#Linear Models with R by Julian Faraway
#chapter 9 Pricipal Component Analysis
library(faraway)
# library(help=faraway)
# A Tecator Infratec Food and Feed Analyzer working
# in the wavelength range of 850 to 1050 nm by the near
# infrared transmission (NIT) principle was used to
# collect data on samples of finely chopped pure meat.
# 215 samples were measured. For each sample, the fat
# content was measured along with a 100 channel spectrum
# of absorbances. Since determining the fat content
# via analytical chemistry is time consuming,
# we would like to build a model to predict the fat content
# of new samples using the 100 absorbances
# which can be measured more easily. See Thodberg (1993).
# The true performance of any model is hard to determine
# based on just the fit to the available data. We need to
# see how well the model does on new data not used in the
# construction of the model. For this reason, we will
# partition the data into two parts—a training sample
# consisting of the first 172 observations that will be
# used to build the models and a testing sample of the
# remaining 43 observations. Let’s start with the least
# squares fit:
data("meatspec")
str(meatspec)
## 'data.frame': 215 obs. of 101 variables:
## $ V1 : num 2.62 2.83 2.58 2.82 2.79 ...
## $ V2 : num 2.62 2.84 2.58 2.82 2.79 ...
## $ V3 : num 2.62 2.84 2.59 2.83 2.79 ...
## $ V4 : num 2.62 2.85 2.59 2.83 2.79 ...
## $ V5 : num 2.62 2.85 2.59 2.83 2.8 ...
## $ V6 : num 2.62 2.86 2.59 2.83 2.8 ...
## $ V7 : num 2.62 2.86 2.59 2.83 2.8 ...
## $ V8 : num 2.62 2.87 2.6 2.84 2.8 ...
## $ V9 : num 2.63 2.87 2.6 2.84 2.81 ...
## $ V10 : num 2.63 2.88 2.6 2.84 2.81 ...
## $ V11 : num 2.63 2.88 2.6 2.84 2.81 ...
## $ V12 : num 2.63 2.89 2.61 2.85 2.82 ...
## $ V13 : num 2.64 2.9 2.61 2.85 2.82 ...
## $ V14 : num 2.64 2.9 2.61 2.85 2.83 ...
## $ V15 : num 2.64 2.91 2.62 2.86 2.83 ...
## $ V16 : num 2.65 2.92 2.62 2.86 2.84 ...
## $ V17 : num 2.65 2.93 2.62 2.86 2.85 ...
## $ V18 : num 2.66 2.94 2.63 2.87 2.85 ...
## $ V19 : num 2.67 2.95 2.63 2.87 2.86 ...
## $ V20 : num 2.67 2.96 2.64 2.88 2.87 ...
## $ V21 : num 2.68 2.97 2.64 2.88 2.88 ...
## $ V22 : num 2.69 2.98 2.65 2.89 2.89 ...
## $ V23 : num 2.69 3 2.65 2.89 2.9 ...
## $ V24 : num 2.7 3.01 2.66 2.9 2.91 ...
## $ V25 : num 2.71 3.02 2.66 2.9 2.92 ...
## $ V26 : num 2.71 3.03 2.67 2.91 2.93 ...
## $ V27 : num 2.72 3.04 2.67 2.92 2.94 ...
## $ V28 : num 2.73 3.05 2.68 2.92 2.95 ...
## $ V29 : num 2.73 3.07 2.68 2.93 2.96 ...
## $ V30 : num 2.74 3.08 2.69 2.93 2.97 ...
## $ V31 : num 2.75 3.1 2.69 2.94 2.99 ...
## $ V32 : num 2.77 3.12 2.7 2.94 3 ...
## $ V33 : num 2.78 3.14 2.71 2.95 3.02 ...
## $ V34 : num 2.79 3.16 2.71 2.95 3.03 ...
## $ V35 : num 2.8 3.18 2.72 2.96 3.05 ...
## $ V36 : num 2.81 3.2 2.72 2.96 3.06 ...
## $ V37 : num 2.83 3.22 2.73 2.97 3.08 ...
## $ V38 : num 2.84 3.24 2.74 2.98 3.1 ...
## $ V39 : num 2.86 3.26 2.75 2.99 3.12 ...
## $ V40 : num 2.88 3.28 2.77 3 3.14 ...
## $ V41 : num 2.89 3.29 2.78 3.02 3.17 ...
## $ V42 : num 2.91 3.3 2.79 3.03 3.18 ...
## $ V43 : num 2.92 3.31 2.81 3.05 3.2 ...
## $ V44 : num 2.93 3.3 2.82 3.06 3.21 ...
## $ V45 : num 2.94 3.3 2.84 3.08 3.23 ...
## $ V46 : num 2.95 3.29 2.85 3.1 3.24 ...
## $ V47 : num 2.96 3.28 2.87 3.12 3.25 ...
## $ V48 : num 2.98 3.29 2.89 3.14 3.26 ...
## $ V49 : num 3 3.29 2.91 3.16 3.28 ...
## $ V50 : num 3.04 3.31 2.94 3.19 3.31 ...
## $ V51 : num 3.07 3.33 2.97 3.22 3.35 ...
## $ V52 : num 3.12 3.36 3.01 3.26 3.39 ...
## $ V53 : num 3.17 3.4 3.05 3.3 3.44 ...
## $ V54 : num 3.22 3.43 3.09 3.35 3.5 ...
## $ V55 : num 3.26 3.46 3.12 3.39 3.55 ...
## $ V56 : num 3.3 3.49 3.15 3.43 3.61 ...
## $ V57 : num 3.33 3.51 3.17 3.46 3.65 ...
## $ V58 : num 3.35 3.53 3.18 3.48 3.68 ...
## $ V59 : num 3.36 3.54 3.19 3.5 3.7 ...
## $ V60 : num 3.37 3.55 3.19 3.51 3.72 ...
## $ V61 : num 3.38 3.55 3.19 3.51 3.73 ...
## $ V62 : num 3.39 3.56 3.19 3.51 3.74 ...
## $ V63 : num 3.39 3.56 3.18 3.51 3.74 ...
## $ V64 : num 3.39 3.56 3.18 3.51 3.74 ...
## $ V65 : num 3.39 3.56 3.17 3.51 3.74 ...
## $ V66 : num 3.39 3.56 3.17 3.5 3.74 ...
## $ V67 : num 3.39 3.56 3.16 3.49 3.74 ...
## $ V68 : num 3.39 3.55 3.15 3.48 3.73 ...
## $ V69 : num 3.38 3.55 3.13 3.47 3.73 ...
## $ V70 : num 3.37 3.54 3.12 3.46 3.72 ...
## $ V71 : num 3.36 3.53 3.1 3.45 3.71 ...
## $ V72 : num 3.35 3.52 3.09 3.43 3.69 ...
## $ V73 : num 3.34 3.52 3.07 3.41 3.68 ...
## $ V74 : num 3.32 3.51 3.05 3.39 3.66 ...
## $ V75 : num 3.31 3.5 3.03 3.38 3.65 ...
## $ V76 : num 3.29 3.49 3.02 3.35 3.63 ...
## $ V77 : num 3.28 3.48 3 3.33 3.61 ...
## $ V78 : num 3.26 3.47 2.98 3.31 3.59 ...
## $ V79 : num 3.25 3.46 2.96 3.29 3.58 ...
## $ V80 : num 3.23 3.44 2.94 3.27 3.56 ...
## $ V81 : num 3.21 3.43 2.92 3.24 3.54 ...
## $ V82 : num 3.19 3.42 2.9 3.22 3.52 ...
## $ V83 : num 3.17 3.41 2.88 3.2 3.5 ...
## $ V84 : num 3.16 3.4 2.86 3.17 3.48 ...
## $ V85 : num 3.13 3.39 2.83 3.15 3.46 ...
## $ V86 : num 3.11 3.38 2.81 3.12 3.44 ...
## $ V87 : num 3.09 3.36 2.79 3.1 3.41 ...
## $ V88 : num 3.07 3.35 2.77 3.07 3.39 ...
## $ V89 : num 3.05 3.33 2.75 3.05 3.37 ...
## $ V90 : num 3.02 3.32 2.73 3.02 3.34 ...
## $ V91 : num 3 3.3 2.71 3 3.32 ...
## $ V92 : num 2.98 3.29 2.69 2.97 3.3 ...
## $ V93 : num 2.96 3.28 2.67 2.95 3.28 ...
## $ V94 : num 2.94 3.27 2.65 2.93 3.26 ...
## $ V95 : num 2.92 3.25 2.63 2.9 3.24 ...
## $ V96 : num 2.9 3.24 2.61 2.88 3.22 ...
## $ V97 : num 2.88 3.23 2.6 2.86 3.2 ...
## $ V98 : num 2.86 3.21 2.58 2.84 3.18 ...
## $ V99 : num 2.84 3.2 2.56 2.82 3.16 ...
## [list output truncated]
names(meatspec)
## [1] "V1" "V2" "V3" "V4" "V5" "V6" "V7" "V8" "V9" "V10"
## [11] "V11" "V12" "V13" "V14" "V15" "V16" "V17" "V18" "V19" "V20"
## [21] "V21" "V22" "V23" "V24" "V25" "V26" "V27" "V28" "V29" "V30"
## [31] "V31" "V32" "V33" "V34" "V35" "V36" "V37" "V38" "V39" "V40"
## [41] "V41" "V42" "V43" "V44" "V45" "V46" "V47" "V48" "V49" "V50"
## [51] "V51" "V52" "V53" "V54" "V55" "V56" "V57" "V58" "V59" "V60"
## [61] "V61" "V62" "V63" "V64" "V65" "V66" "V67" "V68" "V69" "V70"
## [71] "V71" "V72" "V73" "V74" "V75" "V76" "V77" "V78" "V79" "V80"
## [81] "V81" "V82" "V83" "V84" "V85" "V86" "V87" "V88" "V89" "V90"
## [91] "V91" "V92" "V93" "V94" "V95" "V96" "V97" "V98" "V99" "V100"
## [101] "fat"
model <- lm(fat~.,meatspec[1:172,])
summary(model)
##
## Call:
## lm(formula = fat ~ ., data = meatspec[1:172, ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.09837 -0.35779 0.04555 0.38080 2.33860
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.324 2.012 3.143 0.002439 **
## V1 12134.077 3659.798 3.316 0.001443 **
## V2 -12585.857 5971.891 -2.108 0.038605 *
## V3 -5107.556 9390.265 -0.544 0.588200
## V4 23880.493 17143.644 1.393 0.167977
## V5 -40509.555 22129.359 -1.831 0.071360 .
## V6 28469.416 19569.400 1.455 0.150134
## V7 -20901.082 12501.639 -1.672 0.098952 .
## V8 8369.465 7515.467 1.114 0.269193
## V9 -1539.328 5397.505 -0.285 0.776327
## V10 4706.267 7406.895 0.635 0.527217
## V11 7012.943 11720.620 0.598 0.551516
## V12 14891.444 20169.170 0.738 0.462749
## V13 -30963.902 26186.839 -1.182 0.240983
## V14 34338.612 22323.830 1.538 0.128444
## V15 -22235.237 13842.268 -1.606 0.112640
## V16 -7466.797 8558.172 -0.872 0.385890
## V17 6716.653 6561.805 1.024 0.309500
## V18 -2033.071 6741.330 -0.302 0.763851
## V19 8541.212 9419.998 0.907 0.367627
## V20 -1667.207 17300.433 -0.096 0.923500
## V21 -31972.494 24622.615 -1.299 0.198317
## V22 59526.389 27730.712 2.147 0.035244 *
## V23 -49241.388 23117.226 -2.130 0.036632 *
## V24 16184.597 16679.609 0.970 0.335180
## V25 12077.951 10751.912 1.123 0.265081
## V26 -12632.330 6774.573 -1.865 0.066361 .
## V27 -6298.837 7032.334 -0.896 0.373442
## V28 29625.988 9011.227 3.288 0.001573 **
## V29 -39374.835 13561.228 -2.903 0.004914 **
## V30 31251.427 18742.000 1.667 0.099829 .
## V31 -27238.189 21335.756 -1.277 0.205887
## V32 23009.543 19776.156 1.163 0.248522
## V33 -4584.373 14572.471 -0.315 0.753995
## V34 -5437.943 10344.728 -0.526 0.600754
## V35 -6128.931 8762.663 -0.699 0.486564
## V36 5599.605 6652.640 0.842 0.402776
## V37 -5569.160 6670.198 -0.835 0.406557
## V38 97.451 9291.480 0.010 0.991661
## V39 36021.407 12574.711 2.865 0.005488 **
## V40 -54273.400 17144.384 -3.166 0.002280 **
## V41 52084.876 21758.024 2.394 0.019318 *
## V42 -48458.089 23950.549 -2.023 0.046813 *
## V43 29334.488 20232.617 1.450 0.151500
## V44 -18282.834 13508.157 -1.353 0.180200
## V45 22110.934 9725.348 2.274 0.026020 *
## V46 -11735.692 6631.245 -1.770 0.081061 .
## V47 -514.521 3800.612 -0.135 0.892696
## V48 2551.480 6131.893 0.416 0.678592
## V49 3707.639 8970.401 0.413 0.680618
## V50 -25762.703 10934.783 -2.356 0.021236 *
## V51 46844.468 15367.852 3.048 0.003233 **
## V52 -47783.626 18069.344 -2.644 0.010065 *
## V53 26233.604 18822.491 1.394 0.167744
## V54 87.825 17403.836 0.005 0.995988
## V55 -8475.119 13232.005 -0.641 0.523908
## V56 3488.507 7228.428 0.483 0.630858
## V57 -1520.733 4988.093 -0.305 0.761355
## V58 2275.175 5495.630 0.414 0.680124
## V59 -5415.427 5721.475 -0.947 0.347099
## V60 7152.015 4754.317 1.504 0.136935
## V61 -4494.234 4512.937 -0.996 0.322702
## V62 3662.045 4811.634 0.761 0.449129
## V63 13993.987 7098.106 1.972 0.052563 .
## V64 -23252.133 8973.839 -2.591 0.011604 *
## V65 4373.731 10048.591 0.435 0.664695
## V66 4580.913 10146.146 0.451 0.653011
## V67 -837.676 10747.974 -0.078 0.938097
## V68 -7074.425 10852.430 -0.652 0.516587
## V69 9506.571 9739.256 0.976 0.332325
## V70 -2765.099 9519.031 -0.290 0.772295
## V71 -1125.135 8586.061 -0.131 0.896113
## V72 -7295.096 7489.488 -0.974 0.333341
## V73 17059.811 6522.093 2.616 0.010870 *
## V74 -9889.553 6543.945 -1.511 0.135162
## V75 -325.615 6125.973 -0.053 0.957759
## V76 782.219 5421.002 0.144 0.885677
## V77 8058.935 5793.416 1.391 0.168554
## V78 -15869.978 6448.208 -2.461 0.016282 *
## V79 21768.619 6435.678 3.382 0.001172 **
## V80 -28338.145 8180.874 -3.464 0.000906 ***
## V81 8523.317 10053.153 0.848 0.399384
## V82 22319.451 12098.046 1.845 0.069226 .
## V83 -17244.722 13991.685 -1.232 0.221829
## V84 -18325.836 14959.964 -1.225 0.224627
## V85 33345.457 13868.197 2.404 0.018808 *
## V86 -7955.157 14571.278 -0.546 0.586813
## V87 -7837.966 16141.553 -0.486 0.628762
## V88 -1815.552 17261.928 -0.105 0.916532
## V89 631.595 15684.751 0.040 0.967992
## V90 -2701.955 16187.612 -0.167 0.867911
## V91 4375.678 19400.005 0.226 0.822199
## V92 12925.188 16456.244 0.785 0.434816
## V93 -7441.235 12417.883 -0.599 0.550923
## V94 -2464.532 11815.234 -0.209 0.835366
## V95 -2090.635 9666.576 -0.216 0.829394
## V96 10912.352 9950.716 1.097 0.276505
## V97 -20331.405 11022.234 -1.845 0.069270 .
## V98 3948.443 8227.133 0.480 0.632753
## V99 6358.930 8652.372 0.735 0.464800
## V100 -263.365 4104.463 -0.064 0.949019
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.074 on 71 degrees of freedom
## Multiple R-squared: 0.997, Adjusted R-squared: 0.9928
## F-statistic: 237.5 on 100 and 71 DF, p-value: < 2.2e-16
# We see that the fit of this model is already
# very good in terms of R2. How well does this
# model do in predicting the observations in
# the test sample? We need a measure of performance—we
# use root mean square error (RMSE):
rmse <- function(x,y) sqrt(mean((x-y)^2))
rmse(model$fit,meatspec$fat[1:172])
## [1] 0.6903167
rmse(predict(model,meatspec[173:215,]),meatspec$fat[173:215])
