examples/xPCA.md
In WinVector/crosspca: Cross Validated Principal Components Analysis
# see: http://www.win-vector.com/blog/2016/05/pcr_part2_yaware/
# build example where even and odd variables are bringing in noisy images
# of two different signals.
mkData <- function(n) {
for(group in 1:10) {
# y is the sum of two effects yA and yB
yA <- rnorm(n)
yB <- rnorm(n)
if(group==1) {
d <- data.frame(y=yA+yB+rnorm(n))
code <- 'x'
} else {
code <- paste0('noise',group-1)
}
yS <- list(yA,yB)
# these variables are correlated with y in in group 1
for(i in 1:5) {
vi <- yS[[1+(i%%2)]] + rnorm(nrow(d))
d[[paste(code,formatC(i,width=2,flag=0),sep='.')]] <- ncol(d)*vi
}
}
d
}
# make data
set.seed(23525)
dTrain <- mkData(1000)
dTest <- mkData(1000)
## [1] 50
## [1] "std x-only scaling"
## [1] "*******************************************"
## [1] "x-only scaling"
## x.01 x.02 x.03
## Min. :-3.56466 Min. :-3.53178 Min. :-3.30810
## 1st Qu.:-0.71922 1st Qu.:-0.68546 1st Qu.:-0.69234
## Median : 0.01428 Median : 0.02157 Median :-0.01868
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.64729 3rd Qu.: 0.64710 3rd Qu.: 0.68890
## Max. : 3.02949 Max. : 3.44983 Max. : 3.53463
## x.04 x.05 noise1.01
## Min. :-3.024649 Min. :-3.44403 Min. :-3.55505
## 1st Qu.:-0.669618 1st Qu.:-0.70737 1st Qu.:-0.67730
## Median : 0.003458 Median :-0.02962 Median : 0.04075
## Mean : 0.000000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.679310 3rd Qu.: 0.69119 3rd Qu.: 0.66476
## Max. : 3.618095 Max. : 3.25413 Max. : 3.03398
## noise1.02 noise1.03 noise1.04
## Min. :-3.04344 Min. :-3.24553 Min. :-3.17058
## 1st Qu.:-0.67283 1st Qu.:-0.67685 1st Qu.:-0.66255
## Median :-0.01098 Median :-0.04143 Median : 0.02303
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.63123 3rd Qu.: 0.66017 3rd Qu.: 0.68567
## Max. : 3.09969 Max. : 3.46234 Max. : 3.30193
## noise1.05 noise2.01 noise2.02
## Min. :-3.637258 Min. :-3.02967 Min. :-3.11067
## 1st Qu.:-0.716404 1st Qu.:-0.67137 1st Qu.:-0.67677
## Median :-0.009741 Median :-0.02374 Median :-0.03242
## Mean : 0.000000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.669438 3rd Qu.: 0.61202 3rd Qu.: 0.67432
## Max. : 2.989022 Max. : 2.69382 Max. : 3.56327
## noise2.03 noise2.04 noise2.05
## Min. :-3.32724 Min. :-2.96915 Min. :-3.01326
## 1st Qu.:-0.69209 1st Qu.:-0.66348 1st Qu.:-0.67107
## Median : 0.01705 Median :-0.03646 Median :-0.02221
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.67707 3rd Qu.: 0.63654 3rd Qu.: 0.68463
## Max. : 3.64146 Max. : 3.24450 Max. : 3.12544
## noise3.01 noise3.02 noise3.03
## Min. :-3.37021 Min. :-2.90826 Min. :-5.26300
## 1st Qu.:-0.61175 1st Qu.:-0.67123 1st Qu.:-0.63535
## Median :-0.01631 Median :-0.01888 Median : 0.03451
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.63991 3rd Qu.: 0.68101 3rd Qu.: 0.64866
## Max. : 3.13484 Max. : 3.36663 Max. : 3.49695
## noise3.04 noise3.05 noise4.01
## Min. :-3.17697 Min. :-3.30323 Min. :-3.331686
## 1st Qu.:-0.68534 1st Qu.:-0.63505 1st Qu.:-0.672998
## Median : 0.01006 Median : 0.02726 Median :-0.003899
## Mean : 0.00000 Mean : 0.00000 Mean : 0.000000
## 3rd Qu.: 0.71201 3rd Qu.: 0.64763 3rd Qu.: 0.678726
## Max. : 2.80253 Max. : 3.25230 Max. : 3.672058
## noise4.02 noise4.03 noise4.04
## Min. :-3.40526 Min. :-3.50868 Min. :-2.850585
## 1st Qu.:-0.65631 1st Qu.:-0.67795 1st Qu.:-0.642033
## Median :-0.02656 Median :-0.02249 Median :-0.003927
## Mean : 0.00000 Mean : 0.00000 Mean : 0.000000
## 3rd Qu.: 0.71619 3rd Qu.: 0.69348 3rd Qu.: 0.666246
## Max. : 3.14709 Max. : 3.01486 Max. : 2.822614
## noise4.05 noise5.01 noise5.02
## Min. :-2.88875 Min. :-3.28356 Min. :-2.77919
## 1st Qu.:-0.68111 1st Qu.:-0.66186 1st Qu.:-0.68516
## Median :-0.02164 Median : 0.01031 Median :-0.01818
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.68861 3rd Qu.: 0.68392 3rd Qu.: 0.65803
## Max. : 2.99364 Max. : 3.59664 Max. : 2.86640
## noise5.03 noise5.04 noise5.05
## Min. :-3.141748 Min. :-3.372903 Min. :-3.00261
## 1st Qu.:-0.668289 1st Qu.:-0.664215 1st Qu.:-0.69759
## Median : 0.001024 Median : 0.004278 Median : 0.01208
## Mean : 0.000000 Mean : 0.000000 Mean : 0.00000
## 3rd Qu.: 0.694700 3rd Qu.: 0.666247 3rd Qu.: 0.69230
## Max. : 2.882415 Max. : 3.004999 Max. : 2.79255
## noise6.01 noise6.02 noise6.03
## Min. :-3.34363 Min. :-3.457442 Min. :-3.17042
## 1st Qu.:-0.66990 1st Qu.:-0.614116 1st Qu.:-0.68510
## Median : 0.02551 Median : 0.007875 Median :-0.02421
## Mean : 0.00000 Mean : 0.000000 Mean : 0.00000
## 3rd Qu.: 0.70390 3rd Qu.: 0.644664 3rd Qu.: 0.66523
## Max. : 2.76494 Max. : 3.101829 Max. : 3.36585
## noise6.04 noise6.05 noise7.01
## Min. :-3.383278 Min. :-3.08557 Min. :-2.81094
## 1st Qu.:-0.689616 1st Qu.:-0.67565 1st Qu.:-0.70652
## Median :-0.005454 Median : 0.02158 Median : 0.03228
## Mean : 0.000000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.685594 3rd Qu.: 0.66487 3rd Qu.: 0.67877
## Max. : 2.844464 Max. : 2.93981 Max. : 3.43567
## noise7.02 noise7.03 noise7.04
## Min. :-3.219500 Min. :-3.75066 Min. :-2.82669
## 1st Qu.:-0.705328 1st Qu.:-0.67748 1st Qu.:-0.66636
## Median : 0.002837 Median : 0.03481 Median :-0.02026
## Mean : 0.000000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.676359 3rd Qu.: 0.68288 3rd Qu.: 0.65232
## Max. : 3.478201 Max. : 2.78215 Max. : 3.22680
## noise7.05 noise8.01 noise8.02
## Min. :-2.87974 Min. :-3.15106 Min. :-3.36337
## 1st Qu.:-0.66995 1st Qu.:-0.69851 1st Qu.:-0.72149
## Median :-0.01265 Median : 0.03405 Median :-0.04337
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.69144 3rd Qu.: 0.67439 3rd Qu.: 0.68424
## Max. : 3.46219 Max. : 3.31936 Max. : 2.84291
## noise8.03 noise8.04 noise8.05
## Min. :-2.97938 Min. :-2.7641 Min. :-2.78277
## 1st Qu.:-0.69513 1st Qu.:-0.7185 1st Qu.:-0.70907
## Median : 0.02208 Median :-0.0125 Median : 0.03003
## Mean : 0.00000 Mean : 0.0000 Mean : 0.00000
## 3rd Qu.: 0.68959 3rd Qu.: 0.7405 3rd Qu.: 0.68615
## Max. : 3.14059 Max. : 2.9476 Max. : 2.92697
## noise9.01 noise9.02 noise9.03
## Min. :-2.869517 Min. :-3.214109 Min. :-3.112908
## 1st Qu.:-0.697756 1st Qu.:-0.675945 1st Qu.:-0.681257
## Median : 0.002377 Median : 0.002854 Median :-0.008767
## Mean : 0.000000 Mean : 0.000000 Mean : 0.000000
## 3rd Qu.: 0.674219 3rd Qu.: 0.634927 3rd Qu.: 0.694086
## Max. : 2.852684 Max. : 3.250219 Max. : 3.438842
## noise9.04 noise9.05
## Min. :-3.53174 Min. :-3.92015
## 1st Qu.:-0.65046 1st Qu.:-0.68052
## Median :-0.01833 Median : 0.02028
## Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.66983 3rd Qu.: 0.65494
## Max. : 3.47310 Max. : 3.11200
##
## Call:
## lm(formula = formula, data = projectedTrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4461 -0.9468 0.0313 0.9553 4.9620
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.08504 0.04783 1.778 0.075724 .
## PC1 -0.10702 0.03141 -3.407 0.000684 ***
## PC2 -0.04793 0.03181 -1.507 0.132183
## PC3 -0.13593 0.03222 -4.219 2.68e-05 ***
## PC4 -0.16234 0.03250 -4.995 6.94e-07 ***
## PC5 0.35688 0.03325 10.734 < 2e-16 ***
## PC6 0.12649 0.03343 3.783 0.000164 ***
## PC7 0.09255 0.03411 2.713 0.006786 **
## PC8 -0.13425 0.03475 -3.863 0.000119 ***
## PC9 0.28013 0.03516 7.967 4.46e-15 ***
## PC10 0.11262 0.03543 3.179 0.001523 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.513 on 989 degrees of freedom
## Multiple R-squared: 0.2219, Adjusted R-squared: 0.214
## F-statistic: 28.2 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.221881172515066"
## [1] "test rsq 0.26396282224084"
##
## Call:
## lm(formula = formula, data = projectedTrainX)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1926 -1.0522 0.0082 1.0251 5.6872
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.08783 0.05054 1.738 0.082535 .
