Read 2500 items Read 250 items --- APPLYING MODELS TO DATA IN train1x AND train1y SIMPLE LINEAR MODEL Call: lm(formula = trainy ~ trainx) Residuals: Min 1Q Median 3Q Max -1.40576 -0.31558 -0.03542 0.26756 1.95052 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 5.09323 0.44713 11.391 < 2e-16 *** trainxV1 0.21757 0.02145 10.142 < 2e-16 *** trainxV2 1.58882 0.71488 2.222 0.02718 * trainxV3 2.56441 0.60984 4.205 3.68e-05 *** trainxV4 1.90180 0.44280 4.295 2.53e-05 *** trainxV5 -0.65827 0.23777 -2.769 0.00607 ** trainxV6 0.30995 0.29234 1.060 0.29008 trainxV7 0.26580 0.05045 5.268 3.05e-07 *** trainxV8 -0.46711 0.11209 -4.167 4.30e-05 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.5391 on 241 degrees of freedom Multiple R-squared: 0.594, Adjusted R-squared: 0.5805 F-statistic: 44.07 on 8 and 241 DF, p-value: < 2.2e-16 Average test squared error: 0.288 LINEAR MODEL WITH QUADRATIC TERMS Call: lm(formula = trainy ~ trainx2) Residuals: Min 1Q Median 3Q Max -1.29710 -0.25244 -0.01047 0.23797 1.59239 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 14.43298 1.55585 9.277 < 2e-16 *** trainx2V1 0.77631 0.11267 6.890 5.16e-11 *** trainx2V2 5.63565 1.99886 2.819 0.005225 ** trainx2V3 -9.69682 3.41268 -2.841 0.004889 ** trainx2V4 2.24551 4.39913 0.510 0.610223 trainx2V5 0.24796 0.49361 0.502 0.615907 trainx2V6 -0.23047 0.83654 -0.275 0.783179 trainx2V7 -2.33124 0.38882 -5.996 7.66e-09 *** trainx2V8 -1.01865 0.41781 -2.438 0.015514 * trainx2V1 -0.04023 0.00828 -4.859 2.17e-06 *** trainx2V2 -7.76843 3.53533 -2.197 0.028979 * trainx2V3 12.96053 3.48782 3.716 0.000254 *** trainx2V4 -0.99872 3.17141 -0.315 0.753109 trainx2V5 -1.27031 0.66366 -1.914 0.056831 . trainx2V6 1.25527 1.51141 0.831 0.407090 trainx2V7 0.20850 0.03104 6.718 1.40e-10 *** trainx2V8 0.52122 0.39347 1.325 0.186578 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.4662 on 233 degrees of freedom Multiple R-squared: 0.7065, Adjusted R-squared: 0.6863 F-statistic: 35.05 on 16 and 233 DF, p-value: < 2.2e-16 Average test squared error: 0.283 LINEAR MODEL WITH QUADRATIC AND CUBIC TERMS Call: lm(formula = trainy ~ trainx3) Residuals: Min 1Q Median 3Q Max -1.22612 -0.23321 -0.00178 0.26755 1.12009 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.971e+01 6.034e+00 4.923 1.65e-06 *** trainx3V1 6.633e-01 3.679e-01 1.803 0.072714 . trainx3V2 1.510e+01 3.416e+00 4.421 1.53e-05 *** trainx3V3 -6.594e+01 1.278e+01 -5.160 5.42e-07 *** trainx3V4 -1.747e+01 2.445e+01 -0.714 0.475706 trainx3V5 1.404e+00 1.073e+00 1.308 0.192126 trainx3V6 -7.322e-01 1.494e+00 -0.490 0.624443 trainx3V7 -3.368e+00 1.614e+00 -2.087 0.038008 * trainx3V8 7.207e-01 8.548e-01 0.843 0.400074 trainx3V1 -3.598e-02 5.750e-02 -0.626 0.532169 trainx3V2 -6.696e+01 1.754e+01 -3.817 0.000174 *** trainx3V3 1.320e+02 2.642e+01 4.994 1.19e-06 *** trainx3V4 2.843e+01 3.672e+01 0.774 0.439623 trainx3V5 -5.098e+00 3.849e+00 -1.325 0.186652 trainx3V6 2.426e+00 5.551e+00 0.437 