9a234b9f6e3118c3cedaa586bc962d2cc826a609
[ou-jupyter-r-demo.git] / section5.1.ipynb
1 {
2 "cells": [
3 {
4 "cell_type": "markdown",
5 "metadata": {},
6 "source": [
7 "# Section 5.1: Using the model"
8 ]
9 },
10 {
11 "cell_type": "markdown",
12 "metadata": {},
13 "source": [
14 "### Imports and defintions"
15 ]
16 },
17 {
18 "cell_type": "code",
19 "execution_count": 25,
20 "metadata": {
21 "init_cell": true
22 },
23 "outputs": [],
24 "source": [
25 "library(tidyverse)\n",
26 "# library(cowplot)\n",
27 "library(repr)\n",
28 "library(ggfortify)\n",
29 "\n",
30 "# Change plot size to 4 x 3\n",
31 "options(repr.plot.width=6, repr.plot.height=4)"
32 ]
33 },
34 {
35 "cell_type": "code",
36 "execution_count": 26,
37 "metadata": {
38 "init_cell": true
39 },
40 "outputs": [],
41 "source": [
42 "# Multiple plot function\n",
43 "#\n",
44 "# ggplot objects can be passed in ..., or to plotlist (as a list of ggplot objects)\n",
45 "# - cols: Number of columns in layout\n",
46 "# - layout: A matrix specifying the layout. If present, 'cols' is ignored.\n",
47 "#\n",
48 "# If the layout is something like matrix(c(1,2,3,3), nrow=2, byrow=TRUE),\n",
49 "# then plot 1 will go in the upper left, 2 will go in the upper right, and\n",
50 "# 3 will go all the way across the bottom.\n",
51 "#\n",
52 "multiplot <- function(..., plotlist=NULL, file, cols=1, layout=NULL) {\n",
53 " library(grid)\n",
54 "\n",
55 " # Make a list from the ... arguments and plotlist\n",
56 " plots <- c(list(...), plotlist)\n",
57 "\n",
58 " numPlots = length(plots)\n",
59 "\n",
60 " # If layout is NULL, then use 'cols' to determine layout\n",
61 " if (is.null(layout)) {\n",
62 " # Make the panel\n",
63 " # ncol: Number of columns of plots\n",
64 " # nrow: Number of rows needed, calculated from # of cols\n",
65 " layout <- matrix(seq(1, cols * ceiling(numPlots/cols)),\n",
66 " ncol = cols, nrow = ceiling(numPlots/cols))\n",
67 " }\n",
68 "\n",
69 " if (numPlots==1) {\n",
70 " print(plots[[1]])\n",
71 "\n",
72 " } else {\n",
73 " # Set up the page\n",
74 " grid.newpage()\n",
75 " pushViewport(viewport(layout = grid.layout(nrow(layout), ncol(layout))))\n",
76 "\n",
77 " # Make each plot, in the correct location\n",
78 " for (i in 1:numPlots) {\n",
79 " # Get the i,j matrix positions of the regions that contain this subplot\n",
80 " matchidx <- as.data.frame(which(layout == i, arr.ind = TRUE))\n",
81 "\n",
82 " print(plots[[i]], vp = viewport(layout.pos.row = matchidx$row,\n",
83 " layout.pos.col = matchidx$col))\n",
84 " }\n",
85 " }\n",
86 "}"
87 ]
88 },
89 {
90 "cell_type": "code",
91 "execution_count": 27,
92 "metadata": {
93 "init_cell": true
94 },
95 "outputs": [],
96 "source": [
97 "# From https://sejohnston.com/2012/08/09/a-quick-and-easy-function-to-plot-lm-results-in-r/\n",
98 "ggplotRegression <- function (fit) {\n",
99 "\n",
100 "require(ggplot2)\n",
101 "\n",
102 "ggplot(fit$model, aes_string(x = names(fit$model)[2], y = names(fit$model)[1])) + \n",
103 " geom_point() +\n",
104 " stat_smooth(method = \"lm\", col = \"red\") +\n",
105 " labs(title = paste(\"Adj R2 = \",signif(summary(fit)$adj.r.squared, 5),\n",
106 " \"Intercept =\",signif(fit$coef[[1]],5 ),\n",
107 " \" Slope =\",signif(fit$coef[[2]], 5),\n",
108 " \" P =\",signif(summary(fit)$coef[2,4], 5))) + \n",
109 " theme(plot.title = element_text(size=12))\n",
110 "}"
111 ]
112 },
113 {
114 "cell_type": "markdown",
115 "metadata": {},
116 "source": [
117 "## Modelling abrasion loss\n",
118 "\n",
119 "This example concerns the dataset `rubber`, which you first met in Exercise 3.1. The experiment introduced in that exercise concerned an investigation of the resistance of rubber to abrasion (the abrasion loss) and how that resistance depended on various attributes of the rubber. In Exercise 3.1, the only explanatory variable we analysed was hardness; but in Exercise 3.19, a second explanatory variable, tensile strength, was taken into account too. There are 30 datapoints."
