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     "heading_collapsed": true
  14    },
  15    "source": [
  16     "### Imports and defintions"
  17    ]
  18   },
  19   {
  20    "cell_type": "code",
  21    "execution_count": 35,
  22    "metadata": {
  23     "hidden": true
  24    },
  25    "outputs": [],
  26    "source": [
  27     "library(tidyverse)\n",
  28     "# library(cowplot)\n",
  29     "library(repr)\n",
  30     "library(ggfortify)\n",
  31     "\n",
  32     "# Change plot size to 4 x 3\n",
  33     "options(repr.plot.width=6, repr.plot.height=4)"
  34    ]
  35   },
  36   {
  37    "cell_type": "code",
  38    "execution_count": 36,
  39    "metadata": {
  40     "hidden": true
  41    },
  42    "outputs": [],
  43    "source": [
  44     "# Multiple plot function\n",
  45     "#\n",
  46     "# ggplot objects can be passed in ..., or to plotlist (as a list of ggplot objects)\n",
  47     "# - cols:   Number of columns in layout\n",
  48     "# - layout: A matrix specifying the layout. If present, 'cols' is ignored.\n",
  49     "#\n",
  50     "# If the layout is something like matrix(c(1,2,3,3), nrow=2, byrow=TRUE),\n",
  51     "# then plot 1 will go in the upper left, 2 will go in the upper right, and\n",
  52     "# 3 will go all the way across the bottom.\n",
  53     "#\n",
  54     "multiplot <- function(..., plotlist=NULL, file, cols=1, layout=NULL) {\n",
  55     "  library(grid)\n",
  56     "\n",
  57     "  # Make a list from the ... arguments and plotlist\n",
  58     "  plots <- c(list(...), plotlist)\n",
  59     "\n",
  60     "  numPlots = length(plots)\n",
  61     "\n",
  62     "  # If layout is NULL, then use 'cols' to determine layout\n",
  63     "  if (is.null(layout)) {\n",
  64     "    # Make the panel\n",
  65     "    # ncol: Number of columns of plots\n",
  66     "    # nrow: Number of rows needed, calculated from # of cols\n",
  67     "    layout <- matrix(seq(1, cols * ceiling(numPlots/cols)),\n",
  68     "                    ncol = cols, nrow = ceiling(numPlots/cols))\n",
  69     "  }\n",
  70     "\n",
  71     " if (numPlots==1) {\n",
  72     "    print(plots[[1]])\n",
  73     "\n",
  74     "  } else {\n",
  75     "    # Set up the page\n",
  76     "    grid.newpage()\n",
  77     "    pushViewport(viewport(layout = grid.layout(nrow(layout), ncol(layout))))\n",
  78     "\n",
  79     "    # Make each plot, in the correct location\n",
  80     "    for (i in 1:numPlots) {\n",
  81     "      # Get the i,j matrix positions of the regions that contain this subplot\n",
  82     "      matchidx <- as.data.frame(which(layout == i, arr.ind = TRUE))\n",
  83     "\n",
  84     "      print(plots[[i]], vp = viewport(layout.pos.row = matchidx$row,\n",
  85     "                                      layout.pos.col = matchidx$col))\n",
  86     "    }\n",
  87     "  }\n",
  88     "}"
  89    ]
  90   },
  91   {
  92    "cell_type": "markdown",
  93    "metadata": {},
  94    "source": [
  95     "## Modelling abrasion loss\n",
  96     "\n",
  97     "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."