## PC1 -0.12992 0.03752 -3.463 0.000557 ***
## PC2 -0.09055 0.03670 -2.467 0.013795 *
## PC3 -0.07856 0.03697 -2.125 0.033847 *
## PC4 -0.15607 0.03467 -4.502 7.53e-06 ***
## PC5 0.27168 0.03723 7.297 6.05e-13 ***
## PC6 0.13367 0.03751 3.564 0.000383 ***
## PC7 0.15881 0.03637 4.367 1.39e-05 ***
## PC8 -0.03533 0.03770 -0.937 0.348976
## PC9 0.15971 0.03717 4.296 1.91e-05 ***
## PC10 0.08733 0.03654 2.390 0.017052 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.595 on 989 degrees of freedom
## Multiple R-squared: 0.1344, Adjusted R-squared: 0.1256
## F-statistic: 15.35 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.134358541014939"
## [1] "test rsq 0.235021411151901"
## [1] "using direct method"
## [1] "*******************************************"
## [1] "in-sample y-aware scaling"
## x.01 x.02 x.03
## Min. :-2.65396 Min. :-2.51975 Min. :-2.14566
## 1st Qu.:-0.53547 1st Qu.:-0.48904 1st Qu.:-0.44906
## Median : 0.01063 Median : 0.01539 Median :-0.01211
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.48192 3rd Qu.: 0.46167 3rd Qu.: 0.44683
## Max. : 2.25552 Max. : 2.46128 Max. : 2.29259
## x.04 x.05 noise1.01
## Min. :-2.157010 Min. :-2.11879 Min. :-0.24249
## 1st Qu.:-0.477534 1st Qu.:-0.43518 1st Qu.:-0.04620
## Median : 0.002466 Median :-0.01822 Median : 0.00278
## Mean : 0.000000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.484445 3rd Qu.: 0.42523 3rd Qu.: 0.04534
## Max. : 2.580222 Max. : 2.00196 Max. : 0.20695
## noise1.02 noise1.03 noise1.04
## Min. :-0.0917910 Min. :-0.0785730 Min. :-0.0162697
## 1st Qu.:-0.0186927 1st Qu.:-0.0149815 1st Qu.:-0.0033998
## Median : 0.0003253 Median : 0.0009402 Median : 0.0001182
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 0.0199244 3rd Qu.: 0.0153602 3rd Qu.: 0.0035185
## Max. : 0.0901253 Max. : 0.0736528 Max. : 0.0169437
## noise1.05 noise2.01 noise2.02
## Min. :-0.0679766 Min. :-0.173381 Min. :-2.052e-03
## 1st Qu.:-0.0152244 1st Qu.:-0.038421 1st Qu.:-3.884e-04
## Median : 0.0002215 Median :-0.001359 Median : 1.867e-05
## Mean : 0.0000000 Mean : 0.000000 Mean : 0.000e+00
## 3rd Qu.: 0.0162925 3rd Qu.: 0.035024 3rd Qu.: 3.898e-04
## Max. : 0.0827189 Max. : 0.154162 Max. : 1.792e-03
## noise2.03 noise2.04 noise2.05
## Min. :-1.794e-02 Min. :-0.0163329 Min. :-0.0165502
## 1st Qu.:-3.335e-03 1st Qu.:-0.0036497 1st Qu.:-0.0036253
## Median :-8.396e-05 Median :-0.0002006 Median : 0.0001176
## Mean : 0.000e+00 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 3.409e-03 3rd Qu.: 0.0035015 3rd Qu.: 0.0035535
## Max. : 1.639e-02 Max. : 0.0178476 Max. : 0.0159562
## noise3.01 noise3.02 noise3.03
## Min. :-0.1264964 Min. :-0.0218154 Min. :-0.0915218
## 1st Qu.:-0.0258215 1st Qu.:-0.0050351 1st Qu.:-0.0110485
## Median : 0.0006582 Median :-0.0001416 Median : 0.0006002
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 0.0246851 3rd Qu.: 0.0051084 3rd Qu.: 0.0112799
## Max. : 0.1359939 Max. : 0.0252537 Max. : 0.0608108
## noise3.04 noise3.05 noise4.01
## Min. :-0.1837226 Min. :-3.222e-03 Min. :-5.332e-02
## 1st Qu.:-0.0396330 1st Qu.:-6.194e-04 1st Qu.:-9.856e-03
## Median : 0.0005818 Median : 2.659e-05 Median : 5.663e-05
## Mean : 0.0000000 Mean : 0.000e+00 Mean : 0.000e+00
## 3rd Qu.: 0.0411750 3rd Qu.: 6.317e-04 3rd Qu.: 9.773e-03
## Max. : 0.1620686 Max. : 3.172e-03 Max. : 4.838e-02
## noise4.02 noise4.03 noise4.04
## Min. :-0.1187360 Min. :-0.0797358 Min. :-1.002e-02
## 1st Qu.:-0.0228846 1st Qu.:-0.0154065 1st Qu.:-2.365e-03
## Median :-0.0009261 Median :-0.0005111 Median : 1.394e-05
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.000e+00
## 3rd Qu.: 0.0249723 3rd Qu.: 0.0157595 3rd Qu.: 2.279e-03
## Max. : 0.1097340 Max. : 0.0685135 Max. : 1.012e-02
## noise4.05 noise5.01 noise5.02
## Min. :-0.285450 Min. :-0.0936289 Min. :-7.560e-03
## 1st Qu.:-0.065661 1st Qu.:-0.0188727 1st Qu.:-1.864e-03
## Median : 0.002063 Median : 0.0002939 Median :-4.945e-05
## Mean : 0.000000 Mean : 0.0000000 Mean : 0.000e+00
## 3rd Qu.: 0.064945 3rd Qu.: 0.0195017 3rd Qu.: 1.790e-03
## Max. : 0.275449 Max. : 0.1025562 Max. : 7.797e-03
## noise5.03 noise5.04 noise5.05
## Min. :-1.052e-01 Min. :-0.0951126 Min. :-0.1015520
## 1st Qu.:-2.238e-02 1st Qu.:-0.0210877 1st Qu.:-0.0235934
## Median : 3.429e-05 Median :-0.0001354 Median : 0.0004086
## Mean : 0.000e+00 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 2.327e-02 3rd Qu.: 0.0210234 3rd Qu.: 0.0234145
## Max. : 9.655e-02 Max. : 0.1067573 Max. : 0.0944476
## noise6.01 noise6.02 noise6.03
## Min. :-0.0591549 Min. :-0.0671441 Min. :-0.048987
## 1st Qu.:-0.0118519 1st Qu.:-0.0139548 1st Qu.:-0.010586
## Median : 0.0004513 Median :-0.0001705 Median :-0.000374
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.000000
## 3rd Qu.: 0.0124533 3rd Qu.: 0.0132935 3rd Qu.: 0.010279
## Max. : 0.0489168 Max. : 0.0748419 Max. : 0.052007
## noise6.04 noise6.05 noise7.01
## Min. :-3.373e-02 Min. :-0.257923 Min. :-0.17347
## 1st Qu.:-8.129e-03 1st Qu.:-0.058332 1st Qu.:-0.03427
## Median : 6.467e-05 Median :-0.001893 Median :-0.00163
## Mean : 0.000e+00 Mean : 0.000000 Mean : 0.00000
## 3rd Qu.: 8.177e-03 3rd Qu.: 0.059278 3rd Qu.: 0.03567
## Max. : 4.012e-02 Max. : 0.270711 Max. : 0.14192
## noise7.02 noise7.03 noise7.04
## Min. :-6.723e-03 Min. :-0.111783 Min. :-0.0377584
## 1st Qu.:-1.473e-03 1st Qu.:-0.027437 1st Qu.:-0.0089011
## Median : 5.925e-06 Median :-0.001399 Median :-0.0002706
## Mean : 0.000e+00 Mean : 0.000000 Mean : 0.0000000
## 3rd Qu.: 1.412e-03 3rd Qu.: 0.027220 3rd Qu.: 0.0087135
## Max. : 7.263e-03 Max. : 0.150697 Max. : 0.0431029
## noise7.05 noise8.01 noise8.02
## Min. :-0.315530 Min. :-0.0793439 Min. :-0.161566
## 1st Qu.:-0.063015 1st Qu.:-0.0175886 1st Qu.:-0.038886
## Median : 0.001153 Median : 0.0008574 Median : 0.002464
## Mean : 0.000000 Mean : 0.0000000 Mean : 0.000000
## 3rd Qu.: 0.061056 3rd Qu.: 0.0169812 3rd Qu.: 0.041003
## Max. : 0.262448 Max. : 0.0835817 Max. : 0.191144
## noise8.03 noise8.04 noise8.05
## Min. :-0.0672229 Min. :-0.0571279 Min. :-0.127256
## 1st Qu.:-0.0147604 1st Qu.:-0.0148491 1st Qu.:-0.032426
## Median :-0.0004726 Median :-0.0002584 Median : 0.001373
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.000000
## 3rd Qu.: 0.0148790 3rd Qu.: 0.0153044 3rd Qu.: 0.031378
## Max. : 0.0637722 Max. : 0.0609191 Max. : 0.133850
## noise9.01 noise9.02 noise9.03
## Min. :-0.0423694 Min. :-6.255e-02 Min. :-1.752e-02
## 1st Qu.:-0.0100138 1st Qu.:-1.315e-02 1st Qu.:-3.835e-03
## Median :-0.0000353 Median : 5.555e-05 Median :-4.935e-05
## Mean : 0.0000000 Mean : 0.000e+00 Mean : 0.000e+00
## 3rd Qu.: 0.0103634 3rd Qu.: 1.236e-02 3rd Qu.: 3.907e-03
## Max. : 0.0426194 Max. : 6.325e-02 Max. : 1.936e-02
## noise9.04 noise9.05
## Min. :-0.18108 Min. :-0.0654833
## 1st Qu.:-0.03335 1st Qu.:-0.0137813
## Median :-0.00094 Median :-0.0004266
## Mean : 0.00000 Mean : 0.0000000
## 3rd Qu.: 0.03434 3rd Qu.: 0.0143196
## Max. : 0.17808 Max. : 0.0824886
##
## Call:
## lm(formula = formula, data = projectedTrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2028 -0.7853 0.0146 0.8072 3.8040
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.08504 0.03901 2.180 0.0295 *
## PC1 0.78611 0.04080 19.268 <2e-16 ***
## PC2 1.03243 0.04456 23.168 <2e-16 ***
## PC3 0.04029 0.07676 0.525 0.5998
## PC4 0.07607 0.08106 0.938 0.3482
## PC5 0.01020 0.08758 0.116 0.9073
## PC6 0.97950 0.39465 2.482 0.0132 *
## PC7 0.19548 0.40980 0.477 0.6335
## PC8 0.25861 0.44129 0.586 0.5580
## PC9 1.26484 0.54986 2.300 0.0216 *
## PC10 0.51306 0.66129 0.776 0.4380
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.234 on 989 degrees of freedom
## Multiple R-squared: 0.4824, Adjusted R-squared: 0.4772
## F-statistic: 92.18 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.48242177283421"
## [1] "test rsq 0.502942338312764"
##
## Call:
## lm(formula = formula, data = projectedTrainX)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5431 -0.7793 0.0271 0.7785 3.8115
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.081426 0.039360 2.069 0.0388 *
## PC1 0.785442 0.041505 18.924 <2e-16 ***
## PC2 1.013972 0.044635 22.717 <2e-16 ***
## PC3 0.025058 0.079177 0.316 0.7517
## PC4 0.100976 0.080940 1.248 0.2125
## PC5 -0.009149 0.086964 -0.105 0.9162
## PC6 0.946245 0.410214 2.307 0.0213 *
## PC7 0.112232 0.414764 0.271 0.7868
## PC8 0.188555 0.440526 0.428 0.6687
## PC9 1.204269 0.555951 2.166 0.0305 *
## PC10 0.581804 0.696223 0.836 0.4035
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.244 on 989 degrees of freedom
