CAKE (Breakage angle of chocolate cakes) Data: replicate recipe temperature angle temp 1 1 A 175 42 175 2 1 A 185 46 185 3 1 A 195 47 195 4 1 A 205 39 205 5 1 A 215 53 215 6 1 A 225 42 225 7 1 B 175 39 175 8 1 B 185 46 185 9 1 B 195 51 195 10 1 B 205 49 205 11 1 B 215 55 215 12 1 B 225 42 225 13 1 C 175 46 175 14 1 C 185 44 185 15 1 C 195 45 195 16 1 C 205 46 205 17 1 C 215 48 215 18 1 C 225 63 225 19 2 A 175 47 175 20 2 A 185 29 185 21 2 A 195 35 195 22 2 A 205 47 205 23 2 A 215 57 215 24 2 A 225 45 225 25 2 B 175 35 175 26 2 B 185 46 185 27 2 B 195 47 195 28 2 B 205 39 205 29 2 B 215 52 215 30 2 B 225 61 225 31 2 C 175 43 175 32 2 C 185 43 185 33 2 C 195 43 195 34 2 C 205 46 205 35 2 C 215 47 215 36 2 C 225 58 225 37 3 A 175 32 175 38 3 A 185 32 185 39 3 A 195 37 195 40 3 A 205 43 205 41 3 A 215 45 215 42 3 A 225 45 225 43 3 B 175 34 175 44 3 B 185 30 185 45 3 B 195 42 195 46 3 B 205 35 205 47 3 B 215 42 215 48 3 B 225 35 225 49 3 C 175 33 175 50 3 C 185 24 185 51 3 C 195 40 195 52 3 C 205 37 205 53 3 C 215 41 215 54 3 C 225 38 225 55 4 A 175 26 175 56 4 A 185 32 185 57 4 A 195 35 195 58 4 A 205 24 205 59 4 A 215 39 215 60 4 A 225 26 225 61 4 B 175 25 175 62 4 B 185 26 185 63 4 B 195 28 195 64 4 B 205 46 205 65 4 B 215 37 215 66 4 B 225 37 225 67 4 C 175 38 175 68 4 C 185 41 185 69 4 C 195 38 195 70 4 C 205 30 205 71 4 C 215 36 215 72 4 C 225 35 225 73 5 A 175 28 175 74 5 A 185 30 185 75 5 A 195 31 195 76 5 A 205 37 205 77 5 A 215 41 215 78 5 A 225 47 225 79 5 B 175 31 175 80 5 B 185 30 185 81 5 B 195 29 195 82 5 B 205 35 205 83 5 B 215 40 215 84 5 B 225 36 225 85 5 C 175 21 175 86 5 C 185 25 185 87 5 C 195 31 195 88 5 C 205 35 205 89 5 C 215 33 215 90 5 C 225 23 225 91 6 A 175 24 175 92 6 A 185 22 185 93 6 A 195 22 195 94 6 A 205 29 205 95 6 A 215 35 215 96 6 A 225 26 225 97 6 B 175 24 175 98 6 B 185 29 185 99 6 B 195 29 195 100 6 B 205 29 205 101 6 B 215 24 215 102 6 B 225 35 225 103 6 C 175 24 175 104 6 C 185 33 185 105 6 C 195 30 195 106 6 C 205 30 205 107 6 C 215 37 215 108 6 C 225 35 225 109 7 A 175 26 175 110 7 A 185 23 185 111 7 A 195 25 195 112 7 A 205 27 205 113 7 A 215 33 215 114 7 A 225 35 225 115 7 B 175 22 175 116 7 B 185 25 185 117 7 B 195 26 195 118 7 B 205 26 205 119 7 B 215 29 215 120 7 B 225 36 225 121 7 C 175 20 175 122 7 C 185 21 185 123 7 C 195 31 195 124 7 C 205 24 205 125 7 C 215 30 215 126 7 C 225 33 225 127 8 A 175 24 175 128 8 A 185 33 185 129 8 A 195 23 195 130 8 A 205 32 205 131 8 A 215 31 215 132 8 A 225 34 225 133 8 B 175 26 175 134 8 B 185 23 185 135 8 B 195 24 195 136 8 B 205 31 205 137 8 B 215 27 215 138 8 B 225 37 225 139 8 C 175 24 175 140 8 C 185 23 185 141 8 C 195 21 195 142 8 C 205 24 205 143 8 C 215 21 215 144 8 C 225 35 225 145 9 A 175 24 175 146 9 A 185 27 185 147 9 A 195 28 195 148 9 A 205 33 205 149 9 A 215 34 215 150 9 A 225 23 225 151 9 B 175 27 175 152 9 B 185 26 185 153 9 B 195 32 195 154 9 B 205 28 205 155 9 B 215 32 215 156 9 B 225 33 225 157 9 C 175 24 175 158 9 C 185 18 185 159 9 C 195 21 195 160 9 C 205 26 205 161 9 C 215 28 215 162 9 C 225 28 225 163 10 A 175 24 175 164 10 A 185 33 185 165 10 A 195 27 195 166 10 A 205 31 205 167 10 A 215 30 215 168 10 A 225 33 225 169 10 B 175 21 175 170 10 B 185 24 185 171 10 B 195 24 195 172 10 B 205 27 205 173 10 B 215 37 215 174 10 B 225 30 225 175 10 C 175 26 