| Box-Cox Normality Plot | |
| # observations x | 291 |
| maximum correlation | 0.916665444070694 |
| optimal lambda | 1.38 |
| transformation formula | for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda |
| Obs. | Original | Transformed |
| 1 | 0.5 | -0.446218264259418 |
| 2 | 0.5 | -0.446218264259418 |
| 3 | 0.5 | -0.446218264259418 |
| 4 | 0.5 | -0.446218264259418 |
| 5 | 0.5 | -0.446218264259418 |
| 6 | 0.5 | -0.446218264259418 |
| 7 | 0.5 | -0.446218264259418 |
| 8 | 2.5 | 1.84148919688188 |
| 9 | 2.5 | 1.84148919688188 |
| 10 | 2.5 | 1.84148919688188 |
| 11 | 2.5 | 1.84148919688188 |
| 12 | 2.5 | 1.84148919688188 |
| 13 | 2.5 | 1.84148919688188 |
| 14 | 2.5 | 1.84148919688188 |
| 15 | 2.5 | 1.84148919688188 |
| 16 | 3.5 | 3.35794336336114 |
| 17 | 3.5 | 3.35794336336114 |
| 18 | 3.5 | 3.35794336336114 |
| 19 | 3.5 | 3.35794336336114 |
| 20 | 3.5 | 3.35794336336114 |
| 21 | 3.5 | 3.35794336336114 |
| 22 | 3.5 | 3.35794336336114 |
| 23 | 3.5 | 3.35794336336114 |
| 24 | 3.5 | 3.35794336336114 |
| 25 | 3.5 | 3.35794336336114 |
| 26 | 4.5 | 5.05039149406579 |
| 27 | 4.5 | 5.05039149406579 |
| 28 | 4.5 | 5.05039149406579 |
| 29 | 4.5 | 5.05039149406579 |
| 30 | 4.5 | 5.05039149406579 |
| 31 | 4.5 | 5.05039149406579 |
| 32 | 4.5 | 5.05039149406579 |
| 33 | 4.5 | 5.05039149406579 |
| 34 | 4.5 | 5.05039149406579 |
| 35 | 4.5 | 5.05039149406579 |
| 36 | 4.5 | 5.05039149406579 |
| 37 | 4.5 | 5.05039149406579 |
| 38 | 5.5 | 6.89301951703742 |
| 39 | 5.5 | 6.89301951703742 |
| 40 | 5.5 | 6.89301951703742 |
| 41 | 5.5 | 6.89301951703742 |
| 42 | 5.5 | 6.89301951703742 |
| 43 | 5.5 | 6.89301951703742 |
| 44 | 5.5 | 6.89301951703742 |
| 45 | 5.5 | 6.89301951703742 |
| 46 | 5.5 | 6.89301951703742 |
| 47 | 5.5 | 6.89301951703742 |
| 48 | 5.5 | 6.89301951703742 |
| 49 | 5.5 | 6.89301951703742 |
| 50 | 5.5 | 6.89301951703742 |
| 51 | 5.5 | 6.89301951703742 |
| 52 | 5.5 | 6.89301951703742 |
| 53 | 5.5 | 6.89301951703742 |
| 54 | 5.5 | 6.89301951703742 |
| 55 | 5.5 | 6.89301951703742 |
| 56 | 5.5 | 6.89301951703742 |
| 57 | 5.5 | 6.89301951703742 |
| 58 | 5.5 | 6.89301951703742 |
| 59 | 5.5 | 6.89301951703742 |
| 60 | 5.5 | 6.89301951703742 |
| 61 | 5.5 | 6.89301951703742 |
| 62 | 5.5 | 6.89301951703742 |
| 63 | 5.5 | 6.89301951703742 |
| 64 | 5.5 | 6.89301951703742 |
| 65 | 5.5 | 6.89301951703742 |
| 66 | 5.5 | 6.89301951703742 |
| 67 | 5.5 | 6.89301951703742 |
| 68 | 5.5 | 6.89301951703742 |
| 69 | 5.5 | 6.89301951703742 |
| 70 | 5.5 | 6.89301951703742 |
| 71 | 5.5 | 6.89301951703742 |
| 72 | 5.5 | 6.89301951703742 |
| 73 | 6.5 | 8.86807298987499 |