## Multiple R-squared: 0.4737, Adjusted R-squared: 0.4684
## F-statistic: 89.01 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.473673511681592"
## [1] "test rsq 0.50387599242553"
## [1] "vtreat y-aware direct scaling"
## [1] "desigining treatments Thu Jul 14 09:59:08 2016"
## [1] "scoring treatments Thu Jul 14 09:59:08 2016"
## [1] "have treatment plan Thu Jul 14 09:59:08 2016"
## [1] 50
## [1] "*******************************************"
## [1] "vtreat in-sample y-aware scaling"
## x.01_clean x.02_clean x.03_clean
## Min. :-2.65396 Min. :-2.51975 Min. :-2.14566
## 1st Qu.:-0.53547 1st Qu.:-0.48904 1st Qu.:-0.44906
## Median : 0.01063 Median : 0.01539 Median :-0.01211
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.48192 3rd Qu.: 0.46167 3rd Qu.: 0.44683
## Max. : 2.25552 Max. : 2.46128 Max. : 2.29259
## x.04_clean x.05_clean noise1.01_clean
## Min. :-2.157010 Min. :-2.11879 Min. :-0.24249
## 1st Qu.:-0.477534 1st Qu.:-0.43518 1st Qu.:-0.04620
## Median : 0.002466 Median :-0.01822 Median : 0.00278
## Mean : 0.000000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.484445 3rd Qu.: 0.42523 3rd Qu.: 0.04534
## Max. : 2.580222 Max. : 2.00196 Max. : 0.20695
## noise1.02_clean noise1.03_clean noise1.04_clean
## Min. :-0.0917910 Min. :-0.0785730 Min. :-0.0162697
## 1st Qu.:-0.0186927 1st Qu.:-0.0149815 1st Qu.:-0.0033998
## Median : 0.0003253 Median : 0.0009402 Median : 0.0001182
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 0.0199244 3rd Qu.: 0.0153602 3rd Qu.: 0.0035185
## Max. : 0.0901253 Max. : 0.0736528 Max. : 0.0169437
## noise1.05_clean noise2.01_clean noise2.02_clean
## Min. :-0.0679766 Min. :-0.173381 Min. :-2.052e-03
## 1st Qu.:-0.0152244 1st Qu.:-0.038421 1st Qu.:-3.884e-04
## Median : 0.0002215 Median :-0.001359 Median : 1.867e-05
## Mean : 0.0000000 Mean : 0.000000 Mean : 0.000e+00
## 3rd Qu.: 0.0162925 3rd Qu.: 0.035024 3rd Qu.: 3.898e-04
## Max. : 0.0827189 Max. : 0.154162 Max. : 1.792e-03
## noise2.03_clean noise2.04_clean noise2.05_clean
## Min. :-1.794e-02 Min. :-0.0163329 Min. :-0.0165502
## 1st Qu.:-3.335e-03 1st Qu.:-0.0036497 1st Qu.:-0.0036253
## Median :-8.396e-05 Median :-0.0002006 Median : 0.0001176
## Mean : 0.000e+00 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 3.409e-03 3rd Qu.: 0.0035015 3rd Qu.: 0.0035535
## Max. : 1.639e-02 Max. : 0.0178476 Max. : 0.0159562
## noise3.01_clean noise3.02_clean noise3.03_clean
## Min. :-0.1264964 Min. :-0.0218154 Min. :-0.0915218
## 1st Qu.:-0.0258215 1st Qu.:-0.0050351 1st Qu.:-0.0110485
## Median : 0.0006582 Median :-0.0001416 Median : 0.0006002
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 0.0246851 3rd Qu.: 0.0051084 3rd Qu.: 0.0112799
## Max. : 0.1359939 Max. : 0.0252537 Max. : 0.0608108
## noise3.04_clean noise3.05_clean noise4.01_clean
## Min. :-0.1837226 Min. :-3.222e-03 Min. :-5.332e-02
## 1st Qu.:-0.0396330 1st Qu.:-6.194e-04 1st Qu.:-9.856e-03
## Median : 0.0005818 Median : 2.659e-05 Median : 5.663e-05
## Mean : 0.0000000 Mean : 0.000e+00 Mean : 0.000e+00
## 3rd Qu.: 0.0411750 3rd Qu.: 6.317e-04 3rd Qu.: 9.773e-03
## Max. : 0.1620686 Max. : 3.172e-03 Max. : 4.838e-02
## noise4.02_clean noise4.03_clean noise4.04_clean
## Min. :-0.1187360 Min. :-0.0797358 Min. :-1.002e-02
## 1st Qu.:-0.0228846 1st Qu.:-0.0154065 1st Qu.:-2.365e-03
## Median :-0.0009261 Median :-0.0005111 Median : 1.394e-05
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.000e+00
## 3rd Qu.: 0.0249723 3rd Qu.: 0.0157595 3rd Qu.: 2.279e-03
## Max. : 0.1097340 Max. : 0.0685135 Max. : 1.012e-02
## noise4.05_clean noise5.01_clean noise5.02_clean
## Min. :-0.285450 Min. :-0.0936289 Min. :-7.560e-03
## 1st Qu.:-0.065661 1st Qu.:-0.0188727 1st Qu.:-1.864e-03
## Median : 0.002063 Median : 0.0002939 Median :-4.945e-05
## Mean : 0.000000 Mean : 0.0000000 Mean : 0.000e+00
## 3rd Qu.: 0.064945 3rd Qu.: 0.0195017 3rd Qu.: 1.790e-03
## Max. : 0.275449 Max. : 0.1025562 Max. : 7.797e-03
## noise5.03_clean noise5.04_clean noise5.05_clean
## Min. :-1.052e-01 Min. :-0.0951126 Min. :-0.1015520
## 1st Qu.:-2.238e-02 1st Qu.:-0.0210877 1st Qu.:-0.0235934
## Median : 3.429e-05 Median :-0.0001354 Median : 0.0004086
## Mean : 0.000e+00 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 2.327e-02 3rd Qu.: 0.0210234 3rd Qu.: 0.0234145
## Max. : 9.655e-02 Max. : 0.1067573 Max. : 0.0944476
## noise6.01_clean noise6.02_clean noise6.03_clean
## Min. :-0.0591549 Min. :-0.0671441 Min. :-0.048987
## 1st Qu.:-0.0118519 1st Qu.:-0.0139548 1st Qu.:-0.010586
## Median : 0.0004513 Median :-0.0001705 Median :-0.000374
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.000000
## 3rd Qu.: 0.0124533 3rd Qu.: 0.0132935 3rd Qu.: 0.010279
## Max. : 0.0489168 Max. : 0.0748419 Max. : 0.052007
## noise6.04_clean noise6.05_clean noise7.01_clean
## Min. :-3.373e-02 Min. :-0.257923 Min. :-0.17347
## 1st Qu.:-8.129e-03 1st Qu.:-0.058332 1st Qu.:-0.03427
## Median : 6.467e-05 Median :-0.001893 Median :-0.00163
## Mean : 0.000e+00 Mean : 0.000000 Mean : 0.00000
## 3rd Qu.: 8.177e-03 3rd Qu.: 0.059278 3rd Qu.: 0.03567
## Max. : 4.012e-02 Max. : 0.270711 Max. : 0.14192
## noise7.02_clean noise7.03_clean noise7.04_clean
## Min. :-6.723e-03 Min. :-0.111783 Min. :-0.0377584
## 1st Qu.:-1.473e-03 1st Qu.:-0.027437 1st Qu.:-0.0089011
## Median : 5.925e-06 Median :-0.001399 Median :-0.0002706
## Mean : 0.000e+00 Mean : 0.000000 Mean : 0.0000000
## 3rd Qu.: 1.412e-03 3rd Qu.: 0.027220 3rd Qu.: 0.0087135
## Max. : 7.263e-03 Max. : 0.150697 Max. : 0.0431029
## noise7.05_clean noise8.01_clean noise8.02_clean
## Min. :-0.315530 Min. :-0.0793439 Min. :-0.161566
## 1st Qu.:-0.063015 1st Qu.:-0.0175886 1st Qu.:-0.038886
## Median : 0.001153 Median : 0.0008574 Median : 0.002464
## Mean : 0.000000 Mean : 0.0000000 Mean : 0.000000
## 3rd Qu.: 0.061056 3rd Qu.: 0.0169812 3rd Qu.: 0.041003
## Max. : 0.262448 Max. : 0.0835817 Max. : 0.191144
## noise8.03_clean noise8.04_clean noise8.05_clean
## Min. :-0.0672229 Min. :-0.0571279 Min. :-0.127256
## 1st Qu.:-0.0147604 1st Qu.:-0.0148491 1st Qu.:-0.032426
## Median :-0.0004726 Median :-0.0002584 Median : 0.001373
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.000000
## 3rd Qu.: 0.0148790 3rd Qu.: 0.0153044 3rd Qu.: 0.031378
## Max. : 0.0637722 Max. : 0.0609191 Max. : 0.133850
## noise9.01_clean noise9.02_clean noise9.03_clean
## Min. :-0.0423694 Min. :-6.255e-02 Min. :-1.752e-02
## 1st Qu.:-0.0100138 1st Qu.:-1.315e-02 1st Qu.:-3.835e-03
## Median :-0.0000353 Median : 5.555e-05 Median :-4.935e-05
## Mean : 0.0000000 Mean : 0.000e+00 Mean : 0.000e+00
## 3rd Qu.: 0.0103634 3rd Qu.: 1.236e-02 3rd Qu.: 3.907e-03
## Max. : 0.0426194 Max. : 6.325e-02 Max. : 1.936e-02
## noise9.04_clean noise9.05_clean
## Min. :-0.18108 Min. :-0.0654833
## 1st Qu.:-0.03335 1st Qu.:-0.0137813
## Median :-0.00094 Median :-0.0004266
## Mean : 0.00000 Mean : 0.0000000
## 3rd Qu.: 0.03434 3rd Qu.: 0.0143196
## Max. : 0.17808 Max. : 0.0824886
##
## Call:
## lm(formula = formula, data = projectedTrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2028 -0.7853 0.0146 0.8072 3.8040
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.08504 0.03901 2.180 0.0295 *
## PC1 0.78611 0.04080 19.268 <2e-16 ***
## PC2 1.03243 0.04456 23.168 <2e-16 ***
## PC3 0.04029 0.07676 0.525 0.5998
## PC4 0.07607 0.08106 0.938 0.3482
## PC5 0.01020 0.08758 0.116 0.9073
## PC6 0.97950 0.39465 2.482 0.0132 *
## PC7 0.19548 0.40980 0.477 0.6335
## PC8 0.25861 0.44129 0.586 0.5580
## PC9 1.26484 0.54986 2.300 0.0216 *
## PC10 0.51306 0.66129 0.776 0.4380
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.234 on 989 degrees of freedom
## Multiple R-squared: 0.4824, Adjusted R-squared: 0.4772
## F-statistic: 92.18 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.48242177283421"
## [1] "test rsq 0.503254874942015"
##
## Call:
## lm(formula = formula, data = projectedTrainX)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2432 -0.7686 0.0169 0.8154 3.8046
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.083641 0.038830 2.154 0.03148 *
## PC1 0.795175 0.040946 19.420 < 2e-16 ***
## PC2 1.034565 0.044105 23.457 < 2e-16 ***
## PC3 0.052068 0.077986 0.668 0.50450
## PC4 0.096981 0.080222 1.209 0.22699
## PC5 0.002884 0.084751 0.034 0.97286
## PC6 1.037224 0.401609 2.583 0.00995 **
## PC7 -0.093037 0.406995 -0.229 0.81923
## PC8 0.332000 0.437092 0.760 0.44770
## PC9 1.234144 0.548365 2.251 0.02463 *
## PC10 0.591191 0.680856 0.868 0.38544
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.227 on 989 degrees of freedom