## [1] 3.814
# We see that the performance is much worse for the test
# sample. This is not unusual, as the fit to the data we
# have almost always gives an overoptimistic sense of how
# well the model will do with future data. In this case,
# the actual error is about five times greater than the
# model itself suggests.
# Now, it is quite likely that not all 100 predictors are
# necessary to make a good prediction. In fact, some of
# them might just be adding noise to the prediction and
# we could improve matters by eliminating some of them.
# We use the default stepwise model selection:
model2 <- step(model)
## Start: AIC=74.51
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 +
## V22 + V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 +
## V32 + V33 + V34 + V35 + V36 + V37 + V38 + V39 + V40 + V41 +
## V42 + V43 + V44 + V45 + V46 + V47 + V48 + V49 + V50 + V51 +
## V52 + V53 + V54 + V55 + V56 + V57 + V58 + V59 + V60 + V61 +
## V62 + V63 + V64 + V65 + V66 + V67 + V68 + V69 + V70 + V71 +
## V72 + V73 + V74 + V75 + V76 + V77 + V78 + V79 + V80 + V81 +
## V82 + V83 + V84 + V85 + V86 + V87 + V88 + V89 + V90 + V91 +
## V92 + V93 + V94 + V95 + V96 + V97 + V98 + V99 + V100
##
## Df Sum of Sq RSS AIC
## - V54 1 0.0000 81.964 72.512
## - V38 1 0.0001 81.965 72.512
## - V89 1 0.0019 81.966 72.516
## - V75 1 0.0033 81.968 72.519
## - V100 1 0.0048 81.969 72.522
## - V67 1 0.0070 81.971 72.527
## - V20 1 0.0107 81.975 72.534
## - V88 1 0.0128 81.977 72.539
## - V71 1 0.0198 81.984 72.554
## - V47 1 0.0212 81.986 72.556
## - V76 1 0.0240 81.988 72.562
## - V90 1 0.0322 81.997 72.579
## - V94 1 0.0502 82.015 72.617
## - V95 1 0.0540 82.018 72.625
## - V91 1 0.0587 82.023 72.635
## - V9 1 0.0939 82.058 72.709
## - V70 1 0.0974 82.062 72.716
## - V18 1 0.1050 82.069 72.732
## - V57 1 0.1073 82.072 72.737
## - V33 1 0.1143 82.079 72.752
## - V49 1 0.1972 82.162 72.925
## - V58 1 0.1979 82.162 72.927
## - V48 1 0.1999 82.164 72.931
## - V65 1 0.2187 82.183 72.970
## - V66 1 0.2353 82.200 73.005
## - V98 1 0.2659 82.230 73.069
## - V56 1 0.2689 82.233 73.075
## - V87 1 0.2722 82.237 73.082
## - V34 1 0.3190 82.283 73.180
## - V3 1 0.3415 82.306 73.227
## - V86 1 0.3441 82.308 73.233
## - V11 1 0.4133 82.378 73.377
## - V93 1 0.4145 82.379 73.380
## - V10 1 0.4661 82.430 73.487
## - V55 1 0.4736 82.438 73.503
## - V68 1 0.4906 82.455 73.538
## - V35 1 0.5648 82.529 73.693
## - V99 1 0.6235 82.588 73.815
## - V12 1 0.6293 82.594 73.828
## - V62 1 0.6687 82.633 73.910
## - V92 1 0.7122 82.677 74.000
## - V37 1 0.8048 82.769 74.192
## - V36 1 0.8179 82.782 74.220
## - V81 1 0.8298 82.794 74.245
## - V16 1 0.8788 82.843 74.346
## - V27 1 0.9262 82.891 74.445
## - V19 1 0.9491 82.913 74.492
## <none> 81.964 74.512
## - V59 1 1.0342 82.999 74.669
## - V24 1 1.0869 83.051 74.778
## - V72 1 1.0953 83.060 74.795
## - V69 1 1.0999 83.064 74.805
## - V61 1 1.1449 83.109 74.898
## - V17 1 1.2096 83.174 75.032
## - V96 1 1.3883 83.353 75.401
## - V8 1 1.4317 83.396 75.490
## - V25 1 1.4567 83.421 75.542
## - V32 1 1.5628 83.527 75.761
## - V13 1 1.6140 83.578 75.866
## - V84 1 1.7323 83.697 76.109
## - V83 1 1.7536 83.718 76.153
## - V31 1 1.8815 83.846 76.416
## - V21 1 1.9465 83.911 76.549
## - V44 1 2.1148 84.079 76.893
## - V77 1 2.2338 84.198 77.137
## - V4 1 2.2400 84.204 77.149
## - V53 1 2.2425 84.207 77.155
## - V43 1 2.4267 84.391 77.530
## - V6 1 2.4433 84.408 77.564
## - V60 1 2.6124 84.577 77.909
## - V74 1 2.6366 84.601 77.958
## - V14 1 2.7315 84.696 78.150
## - V15 1 2.9788 84.943 78.652
## - V30 1 3.2098 85.174 79.119
## - V7 1 3.2268 85.191 79.153
## - V46 1 3.6157 85.580 79.937
## - V5 1 3.8685 85.833 80.444
## - V97 1 3.9279 85.892 80.563
## - V82 1 3.9292 85.894 80.566
## - V26 1 4.0139 85.978 80.735
## - V63 1 4.4871 86.451 81.679
## - V42 1 4.7257 86.690 82.153
## - V2 1 5.1275 87.092 82.949
## - V23 1 5.2379 87.202 83.167
## - V22 1 5.3194 87.284 83.327
## - V45 1 5.9672 87.932 84.599
## - V50 1 6.4081 88.372 85.459
## - V41 1 6.6153 88.580 85.862
## - V85 1 6.6742 88.639 85.977
## - V78 1 6.9926 88.957 86.593
## - V64 1 7.7506 89.715 88.053
## - V73 1 7.8984 89.863 88.336
## - V52 1 8.0731 90.037 88.670
## - V39 1 9.4731 91.437 91.324
## - V29 1 9.7321 91.696 91.810
## - V51 1 10.7265 92.691 93.665
## - V40 1 11.5690 93.533 95.222
## - V28 1 12.4780 94.442 96.885
## - V1 1 12.6901 94.655 97.271
## - V79 1 13.2081 95.172 98.210
## - V80 1 13.8519 95.816 99.369
##
## Step: AIC=72.51
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 +
## V22 + V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 +
## V32 + V33 + V34 + V35 + V36 + V37 + V38 + V39 + V40 + V41 +
## V42 + V43 + V44 + V45 + V46 + V47 + V48 + V49 + V50 + V51 +
## V52 + V53 + V55 + V56 + V57 + V58 + V59 + V60 + V61 + V62 +
## V63 + V64 + V65 + V66 + V67 + V68 + V69 + V70 + V71 + V72 +
## V73 + V74 + V75 + V76 + V77 + V78 + V79 + V80 + V81 + V82 +
## V83 + V84 + V85 + V86 + V87 + V88 + V89 + V90 + V91 + V92 +
## V93 + V94 + V95 + V96 + V97 + V98 + V99 + V100
##
## Df Sum of Sq RSS AIC
## - V38 1 0.0001 81.965 70.512
## - V89 1 0.0019 81.966 70.516
## - V75 1 0.0035 81.968 70.519
## - V100 1 0.0047 81.969 70.522
## - V67 1 0.0076 81.972 70.528
## - V20 1 0.0107 81.975 70.534
## - V88 1 0.0131 81.978 70.539
## - V71 1 0.0201 81.984 70.554
## - V47 1 0.0216 81.986 70.557
## - V76 1 0.0243 81.989 70.563
## - V90 1 0.0322 81.997 70.580
## - V94 1 0.0504 82.015 70.618
## - V95 1 0.0552 82.020 70.628
## - V91 1 0.0587 82.023 70.635
## - V9 1 0.0939 82.058 70.709
## - V70 1 0.0989 82.063 70.719
## - V18 1 0.1050 82.069 70.732
## - V33 1 0.1146 82.079 70.752
## - V57 1 0.1235 82.088 70.771
## - V49 1 0.2012 82.166 70.934
## - V58 1 0.2141 82.179 70.961
## - V48 1 0.2208 82.185 70.975
## - V65 1 0.2279 82.192 70.990
## - V66 1 0.2357 82.200 71.006
## - V98 1 0.2666 82.231 71.071
## - V87 1 0.2740 82.238 71.086
## - V34 1 0.3267 82.291 71.196
## - V3 1 0.3416 82.306 71.227
## - V86 1 0.3533 82.318 71.252
## - V93 1 0.4165 82.381 71.384
## - V11 1 0.4243 82.389 71.400
## - V10 1 0.4786 82.443 71.513
## - V68 1 0.5216 82.486 71.603
## - V56 1 0.5245 82.489 71.609
## - V35 1 0.5726 82.537 71.710
## - V99 1 0.6251 82.590 71.819
## - V12 1 0.6552 82.620 71.882
## - V62 1 0.6719 82.636 71.916
## - V92 1 0.7164 82.681 72.009
## - V36 1 0.8229 82.787 72.230
## - V37 1 0.8348 82.799 72.255
## - V81 1 0.8712 82.836 72.331
## - V16 1 0.8799 82.844 72.349
## - V27 1 0.9321 82.896 72.457
## - V19 1 0.9498 82.914 72.494
## <none> 81.964 72.512
## - V59 1 1.0844 83.049 72.773
## - V72 1 1.0953 83.060 72.795
## - V24 1 1.1239 83.088 72.854
## - V69 1 1.1381 83.103 72.884
## - V61 1 1.1535 83.118 72.916
## - V17 1 1.2141 83.178 73.041
## - V96 1 1.3968 83.361 73.419
## - V8 1 1.4323 83.397 73.492
## - V25 1 1.4567 83.421 73.542
## - V32 1 1.5629 83.527 73.761
## - V13 1 1.6700 83.634 73.981
## - V83 1 1.8674 83.832 74.387
## - V31 1 1.8897 83.854 74.432
## - V21 1 1.9874 83.952 74.633
## - V84 1 2.0185 83.983 74.697
## - V44 1 2.1226 84.087 74.910
## - V4 1 2.2570 84.221 75.184
## - V77 1 2.2666 84.231 75.204
## - V43 1 2.4424 84.407 75.563
## - V6 1 2.4437 84.408 75.565
## - V60 1 2.7257 84.690 76.139
## - V74 1 2.7516 84.716 76.191
## - V55 1 2.7969 84.761 76.283
## - V14 1 2.8230 84.787 76.336
## - V15 1 3.0649 85.029 76.826
## - V7 1 3.2288 85.193 77.157
## - V30 1 3.2705 85.235 77.242
## - V5 1 3.8742 85.839 78.456
## - V46 1 3.8934 85.858 78.494
## - V97 1 3.9367 85.901 78.581
## - V26 1 4.0179 85.982 78.743
## - V82 1 4.0803 86.045 78.868
## - V63 1 4.4945 86.459 79.694
## - V42 1 4.9341 86.899 80.566
## - V2 1 5.1467 87.111 80.987
## - V22 1 5.7115 87.676 82.098
## - V23 1 5.8132 87.778 82.298
## - V45 1 5.9677 87.932 82.600
## - V50 1 6.8210 88.785 84.261
## - V78 1 6.9928 88.957 84.594
## - V41 1 7.0263 88.991 84.658
## - V85 1 7.5581 89.523 85.683
## - V64 1 8.0604 90.025 86.646
## - V73 1 8.1744 90.139 86.863
## - V39 1 9.8990 91.863 90.123
## - V29 1 9.9135 91.878 90.150
## - V53 1 11.0348 92.999 92.237
## - V40 1 12.1604 94.125 94.306
## - V28 1 12.5323 94.497 94.984
## - V1 1 13.1906 95.155 96.178
## - V79 1 13.2682 95.233 96.318
## - V51 1 14.1805 96.145 97.958
## - V80 1 14.3616 96.326 98.282
## - V52 1 15.3320 97.296 100.006
##
## Step: AIC=70.51
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 +
## V22 + V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 +
## V32 + V33 + V34 + V35 + V36 + V37 + V39 + V40 + V41 + V42 +
## V43 + V44 + V45 + V46 + V47 + V48 + V49 + V50 + V51 + V52 +
## V53 + V55 + V56 + V57 + V58 + V59 + V60 + V61 + V62 + V63 +
## V64 + V65 + V66 + V67 + V68 + V69 + V70 + V71 + V72 + V73 +
## V74 + V75 + V76 + V77 + V78 + V79 + V80 + V81 + V82 + V83 +
## V84 + V85 + V86 + V87 + V88 + V89 + V90 + V91 + V92 + V93 +
## V94 + V95 + V96 + V97 + V98 + V99 + V100
##
## Df Sum of Sq RSS AIC
## - V89 1 0.0019 81.966 68.516
## - V75 1 0.0034 81.968 68.519
## - V100 1 0.0046 81.969 68.522
## - V67 1 0.0077 81.972 68.528
## - V20 1 0.0106 81.975 68.534
## - V88 1 0.0130 81.978 68.540
## - V71 1 0.0205 81.985 68.555
## - V47 1 0.0217 81.986 68.558
## - V76 1 0.0249 81.989 68.565
## - V90 1 0.0332 81.998 68.582
## - V94 1 0.0503 82.015 68.618
## - V95 1 0.0551 82.020 68.628
## - V91 1 0.0599 82.024 68.638
## - V9 1 0.0942 82.059 68.710
## - V70 1 0.0997 82.064 68.721
## - V18 1 0.1049 82.069 68.732
## - V33 1 0.1151 82.080 68.754
## - V57 1 0.1249 82.089 68.774
## - V49 1 0.2104 82.175 68.953
## - V58 1 0.2238 82.188 68.981
## - V65 1 0.2329 82.197 69.000
## - V66 1 0.2426 82.207 69.021
## - V48 1 0.2488 82.213 69.034
## - V98 1 0.2708 82.235 69.080
## - V87 1 0.2741 82.239 69.086
## - V34 1 0.3286 82.293 69.200
## - V3 1 0.3416 82.306 69.228
## - V86 1 0.3535 82.318 69.252
## - V93 1 0.4164 82.381 69.384
## - V11 1 0.4269 82.391 69.406
## - V10 1 0.4794 82.444 69.515
## - V68 1 0.5218 82.486 69.604
## - V56 1 0.5310 82.496 69.623
## - V35 1 0.5752 82.540 69.715
## - V99 1 0.6271 82.592 69.823
## - V12 1 0.6560 82.621 69.883
## - V62 1 0.6757 82.640 69.924
## - V92 1 0.7228 82.687 70.022
## - V36 1 0.8432 82.808 70.273
## - V81 1 0.8739 82.838 70.336
## - V16 1 0.9059 82.870 70.403
## - V27 1 0.9334 82.898 70.460
## - V19 1 0.9534 82.918 70.501
## <none> 81.965 70.512
## - V59 1 1.1038 83.068 70.813
## - V37 1 1.1046 83.069 70.815
## - V24 1 1.1282 83.093 70.864
## - V72 1 1.1391 83.104 70.886
## - V69 1 1.1403 83.105 70.889
## - V61 1 1.1550 83.120 70.919
## - V17 1 1.2857 83.250 71.189
## - V8 1 1.4347 83.399 71.497
## - V25 1 1.4594 83.424 71.548
## - V96 1 1.5537 83.518 71.742
## - V32 1 1.5943 83.559 71.826
## - V13 1 1.6718 83.636 71.985
## - V83 1 1.8783 83.843 72.409
## - V31 1 1.9178 83.882 72.490
## - V21 1 1.9989 83.963 72.657
## - V84 1 2.1479 84.112 72.961
## - V77 1 2.2688 84.233 73.209
## - V4 1 2.2692 84.234 73.209
## - V6 1 2.4470 84.412 73.572
## - V44 1 2.5258 84.490 73.733
## - V60 1 2.7256 84.690 74.139
## - V43 1 2.8040 84.769 74.298
## - V14 1 2.8229 84.787 74.336
## - V55 1 2.8611 84.826 74.414
## - V74 1 2.9463 84.911 74.586
## - V15 1 3.0680 85.033 74.833
## - V7 1 3.2436 85.208 75.188
## - V30 1 3.2818 85.246 75.265
## - V5 1 3.8888 85.853 76.485
## - V46 1 3.8942 85.859 76.496
## - V26 1 4.0203 85.985 76.748
## - V82 1 4.1207 86.085 76.949
## - V63 1 4.4984 86.463 77.702
## - V97 1 4.5127 86.477 77.730
## - V2 1 5.2677 87.232 79.226
## - V42 1 5.5005 87.465 79.684
## - V22 1 5.7384 87.703 80.151
## - V23 1 5.8296 87.794 80.330
## - V45 1 6.4226 88.387 81.488
## - V50 1 6.8406 88.805 82.299
## - V78 1 6.9943 88.959 82.597
## - V41 1 7.4652 89.430 83.505
## - V85 1 7.7699 89.734 84.090
## - V64 1 8.0886 90.053 84.700
## - V73 1 8.9320 90.897 86.303
## - V29 1 9.9348 91.899 88.190
## - V53 1 11.0740 93.039 90.309
## - V28 1 12.6219 94.586 93.147
## - V40 1 13.0363 95.001 93.899
## - V79 1 13.2892 95.254 94.357
## - V1 1 13.8603 95.825 95.385
## - V51 1 14.2041 96.169 96.001
## - V80 1 14.3801 96.345 96.315
## - V52 1 15.3320 97.297 98.006
## - V39 1 18.9076 100.872 104.214
##
## Step: AIC=68.52
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 +
## V22 + V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 +
## V32 + V33 + V34 + V35 + V36 + V37 + V39 + V40 + V41 + V42 +
## V43 + V44 + V45 + V46 + V47 + V48 + V49 + V50 + V51 + V52 +
## V53 + V55 + V56 + V57 + V58 + V59 + V60 + V61 + V62 + V63 +
## V64 + V65 + V66 + V67 + V68 + V69 + V70 + V71 + V72 + V73 +
## V74 + V75 + V76 + V77 + V78 + V79 + V80 + V81 + V82 + V83 +
## V84 + V85 + V86 + V87 + V88 + V90 + V91 + V92 + V93 + V94 +
## V95 + V96 + V97 + V98 + V99 + V100
##
## Df Sum of Sq RSS AIC
## - V100 1 0.0032 81.970 66.523
## - V67 1 0.0065 81.973 66.530
## - V75 1 0.0076 81.974 66.532
## - V20 1 0.0105 81.977 66.538
## - V88 1 0.0174 81.984 66.553
## - V47 1 0.0224 81.989 66.563
## - V71 1 0.0256 81.992 66.570
## - V76 1 0.0353 82.002 66.590
## - V90 1 0.0410 82.007 66.602
## - V94 1 0.0490 82.015 66.619
## - V91 1 0.0581 82.025 66.638
## - V95 1 0.0598 82.026 66.642
## - V9 1 0.0967 82.063 66.719
## - V70 1 0.1013 82.068 66.729
## - V18 1 0.1059 82.072 66.738
## - V33 1 0.1137 82.080 66.755
## - V57 1 0.1278 82.094 66.784
## - V49 1 0.2210 82.188 66.980
## - V58 1 0.2245 82.191 66.987
## - V48 1 0.2468 82.213 67.034
## - V66 1 0.2525 82.219 67.045
## - V98 1 0.2699 82.236 67.082
## - V65 1 0.2801 82.247 67.103
## - V34 1 0.3268 82.293 67.201
## - V87 1 0.3431 82.310 67.235
## - V86 1 0.3538 82.320 67.257
## - V3 1 0.3581 82.325 67.266
## - V93 1 0.4174 82.384 67.390
## - V11 1 0.4307 82.397 67.418
## - V68 1 0.5199 82.486 67.604
## - V10 1 0.5207 82.487 67.606
## - V56 1 0.5731 82.540 67.715
## - V35 1 0.6351 82.602 67.844
## - V99 1 0.6554 82.622 67.886
## - V12 1 0.6681 82.635 67.913
## - V92 1 0.7303 82.697 68.042
## - V62 1 0.7332 82.700 68.048
## - V81 1 0.9059 82.872 68.407
## - V36 1 0.9127 82.879 68.421
## - V16 1 0.9207 82.887 68.438
## - V27 1 0.9317 82.898 68.460
## - V19 1 0.9523 82.919 68.503
## <none> 81.966 68.516
## - V72 1 1.1671 83.134 68.948
## - V59 1 1.1683 83.135 68.951
## - V37 1 1.1761 83.143 68.967
## - V24 1 1.1796 83.146 68.974
## - V69 1 1.1914 83.158 68.998
## - V17 1 1.2867 83.253 69.195
## - V61 1 1.3244 83.291 69.273
## - V8 1 1.4546 83.421 69.542
## - V25 1 1.5069 83.473 69.650
## - V96 1 1.5562 83.523 69.751
## - V32 1 1.6299 83.596 69.903
## - V13 1 1.6772 83.644 70.000
## - V31 1 1.9230 83.890 70.505
## - V83 1 1.9877 83.954 70.638
## - V21 1 2.0072 83.974 70.678
## - V84 1 2.2039 84.170 71.080
## - V4 1 2.2676 84.234 71.210
## - V77 1 2.3346 84.301 71.347
## - V6 1 2.4485 84.415 71.579
## - V44 1 2.5488 84.515 71.783
## - V14 1 2.8672 84.834 72.430
## - V43 1 2.8852 84.852 72.467
## - V60 1 2.9567 84.923 72.611
## - V55 1 2.9683 84.935 72.635
## - V74 1 3.0512 85.018 72.803
## - V15 1 3.0980 85.064 72.897
## - V7 1 3.2672 85.234 73.239
## - V30 1 3.2860 85.253 73.277
## - V5 1 3.8927 85.859 74.497
## - V26 1 4.0230 85.990 74.758
## - V46 1 4.0626 86.029 74.837
## - V82 1 4.1212 86.088 74.954
## - V63 1 4.4998 86.466 75.709
## - V97 1 4.6092 86.576 75.926
## - V2 1 5.3271 87.294 77.347
## - V42 1 5.5483 87.515 77.782
## - V22 1 5.8074 87.774 78.290
## - V23 1 5.9365 87.903 78.543
## - V45 1 6.6466 88.613 79.927
## - V50 1 6.8802 88.847 80.380
## - V41 1 7.4965 89.463 81.569
## - V78 1 7.6168 89.583 81.800
## - V85 1 7.7755 89.742 82.104
## - V64 1 8.2128 90.179 82.941
## - V73 1 8.9331 90.900 84.309
## - V29 1 9.9482 91.915 86.219
## - V53 1 11.2189 93.185 88.581
## - V28 1 12.6379 94.604 91.180
## - V40 1 13.0617 95.028 91.949
## - V79 1 13.4159 95.382 92.589
## - V1 1 14.2044 96.171 94.005
## - V51 1 14.2098 96.176 94.014
## - V80 1 15.0325 96.999 95.480
## - V52 1 15.4047 97.371 96.138
## - V39 1 19.0264 100.993 102.420
##
## Step: AIC=66.52
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 +