120 ]
121 },
122 {
123 "cell_type": "code",
124 "execution_count": 28,
125 "metadata": {
126 "scrolled": true
127 },
128 "outputs": [
129 {
130 "data": {
131 "text/html": [
132 "<table>\n",
133 "<thead><tr><th scope=col>loss</th><th scope=col>hardness</th><th scope=col>strength</th></tr></thead>\n",
134 "<tbody>\n",
135 "\t<tr><td>372</td><td>45 </td><td>162</td></tr>\n",
136 "\t<tr><td>206</td><td>55 </td><td>233</td></tr>\n",
137 "\t<tr><td>175</td><td>61 </td><td>232</td></tr>\n",
138 "\t<tr><td>154</td><td>66 </td><td>231</td></tr>\n",
139 "\t<tr><td>136</td><td>71 </td><td>231</td></tr>\n",
140 "\t<tr><td>112</td><td>71 </td><td>237</td></tr>\n",
141 "\t<tr><td> 55</td><td>81 </td><td>224</td></tr>\n",
142 "\t<tr><td> 45</td><td>86 </td><td>219</td></tr>\n",
143 "\t<tr><td>221</td><td>53 </td><td>203</td></tr>\n",
144 "\t<tr><td>166</td><td>60 </td><td>189</td></tr>\n",
145 "\t<tr><td>164</td><td>64 </td><td>210</td></tr>\n",
146 "\t<tr><td>113</td><td>68 </td><td>210</td></tr>\n",
147 "\t<tr><td> 82</td><td>79 </td><td>196</td></tr>\n",
148 "\t<tr><td> 32</td><td>81 </td><td>180</td></tr>\n",
149 "\t<tr><td>228</td><td>56 </td><td>200</td></tr>\n",
150 "\t<tr><td>196</td><td>68 </td><td>173</td></tr>\n",
151 "\t<tr><td>128</td><td>75 </td><td>188</td></tr>\n",
152 "\t<tr><td> 97</td><td>83 </td><td>161</td></tr>\n",
153 "\t<tr><td> 64</td><td>88 </td><td>119</td></tr>\n",
154 "\t<tr><td>249</td><td>59 </td><td>161</td></tr>\n",
155 "\t<tr><td>219</td><td>71 </td><td>151</td></tr>\n",
156 "\t<tr><td>186</td><td>80 </td><td>165</td></tr>\n",
157 "\t<tr><td>155</td><td>82 </td><td>151</td></tr>\n",
158 "\t<tr><td>114</td><td>89 </td><td>128</td></tr>\n",
159 "\t<tr><td>341</td><td>51 </td><td>161</td></tr>\n",
160 "\t<tr><td>340</td><td>59 </td><td>146</td></tr>\n",
161 "\t<tr><td>283</td><td>65 </td><td>148</td></tr>\n",
162 "\t<tr><td>267</td><td>74 </td><td>144</td></tr>\n",
163 "\t<tr><td>215</td><td>81 </td><td>134</td></tr>\n",
164 "\t<tr><td>148</td><td>86 </td><td>127</td></tr>\n",
165 "</tbody>\n",
166 "</table>\n"
167 ],
168 "text/latex": [
169 "\\begin{tabular}{r|lll}\n",
170 " loss & hardness & strength\\\\\n",
171 "\\hline\n",
172 "\t 372 & 45 & 162\\\\\n",
173 "\t 206 & 55 & 233\\\\\n",
174 "\t 175 & 61 & 232\\\\\n",
175 "\t 154 & 66 & 231\\\\\n",
176 "\t 136 & 71 & 231\\\\\n",
177 "\t 112 & 71 & 237\\\\\n",
178 "\t 55 & 81 & 224\\\\\n",
179 "\t 45 & 86 & 219\\\\\n",
180 "\t 221 & 53 & 203\\\\\n",
181 "\t 166 & 60 & 189\\\\\n",
182 "\t 164 & 64 & 210\\\\\n",
183 "\t 113 & 68 & 210\\\\\n",
184 "\t 82 & 79 & 196\\\\\n",
185 "\t 32 & 81 & 180\\\\\n",
186 "\t 228 & 56 & 200\\\\\n",
187 "\t 196 & 68 & 173\\\\\n",
188 "\t 128 & 75 & 188\\\\\n",
189 "\t 97 & 83 & 161\\\\\n",
190 "\t 64 & 88 & 119\\\\\n",
191 "\t 249 & 59 & 161\\\\\n",
192 "\t 219 & 71 & 151\\\\\n",
193 "\t 186 & 80 & 165\\\\\n",
194 "\t 155 & 82 & 151\\\\\n",
195 "\t 114 & 89 & 128\\\\\n",
196 "\t 341 & 51 & 161\\\\\n",
197 "\t 340 & 59 & 146\\\\\n",
198 "\t 283 & 65 & 148\\\\\n",
199 "\t 267 & 74 & 144\\\\\n",
200 "\t 215 & 81 & 134\\\\\n",
201 "\t 148 & 86 & 127\\\\\n",
202 "\\end{tabular}\n"
203 ],
204 "text/markdown": [
205 "\n",
206 "loss | hardness | strength | \n",
207 "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
208 "| 372 | 45 | 162 | \n",
209 "| 206 | 55 | 233 | \n",
210 "| 175 | 61 | 232 | \n",
211 "| 154 | 66 | 231 | \n",
212 "| 136 | 71 | 231 | \n",
213 "| 112 | 71 | 237 | \n",
214 "| 55 | 81 | 224 | \n",
215 "| 45 | 86 | 219 | \n",
216 "| 221 | 53 | 203 | \n",
217 "| 166 | 60 | 189 | \n",
218 "| 164 | 64 | 210 | \n",
219 "| 113 | 68 | 210 | \n",
220 "| 82 | 79 | 196 | \n",
221 "| 32 | 81 | 180 | \n",
222 "| 228 | 56 | 200 | \n",
223 "| 196 | 68 | 173 | \n",
224 "| 128 | 75 | 188 | \n",
225 "| 97 | 83 | 161 | \n",
226 "| 64 | 88 | 119 | \n",
227 "| 249 | 59 | 161 | \n",
228 "| 219 | 71 | 151 | \n",
229 "| 186 | 80 | 165 | \n",
230 "| 155 | 82 | 151 | \n",
231 "| 114 | 89 | 128 | \n",
232 "| 341 | 51 | 161 | \n",
233 "| 340 | 59 | 146 | \n",
234 "| 283 | 65 | 148 | \n",
235 "| 267 | 74 | 144 | \n",
236 "| 215 | 81 | 134 | \n",
237 "| 148 | 86 | 127 | \n",
238 "\n",
239 "\n"
240 ],
241 "text/plain": [
242 " loss hardness strength\n",
243 "1 372 45 162 \n",
244 "2 206 55 233 \n",
245 "3 175 61 232 \n",
246 "4 154 66 231 \n",
247 "5 136 71 231 \n",
248 "6 112 71 237 \n",
249 "7 55 81 224 \n",
250 "8 45 86 219 \n",
251 "9 221 53 203 \n",
252 "10 166 60 189 \n",
253 "11 164 64 210 \n",
254 "12 113 68 210 \n",
255 "13 82 79 196 \n",
256 "14 32 81 180 \n",
257 "15 228 56 200 \n",
258 "16 196 68 173 \n",
259 "17 128 75 188 \n",
260 "18 97 83 161 \n",
261 "19 64 88 119 \n",
262 "20 249 59 161 \n",
263 "21 219 71 151 \n",
264 "22 186 80 165 \n",
265 "23 155 82 151 \n",
266 "24 114 89 128 \n",
267 "25 341 51 161 \n",
268 "26 340 59 146 \n",
269 "27 283 65 148 \n",
270 "28 267 74 144 \n",
271 "29 215 81 134 \n",
272 "30 148 86 127 "
273 ]
274 },
275 "metadata": {},
276 "output_type": "display_data"
277 }
278 ],
279 "source": [
280 "rubber <- read.csv('rubber.csv')\n",
281 "rubber"
282 ]
283 },
284 {
285 "cell_type": "markdown",
286 "metadata": {},
287 "source": [
288 "The figures below show scatterplots of abrasion loss against hardness and of abrasion loss against strength. (A scatterplot of abrasion loss against hardness also appeared in Solution 3.1.) Figure (a) suggests a strong decreasing linear relationship of abrasion loss with hardness. Figure (b) is much less indicative of any strong dependence of abrasion loss on tensile strength."