## Multiple R-squared: 0.4879, Adjusted R-squared: 0.4827
## F-statistic: 94.22 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.487885192201953"
## [1] "test rsq 0.50274983232389"
## [1] "vtreat y-aware cross scaling"
## [1] 50
## [1] "*******************************************"
## [1] "vtreat out-sample y-aware scaling"
## x.01_clean x.02_clean x.03_clean
## Min. :-2.4928250 Min. :-1.8968518 Min. :-2.0885228
## 1st Qu.:-0.5268214 1st Qu.:-0.4919804 1st Qu.:-0.4492052
## Median : 0.0112782 Median : 0.0128891 Median :-0.0186294
## Mean : 0.0000476 Mean : 0.0003547 Mean :-0.0008096
## 3rd Qu.: 0.4846578 3rd Qu.: 0.4670734 3rd Qu.: 0.4422544
## Max. : 2.3032040 Max. : 1.7843994 Max. : 1.8871384
## x.04_clean x.05_clean noise1.01_clean
## Min. :-2.1991117 Min. :-1.7271045 Min. :-0.426249
## 1st Qu.:-0.4793271 1st Qu.:-0.4362600 1st Qu.:-0.043695
## Median : 0.0065618 Median :-0.0134015 Median :-0.001372
## Mean :-0.0001205 Mean :-0.0004336 Mean :-0.004809
## 3rd Qu.: 0.4976845 3rd Qu.: 0.4260831 3rd Qu.: 0.036954
## Max. : 2.1671205 Max. : 1.9223094 Max. : 0.389958
## noise1.02_clean noise1.03_clean noise1.04_clean
## Min. :-1.643e-01 Min. :-1.930e-01 Min. :-0.1892920
## 1st Qu.:-1.293e-02 1st Qu.:-3.345e-03 1st Qu.:-0.0188442
## Median : 8.440e-06 Median : 1.203e-05 Median :-0.0001182
## Mean :-1.697e-04 Mean : 1.422e-04 Mean : 0.0001067
## 3rd Qu.: 1.164e-02 3rd Qu.: 3.951e-03 3rd Qu.: 0.0202844
## Max. : 1.550e-01 Max. : 2.068e-01 Max. : 0.2137786
## noise1.05_clean noise2.01_clean noise2.02_clean
## Min. :-0.1080511 Min. :-0.3081651 Min. :-0.181633
## 1st Qu.:-0.0084149 1st Qu.:-0.0273283 1st Qu.:-0.021925
## Median : 0.0001153 Median :-0.0009219 Median :-0.001306
## Mean : 0.0010011 Mean :-0.0027857 Mean :-0.001093
## 3rd Qu.: 0.0105288 3rd Qu.: 0.0194300 3rd Qu.: 0.020715
## Max. : 0.0942555 Max. : 0.2854280 Max. : 0.158605
## noise2.03_clean noise2.04_clean noise2.05_clean
## Min. :-9.797e-02 Min. :-0.0995666 Min. :-0.1152369
## 1st Qu.:-1.294e-02 1st Qu.:-0.0096579 1st Qu.:-0.0151831
## Median :-6.684e-05 Median :-0.0002762 Median : 0.0001287
## Mean :-1.585e-03 Mean :-0.0008766 Mean : 0.0008302
## 3rd Qu.: 7.135e-03 3rd Qu.: 0.0071184 3rd Qu.: 0.0165792
## Max. : 1.021e-01 Max. : 0.1057949 Max. : 0.1279297
## noise3.01_clean noise3.02_clean noise3.03_clean
## Min. :-0.1998016 Min. :-0.0604256 Min. :-0.118726
## 1st Qu.:-0.0220991 1st Qu.:-0.0144636 1st Qu.:-0.023373
## Median : 0.0001479 Median :-0.0004227 Median : 0.001961
## Mean : 0.0009997 Mean :-0.0003034 Mean : 0.001188
## 3rd Qu.: 0.0222002 3rd Qu.: 0.0138945 3rd Qu.: 0.028313
## Max. : 0.1828342 Max. : 0.0635209 Max. : 0.125265
## noise3.04_clean noise3.05_clean noise4.01_clean
## Min. :-0.300566 Min. :-0.0703705 Min. :-0.1056500
## 1st Qu.:-0.027579 1st Qu.:-0.0077674 1st Qu.:-0.0161007
## Median : 0.000702 Median :-0.0004022 Median :-0.0003400
## Mean : 0.001242 Mean :-0.0005460 Mean : 0.0006295
## 3rd Qu.: 0.028834 3rd Qu.: 0.0077326 3rd Qu.: 0.0163273
## Max. : 0.263991 Max. : 0.0793515 Max. : 0.1438478
## noise4.02_clean noise4.03_clean noise4.04_clean
## Min. :-1.613e-01 Min. :-0.1198399 Min. :-0.053766
## 1st Qu.:-2.838e-02 1st Qu.:-0.0109753 1st Qu.:-0.010514
## Median : 7.918e-05 Median :-0.0003268 Median :-0.000346
## Mean : 7.489e-04 Mean : 0.0003305 Mean :-0.000778
## 3rd Qu.: 2.987e-02 3rd Qu.: 0.0129833 3rd Qu.: 0.009662
## Max. : 1.822e-01 Max. : 0.1076177 Max. : 0.054513
## noise4.05_clean noise5.01_clean noise5.02_clean
## Min. :-0.3554570 Min. :-0.1587111 Min. :-0.0608793
## 1st Qu.:-0.0618410 1st Qu.:-0.0269446 1st Qu.:-0.0097781
## Median : 0.0022673 Median :-0.0008395 Median : 0.0005607
## Mean :-0.0006985 Mean :-0.0013742 Mean : 0.0003178
## 3rd Qu.: 0.0616620 3rd Qu.: 0.0239865 3rd Qu.: 0.0102144
## Max. : 0.3455270 Max. : 0.1584974 Max. : 0.0668463
## noise5.03_clean noise5.04_clean noise5.05_clean
## Min. :-0.160800 Min. :-0.188312 Min. :-0.1642639
## 1st Qu.:-0.025099 1st Qu.:-0.029240 1st Qu.:-0.0199268
## Median :-0.002182 Median :-0.002763 Median : 0.0003208
## Mean :-0.004084 Mean :-0.001428 Mean :-0.0006798
## 3rd Qu.: 0.018050 3rd Qu.: 0.027289 3rd Qu.: 0.0184161
## Max. : 0.152699 Max. : 0.210413 Max. : 0.1508710
## noise6.01_clean noise6.02_clean noise6.03_clean
## Min. :-0.1409052 Min. :-0.0647908 Min. :-0.1431836
## 1st Qu.:-0.0138004 1st Qu.:-0.0138838 1st Qu.:-0.0119652
## Median : 0.0005295 Median :-0.0001265 Median :-0.0003957
## Mean : 0.0006411 Mean : 0.0001051 Mean :-0.0005282
## 3rd Qu.: 0.0142756 3rd Qu.: 0.0131726 3rd Qu.: 0.0105255
## Max. : 0.1200339 Max. : 0.0846984 Max. : 0.1532759
## noise6.04_clean noise6.05_clean noise7.01_clean
## Min. :-1.339e-01 Min. :-0.2795717 Min. :-2.411e-01
## 1st Qu.:-1.310e-02 1st Qu.:-0.0565541 1st Qu.:-2.822e-02
## Median : 9.779e-05 Median :-0.0013575 Median :-8.754e-05
## Mean : 7.623e-04 Mean :-0.0006809 Mean : 1.016e-03
## 3rd Qu.: 1.379e-02 3rd Qu.: 0.0593673 3rd Qu.: 2.270e-02
## Max. : 1.430e-01 Max. : 0.2907112 Max. : 2.511e-01
## noise7.02_clean noise7.03_clean noise7.04_clean
## Min. :-0.0926229 Min. :-1.574e-01 Min. :-0.174337
## 1st Qu.:-0.0108093 1st Qu.:-2.191e-02 1st Qu.:-0.015499
## Median : 0.0005102 Median :-1.116e-03 Median : 0.003298
## Mean : 0.0005724 Mean :-4.205e-05 Mean : 0.003421
## 3rd Qu.: 0.0114012 3rd Qu.: 2.171e-02 3rd Qu.: 0.021792
## Max. : 0.0888071 Max. : 1.950e-01 Max. : 0.205388
## noise7.05_clean noise8.01_clean noise8.02_clean
## Min. :-0.421940 Min. :-0.1506603 Min. :-0.371298
## 1st Qu.:-0.052708 1st Qu.:-0.0102380 1st Qu.:-0.018444
## Median : 0.001076 Median : 0.0004780 Median : 0.001110
## Mean :-0.002247 Mean : 0.0002121 Mean : 0.001383
## 3rd Qu.: 0.049529 3rd Qu.: 0.0083749 3rd Qu.: 0.019982
## Max. : 0.415175 Max. : 0.1739351 Max. : 0.348457
## noise8.03_clean noise8.04_clean noise8.05_clean
## Min. :-0.0756356 Min. :-0.1115515 Min. :-2.047e-01
## 1st Qu.:-0.0107573 1st Qu.:-0.0128572 1st Qu.:-2.550e-02
## Median :-0.0003162 Median :-0.0005888 Median : 1.406e-04
## Mean : 0.0009101 Mean : 0.0007402 Mean :-1.563e-05
## 3rd Qu.: 0.0116963 3rd Qu.: 0.0125804 3rd Qu.: 2.759e-02
## Max. : 0.0773755 Max. : 0.1206437 Max. : 2.120e-01
## noise9.01_clean noise9.02_clean noise9.03_clean
## Min. :-0.144396 Min. :-0.3035379 Min. :-0.2042942
## 1st Qu.:-0.026123 1st Qu.:-0.0178880 1st Qu.:-0.0346027
## Median : 0.003267 Median :-0.0008822 Median : 0.0012979
## Mean : 0.004086 Mean :-0.0013709 Mean : 0.0009684
## 3rd Qu.: 0.033567 3rd Qu.: 0.0165791 3rd Qu.: 0.0371975
## Max. : 0.141179 Max. : 0.2801319 Max. : 0.2311867
## noise9.04_clean noise9.05_clean
## Min. :-0.2492952 Min. :-0.215547
## 1st Qu.:-0.0277772 1st Qu.:-0.007519
## Median :-0.0007276 Median : 0.001162
## Mean : 0.0006848 Mean : 0.003213
## 3rd Qu.: 0.0278836 3rd Qu.: 0.010409
## Max. : 0.2647385 Max. : 0.277541
##
## Call:
## lm(formula = formula, data = projectedTrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2661 -0.7910 0.0061 0.7893 3.8012
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.08902 0.03926 2.267 0.0236 *
## PC1 0.78437 0.04107 19.097 <2e-16 ***
## PC2 1.04138 0.04515 23.063 <2e-16 ***
## PC3 0.05750 0.07729 0.744 0.4571
## PC4 0.07352 0.08147 0.902 0.3670
## PC5 0.01037 0.08803 0.118 0.9062
## PC6 0.51946 0.34381 1.511 0.1311
## PC7 0.25873 0.40176 0.644 0.5197
## PC8 0.44482 0.41438 1.073 0.2833
## PC9 0.27200 0.43917 0.619 0.5358
## PC10 -0.68763 0.49879 -1.379 0.1683
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.239 on 989 degrees of freedom
## Multiple R-squared: 0.4776, Adjusted R-squared: 0.4723
## F-statistic: 90.41 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.477579027812596"
## [1] "test rsq 0.508026833657251"
##
## Call:
## lm(formula = formula, data = projectedTrainX)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3638 -0.7798 0.0082 0.7805 3.7913
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.086833 0.039378 2.205 0.0277 *
## PC1 0.791402 0.041444 19.096 <2e-16 ***
## PC2 1.036438 0.045209 22.925 <2e-16 ***
## PC3 0.064453 0.078581 0.820 0.4123
## PC4 0.082530 0.080841 1.021 0.3076
## PC5 -0.004644 0.087272 -0.053 0.9576
## PC6 0.534089 0.348692 1.532 0.1259
## PC7 0.240347 0.416181 0.578 0.5637
## PC8 0.090616 0.415384 0.218 0.8274
## PC9 0.162838 0.439745 0.370 0.7112
## PC10 -0.562617 0.526745 -1.068 0.2857
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.243 on 989 degrees of freedom
## Multiple R-squared: 0.4741, Adjusted R-squared: 0.4688
## F-statistic: 89.17 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.474120614572344"
## [1] "test rsq 0.507977629275113"
WinVector/crosspca documentation built on June 24, 2020, 5:09 p.m.