## V22 + V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 +
## V32 + V33 + V34 + V35 + V36 + V37 + V39 + V40 + V41 + V42 +
## V43 + V44 + V45 + V46 + V47 + V48 + V49 + V50 + V51 + V52 +
## V53 + V55 + V56 + V57 + V58 + V59 + V60 + V61 + V62 + V63 +
## V64 + V65 + V66 + V67 + V68 + V69 + V70 + V71 + V72 + V73 +
## V74 + V75 + V76 + V77 + V78 + V79 + V80 + V81 + V82 + V83 +
## V84 + V85 + V86 + V87 + V88 + V90 + V91 + V92 + V93 + V94 +
## V95 + V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V67 1 0.0064 81.976 64.537
## - V75 1 0.0093 81.979 64.543
## - V20 1 0.0119 81.982 64.548
## - V88 1 0.0184 81.988 64.562
## - V47 1 0.0253 81.995 64.576
## - V71 1 0.0254 81.995 64.576
## - V76 1 0.0414 82.011 64.610
## - V90 1 0.0418 82.012 64.611
## - V94 1 0.0470 82.017 64.622
## - V91 1 0.0608 82.030 64.651
## - V95 1 0.0627 82.032 64.655
## - V9 1 0.0966 82.066 64.726
## - V70 1 0.0990 82.069 64.731
## - V18 1 0.1084 82.078 64.750
## - V33 1 0.1108 82.081 64.755
## - V57 1 0.1246 82.094 64.784
## - V58 1 0.2213 82.191 64.987
## - V49 1 0.2345 82.204 65.014
## - V48 1 0.2450 82.215 65.036
## - V66 1 0.2564 82.226 65.060
## - V65 1 0.2781 82.248 65.106
## - V34 1 0.3344 82.304 65.223
## - V87 1 0.3402 82.310 65.235
## - V98 1 0.3651 82.335 65.287
## - V86 1 0.3670 82.337 65.291
## - V3 1 0.3772 82.347 65.313
## - V93 1 0.4222 82.392 65.407
## - V11 1 0.4533 82.423 65.472
## - V68 1 0.5173 82.487 65.605
## - V10 1 0.5192 82.489 65.609
## - V56 1 0.5706 82.540 65.716
## - V35 1 0.6328 82.602 65.846
## - V12 1 0.6963 82.666 65.978
## - V92 1 0.7275 82.697 66.043
## - V62 1 0.7300 82.700 66.048
## - V81 1 0.9030 82.873 66.408
## - V36 1 0.9113 82.881 66.425
## - V16 1 0.9197 82.889 66.442
## - V27 1 0.9385 82.908 66.481
## <none> 81.970 66.523
## - V19 1 0.9780 82.948 66.563
## - V59 1 1.1683 83.138 66.957
## - V72 1 1.1709 83.141 66.963
## - V37 1 1.1740 83.144 66.969
## - V24 1 1.1783 83.148 66.978
## - V69 1 1.1988 83.168 67.020
## - V17 1 1.2957 83.265 67.221
## - V61 1 1.4040 83.374 67.444
## - V8 1 1.4556 83.425 67.551
## - V25 1 1.5147 83.484 67.672
## - V96 1 1.5666 83.536 67.779
## - V32 1 1.6269 83.597 67.904
## - V13 1 1.8338 83.804 68.329
## - V31 1 1.9222 83.892 68.510
## - V21 1 2.0181 83.988 68.706
## - V83 1 2.0446 84.014 68.761
## - V84 1 2.2015 84.171 69.082
## - V4 1 2.2810 84.251 69.244
## - V6 1 2.4472 84.417 69.583
## - V44 1 2.5619 84.532 69.817
## - V77 1 2.8580 84.828 70.418
## - V55 1 2.9724 84.942 70.650
## - V43 1 3.0050 84.975 70.716
## - V60 1 3.0424 85.012 70.792
## - V74 1 3.0666 85.036 70.840
## - V14 1 3.0944 85.064 70.897
## - V15 1 3.1758 85.146 71.061
## - V7 1 3.2665 85.236 71.244
## - V30 1 3.2861 85.256 71.284
## - V5 1 3.8924 85.862 72.503
## - V99 1 3.9454 85.915 72.609
## - V26 1 4.0935 86.063 72.905
## - V46 1 4.1553 86.125 73.029
## - V82 1 4.2376 86.207 73.193
## - V63 1 4.5671 86.537 73.849
## - V97 1 4.6060 86.576 73.926
## - V2 1 5.4522 87.422 75.599
## - V42 1 5.7048 87.674 76.095
## - V22 1 5.8885 87.858 76.456
## - V23 1 5.9912 87.961 76.657
## - V45 1 6.6907 88.660 78.019
## - V50 1 6.9116 88.881 78.447
## - V41 1 7.5028 89.472 79.587
## - V85 1 7.8119 89.782 80.180
## - V64 1 8.4222 90.392 81.346
## - V78 1 8.6146 90.584 81.711
## - V73 1 8.9705 90.940 82.386
## - V29 1 9.9820 91.952 84.288
## - V53 1 11.2851 93.255 86.709
## - V28 1 12.6356 94.605 89.182
## - V40 1 13.1117 95.081 90.045
## - V79 1 13.4182 95.388 90.599
## - V1 1 14.2357 96.205 92.066
## - V51 1 14.5657 96.535 92.655
## - V80 1 15.0418 97.011 93.502
## - V52 1 15.4249 97.395 94.179
## - V39 1 19.0886 101.058 100.531
##
## Step: AIC=64.54
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 +
## V22 + V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 +
## V32 + V33 + V34 + V35 + V36 + V37 + V39 + V40 + V41 + V42 +
## V43 + V44 + V45 + V46 + V47 + V48 + V49 + V50 + V51 + V52 +
## V53 + V55 + V56 + V57 + V58 + V59 + V60 + V61 + V62 + V63 +
## V64 + V65 + V66 + V68 + V69 + V70 + V71 + V72 + V73 + V74 +
## V75 + V76 + V77 + V78 + V79 + V80 + V81 + V82 + V83 + V84 +
## V85 + V86 + V87 + V88 + V90 + V91 + V92 + V93 + V94 + V95 +
## V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V75 1 0.0097 81.986 62.557
## - V71 1 0.0193 81.995 62.577
## - V20 1 0.0208 81.997 62.580
## - V88 1 0.0239 82.000 62.587
## - V47 1 0.0292 82.005 62.598
## - V76 1 0.0363 82.012 62.613
## - V90 1 0.0369 82.013 62.614
## - V94 1 0.0493 82.025 62.640
## - V91 1 0.0571 82.033 62.656
## - V95 1 0.0657 82.042 62.674
## - V9 1 0.1024 82.079 62.751
## - V18 1 0.1121 82.088 62.772
## - V33 1 0.1123 82.088 62.772
## - V70 1 0.1281 82.104 62.805
## - V57 1 0.1483 82.124 62.847
## - V49 1 0.2306 82.207 63.020
## - V48 1 0.3029 82.279 63.171
## - V58 1 0.3078 82.284 63.181
## - V34 1 0.3307 82.307 63.229
## - V87 1 0.3361 82.312 63.240
## - V98 1 0.3637 82.340 63.298
## - V86 1 0.3638 82.340 63.298
## - V3 1 0.3747 82.351 63.321
## - V65 1 0.4047 82.381 63.384
## - V93 1 0.4175 82.394 63.410
## - V11 1 0.4484 82.425 63.475
## - V10 1 0.5228 82.499 63.630
## - V66 1 0.5945 82.571 63.779
## - V35 1 0.6267 82.603 63.847
## - V56 1 0.6558 82.632 63.907
## - V12 1 0.6917 82.668 63.982
## - V62 1 0.7305 82.707 64.062
## - V92 1 0.7366 82.713 64.075
## - V36 1 0.9086 82.885 64.433
## - V16 1 0.9160 82.892 64.448
## - V27 1 0.9359 82.912 64.489
## <none> 81.976 64.537
## - V81 1 1.0040 82.980 64.630
## - V19 1 1.0305 83.007 64.685
## - V24 1 1.2014 83.178 65.039
## - V37 1 1.2389 83.215 65.116
## - V72 1 1.3042 83.280 65.251
## - V17 1 1.4435 83.420 65.539
## - V8 1 1.4622 83.438 65.577
## - V61 1 1.5450 83.521 65.748
## - V69 1 1.5712 83.547 65.802
## - V59 1 1.5767 83.553 65.813
## - V96 1 1.5961 83.572 65.853
## - V32 1 1.6210 83.597 65.904
## - V25 1 1.7143 83.690 66.096
## - V68 1 1.7741 83.750 66.219
## - V13 1 1.8280 83.804 66.330
## - V31 1 1.9166 83.893 66.512
## - V21 1 2.1750 84.151 67.041
## - V4 1 2.3039 84.280 67.304
## - V83 1 2.3469 84.323 67.392
## - V84 1 2.4343 84.410 67.570
## - V6 1 2.4868 84.463 67.677
## - V44 1 2.5757 84.552 67.858
## - V77 1 2.8657 84.842 68.447
## - V43 1 3.0123 84.988 68.744
## - V14 1 3.0954 85.072 68.912
## - V55 1 3.1324 85.109 68.986
## - V15 1 3.1957 85.172 69.114
## - V74 1 3.2504 85.227 69.225
## - V30 1 3.2821 85.258 69.289
## - V7 1 3.2991 85.275 69.323
## - V60 1 3.4256 85.402 69.578
## - V5 1 3.9241 85.900 70.579
## - V99 1 4.1102 86.086 70.951
## - V46 1 4.2509 86.227 71.232
## - V26 1 4.2893 86.265 71.309
## - V63 1 4.6199 86.596 71.967
## - V97 1 4.6640 86.640 72.054
## - V82 1 4.6954 86.672 72.117
## - V2 1 5.5520 87.528 73.808
## - V42 1 5.7647 87.741 74.225
## - V23 1 6.2460 88.222 75.166
## - V22 1 6.2777 88.254 75.228
## - V50 1 6.9412 88.917 76.517
## - V45 1 7.0149 88.991 76.659
## - V41 1 7.5265 89.503 77.645
## - V85 1 7.8470 89.823 78.260
## - V64 1 8.5874 90.563 79.672
## - V78 1 8.6093 90.585 79.713
## - V73 1 8.9812 90.957 80.418
## - V29 1 9.9986 91.975 82.331
## - V53 1 11.2919 93.268 84.733
## - V28 1 12.8147 94.791 87.519
## - V40 1 13.1137 95.090 88.060
## - V79 1 13.6048 95.581 88.946
## - V1 1 14.2484 96.225 90.101
## - V80 1 15.0970 97.073 91.611
## - V51 1 15.1825 97.159 91.762
## - V52 1 15.5837 97.560 92.471
## - V39 1 19.2152 101.191 98.757
##
## Step: AIC=62.56
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 +
## V22 + V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 +
## V32 + V33 + V34 + V35 + V36 + V37 + V39 + V40 + V41 + V42 +
## V43 + V44 + V45 + V46 + V47 + V48 + V49 + V50 + V51 + V52 +
## V53 + V55 + V56 + V57 + V58 + V59 + V60 + V61 + V62 + V63 +
## V64 + V65 + V66 + V68 + V69 + V70 + V71 + V72 + V73 + V74 +
## V76 + V77 + V78 + V79 + V80 + V81 + V82 + V83 + V84 + V85 +
## V86 + V87 + V88 + V90 + V91 + V92 + V93 + V94 + V95 + V96 +
## V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V20 1 0.0165 82.002 60.592
## - V88 1 0.0239 82.010 60.607
## - V47 1 0.0255 82.011 60.611
## - V71 1 0.0268 82.013 60.613
## - V76 1 0.0270 82.013 60.614
## - V94 1 0.0405 82.026 60.642
## - V90 1 0.0474 82.033 60.656
## - V91 1 0.0725 82.058 60.709
## - V95 1 0.0732 82.059 60.710
## - V9 1 0.0965 82.082 60.759
## - V18 1 0.1061 82.092 60.779
## - V33 1 0.1113 82.097 60.790
## - V70 1 0.1372 82.123 60.844
## - V57 1 0.1520 82.138 60.876
## - V49 1 0.2571 82.243 61.096
## - V48 1 0.2974 82.283 61.180
## - V87 1 0.3296 82.315 61.247
## - V58 1 0.3340 82.320 61.256
## - V34 1 0.3655 82.351 61.322
## - V86 1 0.3668 82.353 61.325
## - V98 1 0.3687 82.355 61.329
## - V3 1 0.3753 82.361 61.342
## - V65 1 0.4067 82.393 61.408
## - V11 1 0.4559 82.442 61.511
## - V93 1 0.4608 82.447 61.521
## - V10 1 0.5202 82.506 61.645
## - V66 1 0.5910 82.577 61.792
## - V35 1 0.6254 82.611 61.864
## - V56 1 0.6524 82.638 61.920
## - V12 1 0.6822 82.668 61.982
## - V92 1 0.7270 82.713 62.075
## - V62 1 0.8559 82.842 62.343
## - V36 1 0.8997 82.886 62.434
## - V16 1 0.9279 82.914 62.493
## <none> 81.986 62.557
## - V19 1 1.0264 83.012 62.697
## - V81 1 1.0265 83.012 62.697
## - V27 1 1.0775 83.063 62.803
## - V37 1 1.2343 83.220 63.127
## - V24 1 1.2379 83.224 63.135
## - V72 1 1.4404 83.426 63.553
## - V8 1 1.4527 83.439 63.578
## - V17 1 1.4597 83.446 63.592
## - V61 1 1.5707 83.557 63.821
## - V96 1 1.5991 83.585 63.880
## - V59 1 1.6020 83.588 63.885
## - V32 1 1.6196 83.605 63.922
## - V25 1 1.7052 83.691 64.098
## - V13 1 1.8221 83.808 64.338
## - V69 1 1.8515 83.837 64.398
## - V31 1 1.9071 83.893 64.512
## - V68 1 1.9881 83.974 64.678
## - V4 1 2.3273 84.313 65.371
## - V21 1 2.3300 84.316 65.377
## - V83 1 2.3650 84.351 65.448
## - V84 1 2.4303 84.416 65.581
## - V6 1 2.4779 84.464 65.678
## - V44 1 2.6689 84.655 66.067
## - V77 1 2.8562 84.842 66.447
## - V43 1 3.0390 85.025 66.817
## - V14 1 3.1278 85.114 66.997
## - V55 1 3.1415 85.127 67.024
## - V15 1 3.2203 85.206 67.184
## - V7 1 3.2943 85.280 67.333
## - V30 1 3.3103 85.296 67.365
## - V60 1 3.4163 85.402 67.579
## - V5 1 3.9232 85.909 68.597
## - V99 1 4.1070 86.093 68.964
## - V46 1 4.2457 86.232 69.241
## - V26 1 4.3223 86.308 69.394
## - V63 1 4.6700 86.656 70.085
## - V97 1 4.6705 86.656 70.086
## - V82 1 4.7208 86.707 70.186
## - V2 1 5.5716 87.557 71.866
## - V42 1 5.7562 87.742 72.228
## - V23 1 6.4248 88.411 73.534
## - V22 1 6.5343 88.520 73.747
## - V74 1 7.0580 89.044 74.761
## - V45 1 7.0955 89.081 74.833
## - V50 1 7.1804 89.166 74.997
## - V41 1 7.5746 89.560 75.756
## - V85 1 7.8390 89.825 76.263
## - V64 1 8.5798 90.566 77.676
## - V78 1 8.6846 90.670 77.875
## - V73 1 9.0123 90.998 78.495
## - V29 1 10.2780 92.264 80.871
## - V53 1 11.4895 93.475 83.115
## - V28 1 12.8213 94.807 85.548
## - V40 1 13.4115 95.397 86.616
## - V79 1 13.6257 95.612 87.001
## - V1 1 14.8571 96.843 89.202
## - V80 1 15.2247 97.211 89.854
## - V51 1 15.7472 97.733 90.776
## - V52 1 16.0553 98.041 91.318
## - V39 1 20.1624 102.148 98.376
##
## Step: AIC=60.59
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V21 + V22 +
## V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 +
## V33 + V34 + V35 + V36 + V37 + V39 + V40 + V41 + V42 + V43 +
## V44 + V45 + V46 + V47 + V48 + V49 + V50 + V51 + V52 + V53 +
## V55 + V56 + V57 + V58 + V59 + V60 + V61 + V62 + V63 + V64 +
## V65 + V66 + V68 + V69 + V70 + V71 + V72 + V73 + V74 + V76 +
## V77 + V78 + V79 + V80 + V81 + V82 + V83 + V84 + V85 + V86 +
## V87 + V88 + V90 + V91 + V92 + V93 + V94 + V95 + V96 + V97 +
## V98 + V99
##
## Df Sum of Sq RSS AIC
## - V88 1 0.0247 82.027 58.643
## - V47 1 0.0264 82.029 58.647
## - V76 1 0.0271 82.029 58.648
## - V71 1 0.0291 82.031 58.653
## - V94 1 0.0513 82.054 58.699
## - V90 1 0.0651 82.067 58.728
## - V95 1 0.0750 82.077 58.749
## - V9 1 0.0925 82.095 58.786
## - V91 1 0.0937 82.096 58.788
## - V33 1 0.0979 82.100 58.797
## - V18 1 0.1067 82.109 58.815
## - V70 1 0.1288 82.131 58.862
## - V57 1 0.1953 82.198 59.001
## - V48 1 0.2963 82.299 59.212
## - V49 1 0.2963 82.299 59.212
## - V87 1 0.3144 82.317 59.250
## - V58 1 0.3347 82.337 59.292
## - V98 1 0.3612 82.364 59.348
## - V3 1 0.3774 82.380 59.381
## - V65 1 0.3920 82.394 59.412
## - V86 1 0.4152 82.418 59.460
## - V34 1 0.4331 82.435 59.498
## - V93 1 0.4467 82.449 59.526
## - V11 1 0.4844 82.487 59.605
## - V10 1 0.5763 82.579 59.796
## - V35 1 0.6115 82.614 59.869
## - V66 1 0.6194 82.622 59.886
## - V12 1 0.6868 82.689 60.026
## - V92 1 0.7148 82.717 60.084
## - V56 1 0.7435 82.746 60.144
## - V36 1 0.8832 82.886 60.434
## - V62 1 0.9571 82.959 60.587
## <none> 82.002 60.592
## - V81 1 1.0159 83.018 60.709
## - V16 1 1.0215 83.024 60.721
## - V27 1 1.0756 83.078 60.833
## - V37 1 1.2639 83.266 61.222
## - V72 1 1.4377 83.440 61.581
## - V8 1 1.4534 83.456 61.613
## - V61 1 1.5562 83.559 61.825
## - V59 1 1.5890 83.591 61.893
## - V32 1 1.6319 83.634 61.981
## - V96 1 1.6506 83.653 62.019
## - V17 1 1.6984 83.701 62.118
## - V24 1 1.7109 83.713 62.143
## - V69 1 1.8359 83.838 62.400
## - V25 1 1.8993 83.902 62.530
## - V13 1 1.9280 83.930 62.589
## - V31 1 1.9340 83.936 62.601
## - V68 1 1.9983 84.001 62.733
## - V19 1 2.2187 84.221 63.184
## - V4 1 2.3183 84.321 63.387
## - V84 1 2.4440 84.446 63.643
## - V6 1 2.4653 84.468 63.686
## - V44 1 2.7296 84.732 64.224
## - V77 1 2.8544 84.857 64.477
## - V83 1 2.8698 84.872 64.508
## - V43 1 3.1260 85.128 65.026
## - V55 1 3.1836 85.186 65.143
## - V15 1 3.2193 85.222 65.215
## - V14 1 3.2234 85.226 65.223
## - V7 1 3.3146 85.317 65.407
## - V30 1 3.3340 85.336 65.446
## - V60 1 3.4515 85.454 65.683
## - V5 1 3.9248 85.927 66.633
## - V99 1 4.1005 86.103 66.984
## - V46 1 4.3113 86.314 67.405
## - V26 1 4.3131 86.315 67.408
## - V97 1 4.6595 86.662 68.097
## - V63 1 4.8328 86.835 68.441
## - V82 1 5.2930 87.295 69.350
## - V2 1 5.5557 87.558 69.867
## - V42 1 5.8763 87.879 70.495
## - V45 1 7.0793 89.082 72.834
## - V74 1 7.2057 89.208 73.078
## - V41 1 7.5648 89.567 73.769
## - V85 1 7.8850 89.887 74.383
## - V50 1 8.1661 90.168 74.920
## - V64 1 8.7159 90.718 75.965
## - V78 1 8.7593 90.762 76.048
## - V73 1 8.9965 90.999 76.497
## - V23 1 9.4714 91.474 77.392
## - V29 1 10.2619 92.264 78.872
## - V53 1 11.5156 93.518 81.193
## - V21 1 12.1671 94.169 82.387
## - V28 1 13.0019 95.004 83.905
## - V22 1 13.4689 95.471 84.749
## - V79 1 13.6868 95.689 85.141
## - V40 1 13.8176 95.820 85.376
## - V1 1 15.0412 97.044 87.558
## - V80 1 15.4128 97.415 88.216
## - V52 1 16.2926 98.295 89.762
## - V51 1 16.7762 98.779 90.606
## - V39 1 22.0713 104.074 99.588
##
## Step: AIC=58.64
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V21 + V22 +