  98    ]
  99   },
 100   {
 101    "cell_type": "code",
 102    "execution_count": 37,
 103    "metadata": {
 104     "scrolled": true
 105    },
 106    "outputs": [
 107     {
 108      "data": {
 109       "text/html": [
 110        "<table>\n",
 111        "<thead><tr><th scope=col>loss</th><th scope=col>hardness</th><th scope=col>strength</th></tr></thead>\n",
 112        "<tbody>\n",
 113        "\t<tr><td>372</td><td>45 </td><td>162</td></tr>\n",
 114        "\t<tr><td>206</td><td>55 </td><td>233</td></tr>\n",
 115        "\t<tr><td>175</td><td>61 </td><td>232</td></tr>\n",
 116        "\t<tr><td>154</td><td>66 </td><td>231</td></tr>\n",
 117        "\t<tr><td>136</td><td>71 </td><td>231</td></tr>\n",
 118        "\t<tr><td>112</td><td>71 </td><td>237</td></tr>\n",
 119        "\t<tr><td> 55</td><td>81 </td><td>224</td></tr>\n",
 120        "\t<tr><td> 45</td><td>86 </td><td>219</td></tr>\n",
 121        "\t<tr><td>221</td><td>53 </td><td>203</td></tr>\n",
 122        "\t<tr><td>166</td><td>60 </td><td>189</td></tr>\n",
 123        "\t<tr><td>164</td><td>64 </td><td>210</td></tr>\n",
 124        "\t<tr><td>113</td><td>68 </td><td>210</td></tr>\n",
 125        "\t<tr><td> 82</td><td>79 </td><td>196</td></tr>\n",
 126        "\t<tr><td> 32</td><td>81 </td><td>180</td></tr>\n",
 127        "\t<tr><td>228</td><td>56 </td><td>200</td></tr>\n",
 128        "\t<tr><td>196</td><td>68 </td><td>173</td></tr>\n",
 129        "\t<tr><td>128</td><td>75 </td><td>188</td></tr>\n",
 130        "\t<tr><td> 97</td><td>83 </td><td>161</td></tr>\n",
 131        "\t<tr><td> 64</td><td>88 </td><td>119</td></tr>\n",
 132        "\t<tr><td>249</td><td>59 </td><td>161</td></tr>\n",
 133        "\t<tr><td>219</td><td>71 </td><td>151</td></tr>\n",
 134        "\t<tr><td>186</td><td>80 </td><td>165</td></tr>\n",
 135        "\t<tr><td>155</td><td>82 </td><td>151</td></tr>\n",
 136        "\t<tr><td>114</td><td>89 </td><td>128</td></tr>\n",
 137        "\t<tr><td>341</td><td>51 </td><td>161</td></tr>\n",
 138        "\t<tr><td>340</td><td>59 </td><td>146</td></tr>\n",
 139        "\t<tr><td>283</td><td>65 </td><td>148</td></tr>\n",
 140        "\t<tr><td>267</td><td>74 </td><td>144</td></tr>\n",
 141        "\t<tr><td>215</td><td>81 </td><td>134</td></tr>\n",
 142        "\t<tr><td>148</td><td>86 </td><td>127</td></tr>\n",
 143        "</tbody>\n",
 144        "</table>\n"
 145       ],
 146       "text/latex": [
 147        "\\begin{tabular}{r|lll}\n",
 148        " loss & hardness & strength\\\\\n",
 149        "\\hline\n",
 150        "\t 372 & 45  & 162\\\\\n",
 151        "\t 206 & 55  & 233\\\\\n",
 152        "\t 175 & 61  & 232\\\\\n",
 153        "\t 154 & 66  & 231\\\\\n",
 154        "\t 136 & 71  & 231\\\\\n",
 155        "\t 112 & 71  & 237\\\\\n",
 156        "\t  55 & 81  & 224\\\\\n",
 157        "\t  45 & 86  & 219\\\\\n",
 158        "\t 221 & 53  & 203\\\\\n",
 159        "\t 166 & 60  & 189\\\\\n",
 160        "\t 164 & 64  & 210\\\\\n",
 161        "\t 113 & 68  & 210\\\\\n",
 162        "\t  82 & 79  & 196\\\\\n",
 163        "\t  32 & 81  & 180\\\\\n",
 164        "\t 228 & 56  & 200\\\\\n",
 165        "\t 196 & 68  & 173\\\\\n",
 166        "\t 128 & 75  & 188\\\\\n",
 167        "\t  97 & 83  & 161\\\\\n",
 168        "\t  64 & 88  & 119\\\\\n",
 169        "\t 249 & 59  & 161\\\\\n",
 170        "\t 219 & 71  & 151\\\\\n",
 171        "\t 186 & 80  & 165\\\\\n",