289 ]
290 },
291 {
292 "cell_type": "code",
293 "execution_count": 29,
294 "metadata": {
295 "scrolled": false
296 },
297 "outputs": [
298 {
299 "data": {
300 "image/png": 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R3PUaEzucsxTBd6PnY56kjojSdrDf4J\nHYfQaRf6E+bzMbshdF0d5Vh0feMGrT/QRiF0+juFnTSh30KnsA5PrBRt10cgdPqF3jms9dGX\nTcJhO2s740yhQZYJbQChITQfCG2JQmghEBpCm0BoCoQWAaEhNB8IbYlCaCEQGkKbQGgKhBYB\noSE0HwhtiUJoIRAaQptAaAqEFgGhITQfCG2JQmghEBpCm0BoCoQWAaEhNB8IbYlCaCHpFHrH\njEkrOAkQmguE5uApoT/JU5SD++9JSPC90LsWbucGIXRWC730SO1GjWEJCT4XeufAxkrDbms5\nQQid1UI/yG6lOzohwedC99O+9lWJWyYInd1C99Bvdk7Y/Ppb6NUN2deemhiE0Fkt9GD98TUJ\nCf4W+kv9//jZxCCEzmqhFzfXVuyQhAR/Cz1XF/qtxCCEzmqhA5NOUNdr76KEBH8LHbhA8/n4\njYlBCJ3dQge2fz5hSSCw5737H50dm+BzoRf+TvX52M84QQid5UJrbL2I/mANjZnjM6FXfzwj\n2u+lx6F3vj3sdc7vM4S2tnNahN475cOVsoS0C60/2jTmF8tXQhff00hRWn1kTOJMYQrtnA6h\nJ7ZQlMYPSBLSLnQLJnTv6BxfCT1S+3bNFuqTGRZ6qyCas0J/20Rr/5fFGWkXuhETukt0jq+E\nZs+5VP6hT2ZS6PW9Dlfyni/mRXNWaP1kx9nijLQLfTb7yIejc3wl9EHs63XSJzMo9J4rtU8a\nyYvmrNBXs+Y/SpyRdqEnaZ+YtyE6x1dC57EWvVufzKDQE9knNdvBifpS6I+uPPHCN2xUuZ01\nyh/EGem/Hvrt05RG1yyImeEroZ/QGrTpPH0yg0Lrj6VX5nCifhT6Ze3b/k1SPZVZh2pZr4sz\nMnGB/4adcZO+Err4LrWTcOz7xmQGhTbebMG5xNxe6LVP9x/xCy/qWujw59NKJWFZO0uF3taM\nfd3ZwgyNj1sqSpOHJQm4YyXV49DLJkyNHnzIoNCLm2or+BJe1E7oL49SlzxyGifqRujyvmcQ\ncqOi/HZrBoSeof//PiepH63Z/i8n8y7VNYHQnr1j5dVD1PV7UiEvaiP0zpM0N07Ylhh1I/Q/\nle5krtL3sxb9MiD0d7rQL0nqF8ilewpdbAo9KnRg4aN3vcBx0l7oabockxKjboT+zY2EDD1k\nP7nztxkQevcJWpWbLJbUL5AjQrvdFHpVaHHURugJ4isA3Qjd5ElCrvw/QkY3yYDQgcmNaZVH\nS6qn1SwXhHa7KfSd0IW60PMSo26EPu0msv2gxwm5Iy8TQgfm923f43vvXZyUSMaFdrsp9J3Q\n+gU1PTlRN0I/ePA95zdcXTGm6S0ZEZriwavtEsm40G43hf4TeueDRystBnNOybgSuuyvDRo8\nSX5RTl0HoaW4FdrtptB/Qqts4UfdHYcuLSNk/8zypJsZQmssu+XkvO6xvV0bod1uCn0ptADP\nnlhh+FLotdoBnGNWRefYCO12U+hY6KKJI1+THOX3m9AZPbHC8KXQ+i0Ct0Xn2B6HdrcpdCr0\n6nPo+biJwrjfhM7oiRWGL4U+nwl9VnSOR0+sXKvV8wje8/w0/CZ0Rk+sMHwp9CVM6DbROd48\nsbK2AavoM6IEvwmd2RMrGr4Uehjz5J/ROd48sfKzfvriIVGC34TmHU3aN+aOWx7brG4gx/fp\n+WpNdAiho+y6mGpyXsxRVG+eWNnO7m9TxosS/CY072jSsEHL144qKCFje80v7DuGmEMIHcPu\nMV06PbsrZoZHT6wM0Xz+405R3G9Cc44m7c1fo/4qF0yv7PYTIYs67zeGEFqKgxMrqWwKnQpd\n9GBTpcH1y4RxvwnNOZpU/IHapsGuX63JV2eGOi42hmqo+huVNWWxlJOaMjk1FTYJJGyTEAza\nJISJTUKFbSVJud1n2MSDpIoOokcx7E+spLIpdH5iZfcv3Ms7dfwndO3mmdM3RSwzg6N6l83t\nTMcKZhpD9U9JW5U3RSUBlbA5ZntiJaVNIc4U6tgJ/XUbuo919tex82q/7f3QfjKnCx0vmGEM\n1T/VU1SWH4ilgtQckBOqtEkgYZuEYDB+etZfz2r/ZlnMjAixKaEyZJNQQyrkCeURmxLUX2g6\nKBMIndqmsLSHyuRQDCQkoVYelS8alkQj0qB80YgkGCbSqLTGhEWr+T4vbHTiE598OuKkRoXR\nefuH3DmrlpA1+ZXqD0jHQmPI/eGoj33oD7R+Tr+YOVmwD53apnBfe5V3amMgtRKIPOp80QS2\nfbcuklzBcuSLJlPjEF/o607ZSwe//uYv0Ya/78kKTdyu8wlZ3qnEGHpF6KLj2JGomdFZ2SB0\nSpvCxIb2xC7Hps7qV7jUuIPQk7scxw1lw2HHm7OWdpy1VCVA3hiwYeOgF4g59IjQxtO7n4zO\nygKh3W4KPSH0Tez0qH4M0JNCtzSEPs6cNTVf4wsSHtu752v0aJI+9IjQ83ShR0RnZYHQbjeF\nXhB6md7y/2WTnhT6ut9o7Vzy27/w4xzqW+g97P535YforCwQ2u2m0AtCG69q0W8S9aTQCxqd\n+NSnnz6d12hB1ggd+ES79fa+mDlZILTbTaEXhDbua32PTXpSaDJDexLn7/+XtM/1L3Rgzm0X\n5r8fOyMLhHa7KfSC0IFrNJ9P018O4E2hSWTjjOnrrUeTvC10AlkgtNtNoSeEXnO56vOZxpPd\nPCp0ykBoLnaH7VxuCj0hdCAw8/XPzCuyPCf0FXFAaCnuT6y42xR6ROhYILQAG6G3Pfznax9N\neJdxHFkhdMpAaB5Zv8ux9SztDJvUaI8LnY5fDp8JXZG7Qg9KuNkpEQgti3pO6KKnWilH3S14\nykzA70Kfy4S+QJbjcaHT0dB+EvohbY3eKIz7W+hzmNDnyXIgtCzqNaE36G/V+0KU4G+h9Ue6\nSF/UAqFlUa8J/T/F5tEK/hZ63Yn0y5/MfVG1AYSWRb0m9I+60MLXRPlb6MAv/dqcO0D6DhYI\nnVVCF7fWfD6S+wYsis+F9suJFXcN7SOhA7Nbqj43fU8Yh9AQWhb1nNCBTc8PGrFUHIbQEFoW\n9Z7QOX2mMAChKRBaB0JT0i307tf/9uA38QkQ2hKF0EI8J/RG7WzPv+ISILQlCqGFeE7oAnYg\nNe491VksdPHY7tcP3cSLQmgOPhS6GRO6T2xCFgutPZ2g1SpOFEJz8J/QRQ2Z0N1jE7JX6LfY\nt8nnRCE0B/8JHWCnupThsQnZK7S+A9WUE4XQHHwo9CR293PcFb3ZK3R3JnTj4sQohObgQ6ED\nE1o3PLTjkriE7BV6FBP6Uk4UQnPwo9CBwI49loTsFXrXedTnJrM4UQjNwZ9CJ5C9Qgc2DTzz\nxBtn86IQmkO9CF08vv/Aj6KTEFoETqxkhdA7r6Bb0a5mNwdCi4DQWSH0YNbP+bcxbSf0pk/e\n+UGe4VOhpz/Qb7TknUIQmkN9CK0fKL7GmLYR+qNj1eQOspdF+VToobSV8oQvAofQPOpD6JMt\nR6LkQi87UsvuLcvxpdBfs2b6c2Jk0bi3VwcgNJf6EPp6tqbMFwvJhR6un1kQvm414FOh72df\n/KCEx1Ld3VhRmo6G0FzqQ+g5TemKOna1MS0X+m79NuSVkhxfCj1A/+LrLPNfZLM/g9A86uWw\n3deXH9L0unnmpFzo0Wz9Hb5bkuNLoV9hXzzPOl9/WtVNEJpHPZ1YKYo9lScXekOetv6GyHJ8\nKfTuC7UvPsE6/3gm9OUQmkcWnCmc1Ubdgx5YJEvxpdCBdXe2bHzeBwmzL2JC3waheWSB0IE9\nq+Zulmf4U2h17dRyTqxM0Hw+dDaE5pENQuNMYTzPHqEorSbiKAcXe6E3jf33T7IECF3np763\nfT2LHsSE0BxshX7pUHX71pNzebmB54SeP/E769WjPhNaB0JzsBP6c9YDGSHO8JjQG+hpmzZz\nLAkQ2hJNUujiHyctskSzXOhbmNBnijM8JnRnrb5nWE6v+Vfo3T/zn/2aFqEX0SOH16+Pi2a5\n0FczoVuIM7wl9Ar99No78Qm+FfrxZopy2VxOMB1C72qjtWX86ymyXOg+zI+24gxvCT1D4e4j\n+VXoZ7QvewrnOTTpEHqS3piFsdEsF3rB4dpXmijO8JbQufULXXwM+7YjE4PpEHqM3pifxkaz\nXOjAt6cpylEvShK8JXTgr9oqOD039qE36Mb1TQymQ+gP9eIXxEa9JPQHvW8ZtSO+BvbHoasX\nzJZduek1oTdcp66Bc6xHzn0q9O5DmHEPJgbTIfRO7bWqliuy61joYGUsQRKKmeqpHa/YFZcR\njl8gERKxSaipsUmIEJuEYNgmIUxsalkVW8mlk+YcsCbUkGo6KDfbyR9CB25np8F/Tgym5SjH\nXPog13bxr1upY6GrDsRSQWqiExPZf3OPuIxQ5QE5JGyTEAzaJESITUJlyCahhlTIE8ojNiUE\nWcOUme3kE6G30PuNm73JCabnOHTRjLest3NqQhe+/BzvSSF1u8txC+8IHK7lcEhVWQy1ZRLC\nRBotlwRriDRaqf75ctSb63nBIKmULBoMSoKVRBatqCkre4ru6tyxPzFYTkLasNRt85pIhGbd\nJeXQuAwI7ZBgVQy1VRIiRBoNSoJhIo1WS4IhUiOJ1oQkwWoijYar9JdzPpMYDJKwNqxw27wm\nEqEfY9WIf0oahE5HQ/v21DcHdW11ZSadlRis012ObWfSWjT5Ni4DQqejoXNM6PZM6KMTg3V7\n2G717a2aX/V1fA0gdDoaOseEvpMJfVFiMAtOrEDoJBo6x4ReyN76MSkxCKEpEFqER4UOTDtd\nUY55lROE0BQILcKrQgcCi3/m3rUMoSkQWoR3hRYAoSkQWgSEhtCBwDevf5pwNRWEtkQhtBCP\nCb2WXt1w2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301 "text/plain": [
302 "plot without title"
303 ]
304 },
305 "metadata": {},
306 "output_type": "display_data"
307 }
308 ],
309 "source": [
310 "hardloss <- ggplot(rubber, aes(x=hardness, y=loss)) + geom_point()\n",
311 "strloss <- ggplot(rubber, aes(x=strength, y=loss)) + geom_point()\n",
312 "\n",
313 "multiplot(hardloss, strloss, cols=2)"
314 ]
315 },
316 {
317 "cell_type": "markdown",
318 "metadata": {},
319 "source": [
320 "In exercise 3.5(a) you obtained the following output for the regression of abrasion loss on hardness."