## V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 +
## V33 + V34 + V35 + V36 + V37 + V39 + V40 + V41 + V42 + V43 +
## V44 + V45 + V46 + V47 + V48 + V49 + V50 + V51 + V52 + V53 +
## V55 + V56 + V57 + V58 + V59 + V60 + V61 + V62 + V63 + V64 +
## V65 + V66 + V68 + V69 + V70 + V71 + V72 + V73 + V74 + V76 +
## V77 + V78 + V79 + V80 + V81 + V82 + V83 + V84 + V85 + V86 +
## V87 + V90 + V91 + V92 + V93 + V94 + V95 + V96 + V97 + V98 +
## V99
##
## Df Sum of Sq RSS AIC
## - V47 1 0.0300 82.057 56.706
## - V71 1 0.0365 82.064 56.720
## - V76 1 0.0383 82.065 56.724
## - V94 1 0.0583 82.085 56.766
## - V95 1 0.0625 82.090 56.774
## - V33 1 0.0889 82.116 56.830
## - V9 1 0.0981 82.125 56.849
## - V70 1 0.1148 82.142 56.884
## - V18 1 0.1201 82.147 56.895
## - V91 1 0.1480 82.175 56.953
## - V57 1 0.1804 82.207 57.021
## - V90 1 0.2020 82.229 57.066
## - V48 1 0.2948 82.322 57.260
## - V49 1 0.3227 82.350 57.319
## - V58 1 0.3384 82.365 57.351
## - V98 1 0.3602 82.387 57.397
## - V3 1 0.3608 82.388 57.398
## - V86 1 0.4174 82.444 57.516
## - V65 1 0.4210 82.448 57.524
## - V34 1 0.4331 82.460 57.549
## - V93 1 0.4365 82.464 57.556
## - V11 1 0.4751 82.502 57.637
## - V10 1 0.5822 82.609 57.860
## - V66 1 0.5949 82.622 57.886
## - V35 1 0.6328 82.660 57.965
## - V12 1 0.6781 82.705 58.059
## - V92 1 0.6917 82.719 58.088
## - V56 1 0.7201 82.747 58.147
## <none> 82.027 58.643
## - V36 1 0.9661 82.993 58.657
## - V62 1 0.9865 83.014 58.700
## - V16 1 1.0001 83.027 58.728
## - V81 1 1.0471 83.074 58.825
## - V27 1 1.0755 83.103 58.884
## - V72 1 1.4131 83.440 59.581
## - V37 1 1.4291 83.456 59.614
## - V8 1 1.4311 83.458 59.618
## - V61 1 1.5819 83.609 59.929
## - V32 1 1.6130 83.640 59.993
## - V59 1 1.6242 83.651 60.016
## - V96 1 1.6360 83.663 60.040
## - V17 1 1.6740 83.701 60.118
## - V24 1 1.6862 83.713 60.143
## - V69 1 1.8318 83.859 60.442
## - V87 1 1.8752 83.902 60.531
## - V13 1 1.9050 83.932 60.592
## - V31 1 1.9138 83.941 60.610
## - V68 1 1.9993 84.026 60.785
## - V25 1 2.0555 84.083 60.900
## - V4 1 2.3041 84.331 61.408
## - V19 1 2.3467 84.374 61.495
## - V6 1 2.5144 84.541 61.837
## - V84 1 2.5350 84.562 61.878
## - V77 1 2.8370 84.864 62.492
## - V44 1 2.8391 84.866 62.496
## - V83 1 2.8570 84.884 62.532
## - V55 1 3.1718 85.199 63.169
## - V15 1 3.1961 85.223 63.218
## - V14 1 3.2100 85.237 63.246
## - V30 1 3.3111 85.338 63.450
## - V7 1 3.3954 85.422 63.620
## - V43 1 3.4139 85.441 63.657
## - V60 1 3.4874 85.514 63.805
## - V5 1 4.0113 86.038 64.855
## - V99 1 4.0833 86.110 64.999
## - V46 1 4.3569 86.384 65.545
## - V26 1 4.4850 86.512 65.800
## - V97 1 4.6468 86.674 66.121
## - V63 1 4.8110 86.838 66.447
## - V82 1 5.3790 87.406 67.568
## - V2 1 5.5322 87.559 67.869
## - V42 1 6.7924 88.819 70.327
## - V45 1 7.2206 89.248 71.154
## - V74 1 7.2426 89.270 71.197
## - V85 1 7.8645 89.891 72.391
## - V50 1 8.4463 90.473 73.500
## - V41 1 8.5480 90.575 73.694
## - V78 1 8.7381 90.765 74.054
## - V64 1 8.7611 90.788 74.098
## - V73 1 8.9720 90.999 74.497
## - V23 1 9.4796 91.507 75.454
## - V29 1 10.2630 92.290 76.920
## - V53 1 11.6296 93.657 79.448
## - V21 1 12.3561 94.383 80.777
## - V28 1 12.9814 95.008 81.913
## - V22 1 13.6901 95.717 83.191
## - V79 1 13.8674 95.894 83.510
## - V40 1 14.4471 96.474 84.546
## - V1 1 15.1621 97.189 85.816
## - V80 1 15.4064 97.433 86.248
## - V52 1 16.4790 98.506 88.131
## - V51 1 17.0384 99.065 89.105
## - V39 1 22.7350 104.762 98.722
##
## Step: AIC=56.71
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V21 + V22 +
## V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 +
## V33 + V34 + V35 + V36 + V37 + V39 + V40 + V41 + V42 + V43 +
## V44 + V45 + V46 + V48 + V49 + V50 + V51 + V52 + V53 + V55 +
## V56 + V57 + V58 + V59 + V60 + V61 + V62 + V63 + V64 + V65 +
## V66 + V68 + V69 + V70 + V71 + V72 + V73 + V74 + V76 + V77 +
## V78 + V79 + V80 + V81 + V82 + V83 + V84 + V85 + V86 + V87 +
## V90 + V91 + V92 + V93 + V94 + V95 + V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V71 1 0.0337 82.091 54.777
## - V76 1 0.0392 82.096 54.788
## - V94 1 0.0502 82.107 54.811
## - V95 1 0.0716 82.129 54.856
## - V33 1 0.0852 82.142 54.885
## - V9 1 0.0944 82.151 54.904
## - V70 1 0.1080 82.165 54.932
## - V18 1 0.1202 82.177 54.958
## - V91 1 0.1682 82.225 55.059
## - V57 1 0.1794 82.236 55.082
## - V90 1 0.2337 82.291 55.195
## - V48 1 0.2654 82.322 55.262
## - V49 1 0.3110 82.368 55.357
## - V3 1 0.3390 82.396 55.415
## - V58 1 0.3758 82.433 55.492
## - V98 1 0.3762 82.433 55.493
## - V65 1 0.3925 82.449 55.527
## - V34 1 0.4178 82.475 55.580
## - V86 1 0.4192 82.476 55.583
## - V93 1 0.4349 82.492 55.616
## - V11 1 0.4804 82.537 55.710
## - V66 1 0.6043 82.661 55.968
## - V35 1 0.6298 82.687 56.021
## - V10 1 0.6604 82.717 56.085
## - V12 1 0.6667 82.724 56.098
## - V92 1 0.6732 82.730 56.112
## - V56 1 0.6907 82.748 56.148
## - V36 1 0.9404 82.997 56.666
## <none> 82.057 56.706
## - V16 1 0.9762 83.033 56.740
## - V81 1 1.0347 83.092 56.861
## - V27 1 1.1089 83.166 57.015
## - V62 1 1.1981 83.255 57.199
## - V37 1 1.4033 83.460 57.623
## - V8 1 1.4063 83.463 57.629
## - V72 1 1.4432 83.500 57.705
## - V32 1 1.5905 83.648 58.008
## - V61 1 1.6196 83.677 58.068
## - V59 1 1.6296 83.687 58.089
## - V17 1 1.6474 83.704 58.125
## - V96 1 1.6593 83.716 58.150
## - V69 1 1.8049 83.862 58.448
## - V87 1 1.8490 83.906 58.539
## - V31 1 1.8947 83.952 58.633
## - V13 1 1.9092 83.966 58.662
## - V24 1 1.9600 84.017 58.766
## - V68 1 1.9837 84.041 58.815
## - V25 1 2.0268 84.084 58.903
## - V4 1 2.2742 84.331 59.408
## - V6 1 2.4855 84.543 59.839
## - V84 1 2.5069 84.564 59.882
## - V19 1 2.5120 84.569 59.893
## - V44 1 2.8408 84.898 60.560
## - V83 1 2.8804 84.937 60.640
## - V77 1 2.8950 84.952 60.670
## - V55 1 3.1421 85.199 61.170
## - V14 1 3.2242 85.281 61.335
## - V30 1 3.2856 85.343 61.459
## - V15 1 3.2870 85.344 61.462
## - V7 1 3.3660 85.423 61.621
## - V60 1 3.4638 85.521 61.818
## - V43 1 3.5013 85.558 61.893
## - V5 1 3.9835 86.041 62.860
## - V99 1 4.0563 86.113 63.005
## - V26 1 4.5052 86.562 63.899
## - V97 1 4.6861 86.743 64.259
## - V63 1 5.1789 87.236 65.233
## - V82 1 5.4303 87.487 65.728
## - V2 1 5.5064 87.563 65.877
## - V42 1 6.8303 88.887 68.459
## - V45 1 7.3739 89.431 69.507
## - V74 1 7.4946 89.552 69.739
## - V46 1 7.5983 89.655 69.938
## - V85 1 7.8591 89.916 70.438
## - V50 1 8.4640 90.521 71.591
## - V41 1 8.5200 90.577 71.698
## - V78 1 9.0958 91.153 72.787
## - V64 1 9.1386 91.196 72.868
## - V73 1 9.2069 91.264 72.997
## - V29 1 10.5055 92.563 75.427
## - V23 1 10.5634 92.620 75.535
## - V53 1 11.6221 93.679 77.490
## - V28 1 12.9521 95.009 79.914
## - V21 1 13.1506 95.208 80.273
## - V79 1 14.0203 96.077 81.837
## - V40 1 14.4257 96.483 82.562
## - V22 1 14.7259 96.783 83.096
## - V80 1 15.3773 97.434 84.250
## - V1 1 15.4147 97.472 84.316
## - V52 1 16.4576 98.515 86.146
## - V51 1 17.0339 99.091 87.150
## - V39 1 22.7319 104.789 96.766
##
## Step: AIC=54.78
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V21 + V22 +
## V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 +
## V33 + V34 + V35 + V36 + V37 + V39 + V40 + V41 + V42 + V43 +
## V44 + V45 + V46 + V48 + V49 + V50 + V51 + V52 + V53 + V55 +
## V56 + V57 + V58 + V59 + V60 + V61 + V62 + V63 + V64 + V65 +
## V66 + V68 + V69 + V70 + V72 + V73 + V74 + V76 + V77 + V78 +
## V79 + V80 + V81 + V82 + V83 + V84 + V85 + V86 + V87 + V90 +
## V91 + V92 + V93 + V94 + V95 + V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V76 1 0.0267 82.117 52.833
## - V95 1 0.0683 82.159 52.920
## - V94 1 0.0796 82.170 52.944
## - V33 1 0.0881 82.179 52.961
## - V9 1 0.1085 82.199 53.004
## - V91 1 0.1369 82.228 53.064
## - V18 1 0.1425 82.233 53.075
## - V57 1 0.1848 82.276 53.164
## - V90 1 0.2010 82.292 53.198
## - V49 1 0.2837 82.374 53.370
## - V48 1 0.3135 82.404 53.433
## - V3 1 0.3386 82.429 53.485
## - V65 1 0.3768 82.468 53.565
## - V86 1 0.3915 82.482 53.595
## - V93 1 0.4115 82.502 53.637
## - V58 1 0.4331 82.524 53.682
## - V34 1 0.4350 82.526 53.686
## - V98 1 0.4933 82.584 53.807
## - V11 1 0.5183 82.609 53.859
## - V35 1 0.5992 82.690 54.028
## - V66 1 0.6285 82.719 54.089
## - V12 1 0.6340 82.725 54.100
## - V10 1 0.6435 82.734 54.120
## - V56 1 0.6841 82.775 54.204
## - V92 1 0.7856 82.876 54.415
## - V70 1 0.7981 82.889 54.441
## - V36 1 0.9078 82.999 54.668
## - V16 1 0.9425 83.033 54.740
## <none> 82.091 54.777
## - V27 1 1.0924 83.183 55.051
## - V81 1 1.2134 83.304 55.301
## - V37 1 1.3700 83.461 55.624
## - V62 1 1.4535 83.544 55.796
## - V8 1 1.5088 83.600 55.909
## - V32 1 1.6310 83.722 56.161
## - V17 1 1.6909 83.782 56.284
## - V59 1 1.7283 83.819 56.360
## - V61 1 1.8560 83.947 56.622
## - V13 1 1.8761 83.967 56.664
## - V31 1 1.9529 84.044 56.821
## - V24 1 1.9712 84.062 56.858
## - V68 1 2.0454 84.136 57.010
## - V87 1 2.0729 84.164 57.066
## - V96 1 2.1148 84.206 57.152
## - V25 1 2.1693 84.260 57.263
## - V4 1 2.3015 84.392 57.533
## - V69 1 2.4946 84.585 57.926
## - V84 1 2.5196 84.610 57.977
## - V19 1 2.5318 84.623 58.002
## - V6 1 2.6645 84.755 58.271
## - V44 1 2.8712 84.962 58.690
## - V83 1 2.9073 84.998 58.763
## - V72 1 3.0417 85.132 59.035
## - V55 1 3.1518 85.243 59.257
## - V14 1 3.2001 85.291 59.354
## - V15 1 3.3535 85.444 59.664
## - V30 1 3.3709 85.462 59.699
## - V7 1 3.4703 85.561 59.898
## - V60 1 3.5376 85.628 60.034
## - V77 1 3.5493 85.640 60.057
## - V43 1 3.8687 85.959 60.698
## - V99 1 4.0229 86.114 61.006
## - V5 1 4.1212 86.212 61.202
## - V26 1 5.0151 87.106 62.976
## - V63 1 5.1917 87.282 63.325
## - V82 1 5.4058 87.497 63.746
## - V2 1 5.6003 87.691 64.128
## - V97 1 6.3668 88.458 65.625
## - V42 1 7.3000 89.391 67.430
## - V45 1 7.6270 89.718 68.058
## - V74 1 7.6876 89.778 68.174
## - V85 1 7.8294 89.920 68.446
## - V46 1 7.8792 89.970 68.541
## - V50 1 8.4513 90.542 69.631
## - V41 1 8.8468 90.938 70.381
## - V64 1 9.1214 91.212 70.899
## - V78 1 9.2690 91.360 71.177
## - V73 1 9.9183 92.009 72.396
## - V29 1 10.5118 92.603 73.501
## - V23 1 10.7401 92.831 73.925
## - V53 1 11.6681 93.759 75.636
## - V21 1 13.1207 95.211 78.280
## - V28 1 13.2410 95.332 78.497
## - V79 1 14.0275 96.118 79.911
## - V22 1 14.7237 96.814 81.152
## - V40 1 14.8165 96.907 81.317
## - V1 1 15.4892 97.580 82.506
## - V52 1 16.5782 98.669 84.416
## - V80 1 16.8780 98.969 84.937
## - V51 1 17.2514 99.342 85.585
## - V39 1 22.8604 104.951 95.032
##
## Step: AIC=52.83
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V21 + V22 +
## V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 +
## V33 + V34 + V35 + V36 + V37 + V39 + V40 + V41 + V42 + V43 +
## V44 + V45 + V46 + V48 + V49 + V50 + V51 + V52 + V53 + V55 +
## V56 + V57 + V58 + V59 + V60 + V61 + V62 + V63 + V64 + V65 +
## V66 + V68 + V69 + V70 + V72 + V73 + V74 + V77 + V78 + V79 +
## V80 + V81 + V82 + V83 + V84 + V85 + V86 + V87 + V90 + V91 +
## V92 + V93 + V94 + V95 + V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V95 1 0.0721 82.189 50.984
## - V94 1 0.0805 82.198 51.001
## - V33 1 0.0990 82.216 51.040
## - V91 1 0.1247 82.242 51.094
## - V18 1 0.1308 82.248 51.106
## - V9 1 0.1375 82.255 51.120
## - V90 1 0.1800 82.297 51.209
## - V57 1 0.1868 82.304 51.224
## - V49 1 0.2683 82.386 51.394
## - V48 1 0.3139 82.431 51.489
## - V3 1 0.3318 82.449 51.526
## - V86 1 0.3798 82.497 51.626
## - V65 1 0.4121 82.529 51.694
## - V34 1 0.4129 82.530 51.695
## - V93 1 0.4160 82.533 51.702
## - V58 1 0.4186 82.536 51.707
## - V98 1 0.4867 82.604 51.849
## - V11 1 0.4946 82.612 51.866
## - V35 1 0.5979 82.715 52.081
## - V66 1 0.6033 82.721 52.092
## - V12 1 0.6497 82.767 52.188
## - V56 1 0.7374 82.855 52.370
## - V10 1 0.7684 82.886 52.435
## - V70 1 0.7723 82.890 52.443
## - V92 1 0.7981 82.915 52.496
## - V36 1 0.8823 83.000 52.671
## - V16 1 0.9261 83.043 52.762
## <none> 82.117 52.833
## - V27 1 1.0783 83.196 53.077
## - V37 1 1.3577 83.475 53.653
## - V81 1 1.4484 83.566 53.840
## - V8 1 1.5276 83.645 54.003
## - V62 1 1.6051 83.723 54.162
## - V32 1 1.6235 83.741 54.200
## - V59 1 1.7220 83.839 54.402
## - V17 1 1.7419 83.859 54.443
## - V13 1 1.8929 84.010 54.753
## - V31 1 1.9303 84.048 54.829
## - V61 1 1.9325 84.050 54.834
## - V24 1 1.9550 84.072 54.880
## - V68 1 2.0450 84.162 55.064
## - V87 1 2.1195 84.237 55.216
## - V96 1 2.1801 84.298 55.340
## - V4 1 2.2749 84.392 55.533
## - V25 1 2.2967 84.414 55.577
## - V69 1 2.5434 84.661 56.079
## - V84 1 2.5493 84.667 56.091
## - V19 1 2.5606 84.678 56.114
## - V6 1 2.6676 84.785 56.331
## - V44 1 2.9068 85.024 56.816
## - V83 1 2.9595 85.077 56.923
## - V72 1 3.0333 85.151 57.072
## - V14 1 3.2459 85.363 57.501
## - V55 1 3.3358 85.453 57.682
## - V30 1 3.3795 85.497 57.770
## - V15 1 3.4630 85.580 57.938
## - V7 1 3.5318 85.649 58.076
## - V60 1 3.5359 85.653 58.084
## - V43 1 3.8513 85.969 58.716
## - V99 1 4.0933 86.211 59.200
## - V5 1 4.0947 86.212 59.202
## - V26 1 5.0423 87.160 61.083
## - V63 1 5.3705 87.488 61.729
## - V2 1 5.5740 87.691 62.129
## - V82 1 5.7843 87.902 62.541
## - V97 1 6.4045 88.522 63.750
## - V42 1 7.2841 89.402 65.451
## - V85 1 7.8040 89.921 66.448
## - V77 1 7.8938 90.011 66.620
## - V45 1 8.3479 90.465 67.485
## - V50 1 8.4544 90.572 67.688
## - V46 1 8.6418 90.759 68.043
## - V41 1 8.8207 90.938 68.382
## - V74 1 8.8712 90.989 68.477
## - V64 1 9.1171 91.235 68.942
## - V73 1 10.1198 92.237 70.822
## - V78 1 10.6283 92.746 71.767
## - V29 1 10.7515 92.869 71.995
## - V23 1 10.8231 92.940 72.128
## - V53 1 11.7495 93.867 73.834
## - V28 1 13.2593 95.377 76.579
## - V21 1 13.2594 95.377 76.579
## - V79 1 14.1076 96.225 78.102
## - V22 1 14.8109 96.928 79.354
## - V40 1 14.9002 97.018 79.512
## - V1 1 15.4772 97.595 80.532
## - V52 1 16.5588 98.676 82.428
## - V80 1 17.0463 99.164 83.276
## - V51 1 17.2438 99.361 83.618
## - V39 1 23.2089 105.326 93.646
##
## Step: AIC=50.98
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V21 + V22 +