 172        "\t 155 & 82  & 151\\\\\n",
 173        "\t 114 & 89  & 128\\\\\n",
 174        "\t 341 & 51  & 161\\\\\n",
 175        "\t 340 & 59  & 146\\\\\n",
 176        "\t 283 & 65  & 148\\\\\n",
 177        "\t 267 & 74  & 144\\\\\n",
 178        "\t 215 & 81  & 134\\\\\n",
 179        "\t 148 & 86  & 127\\\\\n",
 180        "\\end{tabular}\n"
 181       ],
 182       "text/markdown": [
 183        "\n",
 184        "loss | hardness | strength | \n",
 185        "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
 186        "| 372 | 45  | 162 | \n",
 187        "| 206 | 55  | 233 | \n",
 188        "| 175 | 61  | 232 | \n",
 189        "| 154 | 66  | 231 | \n",
 190        "| 136 | 71  | 231 | \n",
 191        "| 112 | 71  | 237 | \n",
 192        "|  55 | 81  | 224 | \n",
 193        "|  45 | 86  | 219 | \n",
 194        "| 221 | 53  | 203 | \n",
 195        "| 166 | 60  | 189 | \n",
 196        "| 164 | 64  | 210 | \n",
 197        "| 113 | 68  | 210 | \n",
 198        "|  82 | 79  | 196 | \n",
 199        "|  32 | 81  | 180 | \n",
 200        "| 228 | 56  | 200 | \n",
 201        "| 196 | 68  | 173 | \n",
 202        "| 128 | 75  | 188 | \n",
 203        "|  97 | 83  | 161 | \n",
 204        "|  64 | 88  | 119 | \n",
 205        "| 249 | 59  | 161 | \n",
 206        "| 219 | 71  | 151 | \n",
 207        "| 186 | 80  | 165 | \n",
 208        "| 155 | 82  | 151 | \n",
 209        "| 114 | 89  | 128 | \n",
 210        "| 341 | 51  | 161 | \n",
 211        "| 340 | 59  | 146 | \n",
 212        "| 283 | 65  | 148 | \n",
 213        "| 267 | 74  | 144 | \n",
 214        "| 215 | 81  | 134 | \n",
 215        "| 148 | 86  | 127 | \n",
 216        "\n",
 217        "\n"
 218       ],
 219       "text/plain": [
 220        "   loss hardness strength\n",
 221        "1  372  45       162     \n",
 222        "2  206  55       233     \n",
 223        "3  175  61       232     \n",
 224        "4  154  66       231     \n",
 225        "5  136  71       231     \n",
 226        "6  112  71       237     \n",
 227        "7   55  81       224     \n",
 228        "8   45  86       219     \n",
 229        "9  221  53       203     \n",
 230        "10 166  60       189     \n",
 231        "11 164  64       210     \n",
 232        "12 113  68       210     \n",
 233        "13  82  79       196     \n",
 234        "14  32  81       180     \n",
 235        "15 228  56       200     \n",
 236        "16 196  68       173     \n",
 237        "17 128  75       188     \n",
 238        "18  97  83       161     \n",
 239        "19  64  88       119     \n",
 240        "20 249  59       161     \n",
 241        "21 219  71       151     \n",
 242        "22 186  80       165     \n",
 243        "23 155  82       151     \n",
 244        "24 114  89       128     \n",
 245        "25 341  51       161     \n",
 246        "26 340  59       146     \n",
 247        "27 283  65       148     \n",
 248        "28 267  74       144     \n",
 249        "29 215  81       134     \n",
 250        "30 148  86       127     "
 251       ]
 252      },
 253      "metadata": {},
 254      "output_type": "display_data"
 255     }
 256    ],
 257    "source": [
 258     "rubber <- read.csv('rubber.csv')\n",
 259     "rubber"
 260    ]
 261   },
 262   {
 263    "cell_type": "markdown",
 264    "metadata": {},
 265    "source": [
 266     "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."