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# see: http://www.win-vector.com/blog/2016/05/pcr_part2_yaware/
# build example where even and odd variables are bringing in noisy images
# of two different signals.
mkData <- function(n) {
for(group in 1:10) {
# y is the sum of two effects yA and yB
yA <- rnorm(n)
yB <- rnorm(n)
if(group==1) {
d <- data.frame(y=yA+yB+rnorm(n))
code <- 'x'
} else {
code <- paste0('noise',group-1)
}
yS <- list(yA,yB)
# these variables are correlated with y in in group 1
for(i in 1:5) {
vi <- yS[[1+(i%%2)]] + rnorm(nrow(d))
d[[paste(code,formatC(i,width=2,flag=0),sep='.')]] <- ncol(d)*vi
}
}
d
}
# make data
set.seed(23525)
dTrain <- mkData(1000)
dTest <- mkData(1000)
## [1] 50
## [1] "std x-only scaling"
## [1] "*******************************************"
## [1] "x-only scaling"
## x.01 x.02 x.03
## Min. :-3.56466 Min. :-3.53178 Min. :-3.30810
## 1st Qu.:-0.71922 1st Qu.:-0.68546 1st Qu.:-0.69234
## Median : 0.01428 Median : 0.02157 Median :-0.01868
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.64729 3rd Qu.: 0.64710 3rd Qu.: 0.68890
## Max. : 3.02949 Max. : 3.44983 Max. : 3.53463
## x.04 x.05 noise1.01
## Min. :-3.024649 Min. :-3.44403 Min. :-3.55505
## 1st Qu.:-0.669618 1st Qu.:-0.70737 1st Qu.:-0.67730
## Median : 0.003458 Median :-0.02962 Median : 0.04075
## Mean : 0.000000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.679310 3rd Qu.: 0.69119 3rd Qu.: 0.66476
## Max. : 3.618095 Max. : 3.25413 Max. : 3.03398
## noise1.02 noise1.03 noise1.04
## Min. :-3.04344 Min. :-3.24553 Min. :-3.17058
## 1st Qu.:-0.67283 1st Qu.:-0.67685 1st Qu.:-0.66255
## Median :-0.01098 Median :-0.04143 Median : 0.02303
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.63123 3rd Qu.: 0.66017 3rd Qu.: 0.68567
## Max. : 3.09969 Max. : 3.46234 Max. : 3.30193
## noise1.05 noise2.01 noise2.02
## Min. :-3.637258 Min. :-3.02967 Min. :-3.11067
## 1st Qu.:-0.716404 1st Qu.:-0.67137 1st Qu.:-0.67677
## Median :-0.009741 Median :-0.02374 Median :-0.03242
## Mean : 0.000000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.669438 3rd Qu.: 0.61202 3rd Qu.: 0.67432
## Max. : 2.989022 Max. : 2.69382 Max. : 3.56327
## noise2.03 noise2.04 noise2.05
## Min. :-3.32724 Min. :-2.96915 Min. :-3.01326
## 1st Qu.:-0.69209 1st Qu.:-0.66348 1st Qu.:-0.67107
## Median : 0.01705 Median :-0.03646 Median :-0.02221
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.67707 3rd Qu.: 0.63654 3rd Qu.: 0.68463
## Max. : 3.64146 Max. : 3.24450 Max. : 3.12544
## noise3.01 noise3.02 noise3.03
## Min. :-3.37021 Min. :-2.90826 Min. :-5.26300
## 1st Qu.:-0.61175 1st Qu.:-0.67123 1st Qu.:-0.63535
## Median :-0.01631 Median :-0.01888 Median : 0.03451
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.63991 3rd Qu.: 0.68101 3rd Qu.: 0.64866
## Max. : 3.13484 Max. : 3.36663 Max. : 3.49695
## noise3.04 noise3.05 noise4.01
## Min. :-3.17697 Min. :-3.30323 Min. :-3.331686
## 1st Qu.:-0.68534 1st Qu.:-0.63505 1st Qu.:-0.672998
## Median : 0.01006 Median : 0.02726 Median :-0.003899
## Mean : 0.00000 Mean : 0.00000 Mean : 0.000000
## 3rd Qu.: 0.71201 3rd Qu.: 0.64763 3rd Qu.: 0.678726
## Max. : 2.80253 Max. : 3.25230 Max. : 3.672058
## noise4.02 noise4.03 noise4.04
## Min. :-3.40526 Min. :-3.50868 Min. :-2.850585
## 1st Qu.:-0.65631 1st Qu.:-0.67795 1st Qu.:-0.642033
## Median :-0.02656 Median :-0.02249 Median :-0.003927
## Mean : 0.00000 Mean : 0.00000 Mean : 0.000000
## 3rd Qu.: 0.71619 3rd Qu.: 0.69348 3rd Qu.: 0.666246
## Max. : 3.14709 Max. : 3.01486 Max. : 2.822614
## noise4.05 noise5.01 noise5.02
## Min. :-2.88875 Min. :-3.28356 Min. :-2.77919
## 1st Qu.:-0.68111 1st Qu.:-0.66186 1st Qu.:-0.68516
## Median :-0.02164 Median : 0.01031 Median :-0.01818
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.68861 3rd Qu.: 0.68392 3rd Qu.: 0.65803
## Max. : 2.99364 Max. : 3.59664 Max. : 2.86640
## noise5.03 noise5.04 noise5.05
## Min. :-3.141748 Min. :-3.372903 Min. :-3.00261
## 1st Qu.:-0.668289 1st Qu.:-0.664215 1st Qu.:-0.69759
## Median : 0.001024 Median : 0.004278 Median : 0.01208
## Mean : 0.000000 Mean : 0.000000 Mean : 0.00000
## 3rd Qu.: 0.694700 3rd Qu.: 0.666247 3rd Qu.: 0.69230
## Max. : 2.882415 Max. : 3.004999 Max. : 2.79255
## noise6.01 noise6.02 noise6.03
## Min. :-3.34363 Min. :-3.457442 Min. :-3.17042
## 1st Qu.:-0.66990 1st Qu.:-0.614116 1st Qu.:-0.68510
## Median : 0.02551 Median : 0.007875 Median :-0.02421
## Mean : 0.00000 Mean : 0.000000 Mean : 0.00000
## 3rd Qu.: 0.70390 3rd Qu.: 0.644664 3rd Qu.: 0.66523
## Max. : 2.76494 Max. : 3.101829 Max. : 3.36585
## noise6.04 noise6.05 noise7.01
## Min. :-3.383278 Min. :-3.08557 Min. :-2.81094
## 1st Qu.:-0.689616 1st Qu.:-0.67565 1st Qu.:-0.70652
## Median :-0.005454 Median : 0.02158 Median : 0.03228
## Mean : 0.000000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.685594 3rd Qu.: 0.66487 3rd Qu.: 0.67877
## Max. : 2.844464 Max. : 2.93981 Max. : 3.43567
## noise7.02 noise7.03 noise7.04
## Min. :-3.219500 Min. :-3.75066 Min. :-2.82669
## 1st Qu.:-0.705328 1st Qu.:-0.67748 1st Qu.:-0.66636
## Median : 0.002837 Median : 0.03481 Median :-0.02026
## Mean : 0.000000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.676359 3rd Qu.: 0.68288 3rd Qu.: 0.65232
## Max. : 3.478201 Max. : 2.78215 Max. : 3.22680
## noise7.05 noise8.01 noise8.02
## Min. :-2.87974 Min. :-3.15106 Min. :-3.36337
## 1st Qu.:-0.66995 1st Qu.:-0.69851 1st Qu.:-0.72149
## Median :-0.01265 Median : 0.03405 Median :-0.04337
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.69144 3rd Qu.: 0.67439 3rd Qu.: 0.68424
## Max. : 3.46219 Max. : 3.31936 Max. : 2.84291
## noise8.03 noise8.04 noise8.05
## Min. :-2.97938 Min. :-2.7641 Min. :-2.78277
## 1st Qu.:-0.69513 1st Qu.:-0.7185 1st Qu.:-0.70907
## Median : 0.02208 Median :-0.0125 Median : 0.03003
## Mean : 0.00000 Mean : 0.0000 Mean : 0.00000
## 3rd Qu.: 0.68959 3rd Qu.: 0.7405 3rd Qu.: 0.68615
## Max. : 3.14059 Max. : 2.9476 Max. : 2.92697
## noise9.01 noise9.02 noise9.03
## Min. :-2.869517 Min. :-3.214109 Min. :-3.112908
## 1st Qu.:-0.697756 1st Qu.:-0.675945 1st Qu.:-0.681257
## Median : 0.002377 Median : 0.002854 Median :-0.008767
## Mean : 0.000000 Mean : 0.000000 Mean : 0.000000
## 3rd Qu.: 0.674219 3rd Qu.: 0.634927 3rd Qu.: 0.694086
## Max. : 2.852684 Max. : 3.250219 Max. : 3.438842
## noise9.04 noise9.05
## Min. :-3.53174 Min. :-3.92015
## 1st Qu.:-0.65046 1st Qu.:-0.68052
## Median :-0.01833 Median : 0.02028
## Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.66983 3rd Qu.: 0.65494
## Max. : 3.47310 Max. : 3.11200
##
## Call:
## lm(formula = formula, data = projectedTrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4461 -0.9468 0.0313 0.9553 4.9620
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.08504 0.04783 1.778 0.075724 .
## PC1 -0.10702 0.03141 -3.407 0.000684 ***
## PC2 -0.04793 0.03181 -1.507 0.132183
## PC3 -0.13593 0.03222 -4.219 2.68e-05 ***
## PC4 -0.16234 0.03250 -4.995 6.94e-07 ***
## PC5 0.35688 0.03325 10.734 < 2e-16 ***
## PC6 0.12649 0.03343 3.783 0.000164 ***
## PC7 0.09255 0.03411 2.713 0.006786 **
## PC8 -0.13425 0.03475 -3.863 0.000119 ***
## PC9 0.28013 0.03516 7.967 4.46e-15 ***
## PC10 0.11262 0.03543 3.179 0.001523 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.513 on 989 degrees of freedom
## Multiple R-squared: 0.2219, Adjusted R-squared: 0.214
## F-statistic: 28.2 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.221881172515066"
## [1] "test rsq 0.26396282224084"
##
## Call:
## lm(formula = formula, data = projectedTrainX)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1926 -1.0522 0.0082 1.0251 5.6872
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.08783 0.05054 1.738 0.082535 .