## V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 +
## V33 + V34 + V35 + V36 + V37 + V39 + V40 + V41 + V42 + V43 +
## V44 + V45 + V46 + V48 + V49 + V50 + V51 + V52 + V53 + V55 +
## V56 + V57 + V58 + V59 + V60 + V61 + V62 + V63 + V64 + V65 +
## V66 + V68 + V69 + V70 + V72 + V73 + V74 + V77 + V78 + V79 +
## V80 + V81 + V82 + V83 + V84 + V85 + V86 + V87 + V90 + V91 +
## V92 + V93 + V94 + V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V91 1 0.0993 82.289 49.191
## - V18 1 0.1056 82.295 49.204
## - V9 1 0.1248 82.314 49.245
## - V33 1 0.1253 82.315 49.246
## - V90 1 0.1609 82.350 49.320
## - V57 1 0.2266 82.416 49.457
## - V48 1 0.2821 82.472 49.573
## - V49 1 0.3224 82.512 49.657
## - V3 1 0.3557 82.545 49.726
## - V65 1 0.3684 82.558 49.753
## - V94 1 0.3839 82.573 49.785
## - V93 1 0.3938 82.583 49.806
## - V86 1 0.3939 82.583 49.806
## - V34 1 0.4038 82.593 49.827
## - V98 1 0.4519 82.641 49.927
## - V11 1 0.4564 82.646 49.936
## - V58 1 0.4574 82.647 49.938
## - V35 1 0.5752 82.765 50.183
## - V66 1 0.6362 82.826 50.310
## - V12 1 0.6790 82.868 50.399
## - V56 1 0.7646 82.954 50.576
## - V10 1 0.7657 82.955 50.579
## - V70 1 0.7805 82.970 50.609
## - V92 1 0.9169 83.106 50.892
## - V36 1 0.9221 83.112 50.903
## <none> 82.189 50.984
## - V27 1 1.0413 83.231 51.149
## - V16 1 1.0468 83.236 51.160
## - V37 1 1.4350 83.625 51.961
## - V81 1 1.5291 83.719 52.154
## - V8 1 1.5716 83.761 52.242
## - V62 1 1.5845 83.774 52.268
## - V32 1 1.7003 83.890 52.506
## - V17 1 1.7755 83.965 52.660
## - V59 1 1.7898 83.979 52.689
## - V24 1 1.8952 84.085 52.905
## - V61 1 1.9095 84.099 52.934
## - V31 1 1.9305 84.120 52.977
## - V13 1 1.9420 84.131 53.000
## - V68 1 2.0121 84.202 53.144
## - V87 1 2.1081 84.298 53.340
## - V4 1 2.2871 84.477 53.705
## - V25 1 2.3071 84.497 53.745
## - V84 1 2.5011 84.691 54.140
## - V69 1 2.5111 84.701 54.160
## - V19 1 2.5257 84.715 54.190
## - V6 1 2.6188 84.808 54.379
## - V44 1 2.8490 85.039 54.845
## - V96 1 2.8591 85.049 54.865
## - V83 1 2.9687 85.158 55.087
## - V72 1 3.0137 85.203 55.177
## - V55 1 3.2794 85.469 55.713
## - V14 1 3.2807 85.470 55.716
## - V30 1 3.3408 85.530 55.837
## - V15 1 3.4143 85.604 55.984
## - V7 1 3.4696 85.659 56.095
## - V60 1 3.5986 85.788 56.354
## - V43 1 3.8275 86.017 56.813
## - V5 1 4.0690 86.258 57.295
## - V99 1 4.2861 86.476 57.727
## - V26 1 4.9761 87.166 59.094
## - V63 1 5.3189 87.508 59.769
## - V2 1 5.6512 87.841 60.421
## - V82 1 5.7136 87.903 60.543
## - V97 1 6.3638 88.553 61.811
## - V42 1 7.2298 89.419 63.485
## - V85 1 7.8147 90.004 64.606
## - V77 1 7.8229 90.012 64.622
## - V45 1 8.3074 90.497 65.545
## - V50 1 8.5838 90.773 66.070
## - V41 1 8.8056 90.995 66.489
## - V46 1 8.8760 91.065 66.623
## - V74 1 8.9458 91.135 66.754
## - V64 1 9.0681 91.258 66.985
## - V73 1 10.1993 92.389 69.104
## - V29 1 10.6975 92.887 70.029
## - V78 1 10.7346 92.924 70.098
## - V23 1 10.7537 92.943 70.133
## - V53 1 11.7914 93.981 72.043
## - V28 1 13.1889 95.378 74.581
## - V21 1 13.4463 95.636 75.045
## - V79 1 14.1024 96.292 76.221
## - V22 1 14.8377 97.027 77.529
## - V40 1 15.1217 97.311 78.032
## - V1 1 15.9557 98.145 79.500
## - V52 1 16.6476 98.837 80.708
## - V51 1 17.1743 99.364 81.622
## - V80 1 17.1824 99.372 81.636
## - V39 1 23.4575 105.647 92.169
##
## Step: AIC=49.19
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V21 + V22 +
## V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 +
## V33 + V34 + V35 + V36 + V37 + V39 + V40 + V41 + V42 + V43 +
## V44 + V45 + V46 + V48 + V49 + V50 + V51 + V52 + V53 + V55 +
## V56 + V57 + V58 + V59 + V60 + V61 + V62 + V63 + V64 + V65 +
## V66 + V68 + V69 + V70 + V72 + V73 + V74 + V77 + V78 + V79 +
## V80 + V81 + V82 + V83 + V84 + V85 + V86 + V87 + V90 + V92 +
## V93 + V94 + V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V90 1 0.0770 82.366 47.352
## - V33 1 0.1115 82.400 47.424
## - V18 1 0.1169 82.406 47.436
## - V57 1 0.1726 82.461 47.552
## - V9 1 0.1806 82.469 47.568
## - V49 1 0.2392 82.528 47.691
## - V86 1 0.3078 82.597 47.833
## - V3 1 0.3747 82.663 47.973
## - V94 1 0.3798 82.669 47.983
## - V58 1 0.3803 82.669 47.984
## - V48 1 0.4210 82.710 48.069
## - V11 1 0.4247 82.713 48.077
## - V65 1 0.4375 82.726 48.103
## - V34 1 0.4839 82.773 48.200
## - V35 1 0.4960 82.785 48.225
## - V98 1 0.5268 82.816 48.289
## - V93 1 0.6635 82.952 48.573
## - V66 1 0.6747 82.963 48.596
## - V56 1 0.7216 83.010 48.693
## - V12 1 0.7229 83.012 48.696
## - V10 1 0.7909 83.080 48.837
## - V36 1 0.8354 83.124 48.929
## - V70 1 0.8481 83.137 48.955
## - V27 1 0.9575 83.246 49.181
## <none> 82.289 49.191
## - V16 1 1.0517 83.340 49.376
## - V37 1 1.3923 83.681 50.077
## - V62 1 1.5083 83.797 50.315
## - V32 1 1.6777 83.966 50.663
## - V59 1 1.6937 83.982 50.696
## - V81 1 1.7248 84.014 50.759
## - V17 1 1.7785 84.067 50.869
## - V24 1 1.7975 84.086 50.908
## - V8 1 1.8201 84.109 50.954
## - V31 1 1.9000 84.189 51.118
## - V13 1 1.9547 84.243 51.229
## - V61 1 1.9763 84.265 51.273
## - V68 1 2.3519 84.641 52.038
## - V25 1 2.3984 84.687 52.133
## - V19 1 2.4981 84.787 52.335
## - V4 1 2.5263 84.815 52.392
## - V84 1 2.6781 84.967 52.700
## - V44 1 2.7507 85.039 52.847
## - V83 1 2.8901 85.179 53.128
## - V69 1 3.0430 85.332 53.437
## - V72 1 3.1063 85.395 53.565
## - V6 1 3.1091 85.398 53.570
## - V14 1 3.2326 85.521 53.819
## - V55 1 3.2979 85.587 53.950
## - V30 1 3.3164 85.605 53.987
## - V15 1 3.3418 85.631 54.038
## - V87 1 3.3484 85.637 54.051
## - V96 1 3.3874 85.676 54.130
## - V60 1 3.5862 85.875 54.528
## - V43 1 3.7340 86.023 54.824
## - V7 1 3.9761 86.265 55.308
## - V99 1 4.2666 86.555 55.886
## - V5 1 4.5873 86.876 56.522
## - V26 1 4.8839 87.173 57.108
## - V82 1 5.6893 87.978 58.690
## - V2 1 5.9218 88.211 59.144
## - V92 1 6.0351 88.324 59.365
## - V63 1 6.0616 88.350 59.416
## - V42 1 7.1427 89.431 61.508
## - V97 1 7.3595 89.648 61.925
## - V85 1 7.7158 90.005 62.607
## - V77 1 7.8871 90.176 62.934
## - V45 1 8.2154 90.504 63.559
## - V41 1 8.7098 90.999 64.496
## - V46 1 8.8107 91.099 64.687
## - V50 1 8.8457 91.134 64.753
## - V74 1 9.6975 91.986 66.353
## - V73 1 10.5112 92.800 67.868
## - V64 1 10.5417 92.830 67.924
## - V29 1 10.5983 92.887 68.029
## - V78 1 10.6605 92.949 68.144
## - V23 1 11.1394 93.428 69.028
## - V53 1 11.7025 93.991 70.062
## - V21 1 13.5038 95.793 73.327
## - V28 1 13.8449 96.134 73.938
## - V79 1 14.0481 96.337 74.301
## - V40 1 15.0409 97.330 76.065
## - V22 1 15.1855 97.474 76.320
## - V1 1 16.3292 98.618 78.327
## - V52 1 16.6828 98.972 78.942
## - V80 1 17.4817 99.770 80.325
## - V51 1 17.5772 99.866 80.490
## - V39 1 23.3806 105.669 90.205
##
## Step: AIC=47.35
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V21 + V22 +
## V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 +
## V33 + V34 + V35 + V36 + V37 + V39 + V40 + V41 + V42 + V43 +
## V44 + V45 + V46 + V48 + V49 + V50 + V51 + V52 + V53 + V55 +
## V56 + V57 + V58 + V59 + V60 + V61 + V62 + V63 + V64 + V65 +
## V66 + V68 + V69 + V70 + V72 + V73 + V74 + V77 + V78 + V79 +
## V80 + V81 + V82 + V83 + V84 + V85 + V86 + V87 + V92 + V93 +
## V94 + V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V18 1 0.0965 82.462 45.554
## - V33 1 0.1368 82.502 45.637
## - V57 1 0.1815 82.547 45.731
## - V9 1 0.1910 82.557 45.750
## - V49 1 0.2154 82.581 45.801
## - V86 1 0.2349 82.601 45.842
## - V48 1 0.3935 82.759 46.172
## - V65 1 0.3982 82.764 46.182
## - V3 1 0.4019 82.768 46.189
## - V94 1 0.4491 82.815 46.287
## - V34 1 0.4593 82.825 46.309
## - V35 1 0.4676 82.833 46.326
## - V58 1 0.4848 82.851 46.361
## - V11 1 0.5083 82.874 46.410
## - V98 1 0.5615 82.927 46.521
## - V93 1 0.5885 82.954 46.577
## - V12 1 0.6617 83.027 46.728
## - V56 1 0.7150 83.081 46.839
## - V66 1 0.7398 83.106 46.890
## - V10 1 0.7722 83.138 46.957
## - V36 1 0.8030 83.169 47.021
## - V70 1 0.8934 83.259 47.208
## - V27 1 0.9464 83.312 47.317
## <none> 82.366 47.352
## - V16 1 1.0089 83.375 47.446
## - V37 1 1.3612 83.727 48.171
## - V62 1 1.4501 83.816 48.354
## - V81 1 1.6485 84.014 48.761
## - V32 1 1.6997 84.065 48.865
## - V17 1 1.7208 84.086 48.908
## - V24 1 1.7410 84.107 48.950
## - V8 1 1.8292 84.195 49.130
## - V59 1 1.8436 84.209 49.160
## - V31 1 1.8686 84.234 49.211
## - V13 1 1.8889 84.255 49.252
## - V61 1 1.9850 84.351 49.448
## - V68 1 2.3230 84.689 50.136
## - V19 1 2.4313 84.797 50.356
## - V25 1 2.4448 84.811 50.383
## - V84 1 2.6087 84.974 50.715
## - V4 1 2.7152 85.081 50.931
## - V83 1 2.8396 85.205 51.182
## - V44 1 2.9681 85.334 51.441
## - V69 1 3.1260 85.492 51.759
## - V14 1 3.1995 85.565 51.907
## - V30 1 3.2664 85.632 52.041
## - V96 1 3.3404 85.706 52.190
## - V6 1 3.3478 85.714 52.205
## - V55 1 3.3498 85.715 52.209
## - V15 1 3.3934 85.759 52.296
## - V72 1 3.5365 85.902 52.583
## - V60 1 3.6297 85.995 52.770
## - V99 1 4.1902 86.556 53.887
## - V7 1 4.2734 86.639 54.052
## - V43 1 4.3016 86.667 54.108
## - V26 1 4.8175 87.183 55.129
## - V5 1 4.8476 87.213 55.188
## - V87 1 5.6350 88.001 56.734
## - V82 1 5.6518 88.018 56.767
## - V2 1 5.9066 88.272 57.264
## - V63 1 6.0438 88.410 57.532
## - V97 1 7.3050 89.671 59.968
## - V77 1 7.8105 90.176 60.935
## - V42 1 7.8122 90.178 60.938
## - V85 1 7.8873 90.253 61.081
## - V45 1 8.1384 90.504 61.559
## - V46 1 8.8892 91.255 62.980
## - V50 1 8.9494 91.315 63.093
## - V41 1 9.0691 91.435 63.319
## - V74 1 9.8542 92.220 64.789
## - V92 1 10.3494 92.715 65.710
## - V64 1 10.4648 92.830 65.924
## - V29 1 10.5214 92.887 66.029
## - V78 1 10.8880 93.254 66.707
## - V23 1 11.0726 93.438 67.047
## - V53 1 11.7413 94.107 68.273
## - V73 1 11.7418 94.108 68.274
## - V21 1 13.5030 95.869 71.464
## - V28 1 13.8473 96.213 72.080
## - V79 1 14.0452 96.411 72.433
## - V40 1 15.0873 97.453 74.283
## - V22 1 15.1887 97.554 74.462
## - V1 1 16.2671 98.633 76.352
## - V52 1 16.6090 98.975 76.948
## - V51 1 17.6790 100.045 78.797
## - V80 1 17.7371 100.103 78.897
## - V39 1 23.3148 105.681 88.223
##
## Step: AIC=45.55
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 +
## V12 + V13 + V14 + V15 + V16 + V17 + V19 + V21 + V22 + V23 +
## V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 + V33 +
## V34 + V35 + V36 + V37 + V39 + V40 + V41 + V42 + V43 + V44 +
## V45 + V46 + V48 + V49 + V50 + V51 + V52 + V53 + V55 + V56 +
## V57 + V58 + V59 + V60 + V61 + V62 + V63 + V64 + V65 + V66 +
## V68 + V69 + V70 + V72 + V73 + V74 + V77 + V78 + V79 + V80 +
## V81 + V82 + V83 + V84 + V85 + V86 + V87 + V92 + V93 + V94 +
## V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V9 1 0.1492 82.611 43.864
## - V33 1 0.1646 82.627 43.896
## - V57 1 0.1692 82.631 43.906
## - V86 1 0.2104 82.673 43.992
## - V49 1 0.2746 82.737 44.125
## - V48 1 0.3172 82.780 44.214
## - V65 1 0.3480 82.810 44.278
## - V34 1 0.3872 82.849 44.359
## - V94 1 0.4122 82.874 44.411
## - V3 1 0.4276 82.890 44.443
## - V11 1 0.4424 82.905 44.474
## - V58 1 0.4628 82.925 44.516
## - V98 1 0.5207 82.983 44.636
## - V35 1 0.6102 83.072 44.822
## - V93 1 0.6542 83.116 44.913
## - V56 1 0.7002 83.162 45.008
## - V12 1 0.7949 83.257 45.204
## - V10 1 0.8358 83.298 45.288
## - V66 1 0.8363 83.299 45.289
## - V36 1 0.8387 83.301 45.294
## - V70 1 0.8839 83.346 45.387
## <none> 82.462 45.554
## - V27 1 1.1027 83.565 45.838
## - V16 1 1.3034 83.766 46.251
## - V37 1 1.3355 83.798 46.317
## - V62 1 1.4269 83.889 46.504
## - V81 1 1.6871 84.149 47.037
## - V24 1 1.7419 84.204 47.149
## - V17 1 1.7835 84.246 47.234
## - V32 1 1.7945 84.257 47.256
## - V8 1 1.8943 84.357 47.460
## - V59 1 1.9117 84.374 47.496
## - V61 1 1.9547 84.417 47.583
## - V31 1 2.0074 84.470 47.691
## - V13 1 2.1081 84.570 47.895
## - V25 1 2.3753 84.838 48.438
## - V84 1 2.5129 84.975 48.717
## - V68 1 2.5211 84.983 48.733
## - V83 1 2.8778 85.340 49.454
## - V44 1 2.9226 85.385 49.544
## - V19 1 3.0114 85.474 49.723
## - V4 1 3.0172 85.479 49.734
## - V69 1 3.2380 85.700 50.178
## - V96 1 3.2540 85.716 50.210
## - V14 1 3.2819 85.744 50.266
## - V15 1 3.2981 85.760 50.299
## - V55 1 3.3763 85.839 50.455
## - V30 1 3.3818 85.844 50.467
## - V6 1 3.6517 86.114 51.007
## - V60 1 3.8339 86.296 51.370
## - V72 1 3.9601 86.422 51.621
## - V43 1 4.2865 86.749 52.270
## - V99 1 4.4179 86.880 52.530
## - V26 1 4.7691 87.231 53.224
## - V7 1 4.7730 87.235 53.232
## - V5 1 5.3852 87.847 54.435
## - V82 1 5.5638 88.026 54.784
## - V87 1 5.7084 88.171 55.066
## - V63 1 5.9485 88.411 55.534
## - V2 1 5.9755 88.438 55.586
## - V97 1 7.2259 89.688 58.001
## - V77 1 7.7844 90.247 59.069
## - V85 1 7.8012 90.263 59.101
## - V42 1 8.0688 90.531 59.610
## - V45 1 8.1021 90.564 59.673
## - V46 1 8.7928 91.255 60.980
## - V50 1 8.8609 91.323 61.109
## - V41 1 9.4788 91.941 62.268
## - V74 1 9.8496 92.312 62.961
## - V64 1 10.4982 92.960 64.165
## - V29 1 10.5290 92.991 64.222
## - V92 1 10.6852 93.147 64.511
## - V78 1 10.8281 93.290 64.774
## - V23 1 11.0437 93.506 65.171
## - V53 1 11.8918 94.354 66.724
## - V73 1 12.2871 94.749 67.443
## - V21 1 13.5372 96.000 69.698
## - V28 1 13.9129 96.375 70.370
## - V79 1 13.9775 96.440 70.485
## - V22 1 15.2076 97.670 72.665
## - V40 1 15.2852 97.747 72.801
## - V1 1 16.5291 98.991 74.977
## - V52 1 16.5672 99.029 75.043
## - V51 1 17.6285 100.091 76.876
## - V80 1 17.6408 100.103 76.897
## - V39 1 23.3338 105.796 86.411
##
## Step: AIC=43.86
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V10 + V11 + V12 +
## V13 + V14 + V15 + V16 + V17 + V19 + V21 + V22 + V23 + V24 +
## V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 + V33 + V34 +
## V35 + V36 + V37 + V39 + V40 + V41 + V42 + V43 + V44 + V45 +
## V46 + V48 + V49 + V50 + V51 + V52 + V53 + V55 + V56 + V57 +
## V58 + V59 + V60 + V61 + V62 + V63 + V64 + V65 + V66 + V68 +
## V69 + V70 + V72 + V73 + V74 + V77 + V78 + V79 + V80 + V81 +
## V82 + V83 + V84 + V85 + V86 + V87 + V92 + V93 + V94 + V96 +
## V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V57 1 0.1428 82.754 42.162
## - V86 1 0.1502 82.762 42.177
## - V33 1 0.1605 82.772 42.198
## - V49 1 0.2398 82.851 42.363
## - V65 1 0.3443 82.956 42.580
## - V48 1 0.3599 82.971 42.612
## - V58 1 0.3645 82.976 42.622
## - V34 1 0.3715 82.983 42.636
## - V94 1 0.3991 83.011 42.693
## - V11 1 0.4962 83.108 42.895
## - V3 1 0.5681 83.180 43.043
## - V98 1 0.5689 83.180 43.045
## - V35 1 0.6609 83.272 43.235
## - V93 1 0.6704 83.282 43.255
## - V56 1 0.6788 83.290 43.272
## - V10 1 0.6876 83.299 43.290
## - V12 1 0.7565 83.368 43.432
## - V66 1 0.9038 83.515 43.736
## <none> 82.611 43.864
## - V36 1 1.0099 83.621 43.954
## - V70 1 1.0118 83.623 43.958
## - V27 1 1.2206 83.832 44.387
## - V62 1 1.3896 84.001 44.734
## - V16 1 1.4015 84.013 44.758
## - V37 1 1.5848 84.196 45.133
## - V24 1 1.6067 84.218 45.178
## - V81 1 1.7282 84.340 45.425
## - V59 1 1.7627 84.374 45.496
## - V17 1 1.7761 84.388 45.523
## - V32 1 1.7819 84.393 45.535
## - V8 1 1.8174 84.429 45.607
## - V61 1 1.8825 84.494 45.740
## - V13 1 2.0253 84.637 46.030
## - V31 1 2.0808 84.692 46.143
## - V84 1 2.5891 85.201 47.172
## - V25 1 2.5997 85.211 47.194
## - V83 1 2.7529 85.364 47.503
## - V68 1 2.9827 85.594 47.965
## - V4 1 3.0329 85.644 48.066
## - V44 1 3.0584 85.670 48.117
## - V19 1 3.0945 85.706 48.190
## - V14 1 3.1858 85.797 48.373
## - V15 1 3.2315 85.843 48.464
## - V96 1 3.2773 85.889 48.556
## - V55 1 3.3068 85.918 48.615
## - V6 1 3.5341 86.146 49.069
## - V30 1 3.6580 86.269 49.317
## - V60 1 3.6864 86.298 49.373
## - V69 1 3.7248 86.336 49.450
## - V72 1 3.9973 86.609 49.992
## - V43 1 4.3040 86.915 50.600
## - V99 1 4.4127 87.024 50.815
## - V7 1 4.6243 87.236 51.233
## - V26 1 4.6962 87.308 51.374
## - V5 1 5.2854 87.897 52.531
## - V82 1 5.4726 88.084 52.897
## - V2 1 5.8908 88.502 53.712
## - V63 1 6.0012 88.613 53.926
## - V87 1 6.6244 89.236 55.132
## - V97 1 7.4411 90.053 56.699
## - V85 1 7.6775 90.289 57.149
## - V77 1 7.7362 90.348 57.261
## - V42 1 7.9343 90.546 57.638
## - V45 1 8.3849 90.996 58.492
## - V50 1 8.7196 91.331 59.123
## - V46 1 9.2656 91.877 60.149
## - V41 1 9.3308 91.942 60.271
## - V74 1 10.1560 92.767 61.807
## - V64 1 10.5283 93.140 62.496
## - V78 1 10.6818 93.293 62.780
## - V92 1 10.7280 93.339 62.865
## - V23 1 10.9024 93.514 63.186
## - V29 1 11.6351 94.247 64.528
## - V53 1 11.8159 94.427 64.858
## - V73 1 12.6744 95.286 66.415
## - V21 1 13.4328 96.044 67.778
## - V79 1 13.8523 96.464 68.528
## - V22 1 15.0649 97.676 70.676
## - V40 1 15.1573 97.769 70.839
## - V28 1 15.2563 97.868 71.013
## - V52 1 16.4743 99.086 73.140
## - V51 1 17.4832 100.095 74.883
## - V80 1 17.5866 100.198 75.061
## - V1 1 17.6163 100.228 75.111
## - V39 1 23.7327 106.344 85.300
##
## Step: AIC=42.16
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V10 + V11 + V12 +