 267    ]
 268   },
 269   {
 270    "cell_type": "code",
 271    "execution_count": 38,
 272    "metadata": {
 273     "scrolled": false
 274    },
 275    "outputs": [
 276     {
 277      "data": {
 278       "image/png": 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R3PUaEzucsxTBd6PnY56kjojSdrDf4J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\nCb2WXt1w2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YDieLzsnXeNHRpzrv8ZDi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\nGvgKCA18BYQGvuL/Ad6D8+SrqQ5UAAAAAElFTkSuQmCC",
 279       "text/plain": [
 280        "plot without title"
 281       ]
 282      },
 283      "metadata": {},
 284      "output_type": "display_data"
 285     }
 286    ],
 287    "source": [
 288     "hardloss <- ggplot(rubber, aes(x=hardness, y=loss)) + geom_point()\n",
 289     "strloss <-  ggplot(rubber, aes(x=strength, y=loss)) + geom_point()\n",
 290     "\n",
 291     "multiplot(hardloss, strloss, cols=2)"
 292    ]
 293   },
 294   {
 295    "cell_type": "markdown",
 296    "metadata": {},
 297    "source": [
 298     "In exercise 3.5(a) you obtained the following output for the regression of abrasion loss on hardness."
 299    ]
 300   },
 301   {
 302    "cell_type": "code",
 303    "execution_count": 39,
 304    "metadata": {},
 305    "outputs": [
 306     {
 307      "data": {
 308       "text/plain": [
 309        "\n",
 310        "Call:\n",
 311        "lm(formula = loss ~ hardness, data = rubber)\n",
 312        "\n",
 313        "Residuals:\n",
 314        "   Min     1Q Median     3Q    Max \n",
 315        "-86.15 -46.77 -19.49  54.27 111.49 \n",
 316        "\n",
 317        "Coefficients:\n",
 318        "            Estimate Std. Error t value Pr(>|t|)    \n",
 319        "(Intercept) 550.4151    65.7867   8.367 4.22e-09 ***\n",
 320        "hardness     -5.3366     0.9229  -5.782 3.29e-06 ***\n",
 321        "---\n",
 322        "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
 323        "\n",
 324        "Residual standard error: 60.52 on 28 degrees of freedom\n",
 325        "Multiple R-squared:  0.5442,\tAdjusted R-squared:  0.5279 \n",
 326        "F-statistic: 33.43 on 1 and 28 DF,  p-value: 3.294e-06\n"
 327       ]
 328      },
 329      "metadata": {},
 330      "output_type": "display_data"
 331     },
 332     {
 333      "data": {
 334       "text/html": [
 335        "<table>\n",
 336        "<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",
 337        "<tbody>\n",
 338        "\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",
 339        "\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",
 340        "</tbody>\n",
 341        "</table>\n"
 342       ],
 343       "text/latex": [
 344        "\\begin{tabular}{r|lllll}\n",
 345        "  & Df & Sum Sq & Mean Sq & F value & Pr(>F)\\\\\n",
 346        "\\hline\n",
 347        "\thardness &  1           & 122455.0     & 122455.037   & 33.43276     & 3.294489e-06\\\\\n",
 348        "\tResiduals & 28           & 102556.3     &   3662.726   &       NA     &           NA\\\\\n",
 349        "\\end{tabular}\n"
 350       ],
 351       "text/markdown": [
 352        "\n",
 353        "| <!--/--> | Df | Sum Sq | Mean Sq | F value | Pr(>F) | \n",
 354        "|---|---|\n",
 355        "| hardness |  1           | 122455.0     | 122455.037   | 33.43276     | 3.294489e-06 | \n",
 356        "| Residuals | 28           | 102556.3     |   3662.726   |       NA     |           NA | \n",
 357        "\n",
 358        "\n"
 359       ],
 360       "text/plain": [
 361        "          Df Sum Sq   Mean Sq    F value  Pr(>F)      \n",
 362        "hardness   1 122455.0 122455.037 33.43276 3.294489e-06\n",
 363        "Residuals 28 102556.3   3662.726       NA           NA"
 364       ]
 365      },
 366      "metadata": {},
 367      "output_type": "display_data"
 368     }
 369    ],
 370    "source": [
 371     "fit <- lm(loss ~ hardness, data = rubber)\n",
 372     "summary(fit)\n",
 373     "anova(fit)\n",
 374     "# af <- anova(fit)\n",
 375     "# afss <- af$\"Sum Sq\"\n",
 376     "# print(cbind(af,PctExp=afss/sum(afss)*100))"
 377    ]
 378   },
 379   {
 380    "cell_type": "markdown",
 381    "metadata": {
 382     "solution": "shown",
 383     "solution2": "hidden",
 384     "solution2_first": true,
 385     "solution_first": true
 386    },
 387    "source": [
 388     "### Exercise 5.1\n",
 389     "Now repeat the for the regression of abrasion loss on tensile strength.\n",
 390     "\n",
 391     "Enter your solution in the cell below."
