafYauw8++ICIXn311QcPHrRemp+f/8orrxDR0qVLVX5oXGNnFKZMYc8+\ny0SixwZbWtgzz7ApU5TZceX9+9UcTvJrr8mMPzh/XsjhpMbFtb95UkDATUvLhlZfv7Pe3llW\nVsoUBmK6fI1dW3g83rRp01qPr1+/noiefvrp2tpa5DMYDuSzsdLlfG4zXnUtoPv06RMUFNTS\n0tLWCi0tLYGBgd7e3io/NALaKPzxB7O1ZVFRrKDgz5GCAhYVxWxt2c2bSu77zLRp9URnXn5Z\nkrOZ27blmptfsbPr8C6TIoGgwNT0opPT/TNnxCPlublJgwbVE2Vu26ZkYcB0O6Db4u3tPWzY\nMLmLVqxYQUTjxo0T96yaqQf5DOqFfDZWupzPbcarrgW0ubn5O++80/46cXFxPB5P5YdGQBuL\n9HTm78+ImKcn8/RkRMzfn6Wnq2TfZ6ZPr+RwGohu83jlHE4L0e+enlX5+Z3Z9u6vv2ZaWzOi\nQlPTe2ZmLUR5XO7lTz5RSWGgywHdlqlTp5qbm1dUVMhdunDhQiIyNTVFPoPhQD4bJV3O5zav\ngQ4ICPjpp58qKyttbW1lFq1cubKqqmrjxo3igNYMW1vbO3futL9Obm4unokIXRcYSFevUkbG\nn0+68venp54iE9U8bGjkvn3CjRuv7dlTnZ5e3KuXx8SJw4cO7eS2T4wZQ1VV2ZTahnEAACAA\nSURBVPHxxadOtVRXV4WF9X/tNXcLC5UUBvpo0qRJBw8e3Lt3b0xMTOuln376qVAo/PrrrzVW\nD/IZ1A75DLqmrc76v//9LxF9+eWXba3w5ptvtr8H1XrllVdMTEx2797d1go7d+7kcDhRUVEq\nPzTOcAAYMF0+w9EW8SmMQ4cOtbVCS0vLf/7zn/fff18z9SCfAUAddDmfOYwxuY11dXX1jh07\nevXqNXnyZLkriESiDRs2lJaWrlPFszQ7dPv27aCgoMrKyqeeemrcuHH9+vUTnxqvrKy8efNm\nYmJiRkaGnZ3dpUuXvLy8VHvo7du3x8TEVFdXW1lZqXbPAKB1jY2NPB4vJSUlNDRU27XoK+Qz\nAKiDLudzm5dwWFtbv/POO+1saWJisnjxYjWUJJ+Xl9fvv//+xhtvpKWlXZE3t3lISMiOHTtU\nns56rb6+Pi0t7caNGw4ODgEBAT4+Pgptnp2dnZGRUVZW5uvrGxISYvH436QKCwvT09Pv3bvn\n7e0dFBTk6OioytIFAhIIqLaW/P0pOJi4bX5RNS07mzIyqKyMfH0pJIQM4+909fWUlkY3bpCD\nAwUEkILfEwDkcxcgn1UP+QyapO1T4ApLT09fv3797Nmzp02bNm3atNmzZ69fvz5dRXcSyKWn\nfyLcv3+/i4sLl8vt16+fs7MzEUVERBRIbmFuV0FBwfjx44nI2dm5X79+XC7XxcVl//794qX1\n9fWxsbFmZmbW1tZPPvmkpaWlpaXlypUr27kHXwHZ2Sw0lBGxHj2YlxczMWGenuy331SwZyUV\nFLDx4xkRc3Zm/foxLpe5uLC/PhM9tn8/c3FhXC7r1485OzMiFhHBOvc9MQy6/CdCvYN87iTk\ns4ohnw2ULuez/jXQmqePAX3o0CEul7tmzRrxjN2MsczMzJCQED8/v9ra2va3ra2t9fPzCwkJ\nEQgE4hGhULh69WoulxsfH88Yi4qK6tGjx4kTJ0QiEWOsubl5z549dnZ2KrjgsrCQ9ezJxo1j\nubl/jpSVsQULGI/HtPvfT20t8/NjISHsr8+ECYVs9WrG5bL4eG0WpqRDhxiXy9asYX99T1hm\nJgsJYX5+rKPvicHQ5YCGDiGfkc/IZwOmy/mMBrpjehfQzc3N7u7uy5cvlxmvqKjo2bPnJx1N\nr7N+/fqePXu2niFr+fLlHh4eycnJpqamV65ckVl64sQJLpd7+/ZtpUpfsIANGsQaGmTHo6PZ\nkCFK7VlJ69eznj1Z61nDli9nHh6suVkbNSmtuZm5u7NW3xNWUcF69mRGMw2TLgc0dAj5LIZ8\nRj4bJF3OZ9VMAaMLioqKLl26dOnSJW0Xon3p6ekPHz5csGCBzLitrW10dPSRI0fa3/zIkSPR\n0dGtpy9csGBBfn7+9u3bw8PDAwICZJY+//zzffr0OX78uFKlHzlCc+eSubnseFwcXbhABQVK\n7VwZR45QdDS1+kxowQLKz6f0dG3UpLT0dHr4kFp9T8jWlqKjqaPvCUDnIZ8lkM+qh3wGbdCZ\na/+VtmfPHvHjA1gb84rIdefOnSFDhjQ3N7ezjvgXIIV2q135+fl2dnZOTk6tF/n4+IgnKGx/\nc7m3szg5Odnb29+7d8/Pz0/uhj4+Pnl5eV0o+E+M0YMH8u+QEA/m5xOf3/X9KyM/X35hTk5k\nb0/5+RQSovGalJafT3Z2JO97Qj4+1NH3BKDzkM8SyGfVQz6DNhhOA21nZ9eFW7yfeOKJ/fv3\ntx/Qx48f/+yzzzgcjhLVaZSNjY1QKGxqajIzM5NZVFpaamNj0+HmZWVlrccbGxuFQqGtrW15\nebncDcvKylqfF1EAh0M2NiTv0H8OdlS5GrVVWGMjCYXaLEwZNjYkFFJTE7X6nlBpqb6+KdBJ\nyGcJ5LPqIZ9BK7R7BYle0Ltr7CorK3k8ntyHLIwYMWLevHntbz5v3rwRI0a0Hj906BCPx/vq\nq68cHBwqKytllt67d8/MzOz06dNdrZoxxtiLL7JXXpEzvmkTc3NjKrmLvGvmzWPyPhN26BDj\n8VirT0M/VFYyHo/JfRjHiBGso++JwdDla+y6LCEhYdu2bbmSm70MF/JZDPksZxz5rP90OZ+7\n3kAjoHXZokWL+Hy+5DZtxphIJFq2bJmlpWVOTk772+bk5FhaWi5fvlx8E7eYQCDg8/mLFi2q\nr6/38fGZMGGC5P5xxlhxcXFoaOjw4cOlN+mKlBTG5TKZ518mJzNra7Zpk1J7VlJODrO0ZMuX\nM+k3KBAwPp8tWqS9spS2aBHj85nU94SJRGzZMmZpyTr6nhgMXQ7oLnvuueeIyMzMbN68eQ8f\nPtR2OWqEfGbIZ+Sz4dLlfO76JRyff/75L7/8YmZm9uabby5btoyvrYufQJ61a9fm5eUFBQU9\n//zzAwcOLC0tTUpKys/PP3DgQId/SPXy8jpw4EBUVFR8fHx4eLiDg0NmZmZiYuLEiRPXrl1r\nZmZ27NixiIgIb2/v8ePH9+rVKycnJyEhwdPTMyEhQdk/pIaG0ldf0dy5tGMHjRhBlpZ0+TKd\nPEnz58u5l0KTvLzowAGKiqL4eAoPJwcHysykxESaOJHWrtVmYUpau5by8igoiJ5/ngYOpNJS\nSkqi/Hw6cIDwzAt9Fh4ebmdnd+vWrW3btu3ataumpkbbFcHfkM8qhnwGbWjzUd4dWrduXUZG\nxq1bt65evWphYaHFgC4vL+dyudbW1mrav/4+Kvbnn39OSEi4ceOGvb19QEDArFmzOv97TkFB\nwbfffpuRkVFeXu7r6xsRETFu3DjJ0pqamu++++78+fPiJ12FhYW98sor5q3vzu6a27dp924S\nCKimhvz9aepU0pFneBYU0LffUkYGlZeTry9FRJDUZ6LHfv6ZEhLoxg2yt6eAAJo1S2s3A2mD\nLj8qVnllZWWnT5+eMmWKtgpAPrcF+axiyGdDpMv53PUGWkJjAX337t2PPvooOzs7ICBg6dKl\nTk5Oly5dmjVrlkAg4HA4YWFhX331Vb9+/VR+XP0NaADokC4HtB5BPgOAyulyPqtgFg4HBwcN\ndM8lJSXDhg0rLCwkoqSkpDNnziQmJr7wwguPHj3i8/lFRUXJycmjR4++du2anZ2duosBAAAJ\n5DMAGBu9eZDK559/XlhY+NprryUlJc2fP//KlSvR0dGWlpZZWVkPHz4sLy+fOHHiw4cPN2/e\nrO1KDUpTU5PcKZPERCJRUVGRmg5dX19fWVnZ5c2LiopEIlGbi8vKqKmprYVCoVAoFHb50ADG\nBvmsFchnAG3S9l2MnTVo0CAXF5empibGmEgk6tOnDxH9+OOPkhVKSkosLS2HqOGBovp4l7fy\ndu7cGRAQIJ6p1NXV9Y033igoKJAsTUpKevrpp7t3705ENjY2ERERrR8e2zXNzc2ffvpp//79\nTU1NicjDw2PhwoWtZ2Vqy+XLlyMiIsRzqXbv3v3pp59OSkr6e3FBAXvjDebqyoiYmRkLCGA7\nd0oW1tXVrVixok+fPhwOh8Ph9OnTZ8WKFXV1dSp5X6CzdPkub7m8vLzkToImV3FxsZeXV3Jy\nslpLQj5rGPIZ+WwkdDmf5Z+B9vb2jo+P72QLXlJS4u3tffbsWWX6+A7du3cvODiYy+USEYfD\nCQ4OJqJRo0ZJVnB0dAwKCrp586ZayzASc+fOffvttydMmPC///3v6tWrGzZsuHr1amBgYG5u\nLhHt2rVrzJgxnp6eBw4cyMrK+v77783NzYcOHfrzzz8redzm5uYpU6asWbPm9ddfT05Ovnz5\n8ooVK06cODFkyJCSkpION09MTBw2bBiPx/v++++zsrIOHDjg6ek5ZsyYXbt2ERHdvk2BgXT1\nKm3YQFev0v/+RxMm0Ntv07x5RFRbWztmzJgdO3a88847Fy5cuHDhwjvvvPPNN9+MGTOmtrZW\nyfcFoEK3b9+uqqrq5MrNzc23b99W903eyGdNQj4jn0EnyG2riWin1G9+7SsoKCCixMRElXX1\n8lhYWEybNk3ycs6cOa2Lnzp1KpfLVfmhje0Mx7Fjx8zNzc+dOyc92NjYOHbs2NGjR+fl5Vla\nWm7ZskVmq/fff9/FxaWqqkqZQ2/dulU895b0YFVV1aBBg2bOnNn+tlVVVS4uLkuWLJEZ37x5\nc7du3fLy8tjo0WzsWNbY+Njic+eYmRk7fnzp0qW9evUqLCyUXlhQUODh4bF06dIuvyPQfbp8\nhkMuInrxxReXds4777yDfDYkyGcJ5LMx0OV8bvMmwvj4+JycnM604JqZwM7FxaW0tFTy0sLC\nQvz3KWllZWWOjo4aKMaw7dixIyoqaujQodKDZmZmGzZsGDRo0ObNm5944ol58+bJbLVq1aqv\nv/762LFjUVFRyhw6NjbWx8dHetDa2vrf//73lClTtmzZ0s6N9j/99FNzc/PKlStlxt9+++0v\nvvjixJYtb506RZmZso9FHTqUXn2Vvvlmx/nzq1atcnV1lV7o5ua2dOnSlStXrl69Wo+eFQwG\n79ixY8eOHdN2FX9DPmsM8lkC+Qza1WYDrWsB7evre+3aNcnLTZs2bdq0SWadu3fvenp6arQs\nQ3Tt2rXFixe3Hh84cKC1tfXFixdDQ0NbpxWPxwsKCpL+N+raodesWdN6fPjw4Q0NDTk5OQEB\nAe1sGxwczOPxZMY5HM6wYcNqL14ka2saMEDOlqGhLevWFRYWyp0lZ/jw4YWFhaWlpU5OToq9\nGQD1SExMVHQT8TUV6oN81hjks8yhkc+gLfIbaB0M6GHDhv3yyy95eXkeHh5yV8jIyMjNzZ06\ndapayzAS7fw2r7O/6OtsYQCqNU73Hg+BfNYk5DOALpDfQOtgQC9btuz9999v/furRH19/dq1\nayMjIzVZlUHy8/NLSUmZPXu2zHhmZmZ1dfXgwYN/+uknxphMIDY0NKSnp0dHRyt56NTU1NZf\nv5SUFAsLC29v7/a33b59e0NDg8yXhDF27ty5oZGRdOoUCQRyTnKkppoOHOhWW5uamurv799q\nYSqfz8efnkE3/fDDD8OHD+/du3frRVlZWRkZGa+99poGykA+awzy+fGFyGfQng6vkv7+++9z\nc3PlLhIIBN9//70qL8nWSbhJheEmFTBcunyTSoeIqK0QXr16dWcSXt8hnxnyGQyXLudzx/GK\ngDa2gGaMxcTEdOvW7V//+tfp06evXr36ww8/BAcH8/n827dvM8Z27txpamo6a9asxMTErKys\no0ePTpo0icfjKX+nf1NTU2RkpIODw8cff5ySknL58uVvvvmmX79+/fv3Ly4u7nDzEydO8Hi8\nyZMnHz16NCsr68SJE6+//rqpqemfU8rk5DA+nwUHsx9+YJmZ7PRp9q9/sW7d2Ny5jLGamprQ\n0FB3d/fNmzenpaWlpaV9/vnnPXv2DA0NrampUfJ9gS7T5YDuUDv5vHLlSg6Ho+F6NA/5jHxW\n8n2BLtPlfFaqgUZAGzAtTtS/ceNGJSfqt7W1JUzUD52jywHdoXby+aWXXnJ0dNRwPZqHfEY+\ngwHT5XzmMMbav8aDw+F8//33ci+kmz59+m+//daZGdT12vbt22NiYqqrq9uZo8dQNTU1VVdX\nOzg4yF0qEolKSkpcXFzUcej6+vqGhgZx1HZBUVGRk5OTiUkbD6svKyNra9kpk/4ifk6sEf5z\nG6fGxkYej5eSkiL3Nn/d9PLLL4t/+PHHH4cOHfrEE09IL21pabl//35aWtqECROOHj2qjQI1\nB/mMfAYDpsv53OY0dpKAJqIvvvji+PHj0kulA1qN1YG2mZmZtZXORGRiYqKmdCYiCwsLCwuL\nLm/eQWFtvylCNIPO+/HHHyU/nz9//vz5863XGTp06MaNGzVYFGga8hlAi9psoBHQAAC6KTs7\nW/yDj4/PJ598IjO7hampqaOjo42NjTZKAwAwCm020AhoY/fwIe3cSRkZVF5Ovr4UEUFSsxfV\n1NR8991358+fv3fvnre3d1hY2CuvvGJubv7nYpGI4uPp11/p1i1ydaXBg+n118neXiV1lZWV\n7dq16+LFi48ePerbt+/YsWMnT57c5p8CW/v5Z0pIoBs3yN6eAgJo1izi8/9emplJe/aQQEBE\nNGAARUXRwIEqKbtDqampBw8ezMrK6t69+4ABA2bOnOnl5aWZQyul3e+JslJT6eBBysqi7t1p\nwACaOZP04jNRP8mUYWvXrh03blz7M4iBAUI+I587A/msTm1+rb3/Igloab1790b3bMgSEsjX\nl/buJRcXCg2lvDyKjKTp06mpiYhu3rw5aNCgDz/8kMvlhoeHNzQ0LFy4cOjQoQUFBURE1dX0\nzDM0cyaVl9PIkWRjQ1u2kK8vyfsjhqLOnz//5JNPbtmyxcbGZuTIkWVlZTNnznzmmWeqq6s7\n3ripiaZPp8hIysuj0FBycaE9e6h/f0pI+HOFdesoMJDOnSM/P/Lzo3PnKDCQ1q1Tvuz2Mcbi\n4uLCwsKuX78eHBzs6emZmJjo5+e3c+dOdR9aWe1+T5TCGMXFUVgYXb9OwcHk6UmJieTnR7r/\nmWjWkiVL/Pz8pEfy8vJ279594MCBuro6bVUF6oV8Rj53BvJZ3bpw4+H9+/d37dq1f//+2tpa\n1d7SqJuM7i7vnBxmacmWL2ci0d+DAgHj89miRfX19T4+PhMmTBAKhZKFxcXFoaGhw4cPF4lE\nbPp01r8/u3fv720bG9ns2czJiZWWKlNXSUmJk5PT7NmzG6XmCr17927//v2nT5/e8faLFjE+\nnwkEf4+IRGzZMmZpyXJy2IEDzNycxcc/tkl8PDM3ZwcPKlN2hzZt2mRjY5OcnCw9+OWXX3K5\nXN289fhP7X5PlN35pk3MxoY9/pmwL79kXC5T9Weiy3d5d+jjjz/u27dvWVmZ+GVycrLkCtEB\nAwZ0fnoE/YV8Zgz5rEbIZzmQz4yxzkxjh4A2uoCeN4+NGCFn/NAhxuPt++ore3v71v/u9+7d\nMzMzO//DD4yIXbggu21jI/P2Zh99pExdH330kbe3d1NTk8z4hQsXiCg7O7u9jSsqGI/HDh2S\ns2jECDZvHnvqKfbee3KWvvceCwzscs0damlpcXNz27RpU+tFL7/88osvvqi+Qyur3e8JUyYZ\nWlqYmxuT95mwl19mqv5MdDmgOzRkyJDw8HDpl+bm5v/85z/FT6pbu3atFmvTDOTzn5DPaoB8\nlgP5/JeOr0yKj4/v0aOH/V8XSC1evLixsVEc0AKBYOvWrao8Hw664OxZmjxZzvgLLxBjBUeP\njh07tvUFPL169QoODi6KjycPDwoJkd3WzIwmTKDff1eurrMTJkzgcmUv3A8JCXF3d09JSWlv\n44sXiTF68UU5iyZNouRkunKFpkyRs3TyZLpyhWpqulx2+7KzswsLC6fIO/TkyZN/V+4TU692\nvyeUltb1PWdnU2Fhm/8cuvyZaFxubq7k+cYFBQUXLlx48803P/roo6+//vrpp5/et2+fdssD\n1UM+S0M+twX5rH4dN9AIaKNTXS1/FiFzc7KyYpWVbU2c5ODgIKqoaPNmFAcHqqpSpq6qqqp2\nDl1ZWdn+xmRlJX9iUUdHEm8rd+cODsSYkpW3W1cVEcl9Xw4ODuJH76rp0Mpq93ui1Ccm3rat\nf46qKtLZz0TjKioqJF8ecY8imVp08ODB9+/f11ploCbI58d3jXyWD/msfh030Ahoo+PuTjk5\ncsZLSqi83NTTM0fuUqLs7Gyupyfduyf/HoXsbHJ3V6YuDw8PuYduamq6e/euh4dHexu7u1NF\nBZWWyi+sVy+ysJD/rnNyyMKCnJy6VnOH3N3diUju+8rJyXF3d+dwOGo6tLLa/Z5Q+/8cHe6Z\nqM1/Dnd30tnPROMcHBwePXok/jkpKcnExGTo0KHily0tLeK/foJBQT5LQz63Bfmsfh030Aho\noxMZSTt3UusTBp9/Tu7uwW+9lZSUlJGRIbPwxIkTubm5fgsWkEgk51bcvDw6dIgmTlSursiD\nBw/m5eXJjO/cuZMxNnr06PY2Dgqinj3ps89kxysradcumjSJIiLos89kf3UWieizzygioq1n\nYimPz+cPGTKk9XzqjY2NW7dunajcJ6Ze7X5PKDCw63vm82nIEGo9x3xjI23dquS3yMD4+/sf\nPXr04cOHRUVFP/7447BhwyR/vr9z546bm5t2ywPVQz5LIJ/bgXzWgA6vkh4zZoybm9uDBw8e\nPXrk5OQ0fPhwyaLJkyf36dNHPRdn6xCju0mltpb5+bGQkL9viBYK2erVjMsV3wQdFRXVo0eP\nEydOiEQixlhzc/OePXvs7Ozef/99xhjbvJnxeGzrVtbQ8OfmKSmsXz8WHs5aWpSpq6WlZdSo\nUf369UtNTRWPNDQ0fPHFFzweb8uWLR1vf+gQ43LZmjVMcn96ZiYLCWF+fqy2lv3xB7O1ZVFR\nrKDgz6UFBSwqitnasps3lSm7QykpKTweLy4uTnKrbm5u7nPPPdezZ89Hjx6p9dBK6eh7opSU\nFMbjsbg49tdnwnJz2XPPsZ49mao/E12+SaVDP/30ExGZmpqKZ/ndu3eveFwkEvXo0WPSpEna\nLU8DkM/IZ2XK7hDyWQ7kM2OsM7NwIKCNLqAZYwUFbPx4RsScnVm/fozLZS4ubP9+8cL6+vrY\n2FgzMzNra+snn3zS0tLS0tJy5cqVLZL8/eILZmvLzM2Zry+zt2cmJuzVV5W67fcvlZWVr776\nqomJib29va+vr7m5ua2t7datWzu7/f79zMWFcbmsXz/m7MyIWETE34mcns78/RkR8/Rknp6M\niPn7s/R05cvu0G+//ebp6WliYuLl5dWjRw8iCg0N7eC+dV3Q7vdEWb/9xjw9mYkJ8/JiPXow\nIhYaytTwmehyQHfGzp07Q0NDQ0NDpduUpKQkR0fHL7/8UouFaQbyGfmsbshnOZDPjHFYJy73\n3rVr19dff01EUVFRb7/9tnjwzJkzU6ZMWbNmTUxMjKpPi+uW7du3x8TEVFdXS+bvMxbZ2ZSR\nQWVl5OtLISFkYSG9sLCwMD09Xfykq6CgIEdHx8e2ra6mixf/fNJVUBD16qXCuu7fv5+eni5+\n0tXgwYOtra0V2Li+ni5epOvXycGBAgLIx+expSIRZWT8+aQrf3966inq/DO0lNPc3Hzp0qWs\nrKxu3boNGDBgwIABmjmuCrT7PVFKczNdukRZWdStGw0YQOr5TBobG3k8XkpKSmhoqDr2D2qF\nfEY+awDyWQ6jz+dONdBGzngDGsAI6HJAQ4eQzwAGTJfzWYHf3u7du3fu3LkOJqMBAACNQz4D\nAGiS7Jzncp0/f37OnDmZmZlEdPLkybFjxxLRvn371qxZ88UXX4waNUq9NYKWZGdnZ2RklJWV\n+fr6hoSEWKjwTz8dEQgEAoGgtrbW398/ODi49eT8XVdfT2lpdONGm38ivHKFsrKINP0nQoCu\nQT4bJy3mMwkEJBBQbS35+1NwMCGfwTh1eJX09evXu3fvbmVlFRkZSUQnT54Uj1dXV3fv3v3t\nt99W6zXausAIb1IpKCgYP348ETk7O/fr14/L5bq4uOxX1c0H7crOzhb/paZHjx5eXl4mJiae\nnp6//fabavauqzepgBbp8k0qHUI+I581mc8sO5uFhjIi1qMH8/JiJibM05Mhn0FtdDmfO/7t\nbc2aNU1NTampqd988430uJWV1dNPP63Tj7KELqmrqxs7dmxJSYlAICgqKvrjjz8qKipiY2Oj\noqIOHz6s1kM/evQoPDzcxsYmNzf3wYMHOTk5JSUlEyZMGD9+fGpqqrJ7j4+nqChasIAqKuiP\nP6ioiDIzqbiYxo6lujq6eZNGj6aBA6mggO7coTt3qKCABg6k0aPp1i1VvDkA1UM+Gxst5jM9\nekTh4WRjQ7m59OAB5eRQSQlNmEDjxxPyGYxQhy22q6vr9OnTGWPFxcUkdYaDMfbee+85Ojqq\nsb3XDcZ2hmP9+vU9e/asqKiQGV++fLmHh0dzc7P6Dr1gwYJBgwY1SCYo/Ut0dPSQIUOU2nVz\nM3N3Z8uXy45XVLCePdknn7DJk9mzzzKR6LGlLS3s2WfZlClKHRp0my6f4egQ8hn5LKaBfGYL\nFrBBg1irfGbR0Qz5DOqhy/nc8Rno0tJST09PuYtMTU2rq6tV1suDbjhy5Eh0dLStra3M+IIF\nC/Lz89PT09V66Llz54pnHJcWFxd34cKFgoKCru86PZ0ePqQFC2THbW0pOpoOH6YTJ2jBAtln\nkJqYUGwsJSTIf/gtgLYhn42NFvOZjhyhuXOpVT5TXBxduEDIZzAyHTfQ9vb24nMbrV25coXP\n56u6JNCy/Px8H5lbN4iIyMnJyd7ePj8/X03HZYw9ePBA7qHFg0odOj+f7OzIyUnOIh8fun+f\n6utlb1iRLK2vp5KSrh8aQG2Qz8ZGW/lMjNGDB22GJBEhn8HIdNxADx8+PCEhQXwWXdqpU6dO\nnjwZHh6ulrpAe2xsbMrKylqPNzY2CoVCGxsbNR2Xw+G0dWjxoFKHtrEhoVD+iYrSUhKfzpF3\naCorIw6H1PauAZSBfDY22srnP2OwrZAkUiokkc+ghzpuoN97773i4uJJkyZdv36diOrq6i5e\nvLho0aJx48Zxudx3331X/UWCRoWFhcXHx7ceP378OIfDCQkJUd+hR4wYIffQ8fHxbm5ucs+7\ndFZICHE4dOyYnEWHD9PIkRQYSPIOTfHx9NRT1L171w8NoDbIZ2OjxXymESPaDEk3N/lniDsJ\n+Qz6qDMXSn/55ZetJ+I1MzPbvXu3mi/R1gnGdpNKTk6OpaXl8uXLRVJ3bAgEAj6fv2jRIrUe\nOiUlhcvlfvnll9KDycnJ1tbWmzZtUnbvixYxPp8JBH+PiERs2TJmaclyctiBA8zcnMXHP7ZJ\nfDwzN2cHDyp7aNBhunyTSmcgn5HPmslnlpLCuFz2eD6z5GRmbc2Qz6AeupzPnZr/PCYmJiws\nbNu2befOnSstLbW1tR06dGhsbKyfn5/yHTzoGi8vrwMHDkRFRcXHx4eHt9H/DQAAIABJREFU\nhzs4OGRmZiYmJk6cOHHt2rVqPXRoaOhXX301d+7cHTt2jBgxwtLS8vLlyydPnpw/f/6C1veX\nKGrtWsrLo6Agev55GjiQSkspKYny8+nAAfLyIi8vysmhadNo+HAaMoSI6MIFSkmhNWtoyhTl\n3xqAmiCfjYoW85lCQ+mrr2juXNqxg0aMIEtLunyZTp6k+fPl3P+nKOQz6BsOY0zbNei67du3\nx8TEVFdXW1lZabsWzSkoKPj2228zMjLKy8t9fX0jIiLGjRunmUPfvn179+7dAoGgpqbG399/\n6tSp4kerqMbPP1NCAt24Qfb2FBBAs2aR9I1WmZm0Zw8JBEREAwZQVBQNHKiyQ4NOamxs5PF4\nKSkpqvyagaYgnzWcz3T7Nu3eTQIB1dSQvz9NnUrIZ1AbXc7njhvoH374Yfjw4b179269KCsr\nKyMj47XXXlNPbbrCOAMawEjockB3CPmMfAYwYLqczx3fRDhjxoyUlBS5i44cOTJjxgxVlwQA\nAJ2CfAYA0IqOG+h2tLS0cGQmNgdjIhKJioqKtHPs5mbM/WksKiupvl7bRegf5LORQz6DJhhx\nPivVQF+/ft3BwUFVpYAeOXPmzOjRo21sbFxdXW1tbV944YWMjAwNHfvoURo2jKysyNmZHB3p\n5Zfp9m0NHRo0qbKSFi6kXr3Izo6srMjXlzZtopYWbZelN5DPRgv5DGqHfCZqcxaOl19+WfLz\nF198cfz4cemlLS0t9+/fT0tLmzBhghqrA520a9eu2bNn/9///d/ixYt79ep1+/btXbt2DR06\n9MiRI2q/keXf/6aVKyk2llavJj6frl+nbdsoMJBOnaKgIPUeGjSpuJhGjiTGaMUKCgykujr6\n/XdavZqSkujQITI11XZ9WoZ8hrYgn0HtkM9ibc1v15lthw4devv2bc3NuaclxjbPaPvy8vIs\nLS23bNkiM/7++++7uLhUVVWp8djp6czEhB058tigSMRee435+rLmZjUeGjRs5kw2aBCT+Trd\nvMns7GSnoVWaLs8z2hbkswTyWRryGTQB+cwYY6zNSziy/0JEn3zySfbjcnNzKysrz50716dP\nn85EORiM//73v0888cS8efNkxletWtXc3HxM7qOkVGXnTho9miIjHxvkcGjDBsrOptRUNR4a\nNEkopH376KOPyNr6sfG+fSk2lr75Rktl6RDkM8iFfAa1Qz7/pc1LOLy9vcU/rF27dty4cZKX\nuuPs2bNr165NS0traGjw8vKaMWNGXFxc6ydygWpdu3YtNDS09c1JPB4vKCjo2rVraj02jRwp\nZ9zFhby96do1CgtT49FBY3JyqKFB/uSyoaH0yScaL0jnIJ9BLuQzqB3y+S8dx9mSJUs0UEeH\n3Nzcpk+f/tlnn4lf7t27d8aMGS1/XbF+9erVq1evnj179vDhw7jxXK3w8QLoDuQzSMPHC6Ax\nSs3CoUmPHj2qrKwU/1xaWvrWW28xxpYtW5abm1tWVhYfH8/n848ePbpnzx7t1mnw/Pz8zp07\nx1pdhdnQ0JCenq7epwf7+ZHcKW+Liignh/DgYoPh7U0WFvL/5puaSk8+qfGCoAPIZx2BfAa1\nQz7/RW8aaGkHDx4UCoULFixYvXp179697e3tJ02adPjwYSLavXu3tqszcFFRUXfv3t26davM\n+IoVK7hc7osvvqjGY7/+Op06RUePPjbIGC1aRD4+qnycLGiXlRVNn04ffEDV1Y+N37pFmzfT\n7NlaKgs6BfmsRchnUDvk81/08oq0zMxMInrzzTelB4cMGRIQEKC52S6Nlbu7+9atW2fPnn35\n8uVp06Z5eHiIp0k6ceLEkSNHrGXuKlCtwED68EOaOpViY2n8+L+nSbp0iU6dMqKpc4zB+vU0\nciQNHkyLF/89TdLHH9OoUfT4f/iga5DPWoR8Bk1APhORnjbQdXV1RNS7d2+Z8T59+qj3Jgkg\nIqLo6OjevXuvWrVq6tSpNTU1NjY2YWFh58+fDwgIUPuxly4lf3/6+GPaupUaGsjBgZ55hi5f\nJi8vtR8aNMnZmc6fp5UradUqyssjU1Py8aHlyyk2Fv8n1nHIZ+1CPoPaIZ+JSE8baPEt51VV\nVZaWltLj5eXltra2WirKuIwaNerUqVMikaikpMTFxUWjx46MpMhIam6migpyctLooUGTbG1p\n40bauJEqK4nHIwsLbRcEnYJ81jrkM6gd8lm/Gujvv/9+3759RCQSiYgoKyvL1dVVeoU7d+54\neHhopzijZGJioul0luBykc7GAl2XPkA+6xrkM2iCEeez3jTQ/fr1kxlJS0sbM2aM5OXly5fv\n3r2r9keVAgDA45DPAGBs9KaB/uOPP9pfoaWlZf369dKRDcp4+PDhzp07MzIyysvLfX19IyIi\nHvufX00NffcdnT9P9+6RtzeFhdErr5C5ufbq7ayff/45ISHhxo0b9vb2AQEBs2bN4vP52i4K\nQL8hnzXMUPOZfv6ZEhLoxg2yt6eAAJo1i5DPoKv0cho7uQYPHvzee+899dRT2i7EECQkJPj6\n+u7du9fFxSU0NDQvLy8yMnL69OlNTU1ERDdv0qBB9OGHxOVSeDg1NNDChTR0KBUUaLvw9jQ1\nNU2fPj0yMjIvLy80NNTFxWXPnj39+/dPSEjQdmkABg75rEIGmc/U1ETTp1NkJOXlUWgoubjQ\nnj3Uvz8hn0FnMejItm3biKi6ulrbhWhITk6OpaXl8uXLRSKRZFAgEPD5/EWLFrH6eubjwyZM\nYELh39sUF7PQUDZ8OJPaRNcsWrSIz+cLBALJiEgkWrZsmaWlZU5OjhYLA+1qaGggopSUFG0X\nAl2BfGYGkc9s0SLG5zOpfGYiEVu2jFlaMuSzEdPlfDacBvrRo0cXL168ePGiyvdsbAE9b968\nESNGtB4/dOgQj8er/eorZm/PKitlF9+7x8zM2OnTGqiwCyoqKng83qFDh1ovGjFixLx58zRf\nEugIXQ5og4F8VhWDzGdWUcF4PCYvn9mIEQz5bMR0OZ/15hroDu3Zs2fhwoVExFo9xbQdIpEo\nOTm5ubm5nXVu3LihbHF65ezZs6+//nrr8RdeeIExVnb0aM+xY8nGRnZxr14UHEy//07h4Roo\nUlHi/3PLfRDXpEmT8IA0ALVCPquKQeYzXbxIjJHcByVOmkTIZ9BJhtNA29nZeSk+W/u9e/de\neuml9gNa/AuQQrmv16qrqx0cHFqPm5ubW1lZscpKcneXv6WDA1VWqre4rqqqqrKysjIzM2u9\nyNHRsaqqSvMlARgP5LOqGGQ+U1UVWVmRvHwmR0dCPoNOMpwGOjo6Ojo6WtGtevfuXVRU1P46\n27dvj4mJ4XA4XaxM37i7u+fk5LQeLykpKS8v5/5/e3ceEFW9/3/8M8MyggiIIqigBiKaSO6I\nRJoL5sLF9aqZ15tpUkrptyzFSlwic0/LJfVi2g2tXLLrdnG9brmbuCSg5nbFQGUElEWY3x9z\nLz8uy8gZZubM8nz8pZ9zPmfefBxevjmcc6ZJE1HRViGESE0VERHGLU5fPj4+WVlZ9+/fr1On\nTplNqampPpX9lwPAEMhnQ7HKfBY+PiIrS9y/L8rls0hNrfRHAkBW1vMUDhhKVFRUQkKCuty5\niiVLlvj4+NR7801x4IA4d67stB07xLVrol8/E1UpUbt27Ro2bPjFF1+UGVer1WvXru3fv78s\nVQGAJFaZz6JdO9GwoSiXz0KtFmvXCvIZZokGGmWNHz/e3d09IiLiwoUL2pHc3NzZs2d/9tln\nX3zxhTI8XAwdKvr2FTt3Cu2vTYuKRGKiGDFCvPee8POTs/TK2dnZLV68+LPPPvv0009zc3O1\ng8nJyREREe7u7m+//ba85QFAVVhlPgs7O7F4sfjsM/Hpp+K/+SySk0VEhHB3F+QzzJOMNzBa\nClu7y1uj0dy9e7dPnz5CCE9Pz8DAQHt7+3r16n3//ff/2ZyXp4mJ0Tg4aGrV0jz/vMbJSePk\npImL0xQVyVr1s33//ff16tWzt7cPDAz09PQUQvTt2/fu3bty1wU5mfNd3ngm8tlq8lnz/fea\nevU09vaawECNp6dGCE3fvhry2baZcz4rNJZz70VxcfHGjRsPHjyoUqkiIyN79OhRZocFCxYk\nJSXt2rXLsK+rvcYuOzvbxcXFsEc2c6mpqefOnXvw4EGLFi06duxYo0aN/9mcni5On/7PJ121\na1fBtWtmKS8v7+TJk5cuXfLw8GjdunVAQIDcFUFmBQUFKpXqyJEjnTt3lrsWC0Y+m5hV5rPI\nyxMnT4pLl4SHh2jdWpDPNs+c89libiIsKiqKiooq+dC4JUuWDBw4MCEhwbXU83qSk5N3794t\nU4FWKCAgQFd/6e0t+vY1YTmGUaNGjfDw8PDwcLkLAawH+Wx6VpnPokYNER4uyGdYAotpoFet\nWrV9+3YvL69Jkya5urquXbt28+bNN27c2LNnj7u7u9zVAYDtIp8B2BqLaaDXrVtnb29/8ODB\nwMBAIcS4ceNmzJgxc+bMXr16JSUluZZ/brwJZWdnnzx5MiUlxcvLq127do0aNZKxmKorLi4+\ne/as9k6UoKCgNm3aKJXcVApAMvLZ4MhnwMxZTAN94cKFsLAwbToLIZRK5YwZMzw9PWNiYvr0\n6bN79+6aNWvKUtiyZctiY2OfPHni7++fnp6uVquHDx++bNkyef/PeKYzZ86MGjXqwoULTZo0\nEUL8/vvvQUFB33zzTdu2beUuDYCFIZ8Ni3wGzJ/F/ERbUFBQr169MoMTJkyYN2/ekSNHIiMj\nnzx5Yvqqvvzyy//7v/+Lj4/Pzs6+dOnSgwcPDh06dOrUqaioqOLiYtPXU0VXrlzp1q1bcHDw\n3bt3r1+/fv369bt37wYHB3fr1i0lJUXu6gBYGPLZgMhnwDLI/RiQqmratGloaGiFm6ZPny6E\neOWVV4YPH26Mr6iyxyRlZWXVqlVr5cqVZcZv3rzp4uKSmJho8EoMZeDAgREREcXFxaUHi4qK\nIiIiBg0aJFdVgCzM+TFJloJ8NiDyGShhzvlsMZdwtG7detu2bWq12s3NrcymuLi4R48eLVq0\nyM7OzpQl7d27V6lUvv7662XGfX19Bw0a9NNPPw0bNsyU9VRRYWHhjh07fvzxxzIffqtUKmNi\nYoYMGVJYWOjg4CBXeQAsDvlsKOQzYCks5hKOAQMGFBQUJCYmVrh14cKFY8eOLSoqMmVJt2/f\nbty4cYVZFhAQcPv2bVMWU3WZmZl5eXkVPv8oICAgLy8vMzPT9FUBsFzks6GQz4ClsJgz0JGR\nkYsWLSp/mV2JFStWBAQE3L9/32Qlubq6Pnz4sMJNDx48MNubVGrVqiWEePDgQflNDx48UCgU\nZls5APNEPhsK+QxYCotpoGvVqjVx4kQdOyiVysmTJ5usHiHEiy++eOvWrRMnTnTs2LH0eGFh\n4bZt20aPHm3KYqrOxcWlbdu2mzdv7tSpU5lNmzdvbtOmjVz3ywOwUOSzoZDPgKWwmEs4zFDT\npk2HDh06atSomzdvlgwWFha+/fbbWVlZ48aNk7E23aZOnfrFF19s2bKl9OCWLVuWLFkSGxsr\nV1UAYCjkMwCjspgz0OZp1apV/fv3f/755/v27duiRYu7d+8mJSU9fvz4559/9vDwkLu6Sg0e\nPDgtLW3IkCFhYWEhISFCiOPHjx85cmT27NmDBg2SuzoAMADyGYDxcAa6WmrVqpWUlLR27dra\ntWv/61//evTo0YQJEy5fvlz+t2/mZsqUKWfOnAkNDb148eLFixdDQ0PPnDkzZcoUuesCAMMg\nnwEYD2egq0upVA4ePHjw4MFyFyJZcHBwcHCw3FUAgLGQzwCMhDPQAAAAgAQ00CaiVqvz8vLk\nrqICOTk5OTk5clcBALIhnwFIRQNtXGq1etKkSY0aNXJ3d3dxcWnRosXixYtN/IECFcrLy4uL\ni/P393d1dXV1dfX394+LizPP/0IAwBjIZwB64xpoI8rIyHjppZc0Gs306dPbtm375MmTw4cP\nz5o168CBA5s2bTLxB9uW9vjx4549e968efODDz7Q3k/zyy+/fP7550lJSUlJSc7OznIVBgCm\nQT4DqA4aaCOaPHmySqU6dOiQ9sOlhBCdO3fu379/SEjIqlWroqOj5SosPj7+9u3bp06d8vLy\n0o506NBhyJAhHTt2jI+Pnz17tlyFAYBpkM8AqoNLOIwlJydnw4YN8fHxJems1axZs5iYmNWr\nV8tVmEajWbNmzbRp00rSWcvb23vatGlr1qzRaDRy1QYAJkA+A6gmGmhjSUtLy8/P79y5c/lN\nnTt3vnTpkulL0rp//356enqFhYWFhaWnp9+/f9/0VQGAyZDPAKqJBhoAAACQgAbaWJo2bVqj\nRo2jR4+W33T06NHnn3/e9CVp1alTx9vbu7LC6tevX6dOHdNXBQAmQz4DqCYaaGNxcXEZOnRo\nbGxsdnZ26fGUlJSlS5eOGTNGrsIUCsUbb7zx6aef3rt3r/R4enr67NmzR48erVAo5KoNAEyA\nfAZQTTTQRjRv3rz8/PwOHTqsWbPm7NmzR48enTt3bmhoaJcuXcaOHStjYbGxsT4+Pu3bt//y\nyy9Pnjx58uTJpUuXtm/f3tfXNzY2VsbCAMA0yGcA1cFj7IzI09Pzl19+iYuLmzFjxq1bt+zs\n7AICAj7++OOYmBgZHzIqhHB2dt67d++cOXMWLVp0/fp1IcRzzz03ZsyYKVOm1KhRQ8bCAMA0\nyGcA1aHgmTjPtHLlyujo6OzsbBcXF70PolarVSqVGcaf9nNiq/OlARatoKBApVIdOXKkwkcf\nwMyRz4AVM+d85gy0ibi5ucldQsWIZgA2jnwGIBXXQAMAAAAScAYaZufq1avffPNNcnJybm5u\nUFDQ4MGDq/67m4KCgsTExEOHDqWlpTVu3LhTp05/+ctfatasadSCAcBGkM+AFmegYV4SEhJa\ntmy5c+fOJk2atG/f/tKlS+Hh4e+++25VLta/e/duSEjIpEmT8vPzu3btam9vP3PmzBdeeOHK\nlSsmqBwArBv5DJTgDDTMyNGjR998882lS5dGR0eXDB46dKhv375+fn7vvvuujrkajWbIkCHO\nzs4pKSl169bVDubk5Lz66quRkZHJyckqlcq41QOA9SKfgdI4Aw0zMmfOnCFDhpROZyFEeHj4\nrFmz5syZU1xcrGPuwYMHT5w4kZiYWJLOQggXF5f169dnZmb+8MMPxioaAGwA+QyURgMNM3Lo\n0KGBAweWHx84cGB6enpqaqruue3bt2/UqFGZcTc3tx49ehw+fNiQhQKAjSGfgdJooGEuNBpN\ndna2h4dH+U3awUePHumY/ujRowrnaqer1WqDFAkANoh8BsqggYa5UCgUPj4+aWlp5TdpB318\nfHRMr2yuECI1NdXX19cgRQKADSKfgTJooGFG+vfvv2zZsoKCgjLjixcvDgkJqV+/vo65kZGR\naWlpO3fuLDN+9uzZgwcPRkVFGbhWALAl5DNQGg00zMjUqVMzMzOjoqKuX7+uHXn48OG7776b\nmJi4cOFC3XP9/Pzee++9V199dcOGDdrbWTQazc6dO/v16zds2LCwsDCjVw8A1ot8BkrjMXYw\nI15eXgcOHBg1apSfn1+DBg2cnJyuX7/eqFGjHTt2VOVZ/Z999pmzs/Po0aNHjx793HPP3bp1\nKy8v76233po7d64JigcAK0Y+A6XRQMO8NG3a9MiRI8nJycnJyY8fPw4KCmrfvr29fZXeqEql\ncvr06TExMadOndJ+0lW7du28vb2NXTMA2ALyGShBAw1z1KpVq1atWuk318PDIyIiIiIiwrAl\nAQAE+QwIIbgGGgAAAJCEBhoAAACQgAYaAAAAkIAGGgAAAJCABhoAAACQwPKewqHRaFJSUlJS\nUtRqtUajcXd3b9asWbNmzRQKhdylAYBNI58B2AhLaqCfPHmyYMGCFStW3Llzp8wmHx+fcePG\nvffee05OTrLUBgC2jHwGYFMspoHOzc3t3r378ePHlUplmzZtAgIC3NzcFApFVlZWSkrK+fPn\nP/744+3bt+/du9fZ2VnuYgHAhpDPAGyNxTTQ8fHxx48fHzFixNy5cxs0aFBm6507dyZPnpyY\nmBgfHz979mxZKgQA20Q+A7A1FnMT4YYNG9q1a7du3bry6SyEaNiw4bffftu2bduNGzeavjYA\nsGXkMwBbYzEN9O3bt8PDw5XKSgtWKpXh4eG3bt0yZVUAAPIZgK2xmAbazc3t+vXruve5du2a\nu7u7aeoBAGiRzwBsjcU00D169Pj555/XrVtX2Q5r1679xz/+0b17d1NWBQAgnwHYGou5iXDW\nrFk7duwYNWrU4sWLX3nllcDAQDc3NyGEWq2+cuXKzp07z5075+7uPnPmTLkrBQDbQj4DsDUW\n00D7+/sfPnz4jTfeOHHixNmzZ8vv0LFjxzVr1vj7+5u+tqpQq9UqlapGjRpyFwIABkY+A7A1\nFtNACyGCgoKOHz9+5syZffv2XblyRa1WCyHc3NwCAwO7devWtm1buQusgFqtjouL27Rp061b\nt+zs7AICAsaNGxcTE2NnZyd3aQBgMOQzAJtiSQ20Vtu2bc0zi8vLyMh46aWXNBrN9OnT27Zt\n++TJk8OHD8+aNevAgQObNm0iowFYGfIZgI2wvAbagkyePFmlUh06dKhWrVrakc6dO/fv3z8k\nJGTVqlXR0dHylgcANot8BlAdFvMUjmf6448/Tp06derUKbkL+Y+cnJwNGzbEx8eXpLNWs2bN\nYmJiVq9eLVdhAGBi5DMAK2M9Z6C/++67SZMmCSE0Gk3VZz18+PCjjz56+vSpjn0uX76sRz1p\naWn5+fmdO3cuv6lz587z58/X45gAYInIZwBWxnoaaHd3dyPd4u3i4iKEcHR0NMbBAcDqkc8A\nrIxC0vkA23T06NGwsLD8/HxJGZ2Tk+Pp6blp06Y+ffqU2fTJJ5/s2LHDfH6bCdiygoIClUp1\n5MiRCs9HwsyRz4AVM+d8tp5roM2Ni4vL0KFDY2Njs7OzS4+npKQsXbp0zJgxchUGADaOfAZQ\nTTTQRjRv3rz8/PwOHTqsWbPm7NmzR48enTt3bmhoaJcuXcaOHSt3dQBgu8hnANVhPddAmyFP\nT89ffvklLi5uxowZJQ/q//jjj3lQPwDIi3wGUB2W1EAXFxdv3Ljx4MGDKpUqMjKyR48eZXZY\nsGBBUlLSrl27ZCmvQm5ubosWLVq0aBEfFQvAipHPAGyKxTTQRUVFUVFR27dv1/51yZIlAwcO\nTEhIcHV1LdknOTl59+7dMhX4DG5ubnKXAABGQT4DsDUW00CvWrVq+/btXl5ekyZNcnV1Xbt2\n7ebNm2/cuLFnzx53d3e5qwMA20U+A7A1FnMT4bp16+zt7Q8ePPjhhx++9dZbx44d++STT06f\nPt2rV69Hjx7JXR0A2C7yGYCtsZgz0BcuXAgLCwsMDNT+ValUzpgxw9PTMyYmpk+fPrt3765Z\ns6aRXlr7eFGVSmWk4wOQHZ/EUR3kMwDjMc98tpgGuqCgoF69emUGJ0yYkJeXN3ny5MjIyJLL\n7wyuffv2586d0/1xss/05ptv+vr6Dh482FBVGcqqVauEEGb42KYff/wxLS1typQpchdS1v79\n+3fu3Dl37ly5Cynr3LlzX3755erVq+UupKxbt27FxsauWLHCeF2UfnJzc6OjoxMTE1u0aPHC\nCy/IXY4FI5+NhHyWinyWinzWm8U00L6+vrdv3y4//v777+fk5MyYMWPgwIG1a9c20qtX/x/P\nw8OjVatWr732mkHqMaC9e/cKIcywsCtXruTm5pphYbm5uUeOHDHDwmrXrr1ixQozLOz8+fOx\nsbFDhgzx8PCQu5b/8eDBg+jo6Oeffz44OFjuWiwb+Wwk5LNU5LNU5LPeLKaBbt269bZt29Rq\ndfnbpePi4h49erRo0SIe3gkApkc+A7A1FnMT4YABAwoKChITEyvcunDhwrFjxxYVFZm4KgAA\n+QzA1ljMGejIyMhFixaVv8yuxIoVKwICAu7fv2/KqgAA5DMAW2MxDXStWrUmTpyoYwelUjl5\n8mST1QMA0CKfAdgai7mEAwAAADAHNNAAAACABDTQAAAAgAQ00AAAAIAENNAAAACABBbzFA5L\n5+jo6ODgIHcVFTDPj5gXQjg4OJhnbY6OjhQmiaOjo0KhMMP3v4ODg0KhMM9FgymRz1KRz1KZ\nc2Hks34UGo1G7hpswr1791xcXMzts+aFEA8fPhRCGO9TdvWWm5ubk5Pj5eUldyFlFRQU/PHH\nHz4+PnIXUlZxcfHNmzebNGkidyEVuHbtmp+fn9xVVMBsC4Mpkc9Skc9Skc96MNvCtGigAQAA\nAAm4BhoAAACQgAYaAAAAkIAGGgAAAJCABhoAAACQgAYaAAAAkIAGGgAAAJCABhoAAACQgAYa\nAAAAkIAGGgAAAJCABhoAAACQgAYaAAAAkIAGGgAAAJCABhoAAACQgAYaAAAAkIAGGgAAAJCA\nBrq6mjdvrijH29u7KnOvXr06YsQIb2/vGjVqBAQEfPTRR48fP5a9sOp8RVW3d+/e/v37e3l5\nqVQqX1/fqKioAwcOPHOWUVdM78KMumLffvtt+YOXKCoq0j3deCtWncJM8B7TaDRbtmzp3r27\nj4+Pk5OTn5/fkCFDjh07VpW5JnibwTTIZ/2Qz1VEPuvHOvLZXpZXtTJKpXLkyJGlR9zc3J45\n68KFC+Hh4Wq1ul+/fn5+focOHfr000/37t27b98+JycnGQurzsQqmjp16pw5c1QqVadOnby8\nvDIyMo4cOdKqVauuXbvqmGWCFdOvMGHMFfP39x81alSZwcuXL584ceLll1+2s7PTMdeoK1ad\nwoTx32MTJkxYtmyZm5tbZGRknTp1UlJSNm/evGnTpoSEhPJll2aCtxlMiXyWinyuOvJZP1aS\nzxpUT2BgoEql0mNix44dhRAJCQnavxYVFQ0fPlwIMWvWLHkL03vKd+IRAAANt0lEQVRiFf3t\nb38TQoSGht6+fbtksKioKDMzU/dEY6+Y3oUZe8XK6927txBiw4YNuncz9orpXZixV+zq1atC\niLp16965c6dkcOvWrUIIX19f3XNNv2gwHvJZKvK5+shn3awmn2mgq0u/t9rp06eFEK1bty49\nePv2baVS6ePjU1xcLFdh1ZlYFfn5+d7e3jVr1kxPT5c00dgrpndhGpMH9O+//65UKj09PfPz\n83XsZoL3mH6FaYy/Ynv27BFC9OnTp/RgUVGRvb29k5OTjommXzQYFfksCflcfeTzM1lNPnMJ\nhwEUFxfHx8dfvXrVyckpODh48ODBHh4euqfs27dPCKH9cbBEw4YNg4ODz507l5KSEhgYKEth\n1Zz4TPv27UtPTx8xYoSbm9vGjRsvXLjg5OQUEhLSrVs3hUKhe6Iw5orpXZiW8VasvK+//rq4\nuPj11193dHTUsZtp3mN6FKZl1BVr3ry5nZ3dyZMn09PTSy7d27Fjx9OnT/v166djoukXDcZG\nPlcd+Vx95PMzWU8+m7hhtz7l/8FcXFy+++473bPGjBkjhFi7dm2Z8T//+c9CiG3btslVWHUm\nVsXMmTOFEO+8805AQEDplwgNDdV9asHYK6Z3YRojr1gZhYWF3t7eCoUiNTVV954meI/pV5jG\nJCs2e/ZsIYS7u/vIkSMnTpzYt29fe3v7vn37ZmRk6Jhl4kWDsZHPkpDP1UQ+V5F15DNP4aiu\nUaNGJSUl3b179/HjxxcuXJgwYcLjx49Hjhx56NAhHbPUarWo6Kp8d3d3IURWVpZchVVnYlX8\n8ccfQoivvvpKqVTu378/Ozv7/PnzPXv2PHbs2LBhw3RMNPaK6V2YMPKKlfHTTz+lp6d37969\nadOmuvc0wXtMv8KESVZs2rRp3333XXFx8fr16xcvXrx9+3Z/f/8RI0bUrVtXxywTLxqMjXyW\nhHyuJvK5iqwkn03csNuCadOmCSF69+6tY58hQ4YIIbZs2VJmfOzYsUKI9evXy1WYYSeW99Zb\nbwkh7O3tL1++XDKYk5PToEEDIcTJkycrm2jsFdO7sAoZcMXK6NmzpxDihx9+eOaeJn6PVb2w\nChl8xeLi4hQKxQcffHD9+vXc3NzTp09HREQIIaZOnapjlizfmDAl8lkH8rmayOcqso585gy0\n4b3xxhtCiBMnTujYR/sjlPbHqdIq+wHLZIUZdmJ5tWvXFkI0b968efPmJYM1a9bUfnufOnWq\nsonGXjG9C6uQAVestGvXru3Zs8fLyysqKuqZO5vyPSapsAoZdsX++c9/xsXFDRs27PPPP2/S\npImzs3Pbtm23bt3q6+s7d+7cGzduVDZRlm9MmBL5rAP5XB3kcxVZTT7TQBue9rcJ+fn5OvbR\nXmN05cqVMuOpqalCiGbNmslVmGEnlqf9wrUHLP8SeXl5uicab8X0LqxCBlyx0r7++muNRjN6\n9GgHB4dn7mzK95ikwipk2BXbvn27EOLll18uPejk5NSpU6eioqJz585VNlGWb0yYEvmsA/lc\nHeRzFVlNPtNAG97BgweFEP7+/jr26datmxBi165dpQf//e9///rrrw0bNjTS+6AqhRl2Ynnd\nu3dXKBS//fZbYWFh6fHk5GQhxHPPPVfZRGOvmN6FVciAK1aisLAwISFBoVBof131TCZ7j0kt\nrEKGXbGCggLx3+smS7t3754QQqVSVTZRlm9MmBL5rAP5rDfyueqsJ59NfMmIlTlx4sSvv/5a\neuTkyZPaq7Lmz59fejwhIWHRokX37t0rGdE+D/ybb77R/rWoqGjEiBHCQM8D17uwqk/U28CB\nA4UQ06dPLxn5+eefhRB169bNycmprDCNkVdM78JMsGJaGzduFEL06tWrsh1Mv2L6FWaCFfv7\n3/8uhPD29r5161bJ4LZt2xQKhbOzc1ZWVmW1aUy1aDAB8lkP5LN+yOeqs5p8poGulnnz5gkh\n/P39e/ToMXDgwDZt2mifSfmnP/2poKCg9J7aH91K3+uQnJzs5uamVCqjoqImTpzYrl07IURI\nSMjjx49lLKzqE/V2586dJk2aCCFCQ0PHjx/fr18/pVLp4OCwdetWHYVpjLxiehdmghXT0v7w\nvXnz5sp2MP2K6VeYCVbs6dOn2t8P1qxZc+jQoe+88472WkkhxPLly3XUpjHVosEEyGc9kM/6\nIZ+rzmrymQa6Ws6cOTN27NhWrVp5eHjY29vXrVu3Z8+e69evL/+JOOXfBxqNJi0tbfjw4Z6e\nno6Ojn5+frGxsaV/kpalsKpPrI6MjIyYmJjGjRs7ODjUqVNnwIAB5W+jNvGK6V2YaVYsJSVF\noVDUr1+/sLCwsn1kWTE9CjPNiuXn5y9cuLBjx44uLi52dnaenp6RkZF79+7VXZuWsRcNpkE+\n64d8lop8lso68lmh0WgEAAAAgKrhJkIAAABAAhpoAAAAQAIaaAAAAEACGmgAAABAAhpoAAAA\nQAIaaAAAAEACGmgAAABAAhpoAAAAQAIaaAAAAEACGmgAAABAAhpoAAAAQAIaaAAAAEACGmgA\nAABAAhpoAAAAQAIaaAAAAEACGmgAAABAAhpoAAAAQAIaaAAAAEACGmgAAABAAhpoAAAAQAIa\naAAAAEACGmgAAABAAhpoAAAAQAIaaAAAAEACGmgAAABAAhpoAAAAQAIaaAAAAEACGmgAAABA\nAhpoAAAAQAIaaAAAAEACGmgAAABAAhpoAAAAQAIaaKACu3btUvxX06ZNjfESWVlZilIyMzON\n8SoAYGXIZ5gDGmhYgLS0NIVCMWzYMBMfOTIyMiEhYe7cuVIPu3nz5piYmLCwMBcXl8qO7+zs\nnJCQkJCQEBQUJLluADAP5DNsk73cBQDmKzg4+K9//aseE+Pj40+fPu3q6tqwYcOUlJQK93F0\ndNQefMOGDRcuXKhGmQBgc8hnyIsz0IDhzZ8/PzU1NSsra8GCBXLXAgD4/8hnGAQNNMzdnDlz\nAgIChBAbN24suSLt22+/Ldnh2LFjgwYN8vb2dnR0bNCgwWuvvfbbb7+VPsLOnTt79uzZoEED\nlUpVv379F198cd68eVU5st66du3atGlThUJR/UMBgNkin2GzuIQD5i4yMtLBweH999/v1KnT\n+PHjtYNhYWHaP6xatSo6OrpOnTr9+vWrV6/e9evXf/jhh61bt+7duzckJEQIsW7dulGjRnl7\ne0dFRdWrVy8jI+PixYurV6+ePHmy7iMDAHQjn2GzaKBh7lq2bKlSqd5///3GjRu/9tprpTdd\nvnx5/PjxPXv23LJli5OTk3bw/PnzYWFhb7755q+//iqEWLlypZ2d3enTpxs0aFAy8eHDh7qP\nDAB4JvIZNotLOGDBli1bVlhYGBsbm5ubm/lfDRo06N69+/nz52/cuKHdzc7Ozt7+f35WrF27\nthz1AoCtIJ9h3TgDDQt27NgxIUSXLl0q3Hr37t3GjRsPHz786NGjLVu2HDp0aNeuXV988UVv\nb2/TlgkANod8hnWjgYYFu3//vhBi27ZtJb8fLK1FixZCiAkTJtSuXfurr75avnz5V199JYQI\nDQ2dN28e19IBgPGQz7BuNNCwYG5ubkIIb2/vDh066NhtxIgRI0aMePTo0bFjx7Zu3bpmzZre\nvXtfvHjR19fXVJUCgG0hn2HduAYaFsDOzk4IUVRUVGa8U6dOQogNGzZU5SCurq69evVavnz5\ne++9l52dvW/fPh1HBgBUBfkM20QDDQtQp04dIcTNmzfLjE+YMMHe3n7p0qXatC2Rk5OzceNG\n7Z+TkpKePn1aemtmZqYQwtnZWceRdZgzZ84rr7yyY8cOyV8GAFgd8hm2iUs4YAFcXV1DQkKO\nHz8+fPjw5s2b29nZ9e/fPygoKCgoaOXKlePGjevRo0dERESbNm2Kiop+++23ffv2NWnSZOjQ\noUKI4cOH29vbd+nSpXHjxnZ2dsePH9+/f3/Lli379eun48g6ijl37tzu3bsHDBigY5/Nmzdv\n27ZNCHH79m0hxPHjx7WfClu3bt358+cbbmEAQGbkM2yUBrAEqamp/fr1q127tvbjo9avX1+y\n6ezZsyNHjvT19XV0dKxdu3bLli2jo6P379+v3bp8+fL+/fv7+fk5Ozu7ubkFBwfPnj374cOH\nuo+8c+dOIcS0adPKV9KmTRsHB4dr167pqHbatGkVfrs1bty4/M69evUSQmRkZOizLgAgN/IZ\nNkih0WiM0ZcDFm3Xrl29e/eeOHHihx9+aG9vX7duXe34gwcPPD09o6OjtTeMV4dGo7l3754Q\n4tVXX92/f39GRkbJqwAAKkM+wxxwDTRQqcWLF9evX197K4zW/v37VSrVRx99VP2Dq9Xq+vXr\n169ff//+/dU/GgDYFPIZ8uIMNFCBzMzMU6dOaf9cs2bN8PBwg7/E06dP9+zZU/LX7t27Ozg4\nGPxVAMDKkM8wBzTQAAAAgARcwgEAAABIQAMNAAAASEADDQAAAEhAAw0AAABIQAMNAAAASEAD\nDQAAAEhAAw0AAABIQAMNAAAASEADDQAAAEhAAw0AAABIQAMNAAAASEADDQAAAEhAAw0AAABI\nQAMNAAAASEADDQAAAEhAAw0AAABIQAMNAAAASEADDQAAAEhAAw0AAABIQAMNAAAASEADDQAA\nAEhAAw0AAABIQAMNAAAASEADDQAAAEhAAw0AAABIQAMNAAAASEADDQAAAEjw/wBmR1hpZ5VQ\nGgAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “Predicted”"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"options(repr.plot.width=8, repr.plot.height=4)\n",
"par(mfrow=c(1,2))\n",
"plot(test[,1], test[,2], col=as.integer(test.cls), main=\"Truth\")\n",
"plot(test[,1], test[,2], col=as.integer(test.pred), main=\"Predicted\")"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" test.cls\n",
"test.pred versicolor virginica\n",
" versicolor 25 0\n",
" virginica 3 22"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"table(test.pred, test.cls)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Logistic Regression"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" | Sepal.Length | Sepal.Width | Petal.Length | Petal.Width |
|---|
\n",
"\n",
"\t| 51 | 6.3 | 3.3 | 6.0 | 2.5 |
|---|
\n",
"\t| 31 | 5.5 | 2.4 | 3.8 | 1.1 |
|---|
\n",
"\t| 42 | 6.1 | 3.0 | 4.6 | 1.4 |
|---|
\n",
"\t| 68 | 7.7 | 3.8 | 6.7 | 2.2 |
|---|
\n",
"\t| 9 | 6.6 | 2.9 | 4.6 | 1.3 |
|---|
\n",
"\t| 22 | 6.1 | 2.8 | 4.0 | 1.3 |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|llll}\n",
" & Sepal.Length & Sepal.Width & Petal.Length & Petal.Width\\\\\n",
"\\hline\n",
"\t51 & 6.3 & 3.3 & 6.0 & 2.5\\\\\n",
"\t31 & 5.5 & 2.4 & 3.8 & 1.1\\\\\n",
"\t42 & 6.1 & 3.0 & 4.6 & 1.4\\\\\n",
"\t68 & 7.7 & 3.8 & 6.7 & 2.2\\\\\n",
"\t9 & 6.6 & 2.9 & 4.6 & 1.3\\\\\n",
"\t22 & 6.1 & 2.8 & 4.0 & 1.3\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| | Sepal.Length | Sepal.Width | Petal.Length | Petal.Width | \n",
"|---|---|---|---|---|---|\n",
"| 51 | 6.3 | 3.3 | 6.0 | 2.5 | \n",
"| 31 | 5.5 | 2.4 | 3.8 | 1.1 | \n",
"| 42 | 6.1 | 3.0 | 4.6 | 1.4 | \n",
"| 68 | 7.7 | 3.8 | 6.7 | 2.2 | \n",
"| 9 | 6.6 | 2.9 | 4.6 | 1.3 | \n",
"| 22 | 6.1 | 2.8 | 4.0 | 1.3 | \n",
"\n",
"\n"
],
"text/plain": [
" Sepal.Length Sepal.Width Petal.Length Petal.Width\n",
"51 6.3 3.3 6.0 2.5 \n",
"31 5.5 2.4 3.8 1.1 \n",
"42 6.1 3.0 4.6 1.4 \n",
"68 7.7 3.8 6.7 2.2 \n",
"9 6.6 2.9 4.6 1.3 \n",
"22 6.1 2.8 4.0 1.3 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"head(train)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The warning is due to the fact that vanilla logistic regression does not like perfectly separated data sets. The usual remedy is to add a penalization factor."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning message:\n",