## V13 + V14 + V15 + V16 + V17 + V19 + V21 + V22 + V23 + V24 +
## V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 + V33 + V34 +
## V35 + V36 + V37 + V39 + V40 + V41 + V42 + V43 + V44 + V45 +
## V46 + V48 + V49 + V50 + V51 + V52 + V53 + V55 + V56 + V58 +
## V59 + V60 + V61 + V62 + V63 + V64 + V65 + V66 + V68 + V69 +
## V70 + V72 + V73 + V74 + V77 + V78 + V79 + V80 + V81 + V82 +
## V83 + V84 + V85 + V86 + V87 + V92 + V93 + V94 + V96 + V97 +
## V98 + V99
##
## Df Sum of Sq RSS AIC
## - V33 1 0.1246 82.879 40.420
## - V49 1 0.1466 82.901 40.466
## - V86 1 0.1518 82.906 40.477
## - V58 1 0.2226 82.977 40.624
## - V65 1 0.3051 83.059 40.795
## - V94 1 0.3963 83.151 40.983
## - V11 1 0.4214 83.176 41.035
## - V34 1 0.4246 83.179 41.042
## - V98 1 0.5054 83.260 41.209
## - V3 1 0.5279 83.282 41.255
## - V48 1 0.5735 83.328 41.349
## - V56 1 0.5774 83.332 41.357
## - V35 1 0.6568 83.411 41.521
## - V93 1 0.7110 83.465 41.633
## - V12 1 0.7784 83.533 41.772
## - V10 1 0.8211 83.575 41.860
## <none> 82.754 42.162
## - V70 1 1.0525 83.807 42.335
## - V66 1 1.1725 83.927 42.581
## - V27 1 1.2139 83.968 42.666
## - V36 1 1.2465 84.001 42.733
## - V62 1 1.2690 84.023 42.779
## - V24 1 1.4773 84.232 43.205
## - V16 1 1.5514 84.306 43.356
## - V32 1 1.6784 84.433 43.615
## - V59 1 1.7224 84.477 43.705
## - V8 1 1.7619 84.516 43.785
## - V17 1 1.8177 84.572 43.899
## - V31 1 1.9883 84.743 44.245
## - V13 1 1.9952 84.749 44.259
## - V37 1 2.0822 84.837 44.436
## - V81 1 2.1001 84.854 44.472
## - V61 1 2.1381 84.892 44.549
## - V83 1 2.6110 85.365 45.505
## - V25 1 2.7515 85.506 45.787
## - V4 1 2.9320 85.686 46.150
## - V44 1 2.9367 85.691 46.160
## - V84 1 2.9976 85.752 46.282
## - V19 1 3.0260 85.780 46.339
## - V15 1 3.1059 85.860 46.499
## - V14 1 3.1227 85.877 46.532
## - V96 1 3.1525 85.907 46.592
## - V55 1 3.1641 85.918 46.615
## - V6 1 3.5062 86.261 47.299
## - V68 1 3.5140 86.268 47.314
## - V30 1 3.5762 86.331 47.438
## - V72 1 4.0533 86.808 48.386
## - V69 1 4.1417 86.896 48.561
## - V60 1 4.2420 86.996 48.760
## - V43 1 4.3632 87.117 48.999
## - V99 1 4.5391 87.293 49.346
## - V7 1 4.5562 87.310 49.380
## - V26 1 4.7387 87.493 49.739
## - V5 1 5.2039 87.958 50.651
## - V82 1 5.4217 88.176 51.076
## - V2 1 6.4333 89.188 53.039
## - V87 1 6.7854 89.540 53.716
## - V63 1 7.1772 89.931 54.467
## - V97 1 7.3043 90.059 54.710
## - V77 1 7.9824 90.737 56.000
## - V85 1 8.1457 90.900 56.310
## - V42 1 8.2311 90.985 56.471
## - V45 1 8.2426 90.997 56.493
## - V50 1 8.6068 91.361 57.180
## - V46 1 9.3312 92.086 58.538
## - V41 1 9.3321 92.086 58.540
## - V74 1 10.0421 92.796 59.861
## - V78 1 10.6558 93.410 60.995
## - V23 1 10.8308 93.585 61.317
## - V64 1 11.0109 93.765 61.648
## - V92 1 11.4202 94.174 62.397
## - V29 1 11.6109 94.365 62.745
## - V53 1 11.8539 94.608 63.187
## - V73 1 12.5359 95.290 64.422
## - V21 1 13.3379 96.092 65.864
## - V79 1 13.7450 96.499 66.591
## - V22 1 14.9222 97.676 68.677
## - V40 1 15.0152 97.769 68.840
## - V28 1 15.3770 98.131 69.476
## - V52 1 16.8047 99.559 71.960
## - V51 1 17.6038 100.358 73.335
## - V80 1 18.2498 101.004 74.439
## - V1 1 19.8496 102.604 77.142
## - V39 1 23.7442 106.498 83.549
##
## Step: AIC=40.42
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V10 + V11 + V12 +
## V13 + V14 + V15 + V16 + V17 + V19 + V21 + V22 + V23 + V24 +
## V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 + V34 + V35 +
## V36 + V37 + V39 + V40 + V41 + V42 + V43 + V44 + V45 + V46 +
## V48 + V49 + V50 + V51 + V52 + V53 + V55 + V56 + V58 + V59 +
## V60 + V61 + V62 + V63 + V64 + V65 + V66 + V68 + V69 + V70 +
## V72 + V73 + V74 + V77 + V78 + V79 + V80 + V81 + V82 + V83 +
## V84 + V85 + V86 + V87 + V92 + V93 + V94 + V96 + V97 + V98 +
## V99
##
## Df Sum of Sq RSS AIC
## - V49 1 0.1259 83.005 38.681
## - V86 1 0.1557 83.035 38.743
## - V58 1 0.1764 83.055 38.786
## - V65 1 0.3459 83.225 39.137
## - V11 1 0.3471 83.226 39.139
## - V94 1 0.4278 83.307 39.306
## - V98 1 0.4462 83.325 39.344
## - V3 1 0.4949 83.374 39.444
## - V48 1 0.5522 83.431 39.563
## - V35 1 0.6159 83.495 39.694
## - V93 1 0.6513 83.530 39.767
## - V56 1 0.6541 83.533 39.773
## - V12 1 0.8106 83.689 40.094
## <none> 82.879 40.420
## - V10 1 0.9967 83.876 40.476
## - V70 1 1.0336 83.912 40.552
## - V66 1 1.1230 84.002 40.735
## - V27 1 1.1936 84.072 40.880
## - V36 1 1.2873 84.166 41.071
## - V62 1 1.2962 84.175 41.089
## - V34 1 1.4407 84.320 41.385
## - V24 1 1.5479 84.427 41.603
## - V16 1 1.5806 84.459 41.670
## - V59 1 1.6611 84.540 41.833
## - V8 1 1.6697 84.549 41.851
## - V13 1 1.9538 84.833 42.428
## - V17 1 1.9705 84.849 42.462
## - V61 1 2.0550 84.934 42.633
## - V37 1 2.0849 84.964 42.694
## - V81 1 2.1439 85.023 42.813
## - V31 1 2.3722 85.251 43.274
## - V83 1 2.6439 85.523 43.822
## - V25 1 2.6623 85.541 43.859
## - V4 1 2.8464 85.725 44.228
## - V19 1 2.9209 85.800 44.378
## - V84 1 2.9407 85.820 44.417
## - V14 1 3.0447 85.924 44.626
## - V15 1 3.0469 85.926 44.630
## - V96 1 3.0522 85.931 44.641
## - V44 1 3.0996 85.978 44.736
## - V55 1 3.2511 86.130 45.038
## - V6 1 3.4503 86.329 45.436
## - V68 1 3.5788 86.458 45.692
## - V30 1 3.7133 86.592 45.959
## - V32 1 3.9628 86.842 46.454
## - V60 1 4.1685 87.047 46.861
## - V69 1 4.2269 87.106 46.976
## - V43 1 4.4376 87.316 47.392
## - V7 1 4.4545 87.333 47.425
## - V72 1 4.4681 87.347 47.452
## - V26 1 4.6806 87.559 47.870
## - V99 1 4.8505 87.729 48.203
## - V5 1 5.1060 87.985 48.703
## - V82 1 5.4037 88.283 49.284
## - V2 1 6.6865 89.565 51.765
## - V87 1 6.7508 89.630 51.889
## - V63 1 7.0603 89.939 52.482
## - V97 1 7.1806 90.059 52.712
## - V85 1 8.0709 90.950 54.404
## - V77 1 8.2433 91.122 54.729
## - V42 1 8.2825 91.161 54.804
## - V50 1 8.4840 91.363 55.183
## - V45 1 8.6455 91.524 55.487
## - V41 1 9.3953 92.274 56.890
## - V46 1 9.4495 92.328 56.991
## - V78 1 10.5446 93.423 59.019
## - V23 1 10.7782 93.657 59.449
## - V74 1 10.8479 93.727 59.577
## - V64 1 11.0131 93.892 59.880
## - V92 1 11.3145 94.193 60.431
## - V29 1 11.7474 94.626 61.220
## - V53 1 11.9038 94.783 61.504
## - V21 1 13.2449 96.124 63.920
## - V73 1 13.4256 96.304 64.243
## - V79 1 13.6235 96.502 64.597
## - V22 1 14.8151 97.694 66.707
## - V40 1 15.1785 98.057 67.346
## - V28 1 15.2559 98.135 67.482
## - V52 1 16.7912 99.670 70.152
## - V51 1 17.4863 100.365 71.347
## - V80 1 18.2654 101.144 72.677
## - V1 1 20.2683 103.147 76.050
## - V39 1 24.0723 106.951 82.279
##
## Step: AIC=38.68
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V10 + V11 + V12 +
## V13 + V14 + V15 + V16 + V17 + V19 + V21 + V22 + V23 + V24 +
## V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 + V34 + V35 +
## V36 + V37 + V39 + V40 + V41 + V42 + V43 + V44 + V45 + V46 +
## V48 + V50 + V51 + V52 + V53 + V55 + V56 + V58 + V59 + V60 +
## V61 + V62 + V63 + V64 + V65 + V66 + V68 + V69 + V70 + V72 +
## V73 + V74 + V77 + V78 + V79 + V80 + V81 + V82 + V83 + V84 +
## V85 + V86 + V87 + V92 + V93 + V94 + V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V86 1 0.1133 83.118 36.916
## - V58 1 0.1727 83.177 37.039
## - V11 1 0.3331 83.338 37.370
## - V65 1 0.3838 83.388 37.475
## - V94 1 0.4256 83.430 37.561
## - V3 1 0.5315 83.536 37.779
## - V98 1 0.6043 83.609 37.929
## - V93 1 0.6091 83.614 37.939
## - V35 1 0.6523 83.657 38.028
## - V12 1 0.7811 83.786 38.292
## - V56 1 0.8090 83.814 38.350
## <none> 83.005 38.681
## - V10 1 1.0309 84.036 38.804
## - V66 1 1.1298 84.134 39.007
## - V27 1 1.2448 84.250 39.242
## - V70 1 1.2660 84.271 39.285
## - V36 1 1.2833 84.288 39.320
## - V62 1 1.2878 84.293 39.329
## - V34 1 1.3704 84.375 39.498
## - V24 1 1.4518 84.457 39.664
## - V16 1 1.5224 84.527 39.807
## - V59 1 1.6688 84.673 40.105
## - V8 1 1.7070 84.712 40.183
## - V13 1 1.8709 84.876 40.515
## - V17 1 1.9430 84.948 40.661
## - V37 1 2.1469 85.152 41.073
## - V61 1 2.1671 85.172 41.114
## - V81 1 2.3607 85.365 41.505
## - V83 1 2.5440 85.549 41.874
## - V31 1 2.5915 85.596 41.969
## - V19 1 2.7951 85.800 42.378
## - V4 1 2.9017 85.906 42.592
## - V14 1 2.9440 85.949 42.676
## - V84 1 2.9810 85.986 42.750
## - V15 1 2.9813 85.986 42.751
## - V25 1 3.0935 86.098 42.975
## - V96 1 3.2302 86.235 43.248
## - V44 1 3.2316 86.236 43.251
## - V48 1 3.2616 86.266 43.310
## - V55 1 3.5213 86.526 43.827
## - V6 1 3.5872 86.592 43.958
## - V32 1 4.0355 87.040 44.847
## - V68 1 4.0708 87.076 44.916
## - V60 1 4.1283 87.133 45.030
## - V72 1 4.3454 87.350 45.458
## - V30 1 4.3556 87.360 45.478
## - V43 1 4.4183 87.423 45.602
## - V7 1 4.6056 87.610 45.970
## - V69 1 4.7090 87.714 46.172
## - V99 1 4.7309 87.736 46.215
## - V26 1 4.9110 87.916 46.568
## - V5 1 5.2263 88.231 47.184
## - V82 1 5.2881 88.293 47.304
## - V2 1 6.5783 89.583 49.800
## - V63 1 7.3681 90.373 51.309
## - V87 1 7.4118 90.417 51.392
## - V85 1 7.9730 90.978 52.457
## - V97 1 7.9817 90.986 52.473
## - V77 1 8.1284 91.133 52.750
## - V42 1 8.1818 91.187 52.851
## - V45 1 9.1176 92.122 54.607
## - V41 1 9.2760 92.281 54.903
## - V46 1 10.3192 93.324 56.836
## - V78 1 10.5794 93.584 57.315
## - V23 1 10.6719 93.677 57.485
## - V74 1 10.7293 93.734 57.590
## - V92 1 11.2119 94.217 58.474
## - V64 1 11.2127 94.217 58.475
## - V53 1 12.0207 95.025 59.944
## - V21 1 13.1268 96.132 61.934
## - V29 1 13.2360 96.241 62.130
## - V73 1 13.3302 96.335 62.298
## - V79 1 13.6008 96.606 62.780
## - V50 1 13.8420 96.847 63.209
## - V22 1 14.7432 97.748 64.802
## - V40 1 15.0671 98.072 65.371
## - V28 1 15.7750 98.780 66.609
## - V52 1 16.7003 99.705 68.212
## - V51 1 17.8794 100.884 70.234
## - V80 1 18.3040 101.309 70.957
## - V1 1 20.1702 103.175 74.096
## - V39 1 24.1059 107.111 80.535
##
## Step: AIC=36.92
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V10 + V11 + V12 +
## V13 + V14 + V15 + V16 + V17 + V19 + V21 + V22 + V23 + V24 +
## V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 + V34 + V35 +
## V36 + V37 + V39 + V40 + V41 + V42 + V43 + V44 + V45 + V46 +
## V48 + V50 + V51 + V52 + V53 + V55 + V56 + V58 + V59 + V60 +
## V61 + V62 + V63 + V64 + V65 + V66 + V68 + V69 + V70 + V72 +
## V73 + V74 + V77 + V78 + V79 + V80 + V81 + V82 + V83 + V84 +
## V85 + V87 + V92 + V93 + V94 + V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V58 1 0.178 83.296 35.284
## - V65 1 0.363 83.481 35.666
## - V11 1 0.383 83.501 35.707
## - V94 1 0.505 83.623 35.957
## - V93 1 0.535 83.653 36.019
## - V3 1 0.596 83.714 36.144
## - V98 1 0.604 83.722 36.161
## - V35 1 0.619 83.737 36.192
## - V12 1 0.715 83.833 36.390
## - V56 1 0.891 84.010 36.751
## <none> 83.118 36.916
## - V10 1 1.060 84.178 37.095
## - V66 1 1.123 84.241 37.224
## - V36 1 1.207 84.325 37.395
## - V70 1 1.333 84.451 37.653
## - V27 1 1.378 84.496 37.745
## - V34 1 1.417 84.535 37.823
## - V62 1 1.464 84.582 37.920
## - V24 1 1.558 84.676 38.110
## - V16 1 1.667 84.785 38.330
## - V8 1 1.678 84.796 38.353
## - V59 1 1.813 84.931 38.627
## - V13 1 1.819 84.937 38.638
## - V17 1 1.909 85.027 38.821
## - V37 1 2.062 85.180 39.131
## - V61 1 2.136 85.254 39.281
## - V81 1 2.274 85.392 39.558
## - V31 1 2.601 85.719 40.215
## - V19 1 2.841 85.959 40.696
## - V15 1 2.877 85.995 40.769
## - V14 1 2.894 86.012 40.803
## - V25 1 2.991 86.110 40.998
## - V83 1 3.053 86.171 41.120
## - V84 1 3.134 86.252 41.282
## - V4 1 3.233 86.351 41.479
## - V44 1 3.243 86.361 41.499
## - V48 1 3.383 86.501 41.778
## - V96 1 3.681 86.799 42.369
## - V55 1 3.764 86.882 42.533
## - V6 1 3.815 86.933 42.634
## - V32 1 4.075 87.193 43.148
## - V68 1 4.095 87.213 43.187
## - V60 1 4.203 87.321 43.400
## - V30 1 4.268 87.386 43.529
## - V72 1 4.436 87.554 43.858
## - V43 1 4.531 87.649 44.046
## - V69 1 4.756 87.874 44.487
## - V26 1 4.822 87.940 44.615
## - V7 1 4.832 87.950 44.636
## - V99 1 4.876 87.994 44.721
## - V5 1 5.555 88.673 46.042
## - V82 1 6.201 89.319 47.292
## - V2 1 6.649 89.767 48.152
## - V63 1 7.284 90.402 49.365
## - V77 1 8.035 91.153 50.787
## - V42 1 8.283 91.401 51.256
## - V97 1 8.524 91.642 51.709
## - V45 1 9.150 92.268 52.879
## - V41 1 9.228 92.346 53.024
## - V78 1 10.479 93.597 55.338
## - V23 1 10.642 93.760 55.638
## - V74 1 10.672 93.790 55.693
## - V46 1 10.786 93.904 55.902
## - V92 1 11.103 94.221 56.482
## - V64 1 11.157 94.275 56.580
## - V53 1 12.331 95.449 58.709
## - V21 1 13.047 96.165 59.994
## - V29 1 13.131 96.249 60.145
## - V79 1 13.765 96.883 61.273
## - V73 1 13.776 96.894 61.294
## - V50 1 14.170 97.288 61.991
## - V22 1 14.639 97.757 62.818
## - V40 1 14.979 98.098 63.416
## - V28 1 15.983 99.101 65.167
## - V52 1 16.593 99.711 66.222
## - V51 1 18.269 101.387 69.089
## - V80 1 18.790 101.908 69.972
## - V1 1 20.178 103.296 72.297
## - V85 1 20.223 103.341 72.372
## - V39 1 24.054 107.172 78.633
## - V87 1 48.019 131.137 113.345
##
## Step: AIC=35.28
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V10 + V11 + V12 +