321 ]
322 },
323 {
324 "cell_type": "code",
325 "execution_count": 30,
326 "metadata": {},
327 "outputs": [
328 {
329 "data": {
330 "text/plain": [
331 "\n",
332 "Call:\n",
333 "lm(formula = loss ~ hardness, data = rubber)\n",
334 "\n",
335 "Residuals:\n",
336 " Min 1Q Median 3Q Max \n",
337 "-86.15 -46.77 -19.49 54.27 111.49 \n",
338 "\n",
339 "Coefficients:\n",
340 " Estimate Std. Error t value Pr(>|t|) \n",
341 "(Intercept) 550.4151 65.7867 8.367 4.22e-09 ***\n",
342 "hardness -5.3366 0.9229 -5.782 3.29e-06 ***\n",
343 "---\n",
344 "Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
345 "\n",
346 "Residual standard error: 60.52 on 28 degrees of freedom\n",
347 "Multiple R-squared: 0.5442,\tAdjusted R-squared: 0.5279 \n",
348 "F-statistic: 33.43 on 1 and 28 DF, p-value: 3.294e-06\n"
349 ]
350 },
351 "metadata": {},
352 "output_type": "display_data"
353 },
354 {
355 "data": {
356 "text/html": [
357 "<table>\n",
358 "<thead><tr><th></th><th scope=col>Df</th><th scope=col>Sum Sq</th><th scope=col>Mean Sq</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
359 "<tbody>\n",
360 "\t<tr><th scope=row>hardness</th><td> 1 </td><td>122455.0 </td><td>122455.037 </td><td>33.43276 </td><td>3.294489e-06</td></tr>\n",
361 "\t<tr><th scope=row>Residuals</th><td>28 </td><td>102556.3 </td><td> 3662.726 </td><td> NA </td><td> NA</td></tr>\n",
362 "</tbody>\n",
363 "</table>\n"
364 ],
365 "text/latex": [
366 "\\begin{tabular}{r|lllll}\n",
367 " & Df & Sum Sq & Mean Sq & F value & Pr(>F)\\\\\n",
368 "\\hline\n",
369 "\thardness & 1 & 122455.0 & 122455.037 & 33.43276 & 3.294489e-06\\\\\n",
370 "\tResiduals & 28 & 102556.3 & 3662.726 & NA & NA\\\\\n",
371 "\\end{tabular}\n"
372 ],
373 "text/markdown": [
374 "\n",
375 "| <!--/--> | Df | Sum Sq | Mean Sq | F value | Pr(>F) | \n",
376 "|---|---|\n",
377 "| hardness | 1 | 122455.0 | 122455.037 | 33.43276 | 3.294489e-06 | \n",
378 "| Residuals | 28 | 102556.3 | 3662.726 | NA | NA | \n",
379 "\n",
380 "\n"
381 ],
382 "text/plain": [
383 " Df Sum Sq Mean Sq F value Pr(>F) \n",
384 "hardness 1 122455.0 122455.037 33.43276 3.294489e-06\n",
385 "Residuals 28 102556.3 3662.726 NA NA"
386 ]
387 },
388 "metadata": {},
389 "output_type": "display_data"
390 }
391 ],
392 "source": [
393 "fit <- lm(loss ~ hardness, data = rubber)\n",
394 "summary(fit)\n",
395 "anova(fit)\n",
396 "# af <- anova(fit)\n",
397 "# afss <- af$\"Sum Sq\"\n",
398 "# print(cbind(af,PctExp=afss/sum(afss)*100))"
399 ]
400 },
401 {
402 "cell_type": "code",
403 "execution_count": 31,
404 "metadata": {},
405 "outputs": [
406 {
407 "data": {},
408 "metadata": {},
409 "output_type": "display_data"
410 },
411 {
412 "data": {
413 "image/png": 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MFKpfKLL76Ii4ubNGmSWCy22t7R/bla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\nSUVORK5CYII=",
414 "text/plain": [
415 "plot without title"
416 ]
417 },
418 "metadata": {},
419 "output_type": "display_data"
420 }
421 ],
422 "source": [
423 "ggplot(rubber, aes(x=hardness, y=loss)) + \n",
424 " geom_point() +\n",
425 " stat_smooth(method = \"lm\", col = \"red\")"
426 ]
427 },
428 {
429 "cell_type": "code",
430 "execution_count": 32,
431 "metadata": {},
432 "outputs": [
433 {
434 "data": {},
435 "metadata": {},
436 "output_type": "display_data"
437 },
438 {
439 "data": {
440 "image/png": 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MEHZ8+e1X+GxcSJE2fPnu3GIgEAADdB4PAYThrGIhKJVqxYsWLFCsfutp2Ijo4u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GjQpdulRy/z5XlWwELPxlHRb+4hUs/MU3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\nQmCC",
441 "text/plain": [
442 "plot without title"
443 ]
444 },
445 "metadata": {},
446 "output_type": "display_data"
447 }
448 ],
449 "source": [
450 "ggplotRegression(fit)"
451 ]
452 },
453 {
454 "cell_type": "markdown",
455 "metadata": {
456 "solution": "shown",
457 "solution2": "hidden",
458 "solution2_first": true,
459 "solution_first": true
460 },
461 "source": [
462 "### Exercise 5.1\n",
463 "Now repeat the for the regression of abrasion loss on tensile strength.\n",
464 "\n",
465 "Enter your solution in the cell below."
466 ]
467 },
468 {
469 "cell_type": "code",
470 "execution_count": 33,
471 "metadata": {},
472 "outputs": [],
473 "source": [
474 "# Your solution here"
475 ]
476 },
477 {
478 "cell_type": "markdown",
479 "metadata": {},
480 "source": [
481 "### Solution"
482 ]
483 },
484 {
485 "cell_type": "code",
486 "execution_count": 34,
487 "metadata": {
488 "solution2": "hidden"
489 },
490 "outputs": [
491 {
492 "data": {
493 "text/plain": [
494 "\n",
495 "Call:\n",
496 "lm(formula = loss ~ strength, data = rubber)\n",
497 "\n",
498 "Residuals:\n",
499 " Min 1Q Median 3Q Max \n",
500 "-155.640 -59.919 2.795 61.221 183.285 \n",
501 "\n",
502 "Coefficients:\n",
503 " Estimate Std. Error t value Pr(>|t|) \n",
504 "(Intercept) 305.2248 79.9962 3.815 0.000688 ***\n",
505 "strength -0.7192 0.4347 -1.654 0.109232 \n",
506 "---\n",
507 "Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
508 "\n",
509 "Residual standard error: 85.56 on 28 degrees of freedom\n",
510 "Multiple R-squared: 0.08904,\tAdjusted R-squared: 0.0565 \n",
511 "F-statistic: 2.737 on 1 and 28 DF, p-value: 0.1092\n"
512 ]
513 },
514 "metadata": {},
515 "output_type": "display_data"
516 },
517 {
518 "data": {
519 "text/html": [
520 "<table>\n",
521 "<thead><tr><th></th><th scope=col>Df</th><th scope=col>Sum Sq</th><th scope=col>Mean Sq</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
522 "<tbody>\n",
523 "\t<tr><th scope=row>strength</th><td> 1 </td><td> 20034.77</td><td>20034.772</td><td>2.736769 </td><td>0.1092317</td></tr>\n",
524 "\t<tr><th scope=row>Residuals</th><td>28 </td><td>204976.59</td><td> 7320.593</td><td> NA </td><td> NA</td></tr>\n",
525 "</tbody>\n",
526 "</table>\n"
527 ],
528 "text/latex": [
529 "\\begin{tabular}{r|lllll}\n",