"“glm.fit: algorithm did not converge”Warning message:\n",
"“glm.fit: fitted probabilities numerically 0 or 1 occurred”"
]
}
],
"source": [
"model.logistic <- glm(train.cls ~ .,\n",
" family=binomial(link='logit'), data=train)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"glm(formula = train.cls ~ ., family = binomial(link = \"logit\"), \n",
" data = train)\n",
"\n",
"Deviance Residuals: \n",
" Min 1Q Median 3Q Max \n",
"-2.347e-05 -2.110e-08 2.110e-08 2.110e-08 2.792e-05 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error z value Pr(>|z|)\n",
"(Intercept) 1.658e+00 1.263e+06 0.000 1.000\n",
"Sepal.Length -6.152e+01 9.061e+04 -0.001 0.999\n",
"Sepal.Width -8.214e+01 4.829e+05 0.000 1.000\n",
"Petal.Length 7.759e+01 1.673e+05 0.000 1.000\n",
"Petal.Width 1.453e+02 2.148e+05 0.001 0.999\n",
"\n",
"(Dispersion parameter for binomial family taken to be 1)\n",
"\n",
" Null deviance: 6.8593e+01 on 49 degrees of freedom\n",
"Residual deviance: 2.0984e-09 on 45 degrees of freedom\n",
"AIC: 10\n",
"\n",
"Number of Fisher Scoring iterations: 25\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"summary(model.logistic)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
"test.pred <- ifelse(predict(model.logistic, test) < 0, 1, 2)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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FqIy+XqbvdMaKABAAAAAOSCBhoAAAAA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\nDTQAAAAgAw00AAAAIAMNNAAAACDD/wEqWFxYYpp0SQAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “Predicted”"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"options(repr.plot.width=8, repr.plot.height=4)\n",
"par(mfrow=c(1,2))\n",
"plot(test[,1], test[,2], col=as.integer(test.cls), main=\"Truth\")\n",
"plot(test[,1], test[,2], col=test.pred, main=\"Predicted\")"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" test.cls\n",
"test.pred versicolor virginica\n",
" 1 24 3\n",
" 2 4 19"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"table(test.pred, test.cls)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Overfitting"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [],
"source": [
"set.seed(10)\n",
"\n",
"x <- 1:10 \n",
"y = 0.1*x^2 + 0.2*x + rnorm(10, 0.5, 1)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [],
"source": [
"m1 <- lm(y ~ x)\n",
"m2 <- lm(y ~ poly(x, 2))\n",
"m5 <- lm(y ~ poly(x, 5))\n",
"m9 <- lm(y ~ poly(x, 9))"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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bt2OTMbgPtcvKjKlbVlizZsUECA6TSwEOYz4Er27VP9+nr3XXXpYjoKnt6TC/TJ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hJY/NBwDP9/336tVLp07pjTf8X3op3Ycf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\nGECABgAAAAz4/xFkE32NnykBAAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"options(repr.plot.width=8, repr.plot.height=8)\n",
"\n",
"xp = seq(0, 10, length.out = 100)\n",
"df <- data.frame(x=xp)\n",
"\n",
"par(mfrow=c(2,2))\n",
"plot(x, y, xlim = c(0, 10), pch = 19)\n",
"lines(xp, predict(m1, df), col = \"red\")\n",
"plot(x, y, xlim = c(0, 10), pch = 19)\n",
"lines(xp, predict(m2, df), col = \"red\")\n",
"plot(x, y, xlim = c(0, 10), pch = 19)\n",
"lines(xp, predict(m5, df), col = \"red\")\n",
"plot(x, y, xlim = c(0, 10), pch = 19)\n",
"lines(xp, predict(m9, df), col = \"red\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Evaluate model RSS using `in-sample` testing (Error resubstitution)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] 9.18\n",
"[1] 4.15\n",
"[1] 2.09\n",
"[1] 0\n"
]
}
],
"source": [
"for (model in list(m1, m2, m5, m9)) {\n",
" print(round(sum((predict(model, data.frame(x=x)) - y)^2), 2))\n",
" }"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Evaluate model RSS using `out-of-sample` testing"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"test.x <- runif(10, 0, 10)\n",
"test.y <- 0.1*test.x^2 + 0.2*test.x + rnorm(10, 0.5, 3)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] 112.25\n",
"[1] 103.79\n",
"[1] 99.8\n",
"[1] 111.98\n"
]
}
],
"source": [
"for (model in list(m1, m2, m5, m9)) {\n",
" print(round(sum((predict(model, data.frame(x=test.x)) - test.y)^2), 2))\n",
" }"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Cross-validation"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] 1\n",
" 1 \n",
"17.61035 \n",
"[1] 2\n",
" 1 \n",
"8.68587 \n",
"[1] 3\n",
" 1 \n",
"19.42014 \n",
"[1] 4\n",
" 1 \n",
"20.58078 \n",
"[1] 5\n",
" 1 \n",
"50.26568 \n"
]
}
],
"source": [
"for (k in 1:5) {\n",
" rss <- 0\n",
" for (i in 1:10) {\n",
" xmo <- x[-i]\n",
" ymo <- y[-i]\n",
" model <- lm(ymo ~ poly(xmo, k))\n",
" res <- (predict(model, data.frame(xmo=x[i])) - y[i])^2\n",
" rss <- rss + res\n",
" }\n",
" print(k)\n",
" print(rss)\n",
"} \n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Feature Selection"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [],
"source": [
"suppressPackageStartupMessages(library(genefilter))"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [],
"source": [
"set.seed(123)\n",
"n = 20\n",
"m = 1000\n",
"EXPRS = matrix(rnorm(2 * n * m), 2 * n, m) \n",
"rownames(EXPRS) = paste(\"pt\", 1:(2 * n), sep = \"\") \n",
"colnames(EXPRS) = paste(\"g\", 1:m, sep = \"\")\n",
"grp = as.factor(rep(1:2, c(n, n)))"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" | g1 | g2 | g3 | g4 | g5 | g6 | g7 | g8 | g9 | g10 | ⋯ | g991 | g992 | g993 | g994 | g995 | g996 | g997 | g998 | g999 | g1000 |
|---|
\n",
"\n",
"\t| pt1 | -0.5604756 | -0.6947070 | 0.005764186 | 0.1176466 | 1.052711 | 2.1988103 | -0.7886220 | -1.6674751 | 0.2374303 | -0.2052993 | ⋯ | 0.3780725 | 1.974814 | -0.4535280 | -0.4552866 | -2.3004639 | -0.3804398 | 0.2870161 | -0.2018602 | -1.6727583 | 1.1379048 |
|---|
\n",
"\t| pt2 | -0.2301775 | -0.2079173 | 0.385280401 | -0.9474746 | -1.049177 | 1.3124130 | -0.5021987 | 0.7364960 | 1.2181086 | 0.6511933 | ⋯ | 0.5981352 | -1.021826 | -2.0371182 | 1.5636880 | -0.9501855 | 0.6671640 | -0.6702249 | 1.1181721 | -0.5414325 | 1.2684239 |
|---|
\n",