## V13 + V14 + V15 + V16 + V17 + V19 + V21 + V22 + V23 + V24 +
## V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 + V34 + V35 +
## V36 + V37 + V39 + V40 + V41 + V42 + V43 + V44 + V45 + V46 +
## V48 + V50 + V51 + V52 + V53 + V55 + V56 + V59 + V60 + V61 +
## V62 + V63 + V64 + V65 + V66 + V68 + V69 + V70 + V72 + V73 +
## V74 + V77 + V78 + V79 + V80 + V81 + V82 + V83 + V84 + V85 +
## V87 + V92 + V93 + V94 + V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V11 1 0.304 83.600 33.910
## - V65 1 0.348 83.644 34.002
## - V98 1 0.468 83.764 34.248
## - V94 1 0.481 83.777 34.275
## - V93 1 0.558 83.854 34.432
## - V35 1 0.599 83.895 34.516
## - V3 1 0.718 84.014 34.761
## - V12 1 0.773 84.069 34.874
## <none> 83.296 35.284
## - V10 1 1.177 84.473 35.697
## - V56 1 1.234 84.530 35.813
## - V36 1 1.257 84.553 35.859
## - V66 1 1.268 84.564 35.882
## - V70 1 1.298 84.594 35.943
## - V34 1 1.442 84.738 36.235
## - V27 1 1.525 84.821 36.404
## - V24 1 1.555 84.851 36.466
## - V16 1 1.754 85.050 36.868
## - V13 1 1.787 85.083 36.935
## - V17 1 1.854 85.150 37.070
## - V8 1 1.881 85.177 37.124
## - V62 1 1.946 85.242 37.257
## - V61 1 2.066 85.362 37.498
## - V37 1 2.473 85.769 38.317
## - V31 1 2.575 85.871 38.521
## - V81 1 2.577 85.873 38.524
## - V25 1 2.829 86.125 39.029
## - V15 1 2.837 86.133 39.045
## - V14 1 2.852 86.148 39.075
## - V59 1 2.931 86.227 39.231
## - V84 1 2.964 86.260 39.298
## - V19 1 2.998 86.294 39.365
## - V44 1 3.335 86.631 40.036
## - V48 1 3.385 86.682 40.136
## - V4 1 3.401 86.697 40.167
## - V96 1 3.510 86.806 40.382
## - V83 1 3.711 87.007 40.781
## - V55 1 3.727 87.023 40.813
## - V6 1 3.818 87.114 40.992
## - V30 1 4.145 87.441 41.637
## - V32 1 4.149 87.445 41.645
## - V60 1 4.226 87.522 41.796
## - V68 1 4.297 87.593 41.935
## - V43 1 4.644 87.941 42.617
## - V26 1 4.659 87.955 42.644
## - V7 1 4.913 88.209 43.140
## - V72 1 4.920 88.216 43.155
## - V69 1 4.925 88.221 43.165
## - V99 1 5.345 88.641 43.982
## - V5 1 5.677 88.973 44.625
## - V2 1 6.554 89.850 46.311
## - V82 1 6.605 89.901 46.409
## - V63 1 7.106 90.402 47.365
## - V77 1 7.896 91.192 48.862
## - V42 1 8.525 91.821 50.043
## - V97 1 8.774 92.070 50.509
## - V41 1 9.208 92.504 51.318
## - V45 1 10.045 93.341 52.868
## - V23 1 10.508 93.804 53.718
## - V78 1 10.619 93.915 53.922
## - V64 1 11.209 94.505 54.999
## - V92 1 11.266 94.562 55.102
## - V74 1 11.463 94.759 55.461
## - V53 1 12.244 95.540 56.873
## - V46 1 12.290 95.586 56.956
## - V29 1 12.956 96.252 58.151
## - V21 1 13.382 96.678 58.909
## - V73 1 14.108 97.404 60.196
## - V50 1 14.187 97.483 60.335
## - V79 1 14.187 97.483 60.336
## - V22 1 14.694 97.990 61.229
## - V40 1 14.844 98.140 61.491
## - V28 1 15.826 99.122 63.203
## - V52 1 16.814 100.110 64.909
## - V51 1 18.735 102.031 68.179
## - V85 1 20.083 103.379 70.436
## - V1 1 20.725 104.021 71.501
## - V80 1 21.272 104.568 72.403
## - V39 1 24.357 107.653 77.403
## - V87 1 52.981 136.277 117.958
##
## Step: AIC=33.91
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V10 + V12 + V13 +
## V14 + V15 + V16 + V17 + V19 + V21 + V22 + V23 + V24 + V25 +
## V26 + V27 + V28 + V29 + V30 + V31 + V32 + V34 + V35 + V36 +
## V37 + V39 + V40 + V41 + V42 + V43 + V44 + V45 + V46 + V48 +
## V50 + V51 + V52 + V53 + V55 + V56 + V59 + V60 + V61 + V62 +
## V63 + V64 + V65 + V66 + V68 + V69 + V70 + V72 + V73 + V74 +
## V77 + V78 + V79 + V80 + V81 + V82 + V83 + V84 + V85 + V87 +
## V92 + V93 + V94 + V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V65 1 0.241 83.841 32.406
## - V93 1 0.413 84.013 32.759
## - V98 1 0.471 84.071 32.877
## - V94 1 0.584 84.184 33.108
## - V35 1 0.720 84.320 33.385
## - V3 1 0.858 84.458 33.666
## <none> 83.600 33.910
## - V36 1 1.136 84.736 34.232
## - V34 1 1.200 84.800 34.361
## - V70 1 1.291 84.891 34.547
## - V27 1 1.398 84.998 34.763
## - V56 1 1.508 85.108 34.985
## - V16 1 1.559 85.159 35.089
## - V66 1 1.768 85.368 35.510
## - V17 1 1.878 85.478 35.732
## - V62 1 1.909 85.509 35.794
## - V24 1 1.960 85.560 35.896
## - V61 1 2.077 85.677 36.131
## - V8 1 2.149 85.749 36.276
## - V37 1 2.317 85.917 36.612
## - V31 1 2.421 86.020 36.820
## - V25 1 2.549 86.149 37.077
## - V81 1 2.727 86.327 37.432
## - V84 1 2.731 86.331 37.439
## - V19 1 2.935 86.535 37.846
## - V48 1 3.243 86.843 38.457
## - V44 1 3.251 86.851 38.473
## - V96 1 3.375 86.975 38.718
## - V59 1 3.710 87.310 39.379
## - V32 1 3.867 87.467 39.688
## - V4 1 3.942 87.542 39.836
## - V83 1 4.042 87.641 40.031
## - V30 1 4.086 87.686 40.119
## - V10 1 4.142 87.742 40.228
## - V15 1 4.315 87.915 40.566
## - V13 1 4.339 87.939 40.615
## - V55 1 4.341 87.941 40.618
## - V6 1 4.366 87.966 40.666
## - V43 1 4.428 88.028 40.788
## - V26 1 4.489 88.089 40.906
## - V60 1 4.886 88.486 41.681
## - V14 1 4.914 88.514 41.734
## - V99 1 5.110 88.710 42.115
## - V72 1 5.170 88.770 42.231
## - V68 1 5.212 88.812 42.314
## - V69 1 5.314 88.914 42.511
## - V7 1 5.630 89.230 43.120
## - V12 1 5.702 89.302 43.258
## - V82 1 6.526 90.126 44.839
## - V5 1 6.596 90.196 44.973
## - V2 1 6.597 90.197 44.973
## - V63 1 7.010 90.610 45.760
## - V77 1 8.190 91.790 47.986
## - V42 1 8.281 91.880 48.155
## - V97 1 8.501 92.101 48.568
## - V41 1 8.951 92.551 49.405
## - V45 1 10.248 93.848 51.799
## - V78 1 10.491 94.091 52.244
## - V64 1 10.933 94.533 53.050
## - V92 1 11.193 94.793 53.522
## - V74 1 11.408 95.008 53.913
## - V23 1 11.428 95.028 53.948
## - V46 1 12.294 95.894 55.509
## - V29 1 12.759 96.359 56.341
## - V53 1 13.912 97.512 58.386
## - V73 1 14.001 97.601 58.543
## - V21 1 14.124 97.724 58.760
## - V50 1 14.183 97.783 58.864
## - V79 1 14.496 98.096 59.414
## - V40 1 14.541 98.141 59.492
## - V28 1 15.532 99.132 61.221
## - V22 1 15.749 99.349 61.598
## - V52 1 18.325 101.925 65.999
## - V51 1 19.332 102.932 67.691
## - V85 1 19.785 103.385 68.447
## - V1 1 21.586 105.186 71.416
## - V80 1 21.807 105.407 71.778
## - V39 1 24.054 107.654 75.405
## - V87 1 52.961 136.561 116.315
##
## Step: AIC=32.41
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V10 + V12 + V13 +
## V14 + V15 + V16 + V17 + V19 + V21 + V22 + V23 + V24 + V25 +
## V26 + V27 + V28 + V29 + V30 + V31 + V32 + V34 + V35 + V36 +
## V37 + V39 + V40 + V41 + V42 + V43 + V44 + V45 + V46 + V48 +
## V50 + V51 + V52 + V53 + V55 + V56 + V59 + V60 + V61 + V62 +
## V63 + V64 + V66 + V68 + V69 + V70 + V72 + V73 + V74 + V77 +
## V78 + V79 + V80 + V81 + V82 + V83 + V84 + V85 + V87 + V92 +
## V93 + V94 + V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V93 1 0.308 84.150 31.038
## - V98 1 0.489 84.330 31.406
## - V94 1 0.682 84.523 31.800
## - V35 1 0.699 84.541 31.835
## <none> 83.841 32.406
## - V3 1 1.037 84.878 32.520
## - V36 1 1.079 84.921 32.606
## - V70 1 1.148 84.989 32.744
## - V34 1 1.163 85.005 32.776
## - V16 1 1.431 85.272 33.317
## - V27 1 1.447 85.289 33.350
## - V17 1 1.799 85.641 34.058
## - V61 1 2.031 85.872 34.523
## - V8 1 2.048 85.889 34.557
## - V62 1 2.073 85.914 34.607
## - V56 1 2.263 86.104 34.987
## - V37 1 2.276 86.117 35.012
## - V25 1 2.308 86.150 35.078
## - V31 1 2.329 86.170 35.119
## - V24 1 2.364 86.206 35.190
## - V81 1 2.486 86.327 35.432
## - V84 1 2.492 86.333 35.444
## - V19 1 2.788 86.629 36.033
## - V48 1 3.006 86.848 36.466
## - V96 1 3.279 87.121 37.005
## - V44 1 3.430 87.271 37.302
## - V32 1 3.690 87.531 37.814
## - V59 1 4.098 87.939 38.613
## - V13 1 4.098 87.940 38.615
## - V30 1 4.157 87.998 38.729
## - V4 1 4.190 88.032 38.795
## - V15 1 4.403 88.244 39.210
## - V6 1 4.411 88.253 39.226
## - V26 1 4.414 88.255 39.231
## - V43 1 4.455 88.296 39.311
## - V14 1 4.699 88.540 39.786
## - V10 1 4.766 88.607 39.916
## - V99 1 4.874 88.715 40.125
## - V83 1 4.909 88.750 40.193
## - V60 1 5.129 88.970 40.619
## - V69 1 5.400 89.241 41.142
## - V12 1 5.464 89.305 41.266
## - V7 1 5.596 89.437 41.519
## - V55 1 5.977 89.818 42.250
## - V68 1 6.068 89.909 42.424
## - V2 1 6.375 90.216 43.011
## - V72 1 6.489 90.330 43.228
## - V5 1 6.780 90.621 43.782
## - V82 1 7.260 91.101 44.690
## - V63 1 8.092 91.934 46.254
## - V42 1 8.163 92.004 46.387
## - V77 1 8.187 92.028 46.432
## - V97 1 8.282 92.124 46.610
## - V41 1 8.837 92.679 47.643
## - V66 1 9.085 92.926 48.101
## - V45 1 10.661 94.503 50.995
## - V78 1 10.726 94.568 51.113
## - V92 1 11.072 94.913 51.740
## - V23 1 11.803 95.645 53.061
## - V46 1 12.321 96.162 53.989
## - V74 1 13.108 96.949 55.391
## - V29 1 13.625 97.466 56.306
## - V50 1 13.971 97.813 56.916
## - V21 1 14.049 97.890 57.052
## - V40 1 14.568 98.409 57.962
## - V79 1 14.739 98.580 58.260
## - V22 1 15.978 99.820 60.410
## - V73 1 16.771 100.612 61.770
## - V28 1 17.556 101.398 63.107
## - V53 1 17.821 101.662 63.555
## - V51 1 20.130 103.971 67.418
## - V85 1 20.931 104.773 68.739
## - V52 1 21.488 105.329 69.650
## - V1 1 21.643 105.484 69.904
## - V80 1 21.996 105.837 70.478
## - V39 1 24.186 108.027 74.001
## - V64 1 28.585 112.426 80.866
## - V87 1 55.255 139.096 117.479
##
## Step: AIC=31.04
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V10 + V12 + V13 +
## V14 + V15 + V16 + V17 + V19 + V21 + V22 + V23 + V24 + V25 +
## V26 + V27 + V28 + V29 + V30 + V31 + V32 + V34 + V35 + V36 +
## V37 + V39 + V40 + V41 + V42 + V43 + V44 + V45 + V46 + V48 +
## V50 + V51 + V52 + V53 + V55 + V56 + V59 + V60 + V61 + V62 +
## V63 + V64 + V66 + V68 + V69 + V70 + V72 + V73 + V74 + V77 +
## V78 + V79 + V80 + V81 + V82 + V83 + V84 + V85 + V87 + V92 +
## V94 + V96 + V97 + V98 + V99
##
## Df Sum of Sq RSS AIC
## - V98 1 0.361 84.510 29.773
## - V35 1 0.663 84.813 30.388
## - V36 1 0.965 85.115 31.000
## <none> 84.150 31.038
## - V34 1 1.069 85.218 31.208
## - V70 1 1.095 85.245 31.261
## - V16 1 1.165 85.315 31.403
## - V3 1 1.212 85.362 31.498
## - V27 1 1.272 85.422 31.619
## - V17 1 1.617 85.766 32.311
## - V8 1 1.853 86.003 32.785
## - V56 1 2.137 86.286 33.350
## - V25 1 2.159 86.309 33.396
## - V62 1 2.171 86.321 33.419
## - V31 1 2.187 86.337 33.451
## - V24 1 2.297 86.447 33.670
## - V37 1 2.297 86.447 33.671
## - V61 1 2.400 86.550 33.875
## - V84 1 2.524 86.674 34.120
## - V81 1 2.817 86.967 34.701
## - V19 1 2.935 87.085 34.935
## - V44 1 3.223 87.373 35.503
## - V48 1 3.307 87.457 35.668
## - V32 1 3.489 87.639 36.025
## - V30 1 4.019 88.168 37.062
## - V26 1 4.189 88.339 37.394
## - V13 1 4.367 88.517 37.740
## - V43 1 4.392 88.542 37.788
## - V4 1 4.433 88.582 37.868
## - V6 1 4.501 88.651 38.000
## - V10 1 4.665 88.814 38.317
## - V83 1 4.727 88.877 38.438
## - V59 1 4.899 89.048 38.770
## - V14 1 5.229 89.379 39.407
## - V15 1 5.345 89.495 39.630
## - V96 1 5.364 89.514 39.666
## - V7 1 5.414 89.564 39.763
## - V12 1 5.602 89.752 40.124
## - V69 1 5.623 89.773 40.163
## - V55 1 5.752 89.902 40.410
## - V99 1 5.832 89.982 40.564
## - V2 1 6.144 90.294 41.159
## - V68 1 6.363 90.513 41.576
## - V60 1 6.554 90.704 41.938
## - V72 1 6.729 90.879 42.270
## - V5 1 6.963 91.113 42.712
## - V82 1 6.989 91.138 42.760
## - V63 1 8.055 92.205 44.761
## - V77 1 8.141 92.290 44.920
## - V42 1 8.248 92.397 45.120
## - V97 1 8.495 92.645 45.580
## - V41 1 8.997 93.147 46.510
## - V66 1 9.535 93.684 47.499
## - V45 1 10.373 94.523 49.032
## - V78 1 10.608 94.758 49.459
## - V23 1 11.679 95.829 51.392
## - V46 1 12.351 96.501 52.594
## - V94 1 13.018 97.167 53.778
## - V29 1 13.561 97.710 54.736
## - V74 1 13.711 97.861 55.001
## - V50 1 13.900 98.050 55.333
## - V21 1 14.048 98.198 55.592
## - V40 1 14.956 99.105 57.174
## - V79 1 15.150 99.299 57.511
## - V22 1 15.890 100.040 58.788
## - V73 1 16.972 101.122 60.639
## - V28 1 17.263 101.412 61.133
## - V53 1 17.513 101.663 61.557
## - V51 1 19.849 103.999 65.464
## - V85 1 20.804 104.954 67.037
## - V52 1 21.179 105.329 67.651
## - V1 1 21.362 105.512 67.949
## - V80 1 23.173 107.323 70.876
## - V39 1 25.029 109.179 73.824
## - V92 1 28.190 112.340 78.734
## - V64 1 29.006 113.156 79.978
## - V87 1 55.292 139.442 115.906
##
## Step: AIC=29.77
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V10 + V12 + V13 +
## V14 + V15 + V16 + V17 + V19 + V21 + V22 + V23 + V24 + V25 +
## V26 + V27 + V28 + V29 + V30 + V31 + V32 + V34 + V35 + V36 +
## V37 + V39 + V40 + V41 + V42 + V43 + V44 + V45 + V46 + V48 +
## V50 + V51 + V52 + V53 + V55 + V56 + V59 + V60 + V61 + V62 +
## V63 + V64 + V66 + V68 + V69 + V70 + V72 + V73 + V74 + V77 +
## V78 + V79 + V80 + V81 + V82 + V83 + V84 + V85 + V87 + V92 +
## V94 + V96 + V97 + V99
##
## Df Sum of Sq RSS AIC
## - V35 1 0.786 85.296 29.365
## <none> 84.510 29.773
## - V34 1 1.102 85.612 30.001
## - V36 1 1.131 85.642 30.061
## - V70 1 1.173 85.684 30.145
## - V16 1 1.210 85.720 30.219
## - V3 1 1.295 85.805 30.388
## - V27 1 1.462 85.972 30.723
## - V17 1 1.735 86.245 31.269
## - V8 1 1.863 86.374 31.525
## - V24 1 2.076 86.587 31.948
## - V62 1 2.095 86.605 31.985
## - V84 1 2.203 86.714 32.200
## - V56 1 2.285 86.796 32.363
## - V37 1 2.463 86.974 32.715
## - V25 1 2.529 87.039 32.845
## - V81 1 2.534 87.044 32.854
## - V31 1 2.693 87.204 33.170
## - V61 1 2.720 87.231 33.222
## - V19 1 2.949 87.459 33.672
## - V48 1 3.167 87.678 34.101
## - V44 1 3.303 87.813 34.367
## - V26 1 4.224 88.734 36.162
## - V43 1 4.298 88.808 36.305
## - V32 1 4.298 88.808 36.305
## - V10 1 4.430 88.940 36.561
## - V30 1 4.440 88.950 36.581
## - V6 1 4.458 88.969 36.616
## - V13 1 4.567 89.077 36.826
## - V4 1 4.721 89.231 37.123
## - V96 1 5.242 89.753 38.125
## - V7 1 5.253 89.763 38.145
## - V14 1 5.370 89.880 38.369
## - V15 1 5.448 89.958 38.519
## - V69 1 5.506 90.016 38.630
## - V83 1 5.605 90.115 38.818
## - V12 1 5.999 90.509 39.569
## - V59 1 6.097 90.608 39.756
## - V55 1 6.122 90.633 39.803
## - V68 1 6.249 90.759 40.043
## - V72 1 6.459 90.969 40.441
## - V2 1 6.474 90.984 40.469
## - V5 1 7.183 91.693 41.804
## - V77 1 7.851 92.361 43.052
## - V82 1 8.014 92.525 43.357
## - V42 1 8.206 92.716 43.713
## - V60 1 8.406 92.916 44.083
## - V63 1 8.585 93.095 44.414
## - V41 1 9.147 93.658 45.450
## - V66 1 9.674 94.185 46.416
## - V78 1 10.298 94.808 47.550
## - V45 1 11.301 95.812 49.361
## - V23 1 11.329 95.839 49.410
## - V94 1 12.682 97.193 51.822
## - V46 1 13.203 97.713 52.741
## - V74 1 13.450 97.960 53.175
## - V21 1 13.893 98.403 53.952
## - V29 1 13.966 98.476 54.079
## - V50 1 14.109 98.619 54.329
## - V79 1 14.880 99.391 55.669
## - V40 1 15.506 100.016 56.748
## - V22 1 15.565 100.075 56.850
## - V97 1 15.738 100.249 57.147
## - V73 1 16.612 101.122 58.640
## - V28 1 17.724 102.235 60.522
## - V53 1 19.316 103.826 63.178
## - V85 1 20.513 105.023 65.150
## - V51 1 21.206 105.717 66.282
## - V1 1 22.536 107.047 68.432
## - V80 1 23.007 107.517 69.187
## - V52 1 23.490 108.001 69.959
## - V39 1 26.252 110.762 74.301
## - V92 1 27.882 112.392 76.814
## - V64 1 29.853 114.364 79.805
## - V99 1 32.735 117.245 84.085
## - V87 1 54.956 139.466 113.936
##
## Step: AIC=29.36
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V10 + V12 + V13 +