530 " & Df & Sum Sq & Mean Sq & F value & Pr(>F)\\\\\n",
531 "\\hline\n",
532 "\tstrength & 1 & 20034.77 & 20034.772 & 2.736769 & 0.1092317\\\\\n",
533 "\tResiduals & 28 & 204976.59 & 7320.593 & NA & NA\\\\\n",
534 "\\end{tabular}\n"
535 ],
536 "text/markdown": [
537 "\n",
538 "| <!--/--> | Df | Sum Sq | Mean Sq | F value | Pr(>F) | \n",
539 "|---|---|\n",
540 "| strength | 1 | 20034.77 | 20034.772 | 2.736769 | 0.1092317 | \n",
541 "| Residuals | 28 | 204976.59 | 7320.593 | NA | NA | \n",
542 "\n",
543 "\n"
544 ],
545 "text/plain": [
546 " Df Sum Sq Mean Sq F value Pr(>F) \n",
547 "strength 1 20034.77 20034.772 2.736769 0.1092317\n",
548 "Residuals 28 204976.59 7320.593 NA NA"
549 ]
550 },
551 "metadata": {},
552 "output_type": "display_data"
553 }
554 ],
555 "source": [
556 "fit <- lm(loss ~ strength, data = rubber)\n",
557 "summary(fit)\n",
558 "anova(fit)"
559 ]
560 },
561 {
562 "cell_type": "code",
563 "execution_count": 35,
564 "metadata": {},
565 "outputs": [
566 {
567 "data": {},
568 "metadata": {},
569 "output_type": "display_data"
570 },
571 {
572 "data": {
573 "image/png": 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kPgAAAAAMEhcAAAAIDgEDgAAABAcAgcAAAAIDgEDgAAABAcAgcAAAAIDoEDAAAA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\nASznWhsY1T0PAAAAAElFTkSuQmCC",
574 "text/plain": [
575 "plot without title"
576 ]
577 },
578 "metadata": {},
579 "output_type": "display_data"
580 }
581 ],
582 "source": [
583 "ggplotRegression(fit)"
584 ]
585 },
586 {
587 "cell_type": "markdown",
588 "metadata": {
589 "solution2": "hidden"
590 },
591 "source": [
592 "Individually, then, regression of abrasion loss on hardness seems satisfactory, albeit accounting for a disappointingly small percentage of the variance in the response; regression of abrasion loss on tensile strength, on the other hand, seems to have very little explanatory power. "
593 ]
594 },
595 {
596 "cell_type": "markdown",
597 "metadata": {
598 "solution": "hidden"
599 },
600 "source": [
601 "### Multiple regression\n",
602 "However, back in Exercise 3.19 it was shown that the residuals from the former regression showed a clear relationship with the tensile strength values, and this suggested that a regression model involving both variables is necessary. \n",
603 "\n",
604 "Let us try it. The only change is to include `strength` in the equations being fitted in the `lm()` function. Instead of \n",
605 "\n",
606 "```\n",
607 "lm(loss ~ hardness, data = rubber)\n",
608 "```\n",
609 "use \n",
610 "```\n",
611 "lm(loss ~ hardness + strength, data = rubber)\n",
612 "```"
613 ]
614 },
615 {
616 "cell_type": "code",
617 "execution_count": 36,
618 "metadata": {},
619 "outputs": [
620 {
621 "data": {
622 "text/plain": [
623 "\n",
624 "Call:\n",
625 "lm(formula = loss ~ hardness + strength, data = rubber)\n",
626 "\n",
627 "Residuals:\n",
628 " Min 1Q Median 3Q Max \n",
629 "-79.385 -14.608 3.816 19.755 65.981 \n",
630 "\n",
631 "Coefficients:\n",
632 " Estimate Std. Error t value Pr(>|t|) \n",
633 "(Intercept) 885.1611 61.7516 14.334 3.84e-14 ***\n",
634 "hardness -6.5708 0.5832 -11.267 1.03e-11 ***\n",
635 "strength -1.3743 0.1943 -7.073 1.32e-07 ***\n",
636 "---\n",
637 "Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
638 "\n",
639 "Residual standard error: 36.49 on 27 degrees of freedom\n",
640 "Multiple R-squared: 0.8402,\tAdjusted R-squared: 0.8284 \n",
641 "F-statistic: 71 on 2 and 27 DF, p-value: 1.767e-11\n"
642 ]
643 },
644 "metadata": {},
645 "output_type": "display_data"
646 },
647 {
648 "data": {
649 "text/html": [
650 "<table>\n",
651 "<thead><tr><th></th><th scope=col>Df</th><th scope=col>Sum Sq</th><th scope=col>Mean Sq</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
652 "<tbody>\n",
653 "\t<tr><th scope=row>hardness</th><td> 1 </td><td>122455.04 </td><td>122455.037 </td><td>91.96967 </td><td>3.458255e-10</td></tr>\n",
654 "\t<tr><th scope=row>strength</th><td> 1 </td><td> 66606.59 </td><td> 66606.586 </td><td>50.02477 </td><td>1.324645e-07</td></tr>\n",
655 "\t<tr><th scope=row>Residuals</th><td>27 </td><td> 35949.74 </td><td> 1331.472 </td><td> NA </td><td> NA</td></tr>\n",
656 "</tbody>\n",
657 "</table>\n"
658 ],
659 "text/latex": [
660 "\\begin{tabular}{r|lllll}\n",
661 " & Df & Sum Sq & Mean Sq & F value & Pr(>F)\\\\\n",
662 "\\hline\n",
663 "\thardness & 1 & 122455.04 & 122455.037 & 91.96967 & 3.458255e-10\\\\\n",
664 "\tstrength & 1 & 66606.59 & 66606.586 & 50.02477 & 1.324645e-07\\\\\n",
665 "\tResiduals & 27 & 35949.74 & 1331.472 & NA & NA\\\\\n",
666 "\\end{tabular}\n"
667 ],
668 "text/markdown": [
669 "\n",
670 "| <!--/--> | Df | Sum Sq | Mean Sq | F value | Pr(>F) | \n",
671 "|---|---|---|\n",
672 "| hardness | 1 | 122455.04 | 122455.037 | 91.96967 | 3.458255e-10 | \n",
673 "| strength | 1 | 66606.59 | 66606.586 | 50.02477 | 1.324645e-07 | \n",
674 "| Residuals | 27 | 35949.74 | 1331.472 | NA | NA | \n",
675 "\n",
676 "\n"
677 ],
678 "text/plain": [
679 " Df Sum Sq Mean Sq F value Pr(>F) \n",
680 "hardness 1 122455.04 122455.037 91.96967 3.458255e-10\n",
681 "strength 1 66606.59 66606.586 50.02477 1.324645e-07\n",
682 "Residuals 27 35949.74 1331.472 NA NA"
683 ]
684 },
685 "metadata": {},
686 "output_type": "display_data"
687 }
688 ],
689 "source": [
690 "fit <- lm(loss ~ hardness + strength, data = rubber)\n",
691 "summary(fit)\n",
692 "anova(fit)"
693 ]
694 },
695 {
696 "cell_type": "code",
697 "execution_count": 37,
698 "metadata": {},
699 "outputs": [
700 {
701 "data": {},
702 "metadata": {},
703 "output_type": "display_data"
704 },
705 {
706 "data": {
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AR6/fvf/9aawuH06dPbtm1zVn0AAICxIHAwkcNih95JWtlsaPcy1dmzZ3ULz5w5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OQtMVvXpV9OolUSqDtmwJTk8XGU3Kc795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",
708 "text/plain": [
709 "plot without title"
710 ]
711 },
712 "metadata": {},