| 74 | 6.5 | 8.86807298987499 |
| 75 | 6.5 | 8.86807298987499 |
| 76 | 6.5 | 8.86807298987499 |
| 77 | 6.5 | 8.86807298987499 |
| 78 | 6.5 | 8.86807298987499 |
| 79 | 6.5 | 8.86807298987499 |
| 80 | 6.5 | 8.86807298987499 |
| 81 | 6.5 | 8.86807298987499 |
| 82 | 6.5 | 8.86807298987499 |
| 83 | 6.5 | 8.86807298987499 |
| 84 | 6.5 | 8.86807298987499 |
| 85 | 6.5 | 8.86807298987499 |
| 86 | 6.5 | 8.86807298987499 |
| 87 | 6.5 | 8.86807298987499 |
| 88 | 6.5 | 8.86807298987499 |
| 89 | 6.5 | 8.86807298987499 |
| 90 | 6.5 | 8.86807298987499 |
| 91 | 6.5 | 8.86807298987499 |
| 92 | 6.5 | 8.86807298987499 |
| 93 | 6.5 | 8.86807298987499 |
| 94 | 6.5 | 8.86807298987499 |
| 95 | 6.5 | 8.86807298987499 |
| 96 | 6.5 | 8.86807298987499 |
| 97 | 6.5 | 8.86807298987499 |
| 98 | 6.5 | 8.86807298987499 |
| 99 | 7.5 | 10.9624272546599 |
| 100 | 7.5 | 10.9624272546599 |
| 101 | 7.5 | 10.9624272546599 |
| 102 | 7.5 | 10.9624272546599 |
| 103 | 7.5 | 10.9624272546599 |
| 104 | 7.5 | 10.9624272546599 |
| 105 | 7.5 | 10.9624272546599 |
| 106 | 7.5 | 10.9624272546599 |
| 107 | 7.5 | 10.9624272546599 |
| 108 | 7.5 | 10.9624272546599 |
| 109 | 7.5 | 10.9624272546599 |
| 110 | 7.5 | 10.9624272546599 |
| 111 | 7.5 | 10.9624272546599 |
| 112 | 7.5 | 10.9624272546599 |
| 113 | 7.5 | 10.9624272546599 |
| 114 | 7.5 | 10.9624272546599 |
| 115 | 7.5 | 10.9624272546599 |
| 116 | 7.5 | 10.9624272546599 |
| 117 | 7.5 | 10.9624272546599 |
| 118 | 7.5 | 10.9624272546599 |
| 119 | 7.5 | 10.9624272546599 |
| 120 | 7.5 | 10.9624272546599 |
| 121 | 7.5 | 10.9624272546599 |
| 122 | 7.5 | 10.9624272546599 |
| 123 | 7.5 | 10.9624272546599 |
| 124 | 8.5 | 13.1658991734021 |
| 125 | 8.5 | 13.1658991734021 |
| 126 | 8.5 | 13.1658991734021 |
| 127 | 8.5 | 13.1658991734021 |
| 128 | 8.5 | 13.1658991734021 |
| 129 | 8.5 | 13.1658991734021 |
| 130 | 8.5 | 13.1658991734021 |
| 131 | 8.5 | 13.1658991734021 |
| 132 | 8.5 | 13.1658991734021 |
| 133 | 8.5 | 13.1658991734021 |
| 134 | 8.5 | 13.1658991734021 |
| 135 | 8.5 | 13.1658991734021 |
| 136 | 8.5 | 13.1658991734021 |
| 137 | 8.5 | 13.1658991734021 |
| 138 | 8.5 | 13.1658991734021 |
| 139 | 8.5 | 13.1658991734021 |
| 140 | 8.5 | 13.1658991734021 |
| 141 | 8.5 | 13.1658991734021 |
| 142 | 8.5 | 13.1658991734021 |
| 143 | 8.5 | 13.1658991734021 |
| 144 | 8.5 | 13.1658991734021 |
| 145 | 8.5 | 13.1658991734021 |
| 146 | 9.5 | 15.4703077463909 |
| 147 | 9.5 | 15.4703077463909 |
| 148 | 9.5 | 15.4703077463909 |
| 149 | 9.5 | 15.4703077463909 |
| 150 | 9.5 | 15.4703077463909 |
| 151 | 9.5 | 15.4703077463909 |
| 152 | 9.5 | 15.4703077463909 |