0.662495 trainx3V7 3.864e-01 2.558e-01 1.510 0.132371 trainx3V8 -3.660e+00 1.998e+00 -1.832 0.068279 . trainx3V1 -5.022e-05 2.883e-03 -0.017 0.986118 trainx3V2 7.107e+01 2.026e+01 3.509 0.000544 *** trainx3V3 -8.127e+01 1.780e+01 -4.564 8.25e-06 *** trainx3V4 -1.446e+01 1.818e+01 -0.795 0.427299 trainx3V5 2.948e+00 2.990e+00 0.986 0.325155 trainx3V6 -1.589e+00 5.827e+00 -0.273 0.785314 trainx3V7 -9.835e-03 1.339e-02 -0.735 0.463309 trainx3V8 2.619e+00 1.264e+00 2.072 0.039410 * --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.431 on 225 degrees of freedom Multiple R-squared: 0.7577, Adjusted R-squared: 0.7318 F-statistic: 29.31 on 24 and 225 DF, p-value: < 2.2e-16 Average test squared error: 0.311 GP VERSION OF SIMPLE LINEAR MODEL Average test squared error: 0.288 GP WITH SQUARED EXP TERM, MAX ML, NO RESCALING Initial values: 1 1 1 Maximum log likelihood: -197.8135 user system elapsed 2.256 0.028 2.293 Hyperparameter values: 0.4576304 4.995969 0.1490643 Average test squared error: 0.293 Initial values: 0.2 2 2 Maximum log likelihood: -197.8135 user system elapsed 2.588 0.020 2.619 Hyperparameter values: 0.4576307 4.995961 0.1490643 Average test squared error: 0.293 REMAINING RESULTS AFTER RESCALING... GP WITH SQUARED EXP TERM, MAX ML Initial values: 1 1 1 Maximum log likelihood: -201.0563 user system elapsed 2.072 0.012 2.091 Hyperparameter values: 0.4007889 1.127389 1.946365 Average test squared error: 0.244 Initial values: 0.2 2 2 Maximum log likelihood: -201.0563 user system elapsed 2.472 0.008 2.488 Hyperparameter values: 0.4007879 1.127382 1.946376 Average test squared error: 0.244 GP WITH ABS EXP TERM, MAX ML Initial values: 1 1 1 Maximum log likelihood: -190.4913 user system elapsed 2.088 0.016 2.111 Hyperparameter values: 0.3506279 1.391357 0.2393843 Average test squared error: 0.241 Initial values: 0.2 2 2 Maximum log likelihood: -190.4913 user system elapsed 2.620 0.056 2.683 Hyperparameter values: 0.3506281 1.391364 0.2393816 Average test squared error: 0.241 GP WITH TWO EXP TERMS, MAX ML Initial values: 1 1 1 1 Maximum log likelihood: -190.2402 user system elapsed 5.541 0.028 5.588 Hyperparameter values: 0.3460237 1.161256 1.596204 0.3288235 Average test squared error: 0.237 Initial values: 0.2 2 2 2 Maximum log likelihood: -190.2402 user system elapsed 4.232 0.032 4.278 Hyperparameter values: 0.3460241 1.161258 1.596219 0.3288205 Average test squared error: 0.237 Initial values: 0.4 1 2 1 Maximum log likelihood: -190.2402 user system elapsed 5.512 0.024 5.552 Hyperparameter values: 0.3460267 1.161296 1.596405 0.3287961 Average test squared error: 0.237 Initial values: 0.4 2 1 1 Maximum log likelihood: -190.2402 user system elapsed 4.009 0.024 4.045 Hyperparameter values: 0.3460264 1.161292 1.596631 0.3287964 Average test squared error: 0.237 GP WITH SQUARED EXP TERM, CV Initial values: 1 1 1 Minimum cv error: 0.2722658 user system elapsed 7.740 0.048 7.815 Hyperparameter