 392    ]
 393   },
 394   {
 395    "cell_type": "code",
 396    "execution_count": null,
 397    "metadata": {},
 398    "outputs": [],
 399    "source": [
 400     "# Your solution here"
 401    ]
 402   },
 403   {
 404    "cell_type": "markdown",
 405    "metadata": {},
 406    "source": [
 407     "### Solution"
 408    ]
 409   },
 410   {
 411    "cell_type": "code",
 412    "execution_count": 40,
 413    "metadata": {
 414     "solution2": "hidden"
 415    },
 416    "outputs": [
 417     {
 418      "data": {
 419       "text/plain": [
 420        "\n",
 421        "Call:\n",
 422        "lm(formula = loss ~ strength, data = rubber)\n",
 423        "\n",
 424        "Residuals:\n",
 425        "     Min       1Q   Median       3Q      Max \n",
 426        "-155.640  -59.919    2.795   61.221  183.285 \n",
 427        "\n",
 428        "Coefficients:\n",
 429        "            Estimate Std. Error t value Pr(>|t|)    \n",
 430        "(Intercept) 305.2248    79.9962   3.815 0.000688 ***\n",
 431        "strength     -0.7192     0.4347  -1.654 0.109232    \n",
 432        "---\n",
 433        "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
 434        "\n",
 435        "Residual standard error: 85.56 on 28 degrees of freedom\n",
 436        "Multiple R-squared:  0.08904,\tAdjusted R-squared:  0.0565 \n",
 437        "F-statistic: 2.737 on 1 and 28 DF,  p-value: 0.1092\n"
 438       ]
 439      },
 440      "metadata": {},
 441      "output_type": "display_data"
 442     },
 443     {
 444      "data": {
 445       "text/html": [
 446        "<table>\n",
 447        "<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",
 448        "<tbody>\n",
 449        "\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",
 450        "\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",
 451        "</tbody>\n",
 452        "</table>\n"
 453       ],
 454       "text/latex": [
 455        "\\begin{tabular}{r|lllll}\n",
 456        "  & Df & Sum Sq & Mean Sq & F value & Pr(>F)\\\\\n",
 457        "\\hline\n",
 458        "\tstrength &  1        &  20034.77 & 20034.772 & 2.736769  & 0.1092317\\\\\n",
 459        "\tResiduals & 28        & 204976.59 &  7320.593 &       NA  &        NA\\\\\n",
 460        "\\end{tabular}\n"
 461       ],
 462       "text/markdown": [
 463        "\n",
 464        "| <!--/--> | Df | Sum Sq | Mean Sq | F value | Pr(>F) | \n",
 465        "|---|---|\n",
 466        "| strength |  1        |  20034.77 | 20034.772 | 2.736769  | 0.1092317 | \n",
 467        "| Residuals | 28        | 204976.59 |  7320.593 |       NA  |        NA | \n",
 468        "\n",
 469        "\n"
 470       ],
 471       "text/plain": [
 472        "          Df Sum Sq    Mean Sq   F value  Pr(>F)   \n",
 473        "strength   1  20034.77 20034.772 2.736769 0.1092317\n",
 474        "Residuals 28 204976.59  7320.593       NA        NA"
 475       ]
 476      },
 477      "metadata": {},
 478      "output_type": "display_data"
 479     }
 480    ],
 481    "source": [
 482     "fit <- lm(loss ~ strength, data = rubber)\n",
 483     "summary(fit)\n",
 484     "anova(fit)"
 485    ]
 486   },
 487   {
 488    "cell_type": "markdown",
 489    "metadata": {
 490     "solution2": "hidden"
 491    },
 492    "source": [
 493     "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. "
 494    ]
 495   },
 496   {
 497    "cell_type": "markdown",
 498    "metadata": {
 499     "solution": "hidden"
 500    },
 501    "source": [
 502     "### Multiple regression\n",
 503     "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",
 504     "\n",
 505     "Let us try it. The only change is to include `strength` in the equations being fitted in the `lm()` function. Instead of \n",
 506     "\n",
 507     "```\n",
 508     "lm(loss ~ hardness, data = rubber)\n",
 509     "```\n",
 510     "use \n",
 511     "```\n",
