Executive Salaries
load("EXEXSAL2.Rdata")
names(EXEXSAL2)
## [1] "ID" "Y" "X1" "X2" "X3" "X4" "X5" "X6" "X7" "X8" "X9" "X10"
EXEXSAL2 <-EXEXSAL2[,-1]
names(EXEXSAL2)
## [1] "Y" "X1" "X2" "X3" "X4" "X5" "X6" "X7" "X8" "X9" "X10"
Backward Elimination
reg_full<-lm(Y~., data=EXEXSAL2)
n <-length(reg_full$residuals)
summary(reg_full)
##
## Call:
## lm(formula = Y ~ ., data = EXEXSAL2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.201770 -0.050464 0.004435 0.046826 0.185952
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.002e+01 1.481e-01 67.692 < 2e-16 ***
## X1 2.792e-02 1.773e-03 15.745 < 2e-16 ***
## X2 2.903e-02 3.426e-03 8.475 4.57e-13 ***
## X3 2.243e-01 1.708e-02 13.135 < 2e-16 ***
## X4 5.140e-04 4.922e-05 10.443 < 2e-16 ***
## X5 2.048e-03 5.250e-04 3.901 0.000186 ***
## X6 -1.538e-02 1.686e-02 -0.912 0.364124
## X7 -5.097e-04 1.438e-03 -0.355 0.723795
## X8 -2.633e-03 5.128e-03 -0.513 0.608896
## X9 -2.656e-02 2.037e-02 -1.304 0.195613
## X10 -9.774e-04 2.959e-03 -0.330 0.741955
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07608 on 89 degrees of freedom
## Multiple R-squared: 0.9229, Adjusted R-squared: 0.9142
## F-statistic: 106.5 on 10 and 89 DF, p-value: < 2.2e-16
reg_back_aic <-step(reg_full, direction="backward")
## Start: AIC=-504.84
## Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 + X10
##
## Df Sum of Sq RSS AIC
## - X10 1 0.00063 0.51583 -506.71
## - X7 1 0.00073 0.51593 -506.70
## - X8 1 0.00153 0.51673 -506.54
## - X6 1 0.00482 0.52002 -505.91
## - X9 1 0.00984 0.52504 -504.94
## <none> 0.51520 -504.84
## - X5 1 0.08810 0.60330 -491.05
## - X2 1 0.41581 0.93102 -447.66
## - X4 1 0.63133 1.14653 -426.84
## - X3 1 0.99872 1.51393 -399.05
## - X1 1 1.43512 1.95032 -373.72
##
## Step: AIC=-506.71
## Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9
##
## Df Sum of Sq RSS AIC
## - X7 1 0.00050 0.51633 -508.62
## - X8 1 0.00149 0.51732 -508.43
## - X6 1 0.00448 0.52031 -507.85
## - X9 1 0.00992 0.52575 -506.81
## <none> 0.51583 -506.71
## - X5 1 0.08769 0.60352 -493.01
## - X2 1 0.41593 0.93176 -449.59
## - X4 1 0.63878 1.15461 -428.14
## - X3 1 1.03375 1.54959 -398.72
## - X1 1 1.52826 2.04409 -371.02
##
## Step: AIC=-508.62
## Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X8 + X9
##
## Df Sum of Sq RSS AIC
## - X8 1 0.0015 0.5178 -510.33
## - X6 1 0.0040 0.5203 -509.85
## - X9 1 0.0096 0.5260 -508.77
## <none> 0.5163 -508.62
## - X5 1 0.0898 0.6061 -494.58
## - X2 1 0.4243 0.9406 -450.64
## - X4 1 0.6384 1.1547 -430.13
## - X3 1 1.0503 1.5666 -399.62
## - X1 1 3.9764 4.4927 -294.27
##
## Step: AIC=-510.33
## Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X9