713 "output_type": "display_data"
714 }
715 ],
716 "source": [
717 "ggplotRegression(fit)"
718 ]
719 },
720 {
721 "cell_type": "markdown",
722 "metadata": {},
723 "source": [
724 "Looking at the regression coefficient output next, the estimated model for the mean response is\n",
725 "\n",
726 "$$ \\hat{y} = \\hat{\\alpha} + \\hat{\\beta}_1 x_1 + \\hat{\\beta}_2 x_2 = 885.2 − 6.571 x_1 − 1.374 x_2 $$ \n",
727 "\n",
728 "where $x_1$ and $x_2$ stand for values of hardness and tensile strength, respectively. \n",
729 "\n",
730 "Associated with each estimated parameter, GenStat gives a standard error (details of the calculation of which need not concern us now) and hence a _t_-statistic (estimate divided by standard error) to be compared with the distribution on `d.f. (Residual)`=27 degrees of freedom. GenStat makes the comparison and gives _p_ values, which in this case are all very small, suggesting strong evidence for the non-zeroness (and hence presence) of each parameter, $\\alpha$, $\\beta_1$ and $\\beta_2$, individually."
731 ]
732 },
733 {
734 "cell_type": "markdown",
735 "metadata": {},
736 "source": [
737 "So, even though the single regression of abrasion loss on tensile strength did not suggest a close relationship, when taken in conjunction with the effect of hardness the effect of tensile strength is also a considerable one. A key idea here is that $\\beta_1$ and $\\beta_2$ (and more generally $\\beta_1, \\beta_2, \\ldots , \\beta_k$ in model (5.1)) are partial regression coefficients. That is, $\\beta_1$ measures the effect of an increase of one unit in $x_1$ treating the value of the other variable $x_2$ as fixed. Contrast this with the single regression model $E(Y) = \\alpha + \\beta_1 x_1$ in which $\\beta_1$ represents an increase of one unit in $x_1$ treating $x_2$ as zero. The meaning of $\\beta_1$ in the regression models with one and two explanatory variables is not the same.\n",
738 "\n",
739 "You will notice that the percentage of variance accounted for has increased dramatically in the two-explanatory-variable model to a much more respectable 82.8%. This statistic has the same interpretation — or difficulty of interpretation — as for the case of one explanatory variable (see [Unit 3](unit3.ipynb)).\n",
740 "\n",
741 "Other items in the GenStat output are as for the case of one explanatory variable: the `Standard error of observations` is $\\hat{\\sigma}$, and is the square root of `m.s. (Residual)`; the message about standardised residuals will be clarified below; and the message about leverage will be ignored until [Unit 10](unit10.ipynb).\n",
742 "\n",
743 "The simple residuals are, again, defined as the differences between the observed and predicted responses:\n",
744 "\n",
745 "$$ r_i = y_i - \\left( \\hat{\\alpha} + \\sum_{j=1}^{k} \\hat{\\beta}_j x_{i, j} \\right) ,\\ i = 1, 2, \\ldots, n. $$\n",
746 "\n",
747 "GenStat can obtain these for you and produce a plot of residuals against fitted values. The fitted values are simply $\\hat{Y}_i = \\hat{\\alpha} + \\sum_{j=1}^{k} \\hat{\\beta}_j x_{i, j}$. As in the regression models in [Unit 3](unit3.ipynb), the default in GenStat is to use deviance residuals which, in this context, are equivalent to standardised residuals (simple residuals divided by their estimated standard errors)."
748 ]
749 },
750 {
751 "cell_type": "markdown",
752 "metadata": {},
753 "source": [
754 "## Gratuitous example of more complex maths markup\n",
755 "If \n",
756 "\n",
757 "$$ \\rho(z) = \\rho_c \\exp \\left( - \\frac{z^2}{2H^2} \\right) $$\n",
758 "\n",
759 "then\n",
760 "\n",
761 "\\begin{eqnarray*}\n",
762 "\\frac{\\partial \\rho(z)}{\\partial z} & = & \\rho_c \\frac{\\partial}{\\partial z}\\exp \n",
763 " \\left( - \\frac{z^2}{2H^2} \\right) \\\\\n",
764 "\t& = & \\rho_c \\exp \\left( - \\frac{z^2}{2H^2} \\right) \\cdot \n",
765 "\t \\frac{\\partial}{\\partial z} \\left( - \\frac{z^2}{2H^2} \\right) \\\\\n",
766 "\t& = & \\rho_c \\exp \\left( - \\frac{z^2}{2H^2} \\right) \\cdot \n",
767 "\t - \\frac{z}{H^2} \\\\\n",
768 "\t& = & - \\frac{z}{H^2} \\rho(z) \n",
769 "\\end{eqnarray*}"
770 ]
771 },
772 {
773 "cell_type": "markdown",
774 "metadata": {},
775 "source": [
776 "## Example 5.2\n",
777 "Something about plots of residuals..."
778 ]
779 },
780 {
781 "cell_type": "code",
782 "execution_count": 38,
783 "metadata": {},
784 "outputs": [
785 {
786 "data": {},
787 "metadata": {},
788 "output_type": "display_data"
789 },
790 {
791 "data": {
792 "image/png": 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LhWpCA6Fbm5uUVFRSqNjY2NMO8FAsEoVZqhywBeBKILc/DgQWVXokQi2bdvX6uq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\nEAgEAsEd6HBAIBAIBALBnf8F8z7wZ89es08AAAAASUVORK5CYII=",
793 "text/plain": [
794 "plot without title"
795 ]
796 },
797 "metadata": {},
798 "output_type": "display_data"
799 }
800 ],
801 "source": [
802 "fit <- lm(loss ~ hardness + strength, data = rubber)\n",
803 "autoplot(fit)"
804 ]
805 },
806 {
807 "cell_type": "markdown",
808 "metadata": {},
809 "source": [
810 "These plots are of just the same sort as those in [Unit 3](unit3.ipynb), and are interpreted in the same way. In this case, the normal plot and histogram show some slight suggestion of skewness in the residuals, but there is no obvious cause to doubt the model. In the regression output, GenStat flagged one of the points (number 19) as having a large standardised (i.e. deviance) residual. To decide which points to flag in this way, GenStat uses the same rules as described in [Units 3](unit3.ipynb) and [4](unit4.ipynb). In this case, it warned us about the most negative residual. However, the value of this standardised residual is not very large (at −2.38), and the plot of residuals against fitted values in Figure 5.2 makes it clear that this particular residual is not exceptionally large relative to some of the others, which are almost as large."