| 153 | 9.5 | 15.4703077463909 |
| 154 | 9.5 | 15.4703077463909 |
| 155 | 9.5 | 15.4703077463909 |
| 156 | 9.5 | 15.4703077463909 |
| 157 | 9.5 | 15.4703077463909 |
| 158 | 9.5 | 15.4703077463909 |
| 159 | 9.5 | 15.4703077463909 |
| 160 | 9.5 | 15.4703077463909 |
| 161 | 10.5 | 17.8689050549175 |
| 162 | 10.5 | 17.8689050549175 |
| 163 | 10.5 | 17.8689050549175 |
| 164 | 10.5 | 17.8689050549175 |
| 165 | 10.5 | 17.8689050549175 |
| 166 | 10.5 | 17.8689050549175 |
| 167 | 10.5 | 17.8689050549175 |
| 168 | 10.5 | 17.8689050549175 |
| 169 | 10.5 | 17.8689050549175 |
| 170 | 10.5 | 17.8689050549175 |
| 171 | 10.5 | 17.8689050549175 |
| 172 | 10.5 | 17.8689050549175 |
| 173 | 10.5 | 17.8689050549175 |
| 174 | 10.5 | 17.8689050549175 |
| 175 | 10.5 | 17.8689050549175 |
| 176 | 10.5 | 17.8689050549175 |
| 177 | 10.5 | 17.8689050549175 |
| 178 | 10.5 | 17.8689050549175 |
| 179 | 10.5 | 17.8689050549175 |
| 180 | 10.5 | 17.8689050549175 |
| 181 | 10.5 | 17.8689050549175 |
| 182 | 10.5 | 17.8689050549175 |
| 183 | 10.5 | 17.8689050549175 |
| 184 | 10.5 | 17.8689050549175 |
| 185 | 10.5 | 17.8689050549175 |
| 186 | 10.5 | 17.8689050549175 |
| 187 | 10.5 | 17.8689050549175 |
| 188 | 10.5 | 17.8689050549175 |
| 189 | 10.5 | 17.8689050549175 |
| 190 | 10.5 | 17.8689050549175 |
| 191 | 10.5 | 17.8689050549175 |
| 192 | 10.5 | 17.8689050549175 |
| 193 | 10.5 | 17.8689050549175 |
| 194 | 10.5 | 17.8689050549175 |
| 195 | 10.5 | 17.8689050549175 |
| 196 | 10.5 | 17.8689050549175 |
| 197 | 10.5 | 17.8689050549175 |
| 198 | 10.5 | 17.8689050549175 |
| 199 | 10.5 | 17.8689050549175 |
| 200 | 10.5 | 17.8689050549175 |
| 201 | 10.5 | 17.8689050549175 |
| 202 | 10.5 | 17.8689050549175 |
| 203 | 10.5 | 17.8689050549175 |
| 204 | 10.5 | 17.8689050549175 |
| 205 | 10.5 | 17.8689050549175 |
| 206 | 10.5 | 17.8689050549175 |
| 207 | 10.5 | 17.8689050549175 |
| 208 | 10.5 | 17.8689050549175 |
| 209 | 10.5 | 17.8689050549175 |
| 210 | 10.5 | 17.8689050549175 |
| 211 | 10.5 | 17.8689050549175 |
| 212 | 10.5 | 17.8689050549175 |
| 213 | 10.5 | 17.8689050549175 |
| 214 | 10.5 | 17.8689050549175 |
| 215 | 10.5 | 17.8689050549175 |
| 216 | 10.5 | 17.8689050549175 |
| 217 | 10.5 | 17.8689050549175 |
| 218 | 10.5 | 17.8689050549175 |
| 219 | 10.5 | 17.8689050549175 |
| 220 | 10.5 | 17.8689050549175 |
| 221 | 10.5 | 17.8689050549175 |
| 222 | 10.5 | 17.8689050549175 |
| 223 | 10.5 | 17.8689050549175 |
| 224 | 10.5 | 17.8689050549175 |
| 225 | 10.5 | 17.8689050549175 |
| 226 | 10.5 | 17.8689050549175 |
| 227 | 10.5 | 17.8689050549175 |
| 228 | 10.5 | 17.8689050549175 |
