I'm running a backwards selection process in R using the step() function and it seems to be dropping variables based on lowest AIC associated with that variable. Is this true, and if so, why does it choose the variable with the lowest AIC? I thought lowest AIC meant better fit, hence I would think it's appropriate to drop the variable with the highest AIC.
> full <- lm(mpg ~ ., data=mtcars)
> null <- lm(mpg ~ 1, data=mtcars)
> step(full, data=mtcars, scope=list(upper = full, lower = null), direction="backward")
Start: AIC=70.9
mpg ~ cyl + disp + hp + drat + wt + qsec + vs + am + gear + carb
Df Sum of Sq RSS AIC
- cyl 1 0.0799 147.57 68.915
- vs 1 0.1601 147.66 68.932
- carb 1 0.4067 147.90 68.986
- gear 1 1.3531 148.85 69.190
- drat 1 1.6270 149.12 69.249
- disp 1 3.9167 151.41 69.736
- hp 1 6.8399 154.33 70.348
- qsec 1 8.8641 156.36 70.765
<none> 147.49 70.898
- am 1 10.5467 158.04 71.108
- wt 1 27.0144 174.51 74.280
Step: AIC=68.92
mpg ~ disp + hp + drat + wt + qsec + vs + am + gear + carb
Df Sum of Sq RSS AIC
- vs 1 0.2685 147.84 66.973
- carb 1 0.5201 148.09 67.028
- gear 1 1.8211 149.40 67.308
- drat 1 1.9826 149.56 67.342
- disp 1 3.9009 151.47 67.750
- hp 1 7.3632 154.94 68.473
<none> 147.57 68.915
- qsec 1 10.0933 157.67 69.032
- am 1 11.8359 159.41 69.384
- wt 1 27.0280 174.60 72.297
Step: AIC=66.97
mpg ~ disp + hp + drat + wt + qsec + am + gear + carb
Df Sum of Sq RSS AIC
- carb 1 0.6855 148.53 65.121
- gear 1 2.1437 149.99 65.434
- drat 1 2.2139 150.06 65.449
- disp 1 3.6467 151.49 65.753
- hp 1 7.1060 154.95 66.475
<none> 147.84 66.973
- am 1 11.5694 159.41 67.384
- qsec 1 15.6830 163.53 68.200
- wt 1 27.3799 175.22 70.410
Step: AIC=65.12
mpg ~ disp + hp + drat + wt + qsec + am + gear
Df Sum of Sq RSS AIC
- gear 1 1.565 150.09 63.457
- drat 1 1.932 150.46 63.535
<none> 148.53 65.121
- disp 1 10.110 158.64 65.229
- am 1 12.323 160.85 65.672
- hp 1 14.826 163.35 66.166
- qsec 1 26.408 174.94 68.358
- wt 1 69.127 217.66 75.350
Step: AIC=63.46
mpg ~ disp + hp + drat + wt + qsec + am
Df Sum of Sq RSS AIC
- drat 1 3.345 153.44 62.162
- disp 1 8.545 158.64 63.229
<none> 150.09 63.457
- hp 1 13.285 163.38 64.171
- am 1 20.036 170.13 65.466
- qsec 1 25.574 175.67 66.491
- wt 1 67.572 217.66 73.351
Step: AIC=62.16
mpg ~ disp + hp + wt + qsec + am
Df Sum of Sq RSS AIC
- disp 1 6.629 160.07 61.515
<none> 153.44 62.162
- hp 1 12.572 166.01 62.682
- qsec 1 26.470 179.91 65.255
- am 1 32.198 185.63 66.258
- wt 1 69.043 222.48 72.051
Step: AIC=61.52
mpg ~ hp + wt + qsec + am
Df Sum of Sq RSS AIC
- hp 1 9.219 169.29 61.307
<none> 160.07 61.515
- qsec 1 20.225 180.29 63.323
- am 1 25.993 186.06 64.331
- wt 1 78.494 238.56 72.284
Step: AIC=61.31
mpg ~ wt + qsec + am
Df Sum of Sq RSS AIC
<none> 169.29 61.307
- am 1 26.178 195.46 63.908
- qsec 1 109.034 278.32 75.217
- wt 1 183.347 352.63 82.790
Call:
lm(formula = mpg ~ wt + qsec + am, data = mtcars)
Coefficients:
(Intercept) wt qsec am
9.618 -3.917 1.226 2.936