811 ]
812 },
813 {
814 "cell_type": "markdown",
815 "metadata": {},
816 "source": [
817 "### Exercise 5.2\n",
818 "The table below shows values for the first five datapoints, of 13, of a dataset concerned with predicting the heat evolved when cement sets via knowledge of its constituents. There are two explanatory variables, tricalcium aluminate (TA) and tricalcium silicate (TS), and the response variable is the heat generated in calories per gram (heat).\n",
819 "\n",
820 "heat | TA | TS\n",
821 "-----|----|-----\n",
822 "78.5 | 7 | 26\n",
823 "74.3 | 1 | 29\n",
824 "104.3 | 11 | 56\n",
825 "87.6 | 11 | 31\n",
826 "95.9 | 7 | 52\n",
827 " $\\vdots$ | $\\vdots$ | $\\vdots$\n"
828 ]
829 },
830 {
831 "cell_type": "markdown",
832 "metadata": {},
833 "source": [
834 "a. Load the `cemheat` dataset.\n",
835 "\n",
836 "b. Make scatterplots of heat against each of TA and TS in turn, and comment on what you see.\n",
837 "\n",
838 "c. Use GenStat to fit each individual regression equation (of heat on TA and of heat on TS) in turn, and then to fit the regression equation with two explanatory variables. Does the latter regression equation give you a better model than either of the individual ones?\n",
839 "\n",
840 "d. According to the regression equation with two explanatory variables fitted in part (b), what is the predicted value of heat when TA = 15 and TS = 55?\n",
841 "\n",
842 "e. By looking at the (default) composite residual plots, comment on the appropriateness of the fitted regression model.\n",
843 "\n",
844 "The solution is in the [Section 5.1 solutions](section5.1solutions.ipynb) notebook."
845 ]
846 },
847 {
848 "cell_type": "code",
849 "execution_count": 39,
850 "metadata": {},
851 "outputs": [],
852 "source": [
853 "# Your solution here"
854 ]
855 },
856 {
857 "cell_type": "markdown",
858 "metadata": {},
859 "source": [
860 "### Exercise 5.3: Fitting a quadratic regression model\n",
861 "In Unit 3, the dataset `anaerob` was briefly considered (Example 3.1) and swiftly dismissed as a candidate for simple linear regression modelling. The reason is clear from the figure below, in which the response variable, expired ventilation ($y$), is plotted against the single explanatory variable, oxygen uptake ($x$). (The same plot appeared as Figure 3.1 in Example 3.1.) A model quadratic in $x$, i.e. $E(Y) = \\alpha + \\beta x + \\gamma x^2$, was suggested instead."
862 ]
863 },
864 {
865 "cell_type": "code",
866 "execution_count": 40,
867 "metadata": {},
868 "outputs": [
869 {
870 "data": {},
871 "metadata": {},
872 "output_type": "display_data"
873 },
874 {
875 "data": {
876 "image/png": 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877 "text/plain": [
878 "plot without title"
879 ]
880 },
881 "metadata": {},
882 "output_type": "display_data"
883 }
884 ],
885 "source": [
886 "anaerobic <- read.csv('anaerob.csv')\n",
887 "ggplot(anaerobic, aes(x=oxygen, y=ventil)) + geom_point()"
888 ]
889 },
890 {
891 "cell_type": "markdown",
892 "metadata": {},
893 "source": [
894 "Since this quadratic model is nonetheless linear in its parameters, we can fit it using multiple regression of $y$ on $x$ plus the new variable $x^2$. Even though $x_1 = x$ and $x_2 = x^2$ are closely related, there is no immediate impediment to forgetting this and regressing on them in the usual way. A variable such as $x_2$ is sometimes called a derived variable.\n",
895 "\n",
896 "a. Using GenStat, perform the regression of expired ventilation (`ventil`) on oxygen uptake (`oxygen`). Are you at all surprised by how good this regression model seems?\n",
897 "\n",
898 "b. Now form a new variable `oxy2`, say, by squaring oxygen. (Create a new column in the `anearobic` dataframe which is `anaerobic$oxygen ^ 2`.) Perform the regression of ventil on `oxygen` and `oxy2`. Comment on the fit of this model according to the printed output (and with recourse to Figure 3.2 in Example 3.1).\n",
899 "\n",
900 "c. Make the usual residual plots and comment on the fit of the model again.\n",
901 "\n",
902 "The solution is in the [Section 5.1 solutions](section5.1solutions.ipynb) notebook."
903 ]
904 },
905 {
906 "cell_type": "code",
907 "execution_count": 41,
908 "metadata": {},
909 "outputs": [],
910 "source": [
911 "# Your solution here"
912 ]
913 },
914 {
915 "cell_type": "markdown",
916 "metadata": {},
917 "source": [
918 "## Next steps\n",
919 "Move to the next notebook, or go back to the course material, or something."
920 ]
921 },
922 {
923 "cell_type": "code",
924 "execution_count": null,
925 "metadata": {},
926 "outputs": [],
927 "source": []
928 }
929 ],
930 "metadata": {
931 "kernelspec": {
932 "display_name": "R",
933 "language": "R",
934 "name": "ir"
935 },
936 "language_info": {
937 "codemirror_mode": "r",
938 "file_extension": ".r",
939 "mimetype": "text/x-r-source",
940 "name": "R",
941 "pygments_lexer": "r",
942 "version": "3.4.2"
943 },
944 "toc": {
945 "nav_menu": {},
946 "number_sections": true,
947 "sideBar": true,
948 "skip_h1_title": false,
949 "title_cell": "Table of Contents",
950 "title_sidebar": "Contents",
951 "toc_cell": false,
952 "toc_position": {
953 "height": "calc(100% - 180px)",
954 "left": "10px",
955 "top": "150px",
956 "width": "342px"
957 },
958 "toc_section_display": true,
959 "toc_window_display": true
960 }
961 },
962 "nbformat": 4,
963 "nbformat_minor": 2
964 }