| 229 | 10.5 | 17.8689050549175 |
| 230 | 10.5 | 17.8689050549175 |
| 231 | 10.5 | 17.8689050549175 |
| 232 | 10.5 | 17.8689050549175 |
| 233 | 10.5 | 17.8689050549175 |
| 234 | 10.5 | 17.8689050549175 |
| 235 | 10.5 | 17.8689050549175 |
| 236 | 10.5 | 17.8689050549175 |
| 237 | 10.5 | 17.8689050549175 |
| 238 | 10.5 | 17.8689050549175 |
| 239 | 10.5 | 17.8689050549175 |
| 240 | 10.5 | 17.8689050549175 |
| 241 | 10.5 | 17.8689050549175 |
| 242 | 10.5 | 17.8689050549175 |
| 243 | 10.5 | 17.8689050549175 |
| 244 | 10.5 | 17.8689050549175 |
| 245 | 10.5 | 17.8689050549175 |
| 246 | 10.5 | 17.8689050549175 |
| 247 | 10.5 | 17.8689050549175 |
| 248 | 10.5 | 17.8689050549175 |
| 249 | 10.5 | 17.8689050549175 |
| 250 | 10.5 | 17.8689050549175 |
| 251 | 10.5 | 17.8689050549175 |
| 252 | 10.5 | 17.8689050549175 |
| 253 | 10.5 | 17.8689050549175 |
| 254 | 10.5 | 17.8689050549175 |
| 255 | 10.5 | 17.8689050549175 |
| 256 | 10.5 | 17.8689050549175 |
| 257 | 10.5 | 17.8689050549175 |
| 258 | 10.5 | 17.8689050549175 |
| 259 | 10.5 | 17.8689050549175 |
| 260 | 10.5 | 17.8689050549175 |
| 261 | 10.5 | 17.8689050549175 |
| 262 | 10.5 | 17.8689050549175 |
| 263 | 10.5 | 17.8689050549175 |
| 264 | 10.5 | 17.8689050549175 |
| 265 | 10.5 | 17.8689050549175 |
| 266 | 10.5 | 17.8689050549175 |
| 267 | 10.5 | 17.8689050549175 |
| 268 | 10.5 | 17.8689050549175 |
| 269 | 10.5 | 17.8689050549175 |
| 270 | 10.5 | 17.8689050549175 |
| 271 | 10.5 | 17.8689050549175 |
| 272 | 10.5 | 17.8689050549175 |
| 273 | 10.5 | 17.8689050549175 |
| 274 | 10.5 | 17.8689050549175 |
| 275 | 10.5 | 17.8689050549175 |
| 276 | 10.5 | 17.8689050549175 |
| 277 | 10.5 | 17.8689050549175 |
| 278 | 10.5 | 17.8689050549175 |
| 279 | 10.5 | 17.8689050549175 |
| 280 | 10.5 | 17.8689050549175 |
| 281 | 10.5 | 17.8689050549175 |
| 282 | 10.5 | 17.8689050549175 |
| 283 | 10.5 | 17.8689050549175 |
| 284 | 10.5 | 17.8689050549175 |
| 285 | 10.5 | 17.8689050549175 |
| 286 | 10.5 | 17.8689050549175 |
| 287 | 10.5 | 17.8689050549175 |
| 288 | 10.5 | 17.8689050549175 |
| 289 | 10.5 | 17.8689050549175 |
| 290 | 10.5 | 17.8689050549175 |
| 291 | 12.5 | 22.9267557005424 |
| Maximum Likelihood Estimation of Lambda |
> summary(mypT)
bcPower Transformation to Normality
Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd
x 1.6796 1.68 1.3756 1.9836
Likelihood ratio test that transformation parameter is equal to 0
(log transformation)
LRT df pval
LR test, lambda = (0) 264.7451 1 < 2.22e-16
Likelihood ratio test that no transformation is needed
LRT df pval
LR test, lambda = (1) 24.92264 1 5.9678e-07
|