 512     "lm(loss ~ hardness + strength, data = rubber)\n",
 513     "```"
 514    ]
 515   },
 516   {
 517    "cell_type": "code",
 518    "execution_count": 41,
 519    "metadata": {},
 520    "outputs": [
 521     {
 522      "data": {
 523       "text/plain": [
 524        "\n",
 525        "Call:\n",
 526        "lm(formula = loss ~ hardness + strength, data = rubber)\n",
 527        "\n",
 528        "Residuals:\n",
 529        "    Min      1Q  Median      3Q     Max \n",
 530        "-79.385 -14.608   3.816  19.755  65.981 \n",
 531        "\n",
 532        "Coefficients:\n",
 533        "            Estimate Std. Error t value Pr(>|t|)    \n",
 534        "(Intercept) 885.1611    61.7516  14.334 3.84e-14 ***\n",
 535        "hardness     -6.5708     0.5832 -11.267 1.03e-11 ***\n",
 536        "strength     -1.3743     0.1943  -7.073 1.32e-07 ***\n",
 537        "---\n",
 538        "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
 539        "\n",
 540        "Residual standard error: 36.49 on 27 degrees of freedom\n",
 541        "Multiple R-squared:  0.8402,\tAdjusted R-squared:  0.8284 \n",
 542        "F-statistic:    71 on 2 and 27 DF,  p-value: 1.767e-11\n"
 543       ]
 544      },
 545      "metadata": {},
 546      "output_type": "display_data"
 547     },
 548     {
 549      "data": {
 550       "text/html": [
 551        "<table>\n",
 552        "<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",
 553        "<tbody>\n",
 554        "\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",
 555        "\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",
 556        "\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",
 557        "</tbody>\n",
 558        "</table>\n"
 559       ],
 560       "text/latex": [
 561        "\\begin{tabular}{r|lllll}\n",
 562        "  & Df & Sum Sq & Mean Sq & F value & Pr(>F)\\\\\n",
 563        "\\hline\n",
 564        "\thardness &  1           & 122455.04    & 122455.037   & 91.96967     & 3.458255e-10\\\\\n",
 565        "\tstrength &  1           &  66606.59    &  66606.586   & 50.02477     & 1.324645e-07\\\\\n",
 566        "\tResiduals & 27           &  35949.74    &   1331.472   &       NA     &           NA\\\\\n",
 567        "\\end{tabular}\n"
 568       ],
 569       "text/markdown": [
 570        "\n",
 571        "| <!--/--> | Df | Sum Sq | Mean Sq | F value | Pr(>F) | \n",
 572        "|---|---|---|\n",
 573        "| hardness |  1           | 122455.04    | 122455.037   | 91.96967     | 3.458255e-10 | \n",
 574        "| strength |  1           |  66606.59    |  66606.586   | 50.02477     | 1.324645e-07 | \n",
 575        "| Residuals | 27           |  35949.74    |   1331.472   |       NA     |           NA | \n",
 576        "\n",
 577        "\n"
 578       ],
 579       "text/plain": [
 580        "          Df Sum Sq    Mean Sq    F value  Pr(>F)      \n",
 581        "hardness   1 122455.04 122455.037 91.96967 3.458255e-10\n",
 582        "strength   1  66606.59  66606.586 50.02477 1.324645e-07\n",
 583        "Residuals 27  35949.74   1331.472       NA           NA"
 584       ]
 585      },
 586      "metadata": {},
 587      "output_type": "display_data"
 588     }
 589    ],
 590    "source": [
 591     "fit <- lm(loss ~ hardness + strength, data = rubber)\n",
 592     "summary(fit)\n",
 593     "anova(fit)"
 594    ]
 595   },
 596   {
 597    "cell_type": "markdown",
 598    "metadata": {},
 599    "source": [
 600     "Looking at the regression coefficient output next, the estimated model for the mean response is\n",
 601     "\n",
 602     "$$ \\hat{y} = \\hat{\\alpha} + \\hat{\\beta}_1 x_1 + \\hat{\\beta}_2 x_2 = 885.2 − 6.571 x_1 − 1.374 x_2 $$ \n",
 603     "\n",
 604     "where $x_1$ and $x_2$ stand for values of hardness and tensile strength, respectively. \n",
 605     "\n",
 606     "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."