##
## Df Sum of Sq RSS AIC
## - X6 1 0.0033 0.5211 -511.69
## - X9 1 0.0089 0.5267 -510.64
## <none> 0.5178 -510.33
## - X5 1 0.0885 0.6064 -496.55
## - X2 1 0.4230 0.9408 -452.62
## - X4 1 0.6420 1.1598 -431.69
## - X3 1 1.0490 1.5668 -401.61
## - X1 1 3.9749 4.4927 -296.27
##
## Step: AIC=-511.69
## Y ~ X1 + X2 + X3 + X4 + X5 + X9
##
## Df Sum of Sq RSS AIC
## - X9 1 0.0093 0.5304 -511.93
## <none> 0.5211 -511.69
## - X5 1 0.0947 0.6159 -496.99
## - X2 1 0.4347 0.9558 -453.04
## - X4 1 0.6868 1.2079 -429.63
## - X3 1 1.0466 1.5677 -403.55
## - X1 1 3.9718 4.4929 -298.27
##
## Step: AIC=-511.93
## Y ~ X1 + X2 + X3 + X4 + X5
##
## Df Sum of Sq RSS AIC
## <none> 0.5304 -511.93
## - X5 1 0.0879 0.6183 -498.59
## - X2 1 0.4289 0.9594 -454.67
## - X4 1 0.6908 1.2212 -430.53
## - X3 1 1.0656 1.5961 -403.76
## - X1 1 3.9627 4.4932 -300.26
reg_back_bic <-step(reg_full, direction="backward", k=log(n))
## Start: AIC=-476.18
## Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 + X10
##
## Df Sum of Sq RSS AIC
## - X10 1 0.00063 0.51583 -480.66
## - X7 1 0.00073 0.51593 -480.64
## - X8 1 0.00153 0.51673 -480.49
## - X6 1 0.00482 0.52002 -479.85
## - X9 1 0.00984 0.52504 -478.89
## <none> 0.51520 -476.18
## - X5 1 0.08810 0.60330 -465.00
## - X2 1 0.41581 0.93102 -421.61
## - X4 1 0.63133 1.14653 -400.79
## - X3 1 0.99872 1.51393 -372.99
## - X1 1 1.43512 1.95032 -347.67
##
## Step: AIC=-480.66
## Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9
##
## Df Sum of Sq RSS AIC
## - X7 1 0.00050 0.51633 -485.17
## - X8 1 0.00149 0.51732 -484.98
## - X6 1 0.00448 0.52031 -484.40
## - X9 1 0.00992 0.52575 -483.36
## <none> 0.51583 -480.66
## - X5 1 0.08769 0.60352 -469.57
## - X2 1 0.41593 0.93176 -426.14
## - X4 1 0.63878 1.15461 -404.69
## - X3 1 1.03375 1.54959 -375.27
## - X1 1 1.52826 2.04409 -347.58
##
## Step: AIC=-485.17
## Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X8 + X9
##
## Df Sum of Sq RSS AIC
## - X8 1 0.0015 0.5178 -489.49
## - X6 1 0.0040 0.5203 -489.01
## - X9 1 0.0096 0.5260 -487.93
## <none> 0.5163 -485.17
## - X5 1 0.0898 0.6061 -473.74
## - X2 1 0.4243 0.9406 -429.79
## - X4 1 0.6384 1.1547 -409.29
## - X3 1 1.0503 1.5666 -378.78
## - X1 1 3.9764 4.4927 -273.43
##
## Step: AIC=-489.49
## Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X9
##
## Df Sum of Sq RSS AIC
## - X6 1 0.0033 0.5211 -493.46
## - X9 1 0.0089 0.5267 -492.40
## <none> 0.5178 -489.49
## - X5 1 0.0885 0.6064 -478.31
## - X2 1 0.4230 0.9408 -434.39
## - X4 1 0.6420 1.1598 -413.46
## - X3 1 1.0490 1.5668 -383.38
## - X1 1 3.9749 4.4927 -278.04
##
## Step: AIC=-493.46
## Y ~ X1 + X2 + X3 + X4 + X5 + X9
##
## Df Sum of Sq RSS AIC
## - X9 1 0.0093 0.5304 -496.30
## <none> 0.5211 -493.46
## - X5 1 0.0947 0.6159 -481.36
## - X2 1 0.4347 0.9558 -437.41
## - X4 1 0.6868 1.2079 -413.99
## - X3 1 1.0466 1.5677 -387.92
## - X1 1 3.9718 4.4929 -282.64
##
## Step: AIC=-496.3
## Y ~ X1 + X2 + X3 + X4 + X5
##
## Df Sum of Sq RSS AIC
## <none> 0.5304 -496.30
## - X5 1 0.0879 0.6183 -485.57
## - X2 1 0.4289 0.9594 -441.64
## - X4 1 0.6908 1.2212 -417.51
## - X3 1 1.0656 1.5961 -390.74
## - X1 1 3.9627 4.4932 -287.24
Forward Selection
