df <- mtcars
library(MASS)
kitchen_sink <-
lm(data = df,
formula = mpg ~ .)
plot(kitchen_sink)
?stepAIC
stepAIC(object = kitchen_sink, 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 = df)
Coefficients:
(Intercept) wt qsec am
9.618 -3.917 1.226 2.936
final_model <- lm(data = df,
formula = mpg ~ wt + qsec + am
)
summary(final_model)
Call:
lm(formula = mpg ~ wt + qsec + am, data = df)
Residuals:
Min 1Q Median 3Q Max
-3.4811 -1.5555 -0.7257 1.4110 4.6610
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.6178 6.9596 1.382 0.177915
wt -3.9165 0.7112 -5.507 6.95e-06 ***
qsec 1.2259 0.2887 4.247 0.000216 ***
am 2.9358 1.4109 2.081 0.046716 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2.459 on 28 degrees of freedom
Multiple R-squared: 0.8497, Adjusted R-squared: 0.8336
F-statistic: 52.75 on 3 and 28 DF, p-value: 1.21e-11