175 176 10 C 185 28 185 177 10 C 195 27 195 178 10 C 205 27 205 179 10 C 215 35 215 180 10 C 225 35 225 181 11 A 175 33 175 182 11 A 185 39 185 183 11 A 195 33 195 184 11 A 205 28 205 185 11 A 215 33 215 186 11 A 225 30 225 187 11 B 175 20 175 188 11 B 185 27 185 189 11 B 195 33 195 190 11 B 205 31 205 191 11 B 215 28 215 192 11 B 225 33 225 193 11 C 175 28 175 194 11 C 185 25 185 195 11 C 195 26 195 196 11 C 205 25 205 197 11 C 215 38 215 198 11 C 225 28 225 199 12 A 175 28 175 200 12 A 185 31 185 201 12 A 195 27 195 202 12 A 205 39 205 203 12 A 215 35 215 204 12 A 225 43 225 205 12 B 175 23 175 206 12 B 185 28 185 207 12 B 195 31 195 208 12 B 205 34 205 209 12 B 215 31 215 210 12 B 225 29 225 211 12 C 175 24 175 212 12 C 185 30 185 213 12 C 195 28 195 214 12 C 205 35 205 215 12 C 215 33 215 216 12 C 225 28 225 217 13 A 175 29 175 218 13 A 185 28 185 219 13 A 195 31 195 220 13 A 205 29 205 221 13 A 215 37 215 222 13 A 225 33 225 223 13 B 175 32 175 224 13 B 185 35 185 225 13 B 195 30 195 226 13 B 205 27 205 227 13 B 215 35 215 228 13 B 225 30 225 229 13 C 175 28 175 230 13 C 185 29 185 231 13 C 195 43 195 232 13 C 205 28 205 233 13 C 215 33 215 234 13 C 225 37 225 235 14 A 175 24 175 236 14 A 185 40 185 237 14 A 195 29 195 238 14 A 205 40 205 239 14 A 215 40 215 240 14 A 225 31 225 241 14 B 175 23 175 242 14 B 185 25 185 243 14 B 195 22 195 244 14 B 205 19 205 245 14 B 215 21 215 246 14 B 225 35 225 247 14 C 175 19 175 248 14 C 185 22 185 249 14 C 195 27 195 250 14 C 205 25 205 251 14 C 215 25 215 252 14 C 225 35 225 253 15 A 175 26 175 254 15 A 185 28 185 255 15 A 195 32 195 256 15 A 205 25 205 257 15 A 215 37 215 258 15 A 225 33 225 259 15 B 175 21 175 260 15 B 185 21 185 261 15 B 195 28 195 262 15 B 205 26 205 263 15 B 215 27 215 264 15 B 225 20 225 265 15 C 175 21 175 266 15 C 185 28 185 267 15 C 195 25 195 268 15 C 205 25 205 269 15 C 215 31 215 270 15 C 225 25 225 Description: Data on the breakage angle of chocolate cakes made with three different recipes and baked at six different temperatures. This is a split-plot design with the recipes being whole-units and the different temperatures being applied to sub-units (within replicates). The experimental notes suggest that the replicate numbering represents temporal ordering. Format: A data frame with 270 observations on the following 5 variables. replicate - a factor with levels 1 to 15 recipe - a factor with levels A, B and C temperature - an ordered factor with levels 175 < 185 < 195 < 205 < 215 < 225 angle - a numeric vector giving the angle at which the cake broke. temp - numeric value of the baking temperature (degrees F). Details: The replicate factor is nested within the recipe factor, and temperature is nested within replicate. Source: Original data were presented in Cook (1938), and reported in Cochran and Cox (1957, p. 300). Also cited in Lee, Nelder and Pawitan (2006). References: Cook, F. E. (1938) Chocolate cake, I. Optimum baking temperature. Master's Thesis, Iowa State College. Cochran, W. G., and Cox, G. M. (1957) Experimental designs, 2nd Ed. New York, John Wiley \& Sons. Lee, Y., Nelder, J. A., and Pawitan, Y. (2006) Generalized linear models with random effects. Unified analysis via H-likelihood. Boca Raton, Chapman and Hall/CRC. Task: Model the breakage angle of the chocolate cakes.