reg_forward_start <-lm(Y~1, data=EXEXSAL2)
reg_forward_aic <- step(reg_forward_start,scope=Y~X1+X2+X3+X4+X5+X6+X7+X8+X9+X10, direction="forward" )
## Start: AIC=-268.57
## Y ~ 1
##
## Df Sum of Sq RSS AIC
## + X1 1 4.1364 2.5462 -363.06
## + X7 1 2.6488 4.0338 -317.05
## + X3 1 1.0492 5.6335 -283.64
## + X2 1 0.3264 6.3563 -271.57
## + X4 1 0.2897 6.3930 -271.00
## + X5 1 0.2774 6.4052 -270.81
## <none> 6.6827 -268.57
## + X10 1 0.0201 6.6625 -266.87
## + X8 1 0.0181 6.6646 -266.84
## + X6 1 0.0169 6.6657 -266.82
## + X9 1 0.0002 6.6824 -266.57
##
## Step: AIC=-363.06
## Y ~ X1
##
## Df Sum of Sq RSS AIC
## + X3 1 0.87027 1.6760 -402.88
## + X2 1 0.32522 2.2210 -374.72
## + X4 1 0.31253 2.2337 -374.15
## + X5 1 0.26811 2.2781 -372.18
## <none> 2.5462 -363.06
## + X6 1 0.04591 2.5003 -362.87
## + X10 1 0.04132 2.5049 -362.69
## + X8 1 0.01466 2.5316 -361.63
## + X7 1 0.00843 2.5378 -361.39
## + X9 1 0.00381 2.5424 -361.21
##
## Step: AIC=-402.88
## Y ~ X1 + X3
##
## Df Sum of Sq RSS AIC
## + X4 1 0.60068 1.0753 -445.26
## + X2 1 0.28150 1.3945 -419.27
## + X5 1 0.19195 1.4840 -413.04
## + X6 1 0.10205 1.5739 -407.16
## <none> 1.6760 -402.88
## + X8 1 0.00735 1.6686 -401.32
## + X10 1 0.00137 1.6746 -400.96
## + X9 1 0.00022 1.6757 -400.89
## + X7 1 0.00000 1.6760 -400.88
##
## Step: AIC=-445.26
## Y ~ X1 + X3 + X4
##
## Df Sum of Sq RSS AIC
## + X2 1 0.45697 0.61832 -498.59
## + X5 1 0.11593 0.95936 -454.67
## + X6 1 0.02841 1.04688 -445.94
## <none> 1.07529 -445.26
## + X7 1 0.00623 1.06906 -443.84
## + X8 1 0.00622 1.06907 -443.84
## + X10 1 0.00044 1.07485 -443.30
## + X9 1 0.00003 1.07526 -443.26
##
## Step: AIC=-498.59
## Y ~ X1 + X3 + X4 + X2
##
## Df Sum of Sq RSS AIC
## + X5 1 0.087902 0.53041 -511.93
## <none> 0.61832 -498.59
## + X6 1 0.009688 0.60863 -498.17
## + X9 1 0.002451 0.61587 -496.99
## + X8 1 0.001376 0.61694 -496.82
## + X7 1 0.000343 0.61797 -496.65
## + X10 1 0.000000 0.61832 -496.59
##
## Step: AIC=-511.93
## Y ~ X1 + X3 + X4 + X2 + X5
##
## Df Sum of Sq RSS AIC
## <none> 0.53041 -511.93
## + X9 1 0.0092875 0.52113 -511.69
## + X6 1 0.0037568 0.52666 -510.64
## + X10 1 0.0003588 0.53006 -509.99
## + X8 1 0.0002463 0.53017 -509.97
## + X7 1 0.0000122 0.53040 -509.93
reg_forward_bic <- step(reg_forward_start,scope=Y~X1+X2+X3+X4+X5+X6+X7+X8+X9+X10, direction="forward", k=log(n) )