 607    ]
 608   },
 609   {
 610    "cell_type": "markdown",
 611    "metadata": {},
 612    "source": [
 613     "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",
 614     "\n",
 615     "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",
 616     "\n",
 617     "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",
 618     "\n",
 619     "The simple residuals are, again, defined as the differences between the observed and predicted responses:\n",
 620     "\n",
 621     "$$ r_i = y_i - \\left( \\hat{\\alpha} + \\sum_{j=1}^{k} \\hat{\\beta}_j x_{i, j} \\right) ,\\ i = 1, 2, \\ldots, n. $$\n",
 622     "\n",
 623     "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)."
 624    ]
 625   },
 626   {
 627    "cell_type": "markdown",
 628    "metadata": {},
 629    "source": [
 630     "## Gratuitous example of more complex maths markup\n",
 631     "If \n",
 632     "\n",
 633     "$$ \\rho(z) = \\rho_c \\exp \\left( - \\frac{z^2}{2H^2} \\right) $$\n",
 634     "\n",
 635     "then\n",
 636     "\n",
 637     "\\begin{eqnarray*}\n",
 638     "\\frac{\\partial \\rho(z)}{\\partial z} & = & \\rho_c \\frac{\\partial}{\\partial z}\\exp \n",
 639     "                 \\left( - \\frac{z^2}{2H^2} \\right) \\\\\n",
 640     "\t& = & \\rho_c \\exp \\left( - \\frac{z^2}{2H^2} \\right) \\cdot \n",
 641     "\t             \\frac{\\partial}{\\partial z}  \\left( - \\frac{z^2}{2H^2} \\right) \\\\\n",
 642     "\t& = &  \\rho_c \\exp \\left( - \\frac{z^2}{2H^2} \\right) \\cdot \n",
 643     "\t             - \\frac{z}{H^2} \\\\\n",
 644     "\t& = & - \\frac{z}{H^2} \\rho(z) \n",
 645     "\\end{eqnarray*}"
 646    ]
 647   },
 648   {
 649    "cell_type": "markdown",
 650    "metadata": {},
 651    "source": [
 652     "## Example 5.2\n",
 653     "Something about plots of residuals..."
 654    ]
 655   },
 656   {
 657    "cell_type": "code",
 658    "execution_count": 42,
 659    "metadata": {},
 660    "outputs": [
 661     {
 662      "data": {},
 663      "metadata": {},
 664      "output_type": "display_data"
 665     },
 666     {
 667      "data": {
 668       "image/png": 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g/HZ599BgAwNjaeOXPmzJkzXVxcBALB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\nEAgEAsEd6HBAIBAIBALBnf8F8z7wZ89es08AAAAASUVORK5CYII=",
 669       "text/plain": [
 670        "plot without title"
 671       ]
 672      },
 673      "metadata": {},
 674      "output_type": "display_data"
 675     }
 676    ],
 677    "source": [
 678     "fit <- lm(loss ~ hardness + strength, data = rubber)\n",
 679     "autoplot(fit)"
 680    ]
 681   },
 682   {
 683    "cell_type": "markdown",
 684    "metadata": {},
 685    "source": [
 686     "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."