## V14 + V15 + V16 + V17 + V19 + V21 + V22 + V23 + V24 + V25 +
## V26 + V27 + V28 + V29 + V30 + V31 + V32 + V34 + V36 + V37 +
## V39 + V40 + V41 + V42 + V43 + V44 + V45 + V46 + V48 + V50 +
## V51 + V52 + V53 + V55 + V56 + V59 + V60 + V61 + V62 + V63 +
## V64 + V66 + V68 + V69 + V70 + V72 + V73 + V74 + V77 + V78 +
## V79 + V80 + V81 + V82 + V83 + V84 + V85 + V87 + V92 + V94 +
## V96 + V97 + V99
##
## Df Sum of Sq RSS AIC
## - V36 1 0.431 85.727 28.232
## - V16 1 0.935 86.231 29.240
## <none> 85.296 29.365
## - V70 1 1.165 86.461 29.698
## - V3 1 1.297 86.593 29.960
## - V17 1 1.456 86.752 30.276
## - V27 1 1.617 86.913 30.596
## - V8 1 2.101 87.397 31.551
## - V31 1 2.142 87.438 31.632
## - V24 1 2.208 87.504 31.760
## - V37 1 2.247 87.543 31.837
## - V81 1 2.407 87.703 32.151
## - V25 1 2.531 87.827 32.394
## - V84 1 2.584 87.880 32.499
## - V62 1 2.682 87.978 32.689
## - V44 1 2.876 88.172 33.069
## - V56 1 3.136 88.432 33.575
## - V19 1 3.331 88.627 33.953
## - V61 1 3.371 88.667 34.031
## - V48 1 3.500 88.796 34.283
## - V30 1 3.717 89.013 34.702
## - V43 1 3.837 89.133 34.933
## - V10 1 3.844 89.140 34.947
## - V26 1 4.260 89.555 35.747
## - V13 1 4.404 89.700 36.024
## - V32 1 4.538 89.834 36.281
## - V14 1 5.099 90.395 37.351
## - V4 1 5.118 90.414 37.388
## - V69 1 5.213 90.509 37.569
## - V15 1 5.221 90.517 37.584
## - V6 1 5.302 90.598 37.737
## - V83 1 5.370 90.666 37.866
## - V12 1 5.792 91.088 38.665
## - V68 1 5.931 91.227 38.928
## - V7 1 5.940 91.236 38.945
## - V72 1 6.554 91.850 40.097
## - V2 1 6.889 92.185 40.724
## - V59 1 7.027 92.323 40.981
## - V96 1 7.150 92.446 41.211
## - V55 1 7.338 92.634 41.560
## - V42 1 7.640 92.936 42.120
## - V77 1 7.742 93.038 42.309
## - V5 1 7.864 93.160 42.534
## - V82 1 8.151 93.447 43.062
## - V41 1 8.875 94.171 44.390
## - V63 1 8.997 94.293 44.612
## - V60 1 9.204 94.500 44.990
## - V66 1 10.058 95.354 46.538
## - V78 1 10.522 95.818 47.372
## - V45 1 10.773 96.069 47.823
## - V23 1 12.124 97.420 50.224
## - V94 1 12.926 98.222 51.634
## - V46 1 13.221 98.517 52.150
## - V29 1 13.313 98.609 52.311
## - V34 1 13.629 98.925 52.861
## - V74 1 14.434 99.730 54.255
## - V50 1 14.867 100.163 55.000
## - V21 1 15.244 100.540 55.646
## - V79 1 15.339 100.635 55.809
## - V40 1 16.003 101.299 56.941
## - V22 1 16.782 102.078 58.258
## - V73 1 17.605 102.901 59.639
## - V28 1 18.286 103.582 60.774
## - V97 1 19.104 104.400 62.126
## - V53 1 20.498 105.794 64.408
## - V51 1 22.115 107.411 67.018
## - V85 1 22.218 107.514 67.182
## - V1 1 22.415 107.711 67.497
## - V80 1 23.108 108.404 68.599
## - V52 1 24.435 109.731 70.692
## - V39 1 27.122 112.418 74.854
## - V92 1 27.212 112.508 74.991
## - V64 1 32.310 117.606 82.614
## - V99 1 34.459 119.755 85.729
## - V87 1 56.112 141.408 114.314
##
## Step: AIC=28.23
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V10 + V12 + V13 +
## V14 + V15 + V16 + V17 + V19 + V21 + V22 + V23 + V24 + V25 +
## V26 + V27 + V28 + V29 + V30 + V31 + V32 + V34 + V37 + V39 +
## V40 + V41 + V42 + V43 + V44 + V45 + V46 + V48 + V50 + V51 +
## V52 + V53 + V55 + V56 + V59 + V60 + V61 + V62 + V63 + V64 +
## V66 + V68 + V69 + V70 + V72 + V73 + V74 + V77 + V78 + V79 +
## V80 + V81 + V82 + V83 + V84 + V85 + V87 + V92 + V94 + V96 +
## V97 + V99
##
## Df Sum of Sq RSS AIC
## - V70 1 0.858 86.585 27.944
## - V16 1 0.993 86.720 28.212
## <none> 85.727 28.232
## - V27 1 1.353 87.080 28.926
## - V3 1 1.377 87.104 28.972
## - V17 1 1.652 87.379 29.514
## - V31 1 1.779 87.506 29.764
## - V8 1 2.238 87.966 30.666
## - V81 1 2.240 87.967 30.668
## - V25 1 2.305 88.032 30.795
## - V24 1 2.488 88.215 31.154
## - V62 1 2.682 88.409 31.530
## - V37 1 2.745 88.472 31.653
## - V44 1 2.822 88.549 31.802
## - V56 1 2.921 88.648 31.994
## - V84 1 3.146 88.873 32.430
## - V48 1 3.160 88.887 32.457
## - V61 1 3.188 88.915 32.513
## - V19 1 3.241 88.968 32.615
## - V30 1 3.391 89.118 32.905
## - V10 1 3.539 89.266 33.189
## - V43 1 4.009 89.736 34.093
## - V32 1 4.109 89.836 34.284
## - V26 1 4.304 90.031 34.658
## - V69 1 4.805 90.532 35.613
## - V13 1 4.889 90.616 35.772
## - V83 1 5.160 90.887 36.285
## - V15 1 5.355 91.082 36.654
## - V68 1 5.546 91.273 37.014
## - V14 1 5.579 91.306 37.077
## - V4 1 5.925 91.652 37.727
## - V12 1 6.272 91.999 38.377
## - V6 1 6.829 92.556 39.415
## - V59 1 7.004 92.731 39.741
## - V7 1 7.015 92.742 39.760
## - V96 1 7.086 92.813 39.891
## - V55 1 7.218 92.946 40.137
## - V2 1 7.311 93.038 40.308
## - V72 1 7.572 93.299 40.791
## - V42 1 7.632 93.359 40.901
## - V77 1 7.889 93.616 41.373
## - V82 1 8.276 94.003 42.084
## - V41 1 8.676 94.403 42.813
## - V60 1 9.077 94.805 43.543
## - V5 1 9.517 95.244 44.340
## - V63 1 9.551 95.279 44.401
## - V66 1 10.212 95.939 45.589
## - V45 1 10.541 96.268 46.179
## - V78 1 11.158 96.885 47.277
## - V23 1 12.177 97.904 49.076
## - V94 1 12.563 98.290 49.754
## - V29 1 13.012 98.739 50.537
## - V50 1 14.523 100.250 53.149
## - V46 1 14.869 100.597 53.743
## - V21 1 15.201 100.928 54.309
## - V74 1 15.317 101.044 54.507
## - V40 1 15.669 101.396 55.105
## - V22 1 16.610 102.337 56.693
## - V79 1 16.774 102.501 56.969
## - V28 1 17.864 103.591 58.788
## - V73 1 18.162 103.889 59.282
## - V34 1 18.390 104.117 59.659
## - V97 1 19.745 105.472 61.884
## - V53 1 20.368 106.095 62.896
## - V51 1 21.684 107.411 65.018
## - V80 1 23.106 108.833 67.279
## - V1 1 23.161 108.888 67.365
## - V52 1 24.028 109.755 68.730
## - V85 1 25.265 110.992 70.658
## - V39 1 26.772 112.499 72.978
## - V92 1 27.061 112.788 73.418
## - V64 1 35.670 121.397 86.071
## - V99 1 36.493 122.220 87.232
## - V87 1 59.416 145.143 116.798
##
## Step: AIC=27.94
## fat ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V10 + V12 + V13 +
## V14 + V15 + V16 + V17 + V19 + V21 + V22 + V23 + V24 + V25 +
## V26 + V27 + V28 + V29 + V30 + V31 + V32 + V34 + V37 + V39 +
## V40 + V41 + V42 + V43 + V44 + V45 + V46 + V48 + V50 + V51 +
## V52 + V53 + V55 + V56 + V59 + V60 + V61 + V62 + V63 + V64 +
## V66 + V68 + V69 + V72 + V73 + V74 + V77 + V78 + V79 + V80 +
## V81 + V82 + V83 + V84 + V85 + V87 + V92 + V94 + V96 + V97 +
## V99
##
## Df Sum of Sq RSS AIC
## <none> 86.585 27.944
## - V27 1 1.211 87.795 28.332
## - V16 1 1.212 87.797 28.335
## - V3 1 1.328 87.913 28.562
## - V17 1 1.538 88.123 28.973
## - V25 1 1.798 88.383 29.480
## - V31 1 1.980 88.565 29.834
## - V8 1 2.091 88.676 30.049
## - V81 1 2.229 88.814 30.316
## - V62 1 2.286 88.871 30.427
## - V61 1 2.374 88.959 30.596
## - V84 1 2.463 89.048 30.770
## - V56 1 3.034 89.619 31.868
## - V48 1 3.085 89.670 31.967
## - V30 1 3.218 89.803 32.222
## - V37 1 3.258 89.842 32.297
## - V44 1 3.266 89.851 32.312
## - V10 1 3.764 90.349 33.264
## - V19 1 3.863 90.447 33.451
## - V24 1 3.995 90.579 33.702
## - V26 1 4.559 91.144 34.770
## - V43 1 4.565 91.150 34.783
## - V13 1 4.613 91.198 34.873
## - V32 1 4.728 91.313 35.089
## - V15 1 4.923 91.508 35.456
## - V14 1 5.269 91.854 36.106
## - V68 1 5.919 92.504 37.318
## - V12 1 6.103 92.688 37.660
## - V96 1 6.434 93.018 38.272
## - V4 1 6.434 93.019 38.272
## - V83 1 6.684 93.269 38.735
## - V69 1 6.806 93.391 38.959
## - V59 1 6.845 93.430 39.031
## - V6 1 7.022 93.607 39.357
## - V7 1 7.195 93.780 39.675
## - V2 1 7.525 94.110 40.279
## - V55 1 7.623 94.208 40.457
## - V77 1 8.285 94.869 41.661
## - V60 1 8.320 94.904 41.724
## - V42 1 8.382 94.967 41.838
## - V82 1 8.708 95.293 42.427
## - V63 1 8.764 95.349 42.528
## - V41 1 8.940 95.525 42.846
## - V5 1 10.077 96.662 44.880
## - V66 1 10.466 97.051 45.572
## - V78 1 11.331 97.916 47.097
## - V45 1 11.502 98.086 47.397
## - V94 1 11.976 98.561 48.226
## - V29 1 12.286 98.871 48.767
## - V50 1 13.699 100.284 51.208
## - V23 1 14.791 101.376 53.070
## - V40 1 15.385 101.969 54.075
## - V46 1 15.955 102.540 55.034
## - V79 1 16.728 103.313 56.326
## - V28 1 17.183 103.768 57.082
## - V21 1 17.600 104.185 57.772
## - V74 1 18.853 105.438 59.827
## - V22 1 19.074 105.659 60.188
## - V34 1 19.118 105.702 60.259
## - V97 1 19.247 105.832 60.469
## - V53 1 20.613 107.198 62.675
## - V51 1 20.827 107.412 63.018
## - V72 1 21.057 107.642 63.387
## - V80 1 22.638 109.223 65.894
## - V1 1 22.789 109.374 66.131
## - V52 1 23.419 110.004 67.120
## - V85 1 24.552 111.137 68.882
## - V73 1 25.125 111.709 69.766
## - V39 1 26.614 113.199 72.044
## - V92 1 27.172 113.756 72.889
## - V64 1 35.632 122.216 85.227
## - V99 1 37.819 124.404 88.279
## - V87 1 58.567 145.152 114.810
rmse(model2$fit,meatspec$fat[1:172])
## [1] 0.7095069
rmse(predict(model2,meatspec[173:215,]),meatspec$fat[173:215])
## [1] 3.590245
# The model selection step removed 28 variables. Of course,
# the nominal fit got a little worse as it always will
# when predictors are removed, but the actual
# performance improved somewhat from 3.81 to 3.59.
# Now let’s compute the PCA on the training sample
# predictors:
library(MVA)
## Loading required package: HSAUR2
## Loading required package: tools
##
## Attaching package: 'HSAUR2'
## The following objects are masked from 'package:faraway':
##
## epilepsy, toenail
meatpca <- prcomp(meatspec[1:172,-101])
summary(meatpca)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 5.0554 0.51114 0.28176 0.16771 0.03817 0.02457
## Proportion of Variance 0.9857 0.01008 0.00306 0.00108 0.00006 0.00002
## Cumulative Proportion 0.9857 0.99576 0.99882 0.99991 0.99996 0.99999
## PC7 PC8 PC9 PC10 PC11 PC12
## Standard deviation 0.01432 0.0108 0.004533 0.003432 0.002099 0.001759
## Proportion of Variance 0.00001 0.0000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.99999 1.0000 1.000000 1.000000 1.000000 1.000000
## PC13 PC14 PC15 PC16 PC17
## Standard deviation 0.000998 0.0007307 0.0005441 0.0004426 0.0003933
## Proportion of Variance 0.000000 0.0000000 0.0000000 0.0000000 0.0000000
## Cumulative Proportion 1.000000 1.0000000 1.0000000 1.0000000 1.0000000
## PC18 PC19 PC20 PC21 PC22
## Standard deviation 0.0003409 0.0002888 0.0002046 0.0001958 0.0001904
## Proportion of Variance 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## Cumulative Proportion 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## PC23 PC24 PC25 PC26 PC27
## Standard deviation 0.0001646 0.0001423 0.0001125 0.0001059 0.0001019
## Proportion of Variance 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## Cumulative Proportion 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## PC28 PC29 PC30 PC31 PC32
## Standard deviation 9.614e-05 8.896e-05 8.082e-05 7.738e-05 7.372e-05
## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## PC33 PC34 PC35 PC36 PC37
## Standard deviation 6.861e-05 6.326e-05 5.761e-05 5.392e-05 4.801e-05
## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## PC38 PC39 PC40 PC41 PC42
## Standard deviation 4.685e-05 4.418e-05 4.271e-05 3.768e-05 3.534e-05
## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## PC43 PC44 PC45 PC46 PC47
## Standard deviation 3.435e-05 3.291e-05 3.117e-05 2.803e-05 2.662e-05
## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## PC48 PC49 PC50 PC51 PC52
## Standard deviation 2.635e-05 2.343e-05 2.193e-05 2.14e-05 2.082e-05
## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.00e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.00e+00 1.000e+00
## PC53 PC54 PC55 PC56 PC57
## Standard deviation 1.95e-05 1.85e-05 1.752e-05 1.746e-05 1.633e-05
## Proportion of Variance 0.00e+00 0.00e+00 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.00e+00 1.00e+00 1.000e+00 1.000e+00 1.000e+00
## PC58 PC59 PC60 PC61 PC62
## Standard deviation 1.596e-05 1.552e-05 1.485e-05 1.415e-05 1.358e-05
## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## PC63 PC64 PC65 PC66 PC67
## Standard deviation 1.275e-05 1.256e-05 1.231e-05 1.158e-05 1.131e-05
## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## PC68 PC69 PC70 PC71 PC72
## Standard deviation 1.092e-05 1.006e-05 9.678e-06 9.43e-06 9.144e-06
## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.00e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.00e+00 1.000e+00
## PC73 PC74 PC75 PC76 PC77
## Standard deviation 9.038e-06 8.83e-06 8.384e-06 8.112e-06 7.9e-06
## Proportion of Variance 0.000e+00 0.00e+00 0.000e+00 0.000e+00 0.0e+00
## Cumulative Proportion 1.000e+00 1.00e+00 1.000e+00 1.000e+00 1.0e+00
## PC78 PC79 PC80 PC81 PC82
## Standard deviation 7.64e-06 7.074e-06 7.007e-06 6.512e-06 6.113e-06
## Proportion of Variance 0.00e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.00e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## PC83 PC84 PC85 PC86 PC87
## Standard deviation 5.902e-06 5.721e-06 5.579e-06 5.047e-06 4.531e-06
## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## PC88 PC89 PC90 PC91 PC92
## Standard deviation 4.399e-06 4.037e-06 3.989e-06 3.856e-06 3.664e-06
## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## PC93 PC94 PC95 PC96 PC97
## Standard deviation 3.359e-06 2.81e-06 2.51e-06 2.312e-06 2.18e-06
## Proportion of Variance 0.000e+00 0.00e+00 0.00e+00 0.000e+00 0.00e+00
## Cumulative Proportion 1.000e+00 1.00e+00 1.00e+00 1.000e+00 1.00e+00
## PC98 PC99 PC100
## Standard deviation 1.96e-06 1.828e-06 1.546e-06
## Proportion of Variance 0.00e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.00e+00 1.000e+00 1.000e+00
str(meatpca)
## List of 5
## $ sdev : num [1:100] 5.0554 0.5111 0.2818 0.1677 0.0382 ...
## $ rotation: num [1:100, 1:100] 0.0785 0.079 0.0795 0.0799 0.0804 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:100] "V1" "V2" "V3" "V4" ...
## .. ..$ : chr [1:100] "PC1" "PC2" "PC3" "PC4" ...
## $ center : Named num [1:100] 2.81 2.82 2.82 2.82 2.82 ...
## ..- attr(*, "names")= chr [1:100] "V1" "V2" "V3" "V4" ...
## $ scale : logi FALSE
## $ x : num [1:172, 1:100] -2.245 0.442 -3.831 -1.085 0.538 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:172] "1" "2" "3" "4" ...
## .. ..$ : chr [1:100] "PC1" "PC2" "PC3" "PC4" ...
## - attr(*, "class")= chr "prcomp"
round(meatpca$sdev,3)
## [1] 5.055 0.511 0.282 0.168 0.038 0.025 0.014 0.011 0.005 0.003 0.002
## [12] 0.002 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## [23] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## [34] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## [45] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## [56] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## [67] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## [78] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## [89] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## [100] 0.000
# It is better to examine the square roots because the
# eigenvalues themselves are the variances of the PCs,
# but standard deviations are a better scale for comparison.
# We see that the first PC accounts for about ten times more
# variation than the second. The contribution drops off
# sharply. This suggests that most of the variation in the
# predictors can be explained with just a few dimensions.
# The eigenvalues can be found in the object meatpca$rotat
# ion. We plot these vectors against the predictor number
# (which represents a range of frequencies in this case
matplot(1:100,meatpca$rotation[,1:3],type = "l",
xlab = "Frequency",ylab = "")
# We can get the PCs themselves from the columns of the
# object meatpca$x. Let’s use the first four PCs to predict
# the response:
model3 <- lm(fat~ meatpca$x[,1:4],meatspec[1:172,])
rmse(model3$fit,meatspec$fat[1:172])
## [1] 4.064745
# We do not expect as good a fit using only four variables
# instead of the 100. Even so, considering that, the fit
# is not much worse than the much bigger models