## Start: AIC=-265.96
## Y ~ 1
##
## Df Sum of Sq RSS AIC
## + X1 1 4.1364 2.5462 -357.85
## + X7 1 2.6488 4.0338 -311.84
## + X3 1 1.0492 5.6335 -278.43
## + X2 1 0.3264 6.3563 -266.36
## <none> 6.6827 -265.96
## + X4 1 0.2897 6.3930 -265.79
## + X5 1 0.2774 6.4052 -265.60
## + X10 1 0.0201 6.6625 -261.66
## + X8 1 0.0181 6.6646 -261.63
## + X6 1 0.0169 6.6657 -261.61
## + X9 1 0.0002 6.6824 -261.36
##
## Step: AIC=-357.85
## Y ~ X1
##
## Df Sum of Sq RSS AIC
## + X3 1 0.87027 1.6760 -395.06
## + X2 1 0.32522 2.2210 -366.91
## + X4 1 0.31253 2.2337 -366.34
## + X5 1 0.26811 2.2781 -364.37
## <none> 2.5462 -357.85
## + X6 1 0.04591 2.5003 -355.06
## + X10 1 0.04132 2.5049 -354.88
## + X8 1 0.01466 2.5316 -353.82
## + X7 1 0.00843 2.5378 -353.57
## + X9 1 0.00381 2.5424 -353.39
##
## Step: AIC=-395.06
## Y ~ X1 + X3
##
## Df Sum of Sq RSS AIC
## + X4 1 0.60068 1.0753 -434.84
## + X2 1 0.28150 1.3945 -408.85
## + X5 1 0.19195 1.4840 -402.62
## + X6 1 0.10205 1.5739 -396.74
## <none> 1.6760 -395.06
## + X8 1 0.00735 1.6686 -390.90
## + X10 1 0.00137 1.6746 -390.54
## + X9 1 0.00022 1.6757 -390.47
## + X7 1 0.00000 1.6760 -390.46
##
## Step: AIC=-434.84
## Y ~ X1 + X3 + X4
##
## Df Sum of Sq RSS AIC
## + X2 1 0.45697 0.61832 -485.57
## + X5 1 0.11593 0.95936 -441.64
## <none> 1.07529 -434.84
## + X6 1 0.02841 1.04688 -432.91
## + X7 1 0.00623 1.06906 -430.81
## + X8 1 0.00622 1.06907 -430.81
## + X10 1 0.00044 1.07485 -430.27
## + X9 1 0.00003 1.07526 -430.23
##
## Step: AIC=-485.57
## Y ~ X1 + X3 + X4 + X2
##
## Df Sum of Sq RSS AIC
## + X5 1 0.087902 0.53041 -496.30
## <none> 0.61832 -485.57
## + X6 1 0.009688 0.60863 -482.54
## + X9 1 0.002451 0.61587 -481.36
## + X8 1 0.001376 0.61694 -481.18
## + X7 1 0.000343 0.61797 -481.02
## + X10 1 0.000000 0.61832 -480.96
##
## Step: AIC=-496.3
## Y ~ X1 + X3 + X4 + X2 + X5
##
## Df Sum of Sq RSS AIC
## <none> 0.53041 -496.30
## + X9 1 0.0092875 0.52113 -493.46
## + X6 1 0.0037568 0.52666 -492.40
## + X10 1 0.0003588 0.53006 -491.76
## + X8 1 0.0002463 0.53017 -491.74
## + X7 1 0.0000122 0.53040 -491.69
Stepwise regression
reg_forward_step <- step(reg_forward_start,scope=Y~X1+X2+X3+X4+X5+X6+X7+X8+X9+X10, direction="both" )
## Start: AIC=-268.57
## Y ~ 1
##
## Df Sum of Sq RSS AIC
## + X1 1 4.1364 2.5462 -363.06
## + X7 1 2.6488 4.0338 -317.05
## + X3 1 1.0492 5.6335 -283.64
## + X2 1 0.3264 6.3563 -271.57
## + X4 1 0.2897 6.3930 -271.00
## + X5 1 0.2774 6.4052 -270.81
## <none> 6.6827 -268.57
## + X10 1 0.0201 6.6625 -266.87
## + X8 1 0.0181 6.6646 -266.84
## + X6 1 0.0169 6.6657 -266.82
## + X9 1 0.0002 6.6824 -266.57
##
## Step: AIC=-363.06
## Y ~ X1
##
## Df Sum of Sq RSS AIC
## + X3 1 0.8703 1.6760 -402.88
## + X2 1 0.3252 2.2210 -374.72
## + X4 1 0.3125 2.2337 -374.15
## + X5 1 0.2681 2.2781 -372.18
## <none> 2.5462 -363.06
## + X6 1 0.0459 2.5003 -362.87
## + X10 1 0.0413 2.5049 -362.69
## + X8 1 0.0147 2.5316 -361.63
## + X7 1 0.0084 2.5378 -361.39
## + X9 1 0.0038 2.5424 -361.21
## - X1 1 4.1364 6.6827 -268.57
##
## Step: AIC=-402.88
## Y ~ X1 + X3
##
## Df Sum of Sq RSS AIC
## + X4 