"\t| pt3 | 1.5587083 | -1.2653964 | -0.370660032 | -0.4905574 | -1.260155 | -0.2651451 | 1.4960607 | 0.3860266 | -1.3387743 | 0.2737665 | ⋯ | 0.5774870 | 0.853561 | -0.3030158 | -0.1434414 | -0.8478627 | 0.2413405 | -0.5417177 | 0.1625707 | 0.1995339 | 0.0427062 |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll}\n",
" & g1 & g2 & g3 & g4 & g5 & g6 & g7 & g8 & g9 & g10 & ⋯ & g991 & g992 & g993 & g994 & g995 & g996 & g997 & g998 & g999 & g1000\\\\\n",
"\\hline\n",
"\tpt1 & -0.5604756 & -0.6947070 & 0.005764186 & 0.1176466 & 1.052711 & 2.1988103 & -0.7886220 & -1.6674751 & 0.2374303 & -0.2052993 & ⋯ & 0.3780725 & 1.974814 & -0.4535280 & -0.4552866 & -2.3004639 & -0.3804398 & 0.2870161 & -0.2018602 & -1.6727583 & 1.1379048 \\\\\n",
"\tpt2 & -0.2301775 & -0.2079173 & 0.385280401 & -0.9474746 & -1.049177 & 1.3124130 & -0.5021987 & 0.7364960 & 1.2181086 & 0.6511933 & ⋯ & 0.5981352 & -1.021826 & -2.0371182 & 1.5636880 & -0.9501855 & 0.6671640 & -0.6702249 & 1.1181721 & -0.5414325 & 1.2684239 \\\\\n",
"\tpt3 & 1.5587083 & -1.2653964 & -0.370660032 & -0.4905574 & -1.260155 & -0.2651451 & 1.4960607 & 0.3860266 & -1.3387743 & 0.2737665 & ⋯ & 0.5774870 & 0.853561 & -0.3030158 & -0.1434414 & -0.8478627 & 0.2413405 & -0.5417177 & 0.1625707 & 0.1995339 & 0.0427062 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| | g1 | g2 | g3 | g4 | g5 | g6 | g7 | g8 | g9 | g10 | ⋯ | g991 | g992 | g993 | g994 | g995 | g996 | g997 | g998 | g999 | g1000 | \n",
"|---|---|---|\n",
"| pt1 | -0.5604756 | -0.6947070 | 0.005764186 | 0.1176466 | 1.052711 | 2.1988103 | -0.7886220 | -1.6674751 | 0.2374303 | -0.2052993 | ⋯ | 0.3780725 | 1.974814 | -0.4535280 | -0.4552866 | -2.3004639 | -0.3804398 | 0.2870161 | -0.2018602 | -1.6727583 | 1.1379048 | \n",
"| pt2 | -0.2301775 | -0.2079173 | 0.385280401 | -0.9474746 | -1.049177 | 1.3124130 | -0.5021987 | 0.7364960 | 1.2181086 | 0.6511933 | ⋯ | 0.5981352 | -1.021826 | -2.0371182 | 1.5636880 | -0.9501855 | 0.6671640 | -0.6702249 | 1.1181721 | -0.5414325 | 1.2684239 | \n",
"| pt3 | 1.5587083 | -1.2653964 | -0.370660032 | -0.4905574 | -1.260155 | -0.2651451 | 1.4960607 | 0.3860266 | -1.3387743 | 0.2737665 | ⋯ | 0.5774870 | 0.853561 | -0.3030158 | -0.1434414 | -0.8478627 | 0.2413405 | -0.5417177 | 0.1625707 | 0.1995339 | 0.0427062 | \n",
"\n",
"\n"
],
"text/plain": [
" g1 g2 g3 g4 g5 g6 \n",
"pt1 -0.5604756 -0.6947070 0.005764186 0.1176466 1.052711 2.1988103\n",
"pt2 -0.2301775 -0.2079173 0.385280401 -0.9474746 -1.049177 1.3124130\n",
"pt3 1.5587083 -1.2653964 -0.370660032 -0.4905574 -1.260155 -0.2651451\n",
" g7 g8 g9 g10 ⋯ g991 g992 \n",
"pt1 -0.7886220 -1.6674751 0.2374303 -0.2052993 ⋯ 0.3780725 1.974814\n",
"pt2 -0.5021987 0.7364960 1.2181086 0.6511933 ⋯ 0.5981352 -1.021826\n",
"pt3 1.4960607 0.3860266 -1.3387743 0.2737665 ⋯ 0.5774870 0.853561\n",
" g993 g994 g995 g996 g997 g998 \n",
"pt1 -0.4535280 -0.4552866 -2.3004639 -0.3804398 0.2870161 -0.2018602\n",
"pt2 -2.0371182 1.5636880 -0.9501855 0.6671640 -0.6702249 1.1181721\n",
"pt3 -0.3030158 -0.1434414 -0.8478627 0.2413405 -0.5417177 0.1625707\n",
" g999 g1000 \n",
"pt1 -1.6727583 1.1379048\n",
"pt2 -0.5414325 1.2684239\n",
"pt3 0.1995339 0.0427062"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"head(EXPRS, 3)"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [],
"source": [
"stats = abs(rowttests(t(EXPRS), grp)$statistic) "
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- 0.674624258566226
\n",
"\t- 0.741717473727548
\n",
"\t- 3.02542265710511
\n",
"
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 0.674624258566226\n",
"\\item 0.741717473727548\n",
"\\item 3.02542265710511\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 0.674624258566226\n",
"2. 0.741717473727548\n",
"3. 3.02542265710511\n",
"\n",
"\n"
],
"text/plain": [
"[1] 0.6746243 0.7417175 3.0254227"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"head(stats,3)"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [],
"source": [
"ii <- order(-stats)"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [],
"source": [
"TOPEXPRS <- EXPRS[, ii[1:10]]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Error Resubstitution (In-sample error)"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" grp\n",
"mod0 1 2\n",
" 1 17 0\n",
" 2 3 20"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mod0 = knn(train = TOPEXPRS, test = TOPEXPRS, cl = grp, k = 3) \n",
"table(mod0, grp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Optimistic Cross-validated predictions\n",
"\n",
"Note: Feature selection is not part of the CV process, and so the results are OVER-OPTIMISTIC"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" grp\n",
"mode1 1 2\n",
" 1 16 0\n",
" 2 4 20"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mode1 = knn.cv(TOPEXPRS, grp, k = 3) \n",
"table(mode1, grp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Cross-validation done right (fancy version)"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [],
"source": [
"suppressPackageStartupMessages(library(multtest))"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [],
"source": [
"top.features <- function(EXP, resp, test, fsnum) {\n",
" top.features.i <- function(i, EXP, resp, test, fsnum) {\n",
" stats <- abs(mt.teststat(EXP[, -i], resp[-i], test = test)) \n",
" ii <- order(-stats)[1:fsnum]\n",
" rownames(EXP)[ii]\n",
" }\n",
" sapply(1:ncol(EXP), top.features.i, \n",
" EXP = EXP, resp = resp, test = test, fsnum = fsnum)\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [],
"source": [
"# This function evaluates the knn\n",
"knn.loocv <- function(EXP, resp, test, k, fsnum, tabulate = FALSE, permute = FALSE) {\n",
" if (permute) {\n",
" resp = sample(resp)\n",
" }\n",
" topfeat = top.features(EXP, resp, test, fsnum) \n",
" pids = rownames(EXP)\n",
" EXP = t(EXP)\n",
" colnames(EXP) = as.character(pids)\n",
" knn.loocv.i = function(i, EXP, resp, k, topfeat) {\n",
" ii = topfeat[, i]\n",
" mod = knn(train = EXP[-i, ii], test = EXP[i, ii], cl = resp[-i], k = k)[1] }\n",
" out = sapply(1:nrow(EXP), knn.loocv.i, \n",
" EXP = EXP, resp = resp, k\n",
" = k, topfeat = topfeat) \n",
" if (tabulate)\n",