 687    ]
 688   },
 689   {
 690    "cell_type": "markdown",
 691    "metadata": {},
 692    "source": [
 693     "### Exercise 5.2\n",
 694     "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",
 695     "\n",
 696     "heat | TA |  TS\n",
 697     "-----|----|-----\n",
 698     "78.5 |  7 | 26\n",
 699     "74.3 |  1 | 29\n",
 700     "104.3 |  11 |  56\n",
 701     "87.6 |  11 |  31\n",
 702     "95.9 |  7 | 52\n",
 703     " $\\vdots$ | $\\vdots$ | $\\vdots$\n"
 704    ]
 705   },
 706   {
 707    "cell_type": "markdown",
 708    "metadata": {},
 709    "source": [
 710     "a. Load the `cemheat` dataset.\n",
 711     "\n",
 712     "b. Make scatterplots of heat against each of TA and TS in turn, and comment on what you see.\n",
 713     "\n",
 714     "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",
 715     "\n",
 716     "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",
 717     "\n",
 718     "e. By looking at the (default) composite residual plots, comment on the appropriateness of the fitted regression model.\n",
 719     "\n",
 720     "The solution is in the [Section 5.1 solutions](section5.1solutions.ipynb) notebook."
 721    ]
 722   },
 723   {
 724    "cell_type": "code",
 725    "execution_count": 43,
 726    "metadata": {},
 727    "outputs": [],
 728    "source": [
 729     "# Your solution here"
 730    ]
 731   },
 732   {
 733    "cell_type": "markdown",
 734    "metadata": {},
 735    "source": [
 736     "### Exercise 5.3: Fitting a quadratic regression model\n",
 737     "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."
 738    ]
 739   },
 740   {
 741    "cell_type": "code",
 742    "execution_count": 44,
 743    "metadata": {},
 744    "outputs": [
 745     {
 746      "data": {},
 747      "metadata": {},
 748      "output_type": "display_data"
 749     },
 750     {
 751      "data": {
 752       "image/png": 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 753       "text/plain": [
 754        "plot without title"
 755       ]
 756      },
 757      "metadata": {},
 758      "output_type": "display_data"
 759     }
 760    ],
 761    "source": [
 762     "anaerobic <- read.csv('anaerob.csv')\n",
 763     "ggplot(anaerobic, aes(x=oxygen, y=ventil)) + geom_point()"
 764    ]
 765   },
 766   {
 767    "cell_type": "markdown",
 768    "metadata": {},
 769    "source": [
 770     "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",
 771     "\n",
 772     "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",
 773     "\n",
 774     "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",
 775     "\n",
 776     "c. Make the usual residual plots and comment on the fit of the model again.\n",
 777     "\n",
 778     "The solution is in the [Section 5.1 solutions](section5.1solutions.ipynb) notebook."
 779    ]
 780   },
 781   {
 782    "cell_type": "code",
 783    "execution_count": 45,
 784    "metadata": {},
 785    "outputs": [],
 786    "source": [
 787     "# Your solution here"
 788    ]
 789   },
 790   {
 791    "cell_type": "markdown",
 792    "metadata": {},
 793    "source": [
 794     "## Next steps\n",
 795     "Move to the next notebook, or go back to the course material, or something."
 796    ]
 797   },
 798   {
 799    "cell_type": "code",
 800    "execution_count": null,
 801    "metadata": {},
 802    "outputs": [],
 803    "source": []
 804   }
 805  ],
 806  "metadata": {
 807   "kernelspec": {
 808    "display_name": "R",
 809    "language": "R",
 810    "name": "ir"
 811   },
 812   "language_info": {
 813    "codemirror_mode": "r",
 814    "file_extension": ".r",
 815    "mimetype": "text/x-r-source",
 816    "name": "R",
 817    "pygments_lexer": "r",
 818    "version": "3.4.2"
 819   },
 820   "toc": {
 821    "nav_menu": {},
 822    "number_sections": true,
 823    "sideBar": true,
 824    "skip_h1_title": false,
 825    "title_cell": "Table of Contents",
 826    "title_sidebar": "Contents",
 827    "toc_cell": false,
 828    "toc_position": {
 829     "height": "calc(100% - 180px)",
 830     "left": "10px",
 831     "top": "150px",
 832     "width": "342px"
 833    },
 834    "toc_section_display": true,
 835    "toc_window_display": true
 836   }
 837  },
 838  "nbformat": 4,
 839  "nbformat_minor": 2
 840 }