1 0.6007 1.0753 -445.26
## + X2 1 0.2815 1.3945 -419.27
## + X5 1 0.1919 1.4840 -413.04
## + X6 1 0.1021 1.5739 -407.16
## <none> 1.6760 -402.88
## + X8 1 0.0073 1.6686 -401.32
## + X10 1 0.0014 1.6746 -400.96
## + X9 1 0.0002 1.6757 -400.89
## + X7 1 0.0000 1.6760 -400.88
## - X3 1 0.8703 2.5462 -363.06
## - X1 1 3.9575 5.6335 -283.64
##
## Step: AIC=-445.26
## Y ~ X1 + X3 + X4
##
## Df Sum of Sq RSS AIC
## + X2 1 0.4570 0.6183 -498.59
## + X5 1 0.1159 0.9594 -454.67
## + X6 1 0.0284 1.0469 -445.94
## <none> 1.0753 -445.26
## + X7 1 0.0062 1.0691 -443.84
## + X8 1 0.0062 1.0691 -443.84
## + X10 1 0.0004 1.0748 -443.30
## + X9 1 0.0000 1.0753 -443.26
## - X4 1 0.6007 1.6760 -402.88
## - X3 1 1.1584 2.2337 -374.15
## - X1 1 3.9592 5.0345 -292.89
##
## Step: AIC=-498.59
## Y ~ X1 + X3 + X4 + X2
##
## Df Sum of Sq RSS AIC
## + X5 1 0.0879 0.5304 -511.93
## <none> 0.6183 -498.59
## + X6 1 0.0097 0.6086 -498.17
## + X9 1 0.0025 0.6159 -496.99
## + X8 1 0.0014 0.6169 -496.82
## + X7 1 0.0003 0.6180 -496.65
## + X10 1 0.0000 0.6183 -496.59
## - X2 1 0.4570 1.0753 -445.26
## - X4 1 0.7761 1.3945 -419.27
## - X3 1 1.1508 1.7692 -395.47
## - X1 1 3.9635 4.5818 -300.31
##
## Step: AIC=-511.93
## Y ~ X1 + X3 + X4 + X2 + X5
##
## Df Sum of Sq RSS AIC
## <none> 0.5304 -511.93
## + X9 1 0.0093 0.5211 -511.69
## + X6 1 0.0038 0.5267 -510.64
## + X10 1 0.0004 0.5301 -509.99
## + X8 1 0.0002 0.5302 -509.97
## + X7 1 0.0000 0.5304 -509.93
## - X5 1 0.0879 0.6183 -498.59
## - X2 1 0.4289 0.9594 -454.67
## - X4 1 0.6908 1.2212 -430.53
## - X3 1 1.0656 1.5961 -403.76
## - X1 1 3.9627 4.4932 -300.26
summary(reg_forward_step)$adj.r.squared
## [1] 0.9164065
summary(reg_forward_step)$r.squared
## [1] 0.9206284
Exhaustive Search
library(leaps)
## Warning: package 'leaps' was built under R version 4.0.5
reg_all_search <- summary(regsubsets(Y~., data=EXEXSAL2, nvmax=10))
reg_all_search
## Subset selection object
## Call: regsubsets.formula(Y ~ ., data = EXEXSAL2, nvmax = 10)
## 10 Variables (and intercept)
## Forced in Forced out
## X1 FALSE FALSE
## X2 FALSE FALSE
## X3 FALSE FALSE
## X4 FALSE FALSE
## X5 FALSE FALSE
## X6 FALSE FALSE
## X7 FALSE FALSE
## X8 FALSE FALSE
## X9 FALSE FALSE
## X10 FALSE FALSE
## 1 subsets of each size up to 10
## Selection Algorithm: exhaustive
## X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
## 1 ( 1 ) "*" " " " " " " " " " " " " " " " " " "
## 2 ( 1 ) "*" " " "*" " " " " " " " " " " " " " "
## 3 ( 1 ) "*" " " "*" "*" " " " " " " " " " " " "
## 4 ( 1 ) "*" "*" "*" "*" " " " " " " " " " " " "
## 5 ( 1 ) "*" "*" "*" "*" "*" " " " " " " " " " "
## 6 ( 1 ) "*" "*" "*" "*" "*" " " " " " " "*" " "
## 7 ( 1 ) "*" "*" "*" "*" "*" "*" " " " " "*" " "
## 8 ( 1 ) "*" "*" "*" "*" "*" "*" " " "*" "*" " "
## 9 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*" " "
## 10 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*" "*"
names(reg_all_search)