" out = ftable(pred = out, obs = resp) \n",
" return(out)\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Reminder of what the data look like"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" | g1 | g2 | g3 | g4 | g5 |
|---|
\n",
"\n",
"\t| pt1 | -0.56047565 | -0.6947070 | 0.005764186 | 0.1176466 | 1.0527115 |
|---|
\n",
"\t| pt2 | -0.23017749 | -0.2079173 | 0.385280401 | -0.9474746 | -1.0491770 |
|---|
\n",
"\t| pt3 | 1.55870831 | -1.2653964 | -0.370660032 | -0.4905574 | -1.2601552 |
|---|
\n",
"\t| pt4 | 0.07050839 | 2.1689560 | 0.644376549 | -0.2560922 | 3.2410399 |
|---|
\n",
"\t| pt5 | 0.12928774 | 1.2079620 | -0.220486562 | 1.8438620 | -0.4168576 |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|lllll}\n",
" & g1 & g2 & g3 & g4 & g5\\\\\n",
"\\hline\n",
"\tpt1 & -0.56047565 & -0.6947070 & 0.005764186 & 0.1176466 & 1.0527115 \\\\\n",
"\tpt2 & -0.23017749 & -0.2079173 & 0.385280401 & -0.9474746 & -1.0491770 \\\\\n",
"\tpt3 & 1.55870831 & -1.2653964 & -0.370660032 & -0.4905574 & -1.2601552 \\\\\n",
"\tpt4 & 0.07050839 & 2.1689560 & 0.644376549 & -0.2560922 & 3.2410399 \\\\\n",
"\tpt5 & 0.12928774 & 1.2079620 & -0.220486562 & 1.8438620 & -0.4168576 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| | g1 | g2 | g3 | g4 | g5 | \n",
"|---|---|---|---|---|\n",
"| pt1 | -0.56047565 | -0.6947070 | 0.005764186 | 0.1176466 | 1.0527115 | \n",
"| pt2 | -0.23017749 | -0.2079173 | 0.385280401 | -0.9474746 | -1.0491770 | \n",
"| pt3 | 1.55870831 | -1.2653964 | -0.370660032 | -0.4905574 | -1.2601552 | \n",
"| pt4 | 0.07050839 | 2.1689560 | 0.644376549 | -0.2560922 | 3.2410399 | \n",
"| pt5 | 0.12928774 | 1.2079620 | -0.220486562 | 1.8438620 | -0.4168576 | \n",
"\n",
"\n"
],
"text/plain": [
" g1 g2 g3 g4 g5 \n",
"pt1 -0.56047565 -0.6947070 0.005764186 0.1176466 1.0527115\n",
"pt2 -0.23017749 -0.2079173 0.385280401 -0.9474746 -1.0491770\n",
"pt3 1.55870831 -1.2653964 -0.370660032 -0.4905574 -1.2601552\n",
"pt4 0.07050839 2.1689560 0.644376549 -0.2560922 3.2410399\n",
"pt5 0.12928774 1.2079620 -0.220486562 1.8438620 -0.4168576"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"EXPRS[1:5, 1:5]"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- '1'
\n",
"\t- '2'
\n",
"
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item '1'\n",
"\\item '2'\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. '1'\n",
"2. '2'\n",
"\n",
"\n"
],
"text/plain": [
"[1] \"1\" \"2\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"levels(grp)"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" obs 1 2\n",
"pred \n",
"1 7 7\n",
"2 13 13"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"knn.loocv(t(EXPRS), grp, \"t.equalvar\", 3, 10, TRUE)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Cross-validation done right (simple version)"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [],
"source": [
"pred <- numeric(2*n)\n",
"for (i in 1:(2*n)) {\n",
" stats = abs(rowttests(t(EXPRS[-i,]), grp[-i])$statistic) \n",
" ii <- order(-stats)\n",
" TOPEXPRS <- EXPRS[-i, ii[1:10]]\n",
" pred[i] = knn(TOPEXPRS, EXPRS[i, ii[1:10]], grp[-i], k = 3) \n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" grp\n",
"pred 1 2\n",
" 1 7 7\n",
" 2 13 13"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"table(pred, grp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise\n",
"\n",
"- Repeat the last experiment with a noisy quantitative outcome\n",
"- First simulate a data matrix of dimension n = 50 (patients) and m (genes)\n",
"- Next draw the outcome for n=50 patients from a standard normal distribution independent of the data matrix\n",
"- There is no relationship between the expressions and the outcome (by design)\n",
"- We consider m=45 and m=50000\n",
"- We conduct Naive LOOCV using the top 10 features"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Data Generation"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [],
"source": [
"set.seed(123)\n",
"n <- 50\n",
"m <- 50000\n",
"EXPRS <- matrix(rnorm(n*m), n, m)\n",
"rownames(EXPRS) = paste(\"pt\", 1:n, sep = \"\") \n",
"colnames(EXPRS) = paste(\"g\", 1:m, sep = \"\")\n",
"OUTCOMES <- rnorm(n)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Proper cross-validation"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [],
"source": [
"pred0 <- numeric(n)\n",
"for (i in 1:n) {\n",
" \n",
" stats <- abs(cor(OUTCOMES[-i], EXPRS[-i,]))\n",
" ii <- order(-stats)\n",
" TOPEXPRS <- EXPRS[, ii[1:10]]\n",
" \n",
" data <- data.frame(y = OUTCOMES, x = I(TOPEXPRS))\n",
" model <- lm(y ~ x, data=data[-i,])\n",
" pred0[i] <- predict(model, data[i,])\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Naive cross-validation"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [],
"source": [
"stats <- abs(cor(OUTCOMES, EXPRS))\n",
"ii <- order(-stats)\n",
"TOPEXPRS <- EXPRS[, ii[1:10]]"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [],
"source": [
"pred <- numeric(n)\n",
"for (i in 1:n) {\n",
" data <- data.frame(y = OUTCOMES, x = I(TOPEXPRS))\n",
" model <- lm(y ~ x, data=data[-i,])\n",
" pred[i] <- predict(model, data[i,])\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
{
"ename": "ERROR",
"evalue": "Error in xy.coords(x, y): object 'pred.0' not found\n",
"output_type": "error",
"traceback": [
"Error in xy.coords(x, y): object 'pred.0' not found\nTraceback:\n",
"1. points(OUTCOMES, pred.0, pch = 4, col = \"blue\")",
"2. points.default(OUTCOMES, pred.0, pch = 4, col = \"blue\")",
"3. plot.xy(xy.coords(x, y), type = type, ...)",
"4. xy.coords(x, y)"
]
},
{
"data": {
"image/png": 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jIXQ8NO+MUCAOABvPCC/P21fPmdrtay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\nUKABAAAAAyjQAAAAgAEUaAAAAMCA/w8fKxtC6uP3zAAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(OUTCOMES, pred, col='red', xlab=\"Observed Values\", ylab=\"Predicted Values\")\n",
"points(OUTCOMES, pred.0, pch=4, col='blue')\n",
"abline(lm(pred ~ OUTCOMES), col='red')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
"version": "3.4.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}