values: 0.4463586 1.496999 2.797199 Average test squared error: 0.276 Initial values: 0.2 2 2 Minimum cv error: 0.2722658 user system elapsed 6.897 0.068 6.988 Hyperparameter values: 0.5189467 1.740479 2.797195 Average test squared error: 0.276 GP WITH ABS EXP TERM, CV Initial values: 1 1 1 Minimum cv error: 0.2450894 user system elapsed 24.613 0.296 24.989 Hyperparameter values: 0.2148079 1.963471 0.01 Average test squared error: 0.24 Initial values: 0.2 2 2 Minimum cv error: 0.2450892 user system elapsed 58.012 0.468 58.664 Hyperparameter values: 0.09318134 0.8515003 0.01000001 Average test squared error: 0.24 GP WITH TWO EXP TERMS, CV Initial values: 1 1 1 1 Minimum cv error: 0.2450897 user system elapsed 78.769 0.232 79.249 Hyperparameter values: 0.2919587 2.66844 0.3992143 0.01 Average test squared error: 0.24 GP WITH SQUARED EXP TERM, IMPORTANCE SAMPLING user system elapsed 136.348 0.564 137.343 Mean hyperparameter values: 0.3967963 1.19196 2.052404 Marginal likelihood: 1.960152e-182 Average test squared error: 0.246 GP WITH ABS EXP TERM, IMPORTANCE SAMPLING user system elapsed 133.293 0.404 134.114 Mean hyperparameter values: 0.3394469 1.396018 0.3152587 Marginal likelihood: 2.536979e-182 Average test squared error: 0.24 GP WITH TWO EXP TERMS, IMPORTANCE SAMPLING user system elapsed 232.986 0.640 234.362 Mean hyperparameter values: 0.3260324 1.016188 1.072945 0.6030058 Marginal likelihood: 2.053783e-117 Average test squared error: 0.236 Read 2500 items Read 250 items --- APPLYING MODELS TO DATA IN train2x AND train2y SIMPLE LINEAR MODEL Call: lm(formula = trainy ~ trainx) Residuals: Min 1Q Median 3Q Max -1.91644 -0.35931 -0.04272 0.28533 1.51851 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3.65871 0.50774 7.206 7.37e-12 *** trainxV1 0.22675 0.02337 9.702 < 2e-16 *** trainxV2 1.87513 0.51645 3.631 0.000345 *** trainxV3 3.54124 0.56759 6.239 1.96e-09 *** trainxV4 2.27922 0.44962 5.069 7.96e-07 *** trainxV5 -0.39567 0.25773 -1.535 0.126052 trainxV6 -0.31757 0.29558 -1.074 0.283716 trainxV7 0.35901 0.04689 7.656 4.63e-13 *** trainxV8 -0.15237 0.10944 -1.392 0.165142 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.5144 on 241 degrees of freedom Multiple R-squared: 0.6517, Adjusted R-squared: 0.6401 F-statistic: 56.36 on 8 and 241 DF, p-value: < 2.2e-16 Average test squared error: 0.289 LINEAR MODEL WITH QUADRATIC TERMS Call: lm(formula = trainy ~ trainx2) Residuals: Min 1Q Median 3Q Max -1.91464 -0.26443 -0.03839 0.26327 1.31942 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 4.62303 1.84789 2.502 0.013044 * trainx2V1 0.60569 0.15415 3.929 0.000112 *** trainx2V2 10.68342 2.04017 5.237 3.65e-07 *** trainx2V3 3.52522 3.40320 1.036 0.301344 trainx2V4 2.26614 4.99393 0.454 0.650410 trainx2V5 -0.46156 0.56769 -0.813 0.417023 trainx2V6 -1.49494 0.73344 -2.038 0.042653 * trainx2V7 -0.18990 0.29193 -0.650 0.516012 trainx2V8 0.51096 0.41822 1.222 0.223036 trainx2V1 -0.03230 