## [1] "which" "rsq" "rss" "adjr2" "cp" "bic" "outmat" "obj"
reg_all_search$which
## (Intercept) X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
## 1 TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 TRUE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 3 TRUE TRUE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## 4 TRUE TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## 5 TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE FALSE
## 6 TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE FALSE TRUE FALSE
## 7 TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE FALSE
## 8 TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE FALSE
## 9 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE
## 10 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
reg_all_search$adjr2
## [1] 0.6150915 0.7440365 0.8340647 0.9035788 0.9164065 0.9169871 0.9166195
## [8] 0.9159429 0.9150913 0.9142424
reg_all_search$rsq
## [1] 0.6189795 0.7492075 0.8390930 0.9074746 0.9206284 0.9220182 0.9225151
## [8] 0.9227354 0.9228103 0.9229048
reg_all_search$cp
## [1] 343.856582 195.519164 93.753768 16.812839 3.627915 4.023513
## [7] 5.449923 7.195556 9.109093 11.000000
reg_all_search$bic
## [1] -87.27986 -124.49741 -164.27219 -215.00141 -225.73045 -222.89179
## [7] -218.92582 -214.60542 -210.09723 -205.61456
reg_all_search$rss
## [1] 2.5462337 1.6759632 1.0752880 0.6183162 0.5304140 0.5211265 0.5178061
## [8] 0.5163336 0.5158331 0.5152016
reg_all_search$outmat
## X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
## 1 ( 1 ) "*" " " " " " " " " " " " " " " " " " "
## 2 ( 1 ) "*" " " "*" " " " " " " " " " " " " " "
## 3 ( 1 ) "*" " " "*" "*" " " " " " " " " " " " "
## 4 ( 1 ) "*" "*" "*" "*" " " " " " " " " " " " "
## 5 ( 1 ) "*" "*" "*" "*" "*" " " " " " " " " " "
## 6 ( 1 ) "*" "*" "*" "*" "*" " " " " " " "*" " "
## 7 ( 1 ) "*" "*" "*" "*" "*" "*" " " " " "*" " "
## 8 ( 1 ) "*" "*" "*" "*" "*" "*" " " "*" "*" " "
## 9 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*" " "
## 10 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*" "*"
reg_all_search$obj
## Subset selection object
## Call: regsubsets.formula(Y ~ ., data = EXEXSAL2, nvmax = 10)
## 10 Variables (and intercept)
## Forced in Forced out
## X1 FALSE FALSE
## X2 FALSE FALSE
## X3 FALSE FALSE
## X4 FALSE FALSE
## X5 FALSE FALSE
## X6 FALSE FALSE
## X7 FALSE FALSE
## X8 FALSE FALSE
## X9 FALSE FALSE
## X10 FALSE FALSE
## 1 subsets of each size up to 10
## Selection Algorithm: exhaustive
reg_aic <- n*log(reg_all_search$rss/n)+2*(1:10)
plot(reg_aic~I(1:10), ylab ="AIC", xlab="p, number of independent variables in the model ", pch=20, col="dodgerblue", type="b", cex=2, main="AIC vs Model Complexity")