## PC1 -0.12992 0.03752 -3.463 0.000557 ***
## PC2 -0.09055 0.03670 -2.467 0.013795 *
## PC3 -0.07856 0.03697 -2.125 0.033847 *
## PC4 -0.15607 0.03467 -4.502 7.53e-06 ***
## PC5 0.27168 0.03723 7.297 6.05e-13 ***
## PC6 0.13367 0.03751 3.564 0.000383 ***
## PC7 0.15881 0.03637 4.367 1.39e-05 ***
## PC8 -0.03533 0.03770 -0.937 0.348976
## PC9 0.15971 0.03717 4.296 1.91e-05 ***
## PC10 0.08733 0.03654 2.390 0.017052 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.595 on 989 degrees of freedom
## Multiple R-squared: 0.1344, Adjusted R-squared: 0.1256
## F-statistic: 15.35 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.134358541014939"
## [1] "test rsq 0.235021411151901"
## [1] "using direct method"
## [1] "*******************************************"
## [1] "in-sample y-aware scaling"
## x.01 x.02 x.03
## Min. :-2.65396 Min. :-2.51975 Min. :-2.14566
## 1st Qu.:-0.53547 1st Qu.:-0.48904 1st Qu.:-0.44906
## Median : 0.01063 Median : 0.01539 Median :-0.01211
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.48192 3rd Qu.: 0.46167 3rd Qu.: 0.44683
## Max. : 2.25552 Max. : 2.46128 Max. : 2.29259
## x.04 x.05 noise1.01
## Min. :-2.157010 Min. :-2.11879 Min. :-0.24249
## 1st Qu.:-0.477534 1st Qu.:-0.43518 1st Qu.:-0.04620
## Median : 0.002466 Median :-0.01822 Median : 0.00278
## Mean : 0.000000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.484445 3rd Qu.: 0.42523 3rd Qu.: 0.04534
## Max. : 2.580222 Max. : 2.00196 Max. : 0.20695
## noise1.02 noise1.03 noise1.04
## Min. :-0.0917910 Min. :-0.0785730 Min. :-0.0162697
## 1st Qu.:-0.0186927 1st Qu.:-0.0149815 1st Qu.:-0.0033998
## Median : 0.0003253 Median : 0.0009402 Median : 0.0001182
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 0.0199244 3rd Qu.: 0.0153602 3rd Qu.: 0.0035185
## Max. : 0.0901253 Max. : 0.0736528 Max. : 0.0169437
## noise1.05 noise2.01 noise2.02
## Min. :-0.0679766 Min. :-0.173381 Min. :-2.052e-03
## 1st Qu.:-0.0152244 1st Qu.:-0.038421 1st Qu.:-3.884e-04
## Median : 0.0002215 Median :-0.001359 Median : 1.867e-05
## Mean : 0.0000000 Mean : 0.000000 Mean : 0.000e+00
## 3rd Qu.: 0.0162925 3rd Qu.: 0.035024 3rd Qu.: 3.898e-04
## Max. : 0.0827189 Max. : 0.154162 Max. : 1.792e-03
## noise2.03 noise2.04 noise2.05
## Min. :-1.794e-02 Min. :-0.0163329 Min. :-0.0165502
## 1st Qu.:-3.335e-03 1st Qu.:-0.0036497 1st Qu.:-0.0036253
## Median :-8.396e-05 Median :-0.0002006 Median : 0.0001176
## Mean : 0.000e+00 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 3.409e-03 3rd Qu.: 0.0035015 3rd Qu.: 0.0035535
## Max. : 1.639e-02 Max. : 0.0178476 Max. : 0.0159562
## noise3.01 noise3.02 noise3.03
## Min. :-0.1264964 Min. :-0.0218154 Min. :-0.0915218
## 1st Qu.:-0.0258215 1st Qu.:-0.0050351 1st Qu.:-0.0110485
## Median : 0.0006582 Median :-0.0001416 Median : 0.0006002
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 0.0246851 3rd Qu.: 0.0051084 3rd Qu.: 0.0112799
## Max. : 0.1359939 Max. : 0.0252537 Max. : 0.0608108
## noise3.04 noise3.05 noise4.01
## Min. :-0.1837226 Min. :-3.222e-03 Min. :-5.332e-02
## 1st Qu.:-0.0396330 1st Qu.:-6.194e-04 1st Qu.:-9.856e-03
## Median : 0.0005818 Median : 2.659e-05 Median : 5.663e-05
## Mean : 0.0000000 Mean : 0.000e+00 Mean : 0.000e+00
## 3rd Qu.: 0.0411750 3rd Qu.: 6.317e-04 3rd Qu.: 9.773e-03
## Max. : 0.1620686 Max. : 3.172e-03 Max. : 4.838e-02
## noise4.02 noise4.03 noise4.04
## Min. :-0.1187360 Min. :-0.0797358 Min. :-1.002e-02
## 1st Qu.:-0.0228846 1st Qu.:-0.0154065 1st Qu.:-2.365e-03
## Median :-0.0009261 Median :-0.0005111 Median : 1.394e-05
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.000e+00
## 3rd Qu.: 0.0249723 3rd Qu.: 0.0157595 3rd Qu.: 2.279e-03
## Max. : 0.1097340 Max. : 0.0685135 Max. : 1.012e-02
## noise4.05 noise5.01 noise5.02
## Min. :-0.285450 Min. :-0.0936289 Min. :-7.560e-03
## 1st Qu.:-0.065661 1st Qu.:-0.0188727 1st Qu.:-1.864e-03
## Median : 0.002063 Median : 0.0002939 Median :-4.945e-05
## Mean : 0.000000 Mean : 0.0000000 Mean : 0.000e+00
## 3rd Qu.: 0.064945 3rd Qu.: 0.0195017 3rd Qu.: 1.790e-03
## Max. : 0.275449 Max. : 0.1025562 Max. : 7.797e-03
## noise5.03 noise5.04 noise5.05
## Min. :-1.052e-01 Min. :-0.0951126 Min. :-0.1015520
## 1st Qu.:-2.238e-02 1st Qu.:-0.0210877 1st Qu.:-0.0235934
## Median : 3.429e-05 Median :-0.0001354 Median : 0.0004086
## Mean : 0.000e+00 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 2.327e-02 3rd Qu.: 0.0210234 3rd Qu.: 0.0234145
## Max. : 9.655e-02 Max. : 0.1067573 Max. : 0.0944476
## noise6.01 noise6.02 noise6.03
## Min. :-0.0591549 Min. :-0.0671441 Min. :-0.048987
## 1st Qu.:-0.0118519 1st Qu.:-0.0139548 1st Qu.:-0.010586
## Median : 0.0004513 Median :-0.0001705 Median :-0.000374
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.000000
## 3rd Qu.: 0.0124533 3rd Qu.: 0.0132935 3rd Qu.: 0.010279
## Max. : 0.0489168 Max. : 0.0748419 Max. : 0.052007
## noise6.04 noise6.05 noise7.01
## Min. :-3.373e-02 Min. :-0.257923 Min. :-0.17347
## 1st Qu.:-8.129e-03 1st Qu.:-0.058332 1st Qu.:-0.03427
## Median : 6.467e-05 Median :-0.001893 Median :-0.00163
## Mean : 0.000e+00 Mean : 0.000000 Mean : 0.00000
## 3rd Qu.: 8.177e-03 3rd Qu.: 0.059278 3rd Qu.: 0.03567
## Max. : 4.012e-02 Max. : 0.270711 Max. : 0.14192
## noise7.02 noise7.03 noise7.04
## Min. :-6.723e-03 Min. :-0.111783 Min. :-0.0377584
## 1st Qu.:-1.473e-03 1st Qu.:-0.027437 1st Qu.:-0.0089011
## Median : 5.925e-06 Median :-0.001399 Median :-0.0002706
## Mean : 0.000e+00 Mean : 0.000000 Mean : 0.0000000
## 3rd Qu.: 1.412e-03 3rd Qu.: 0.027220 3rd Qu.: 0.0087135
## Max. : 7.263e-03 Max. : 0.150697 Max. : 0.0431029
## noise7.05 noise8.01 noise8.02
## Min. :-0.315530 Min. :-0.0793439 Min. :-0.161566
## 1st Qu.:-0.063015 1st Qu.:-0.0175886 1st Qu.:-0.038886
## Median : 0.001153 Median : 0.0008574 Median : 0.002464
## Mean : 0.000000 Mean : 0.0000000 Mean : 0.000000
## 3rd Qu.: 0.061056 3rd Qu.: 0.0169812 3rd Qu.: 0.041003
## Max. : 0.262448 Max. : 0.0835817 Max. : 0.191144
## noise8.03 noise8.04 noise8.05
## Min. :-0.0672229 Min. :-0.0571279 Min. :-0.127256
## 1st Qu.:-0.0147604 1st Qu.:-0.0148491 1st Qu.:-0.032426
## Median :-0.0004726 Median :-0.0002584 Median : 0.001373
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.000000
## 3rd Qu.: 0.0148790 3rd Qu.: 0.0153044 3rd Qu.: 0.031378
## Max. : 0.0637722 Max. : 0.0609191 Max. : 0.133850
## noise9.01 noise9.02 noise9.03
## Min. :-0.0423694 Min. :-6.255e-02 Min. :-1.752e-02
## 1st Qu.:-0.0100138 1st Qu.:-1.315e-02 1st Qu.:-3.835e-03
## Median :-0.0000353 Median : 5.555e-05 Median :-4.935e-05
## Mean : 0.0000000 Mean : 0.000e+00 Mean : 0.000e+00
## 3rd Qu.: 0.0103634 3rd Qu.: 1.236e-02 3rd Qu.: 3.907e-03
## Max. : 0.0426194 Max. : 6.325e-02 Max. : 1.936e-02
## noise9.04 noise9.05
## Min. :-0.18108 Min. :-0.0654833
## 1st Qu.:-0.03335 1st Qu.:-0.0137813
## Median :-0.00094 Median :-0.0004266
## Mean : 0.00000 Mean : 0.0000000
## 3rd Qu.: 0.03434 3rd Qu.: 0.0143196
## Max. : 0.17808 Max. : 0.0824886
##
## Call:
## lm(formula = formula, data = projectedTrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2028 -0.7853 0.0146 0.8072 3.8040
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.08504 0.03901 2.180 0.0295 *
## PC1 0.78611 0.04080 19.268 <2e-16 ***
## PC2 1.03243 0.04456 23.168 <2e-16 ***
## PC3 0.04029 0.07676 0.525 0.5998
## PC4 0.07607 0.08106 0.938 0.3482
## PC5 0.01020 0.08758 0.116 0.9073
## PC6 0.97950 0.39465 2.482 0.0132 *
## PC7 0.19548 0.40980 0.477 0.6335
## PC8 0.25861 0.44129 0.586 0.5580
## PC9 1.26484 0.54986 2.300 0.0216 *
## PC10 0.51306 0.66129 0.776 0.4380
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.234 on 989 degrees of freedom
## Multiple R-squared: 0.4824, Adjusted R-squared: 0.4772
## F-statistic: 92.18 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.48242177283421"
## [1] "test rsq 0.502942338312764"
##
## Call:
## lm(formula = formula, data = projectedTrainX)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5431 -0.7793 0.0271 0.7785 3.8115
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.081426 0.039360 2.069 0.0388 *
## PC1 0.785442 0.041505 18.924 <2e-16 ***
## PC2 1.013972 0.044635 22.717 <2e-16 ***
## PC3 0.025058 0.079177 0.316 0.7517
## PC4 0.100976 0.080940 1.248 0.2125
## PC5 -0.009149 0.086964 -0.105 0.9162
## PC6 0.946245 0.410214 2.307 0.0213 *
## PC7 0.112232 0.414764 0.271 0.7868
## PC8 0.188555 0.440526 0.428 0.6687
## PC9 1.204269 0.555951 2.166 0.0305 *
## PC10 0.581804 0.696223 0.836 0.4035
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.244 on 989 degrees of freedom