0.01144 -2.824 0.005161 ** trainx2V2 -13.08370 2.94569 -4.442 1.38e-05 *** trainx2V3 -0.29648 3.23605 -0.092 0.927081 trainx2V4 -0.41273 3.45251 -0.120 0.904947 trainx2V5 0.12392 0.80810 0.153 0.878256 trainx2V6 2.13361 1.28496 1.660 0.098168 . trainx2V7 0.04197 0.02322 1.808 0.071941 . trainx2V8 -0.62043 0.39922 -1.554 0.121520 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.4881 on 233 degrees of freedom Multiple R-squared: 0.6969, Adjusted R-squared: 0.676 F-statistic: 33.48 on 16 and 233 DF, p-value: < 2.2e-16 Average test squared error: 0.258 LINEAR MODEL WITH QUADRATIC AND CUBIC TERMS Call: lm(formula = trainy ~ trainx3) Residuals: Min 1Q Median 3Q Max -1.80535 -0.23550 -0.01783 0.27297 1.42083 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.932e+01 1.031e+01 2.845 0.004853 ** trainx3V1 -5.629e-01 6.570e-01 -0.857 0.392499 trainx3V2 1.692e+01 3.940e+00 4.295 2.59e-05 *** trainx3V3 -5.128e+01 1.432e+01 -3.580 0.000420 *** trainx3V4 -5.300e+01 4.036e+01 -1.313 0.190483 trainx3V5 -2.785e-01 1.291e+00 -0.216 0.829410 trainx3V6 -1.261e+00 1.675e+00 -0.752 0.452567 trainx3V7 -1.321e-01 1.170e+00 -0.113 0.910251 trainx3V8 1.576e+00 9.011e-01 1.749 0.081628 . trainx3V1 1.542e-01 1.035e-01 1.489 0.137805 trainx3V2 -5.226e+01 1.963e+01 -2.662 0.008320 ** trainx3V3 1.026e+02 2.605e+01 3.940 0.000109 *** trainx3V4 7.744e+01 5.622e+01 1.377 0.169768 trainx3V5 -1.878e-01 4.803e+00 -0.039 0.968851 trainx3V6 3.574e-01 6.956e+00 0.051 0.959065 trainx3V7 2.897e-02 1.956e-01 0.148 0.882423 trainx3V8 -3.206e+00 2.113e+00 -1.517 0.130637 trainx3V1 -9.642e-03 5.251e-03 -1.836 0.067624 . trainx3V2 4.327e+01 2.084e+01 2.076 0.039018 * trainx3V3 -6.196e+01 1.524e+01 -4.067 6.60e-05 *** trainx3V4 -3.648e+01 2.586e+01 -1.411 0.159706 trainx3V5 3.366e-01 3.824e+00 0.088 0.929950 trainx3V6 2.314e+00 7.555e+00 0.306 0.759690 trainx3V7 6.727e-04 1.066e-02 0.063 0.949726 trainx3V8 1.631e+00 1.340e+00 1.217 0.224815 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.4668 on 225 degrees of freedom Multiple R-squared: 0.7322, Adjusted R-squared: 0.7036 F-statistic: 25.63 on 24 and 225 DF, p-value: < 2.2e-16 Average test squared error: 0.251 GP VERSION OF SIMPLE LINEAR MODEL Average test squared error: 0.289 GP WITH SQUARED EXP TERM, MAX ML, NO RESCALING Initial values: 1 1 1 Maximum log likelihood: -209.0035 user system elapsed 2.128 0.056 2.191 Hyperparameter values: 0.4913552 15.49997 0.0623874 Average test squared error: 0.257 Initial values: 0.2 2 2 Maximum log likelihood: -209.0035 user system elapsed 2.088 0.020 2.116 Hyperparameter values: 0.4913551 15.50079 0.06238547 Average test squared error: 0.257 REMAINING RESULTS AFTER RESCALING... GP WITH SQUARED EXP TERM, MAX ML Initial values: 1 1 1 Maximum log likelihood: -203.1627 user system elapsed 1.733 0.032 1.771 Hyperparameter values: 0.4485648 1.678319 1.114696 Average test squared error: 0.245 Initial values: 0.2 2 2 Maximum log likelihood: -203.1627 user system elapsed 2.528 0.032 2.572 Hyperparameter values: 0.4485651 1.678316 1.114696 Average test squared error: 0.245 GP WITH ABS EXP TERM, MAX ML Initial values: 1 1 1 Maximum log likelihood: -205.8753 user system elapsed 2.096 0.036 2.139 Hyperparameter values: 0.4241969 1.319925 0.1871104 Average test squared error: 0.216 Initial values: 0.2 2 2 Maximum log likelihood: -205.8753 user system elapsed 1.916 0.020 1.940 Hyperparameter values: 0.4241975 1.31993 0.1871069 Average test squared error: 0.216 GP WITH TWO EXP TERMS, MAX ML Initial values: 1 1 1 1 Maximum log likelihood: -202.9812 user system elapsed 5.580 0.060 5.658 Hyperparameter values: 0.4351322 0.2624448 1.657376 1.029149 Average test squared error: 0.236 Initial values: 0.2 2 2 2 Maximum log likelihood: -202.9445 user system elapsed 4.209 0.064 4.286 Hyperparameter values: 0.4301802 0.7092909 2.668137 0.3984788 Average test squared error: 0.221 Initial values: 0.4 1 2 1 Maximum log likelihood: -202.9445 user system elapsed 4.144 0.028 4.191 Hyperparameter values: 0.4301806 0.7092681 2.668062 0.3985003 Average test squared error: 0.221 Initial values: 0.4 2 1 1 Maximum log likelihood: -202.9445 user system elapsed 4.232 0.012 4.260 Hyperparameter values: 0.4301804 0.7092665 2.668041 0.3985036 Average test squared error: 0.221 GP WITH SQUARED EXP TERM, CV Initial values: 1 1 1 Minimum cv error: 0.2577546 user system elapsed 34.614 0.432 35.176 Hyperparameter values: 0.1488616 0.4841947 1.183449 Average test squared error: 0.244 Initial values: 0.2 2 2 Minimum cv error: 0.2577545 user system elapsed 47.083 0.312 47.559 Hyperparameter values: 0.09152418 0.2976826 1.183455 Average test squared error: 0.244 GP WITH ABS EXP TERM, CV Initial values: 1 1 1 Minimum cv error: 0.2565918 user system elapsed 11.721 0.076 11.842 Hyperparameter values: 0.5891221 1.46671 0.1749574 Average test squared error: 0.219 Initial values: 0.2 2 2 Minimum cv error: 0.2565925 user system elapsed 12.973 0.060 13.081 Hyperparameter values: 0.8368711 2.083516 0.174964 Average test squared error: 0.219 GP WITH TWO EXP TERMS, CV Initial values: 1 1 1 1 Minimum cv error: 0.2522393 user system elapsed 30.766 0.156 31.032 Hyperparameter values: 0.3651379 0.6299946 2.255033 0.2521128 Average test squared error: 0.222 GP WITH SQUARED EXP TERM, IMPORTANCE SAMPLING user system elapsed 137.280 0.472 138.256 Mean hyperparameter values: 0.4442959 1.593949 1.152257 Marginal likelihood: 4.428472e-183 Average test squared error: 0.244 GP WITH ABS EXP TERM, IMPORTANCE SAMPLING user system elapsed 133.761 0.460 134.698 Mean hyperparameter values: 0.3945411 1.307972 0.3271287 Marginal likelihood: 5.988985e-183 Average test squared error: 0.215 GP WITH TWO EXP TERMS, IMPORTANCE SAMPLING user system elapsed 233.434 0.700 234.962 Mean hyperparameter values: 0.417513 0.4994006 2.195435 0.648123 Marginal likelihood: 1.749671e-118 Average test squared error: 0.225