## Multiple R-squared: 0.4737, Adjusted R-squared: 0.4684
## F-statistic: 89.01 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.473673511681592"
## [1] "test rsq 0.50387599242553"
## [1] "vtreat y-aware direct scaling"
## [1] "desigining treatments Thu Jul 14 09:59:08 2016"
## [1] "scoring treatments Thu Jul 14 09:59:08 2016"
## [1] "have treatment plan Thu Jul 14 09:59:08 2016"
## [1] 50
## [1] "*******************************************"
## [1] "vtreat in-sample y-aware scaling"
## x.01_clean x.02_clean x.03_clean
## Min. :-2.65396 Min. :-2.51975 Min. :-2.14566
## 1st Qu.:-0.53547 1st Qu.:-0.48904 1st Qu.:-0.44906
## Median : 0.01063 Median : 0.01539 Median :-0.01211
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.48192 3rd Qu.: 0.46167 3rd Qu.: 0.44683
## Max. : 2.25552 Max. : 2.46128 Max. : 2.29259
## x.04_clean x.05_clean noise1.01_clean
## Min. :-2.157010 Min. :-2.11879 Min. :-0.24249
## 1st Qu.:-0.477534 1st Qu.:-0.43518 1st Qu.:-0.04620
## Median : 0.002466 Median :-0.01822 Median : 0.00278
## Mean : 0.000000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.484445 3rd Qu.: 0.42523 3rd Qu.: 0.04534
## Max. : 2.580222 Max. : 2.00196 Max. : 0.20695
## noise1.02_clean noise1.03_clean noise1.04_clean
## Min. :-0.0917910 Min. :-0.0785730 Min. :-0.0162697
## 1st Qu.:-0.0186927 1st Qu.:-0.0149815 1st Qu.:-0.0033998
## Median : 0.0003253 Median : 0.0009402 Median : 0.0001182
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 0.0199244 3rd Qu.: 0.0153602 3rd Qu.: 0.0035185
## Max. : 0.0901253 Max. : 0.0736528 Max. : 0.0169437
## noise1.05_clean noise2.01_clean noise2.02_clean
## Min. :-0.0679766 Min. :-0.173381 Min. :-2.052e-03
## 1st Qu.:-0.0152244 1st Qu.:-0.038421 1st Qu.:-3.884e-04
## Median : 0.0002215 Median :-0.001359 Median : 1.867e-05
## Mean : 0.0000000 Mean : 0.000000 Mean : 0.000e+00
## 3rd Qu.: 0.0162925 3rd Qu.: 0.035024 3rd Qu.: 3.898e-04
## Max. : 0.0827189 Max. : 0.154162 Max. : 1.792e-03
## noise2.03_clean noise2.04_clean noise2.05_clean
## Min. :-1.794e-02 Min. :-0.0163329 Min. :-0.0165502
## 1st Qu.:-3.335e-03 1st Qu.:-0.0036497 1st Qu.:-0.0036253
## Median :-8.396e-05 Median :-0.0002006 Median : 0.0001176
## Mean : 0.000e+00 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 3.409e-03 3rd Qu.: 0.0035015 3rd Qu.: 0.0035535
## Max. : 1.639e-02 Max. : 0.0178476 Max. : 0.0159562
## noise3.01_clean noise3.02_clean noise3.03_clean
## Min. :-0.1264964 Min. :-0.0218154 Min. :-0.0915218
## 1st Qu.:-0.0258215 1st Qu.:-0.0050351 1st Qu.:-0.0110485
## Median : 0.0006582 Median :-0.0001416 Median : 0.0006002
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 0.0246851 3rd Qu.: 0.0051084 3rd Qu.: 0.0112799
## Max. : 0.1359939 Max. : 0.0252537 Max. : 0.0608108
## noise3.04_clean noise3.05_clean noise4.01_clean
## Min. :-0.1837226 Min. :-3.222e-03 Min. :-5.332e-02
## 1st Qu.:-0.0396330 1st Qu.:-6.194e-04 1st Qu.:-9.856e-03
## Median : 0.0005818 Median : 2.659e-05 Median : 5.663e-05
## Mean : 0.0000000 Mean : 0.000e+00 Mean : 0.000e+00
## 3rd Qu.: 0.0411750 3rd Qu.: 6.317e-04 3rd Qu.: 9.773e-03
## Max. : 0.1620686 Max. : 3.172e-03 Max. : 4.838e-02
## noise4.02_clean noise4.03_clean noise4.04_clean
## Min. :-0.1187360 Min. :-0.0797358 Min. :-1.002e-02
## 1st Qu.:-0.0228846 1st Qu.:-0.0154065 1st Qu.:-2.365e-03
## Median :-0.0009261 Median :-0.0005111 Median : 1.394e-05
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.000e+00
## 3rd Qu.: 0.0249723 3rd Qu.: 0.0157595 3rd Qu.: 2.279e-03
## Max. : 0.1097340 Max. : 0.0685135 Max. : 1.012e-02
## noise4.05_clean noise5.01_clean noise5.02_clean
## Min. :-0.285450 Min. :-0.0936289 Min. :-7.560e-03
## 1st Qu.:-0.065661 1st Qu.:-0.0188727 1st Qu.:-1.864e-03
## Median : 0.002063 Median : 0.0002939 Median :-4.945e-05
## Mean : 0.000000 Mean : 0.0000000 Mean : 0.000e+00
## 3rd Qu.: 0.064945 3rd Qu.: 0.0195017 3rd Qu.: 1.790e-03
## Max. : 0.275449 Max. : 0.1025562 Max. : 7.797e-03
## noise5.03_clean noise5.04_clean noise5.05_clean
## Min. :-1.052e-01 Min. :-0.0951126 Min. :-0.1015520
## 1st Qu.:-2.238e-02 1st Qu.:-0.0210877 1st Qu.:-0.0235934
## Median : 3.429e-05 Median :-0.0001354 Median : 0.0004086
## Mean : 0.000e+00 Mean : 0.0000000 Mean : 0.0000000
## 3rd Qu.: 2.327e-02 3rd Qu.: 0.0210234 3rd Qu.: 0.0234145
## Max. : 9.655e-02 Max. : 0.1067573 Max. : 0.0944476
## noise6.01_clean noise6.02_clean noise6.03_clean
## Min. :-0.0591549 Min. :-0.0671441 Min. :-0.048987
## 1st Qu.:-0.0118519 1st Qu.:-0.0139548 1st Qu.:-0.010586
## Median : 0.0004513 Median :-0.0001705 Median :-0.000374
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.000000
## 3rd Qu.: 0.0124533 3rd Qu.: 0.0132935 3rd Qu.: 0.010279
## Max. : 0.0489168 Max. : 0.0748419 Max. : 0.052007
## noise6.04_clean noise6.05_clean noise7.01_clean
## Min. :-3.373e-02 Min. :-0.257923 Min. :-0.17347
## 1st Qu.:-8.129e-03 1st Qu.:-0.058332 1st Qu.:-0.03427
## Median : 6.467e-05 Median :-0.001893 Median :-0.00163
## Mean : 0.000e+00 Mean : 0.000000 Mean : 0.00000
## 3rd Qu.: 8.177e-03 3rd Qu.: 0.059278 3rd Qu.: 0.03567
## Max. : 4.012e-02 Max. : 0.270711 Max. : 0.14192
## noise7.02_clean noise7.03_clean noise7.04_clean
## Min. :-6.723e-03 Min. :-0.111783 Min. :-0.0377584
## 1st Qu.:-1.473e-03 1st Qu.:-0.027437 1st Qu.:-0.0089011
## Median : 5.925e-06 Median :-0.001399 Median :-0.0002706
## Mean : 0.000e+00 Mean : 0.000000 Mean : 0.0000000
## 3rd Qu.: 1.412e-03 3rd Qu.: 0.027220 3rd Qu.: 0.0087135
## Max. : 7.263e-03 Max. : 0.150697 Max. : 0.0431029
## noise7.05_clean noise8.01_clean noise8.02_clean
## Min. :-0.315530 Min. :-0.0793439 Min. :-0.161566
## 1st Qu.:-0.063015 1st Qu.:-0.0175886 1st Qu.:-0.038886
## Median : 0.001153 Median : 0.0008574 Median : 0.002464
## Mean : 0.000000 Mean : 0.0000000 Mean : 0.000000
## 3rd Qu.: 0.061056 3rd Qu.: 0.0169812 3rd Qu.: 0.041003
## Max. : 0.262448 Max. : 0.0835817 Max. : 0.191144
## noise8.03_clean noise8.04_clean noise8.05_clean
## Min. :-0.0672229 Min. :-0.0571279 Min. :-0.127256
## 1st Qu.:-0.0147604 1st Qu.:-0.0148491 1st Qu.:-0.032426
## Median :-0.0004726 Median :-0.0002584 Median : 0.001373
## Mean : 0.0000000 Mean : 0.0000000 Mean : 0.000000
## 3rd Qu.: 0.0148790 3rd Qu.: 0.0153044 3rd Qu.: 0.031378
## Max. : 0.0637722 Max. : 0.0609191 Max. : 0.133850
## noise9.01_clean noise9.02_clean noise9.03_clean
## Min. :-0.0423694 Min. :-6.255e-02 Min. :-1.752e-02
## 1st Qu.:-0.0100138 1st Qu.:-1.315e-02 1st Qu.:-3.835e-03
## Median :-0.0000353 Median : 5.555e-05 Median :-4.935e-05
## Mean : 0.0000000 Mean : 0.000e+00 Mean : 0.000e+00
## 3rd Qu.: 0.0103634 3rd Qu.: 1.236e-02 3rd Qu.: 3.907e-03
## Max. : 0.0426194 Max. : 6.325e-02 Max. : 1.936e-02
## noise9.04_clean noise9.05_clean
## Min. :-0.18108 Min. :-0.0654833
## 1st Qu.:-0.03335 1st Qu.:-0.0137813
## Median :-0.00094 Median :-0.0004266
## Mean : 0.00000 Mean : 0.0000000
## 3rd Qu.: 0.03434 3rd Qu.: 0.0143196
## Max. : 0.17808 Max. : 0.0824886
##
## Call:
## lm(formula = formula, data = projectedTrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2028 -0.7853 0.0146 0.8072 3.8040
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.08504 0.03901 2.180 0.0295 *
## PC1 0.78611 0.04080 19.268 <2e-16 ***
## PC2 1.03243 0.04456 23.168 <2e-16 ***
## PC3 0.04029 0.07676 0.525 0.5998
## PC4 0.07607 0.08106 0.938 0.3482
## PC5 0.01020 0.08758 0.116 0.9073
## PC6 0.97950 0.39465 2.482 0.0132 *
## PC7 0.19548 0.40980 0.477 0.6335
## PC8 0.25861 0.44129 0.586 0.5580
## PC9 1.26484 0.54986 2.300 0.0216 *
## PC10 0.51306 0.66129 0.776 0.4380
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.234 on 989 degrees of freedom
## Multiple R-squared: 0.4824, Adjusted R-squared: 0.4772
## F-statistic: 92.18 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.48242177283421"
## [1] "test rsq 0.503254874942015"
##
## Call:
## lm(formula = formula, data = projectedTrainX)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2432 -0.7686 0.0169 0.8154 3.8046
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.083641 0.038830 2.154 0.03148 *
## PC1 0.795175 0.040946 19.420 < 2e-16 ***
## PC2 1.034565 0.044105 23.457 < 2e-16 ***
## PC3 0.052068 0.077986 0.668 0.50450
## PC4 0.096981 0.080222 1.209 0.22699
## PC5 0.002884 0.084751 0.034 0.97286
## PC6 1.037224 0.401609 2.583 0.00995 **
## PC7 -0.093037 0.406995 -0.229 0.81923
## PC8 0.332000 0.437092 0.760 0.44770
## PC9 1.234144 0.548365 2.251 0.02463 *
## PC10 0.591191 0.680856 0.868 0.38544
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.227 on 989 degrees of freedom
## Multiple R-squared: 0.4879, Adjusted R-squared: 0.4827
## F-statistic: 94.22 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.487885192201953"
## [1] "test rsq 0.50274983232389"
## [1] "vtreat y-aware cross scaling"
## [1] 50
## [1] "*******************************************"
## [1] "vtreat out-sample y-aware scaling"
## x.01_clean x.02_clean x.03_clean
## Min. :-2.4928250 Min. :-1.8968518 Min. :-2.0885228
## 1st Qu.:-0.5268214 1st Qu.:-0.4919804 1st Qu.:-0.4492052
## Median : 0.0112782 Median : 0.0128891 Median :-0.0186294
## Mean : 0.0000476 Mean : 0.0003547 Mean :-0.0008096
## 3rd Qu.: 0.4846578 3rd Qu.: 0.4670734 3rd Qu.: 0.4422544
## Max. : 2.3032040 Max. : 1.7843994 Max. : 1.8871384
## x.04_clean x.05_clean noise1.01_clean
## Min. :-2.1991117 Min. :-1.7271045 Min. :-0.426249
## 1st Qu.:-0.4793271 1st Qu.:-0.4362600 1st Qu.:-0.043695
## Median : 0.0065618 Median :-0.0134015 Median :-0.001372
## Mean :-0.0001205 Mean :-0.0004336 Mean :-0.004809
## 3rd Qu.: 0.4976845 3rd Qu.: 0.4260831 3rd Qu.: 0.036954
## Max. : 2.1671205 Max. : 1.9223094 Max. : 0.389958
## noise1.02_clean noise1.03_clean noise1.04_clean
## Min. :-1.643e-01 Min. :-1.930e-01 Min. :-0.1892920
## 1st Qu.:-1.293e-02 1st Qu.:-3.345e-03 1st Qu.:-0.0188442
## Median : 8.440e-06 Median : 1.203e-05 Median :-0.0001182
## Mean :-1.697e-04 Mean : 1.422e-04 Mean : 0.0001067
## 3rd Qu.: 1.164e-02 3rd Qu.: 3.951e-03 3rd Qu.: 0.0202844
## Max. : 1.550e-01 Max. : 2.068e-01 Max. : 0.2137786
## noise1.05_clean noise2.01_clean noise2.02_clean
## Min. :-0.1080511 Min. :-0.3081651 Min. :-0.181633
## 1st Qu.:-0.0084149 1st Qu.:-0.0273283 1st Qu.:-0.021925
## Median : 0.0001153 Median :-0.0009219 Median :-0.001306
## Mean : 0.0010011 Mean :-0.0027857 Mean :-0.001093
## 3rd Qu.: 0.0105288 3rd Qu.: 0.0194300 3rd Qu.: 0.020715
## Max. : 0.0942555 Max. : 0.2854280 Max. : 0.158605
## noise2.03_clean noise2.04_clean noise2.05_clean
## Min. :-9.797e-02 Min. :-0.0995666 Min. :-0.1152369
## 1st Qu.:-1.294e-02 1st Qu.:-0.0096579 1st Qu.:-0.0151831
## Median :-6.684e-05 Median :-0.0002762 Median : 0.0001287
## Mean :-1.585e-03 Mean :-0.0008766 Mean : 0.0008302
## 3rd Qu.: 7.135e-03 3rd Qu.: 0.0071184 3rd Qu.: 0.0165792
## Max. : 1.021e-01 Max. : 0.1057949 Max. : 0.1279297
## noise3.01_clean noise3.02_clean noise3.03_clean
## Min. :-0.1998016 Min. :-0.0604256 Min. :-0.118726
## 1st Qu.:-0.0220991 1st Qu.:-0.0144636 1st Qu.:-0.023373
## Median : 0.0001479 Median :-0.0004227 Median : 0.001961
## Mean : 0.0009997 Mean :-0.0003034 Mean : 0.001188
## 3rd Qu.: 0.0222002 3rd Qu.: 0.0138945 3rd Qu.: 0.028313
## Max. : 0.1828342 Max. : 0.0635209 Max. : 0.125265
## noise3.04_clean noise3.05_clean noise4.01_clean
## Min. :-0.300566 Min. :-0.0703705 Min. :-0.1056500
## 1st Qu.:-0.027579 1st Qu.:-0.0077674 1st Qu.:-0.0161007
## Median : 0.000702 Median :-0.0004022 Median :-0.0003400
## Mean : 0.001242 Mean :-0.0005460 Mean : 0.0006295
## 3rd Qu.: 0.028834 3rd Qu.: 0.0077326 3rd Qu.: 0.0163273
## Max. : 0.263991 Max. : 0.0793515 Max. : 0.1438478
## noise4.02_clean noise4.03_clean noise4.04_clean
## Min. :-1.613e-01 Min. :-0.1198399 Min. :-0.053766
## 1st Qu.:-2.838e-02 1st Qu.:-0.0109753 1st Qu.:-0.010514
## Median : 7.918e-05 Median :-0.0003268 Median :-0.000346
## Mean : 7.489e-04 Mean : 0.0003305 Mean :-0.000778
## 3rd Qu.: 2.987e-02 3rd Qu.: 0.0129833 3rd Qu.: 0.009662
## Max. : 1.822e-01 Max. : 0.1076177 Max. : 0.054513
## noise4.05_clean noise5.01_clean noise5.02_clean
## Min. :-0.3554570 Min. :-0.1587111 Min. :-0.0608793
## 1st Qu.:-0.0618410 1st Qu.:-0.0269446 1st Qu.:-0.0097781
## Median : 0.0022673 Median :-0.0008395 Median : 0.0005607
## Mean :-0.0006985 Mean :-0.0013742 Mean : 0.0003178
## 3rd Qu.: 0.0616620 3rd Qu.: 0.0239865 3rd Qu.: 0.0102144
## Max. : 0.3455270 Max. : 0.1584974 Max. : 0.0668463
## noise5.03_clean noise5.04_clean noise5.05_clean
## Min. :-0.160800 Min. :-0.188312 Min. :-0.1642639
## 1st Qu.:-0.025099 1st Qu.:-0.029240 1st Qu.:-0.0199268
## Median :-0.002182 Median :-0.002763 Median : 0.0003208
## Mean :-0.004084 Mean :-0.001428 Mean :-0.0006798
## 3rd Qu.: 0.018050 3rd Qu.: 0.027289 3rd Qu.: 0.0184161
## Max. : 0.152699 Max. : 0.210413 Max. : 0.1508710
## noise6.01_clean noise6.02_clean noise6.03_clean
## Min. :-0.1409052 Min. :-0.0647908 Min. :-0.1431836
## 1st Qu.:-0.0138004 1st Qu.:-0.0138838 1st Qu.:-0.0119652
## Median : 0.0005295 Median :-0.0001265 Median :-0.0003957
## Mean : 0.0006411 Mean : 0.0001051 Mean :-0.0005282
## 3rd Qu.: 0.0142756 3rd Qu.: 0.0131726 3rd Qu.: 0.0105255
## Max. : 0.1200339 Max. : 0.0846984 Max. : 0.1532759
## noise6.04_clean noise6.05_clean noise7.01_clean
## Min. :-1.339e-01 Min. :-0.2795717 Min. :-2.411e-01
## 1st Qu.:-1.310e-02 1st Qu.:-0.0565541 1st Qu.:-2.822e-02
## Median : 9.779e-05 Median :-0.0013575 Median :-8.754e-05
## Mean : 7.623e-04 Mean :-0.0006809 Mean : 1.016e-03
## 3rd Qu.: 1.379e-02 3rd Qu.: 0.0593673 3rd Qu.: 2.270e-02
## Max. : 1.430e-01 Max. : 0.2907112 Max. : 2.511e-01
## noise7.02_clean noise7.03_clean noise7.04_clean
## Min. :-0.0926229 Min. :-1.574e-01 Min. :-0.174337
## 1st Qu.:-0.0108093 1st Qu.:-2.191e-02 1st Qu.:-0.015499
## Median : 0.0005102 Median :-1.116e-03 Median : 0.003298
## Mean : 0.0005724 Mean :-4.205e-05 Mean : 0.003421
## 3rd Qu.: 0.0114012 3rd Qu.: 2.171e-02 3rd Qu.: 0.021792
## Max. : 0.0888071 Max. : 1.950e-01 Max. : 0.205388
## noise7.05_clean noise8.01_clean noise8.02_clean
## Min. :-0.421940 Min. :-0.1506603 Min. :-0.371298
## 1st Qu.:-0.052708 1st Qu.:-0.0102380 1st Qu.:-0.018444
## Median : 0.001076 Median : 0.0004780 Median : 0.001110
## Mean :-0.002247 Mean : 0.0002121 Mean : 0.001383
## 3rd Qu.: 0.049529 3rd Qu.: 0.0083749 3rd Qu.: 0.019982
## Max. : 0.415175 Max. : 0.1739351 Max. : 0.348457
## noise8.03_clean noise8.04_clean noise8.05_clean
## Min. :-0.0756356 Min. :-0.1115515 Min. :-2.047e-01
## 1st Qu.:-0.0107573 1st Qu.:-0.0128572 1st Qu.:-2.550e-02
## Median :-0.0003162 Median :-0.0005888 Median : 1.406e-04
## Mean : 0.0009101 Mean : 0.0007402 Mean :-1.563e-05
## 3rd Qu.: 0.0116963 3rd Qu.: 0.0125804 3rd Qu.: 2.759e-02
## Max. : 0.0773755 Max. : 0.1206437 Max. : 2.120e-01
## noise9.01_clean noise9.02_clean noise9.03_clean
## Min. :-0.144396 Min. :-0.3035379 Min. :-0.2042942
## 1st Qu.:-0.026123 1st Qu.:-0.0178880 1st Qu.:-0.0346027
## Median : 0.003267 Median :-0.0008822 Median : 0.0012979
## Mean : 0.004086 Mean :-0.0013709 Mean : 0.0009684
## 3rd Qu.: 0.033567 3rd Qu.: 0.0165791 3rd Qu.: 0.0371975
## Max. : 0.141179 Max. : 0.2801319 Max. : 0.2311867
## noise9.04_clean noise9.05_clean
## Min. :-0.2492952 Min. :-0.215547
## 1st Qu.:-0.0277772 1st Qu.:-0.007519
## Median :-0.0007276 Median : 0.001162
## Mean : 0.0006848 Mean : 0.003213
## 3rd Qu.: 0.0278836 3rd Qu.: 0.010409
## Max. : 0.2647385 Max. : 0.277541
##
## Call:
## lm(formula = formula, data = projectedTrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2661 -0.7910 0.0061 0.7893 3.8012
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.08902 0.03926 2.267 0.0236 *
## PC1 0.78437 0.04107 19.097 <2e-16 ***
## PC2 1.04138 0.04515 23.063 <2e-16 ***
## PC3 0.05750 0.07729 0.744 0.4571
## PC4 0.07352 0.08147 0.902 0.3670
## PC5 0.01037 0.08803 0.118 0.9062
## PC6 0.51946 0.34381 1.511 0.1311
## PC7 0.25873 0.40176 0.644 0.5197
## PC8 0.44482 0.41438 1.073 0.2833
## PC9 0.27200 0.43917 0.619 0.5358
## PC10 -0.68763 0.49879 -1.379 0.1683
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.239 on 989 degrees of freedom
## Multiple R-squared: 0.4776, Adjusted R-squared: 0.4723
## F-statistic: 90.41 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.477579027812596"
## [1] "test rsq 0.508026833657251"
##
## Call:
## lm(formula = formula, data = projectedTrainX)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3638 -0.7798 0.0082 0.7805 3.7913
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.086833 0.039378 2.205 0.0277 *
## PC1 0.791402 0.041444 19.096 <2e-16 ***
## PC2 1.036438 0.045209 22.925 <2e-16 ***
## PC3 0.064453 0.078581 0.820 0.4123
## PC4 0.082530 0.080841 1.021 0.3076
## PC5 -0.004644 0.087272 -0.053 0.9576
## PC6 0.534089 0.348692 1.532 0.1259
## PC7 0.240347 0.416181 0.578 0.5637
## PC8 0.090616 0.415384 0.218 0.8274
## PC9 0.162838 0.439745 0.370 0.7112
## PC10 -0.562617 0.526745 -1.068 0.2857
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.243 on 989 degrees of freedom
## Multiple R-squared: 0.4741, Adjusted R-squared: 0.4688
## F-statistic: 89.17 on 10 and 989 DF, p-value: < 2.2e-16
## [1] "train rsq 0.474120614572344"
## [1] "test rsq 0.507977629275113"
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