Stepwise Regression
F-to-Enter: 4.00 F-to-Remove: 4.00
Response is mpg on 7 predictors, with N = 392
Step 1 2 3
Constant 46.22 -14.35 -18.05
weight -0.00765 -0.00663 -0.00599
T-Value -29.65 -30.91 -23.59
year 0.757 0.757
T-Value 15.31 15.67
origin 1.15
T-Value 4.44
S 4.33 3.43 3.35
R-Sq 69.26 80.82 81.75
The only three variables entered by the method are
weight, year, and origin. Of course,
origin doesn't make much sense (see description
in Section 2.1). We recoded it into two variables
as described in Section 2.1 and reran the stepwise
procedure:
Stepwise Regression
F-to-Enter: 4.00 F-to-Remove: 4.00
Response is mpg on 8 predictors, with N = 392
Step 1 2 3 4
Constant 46.22 -14.35 -14.68 -18.31
weight -0.00765 -0.00663 -0.00635 -0.00589
T-Value -29.65 -30.91 -27.20 -22.65
year 0.757 0.747 0.770
T-Value 15.31 15.20 15.82
japan 1.39 2.21
T-Value 2.89 4.27
euro 1.98
T-Value 3.82
S 4.33 3.43 3.40 3.34
R-Sq 69.26 80.82 81.22 81.90
Now both coded values of the origin variable
enter.
It might be a little surprising that year enters in as a predictor variable, second only to weight, which makes sense. Those of you familiar with ancient history know that the years 1974-1982 were marked with huge increases in petroleum prices forcing consumers and car manufacturers to become more fuel efficient.
Interestingly, after dropping the variables cylinder and acc, and taking the random subset of test data out, Stepwise selected all variables remaining:
Stepwise Regression
F-to-Enter: 4.00 F-to-Remove: 4.00
Response is mpg on 6 predictors, with N = 329
Step 1 2 3 4 5 6
Constant 46.93 -13.72 -14.21 -17.12 -18.73 -16.40
weight -0.00785 -0.00683 -0.00657 -0.00615 -0.00746 -0.00717
T-Value -27.21 -28.49 -24.86 -21.42 -11.80 -11.13
year 0.757 0.750 0.766 0.803 0.777
T-Value 13.97 13.90 14.37 14.53 13.79
japan 1.19 1.97 2.27 2.62
T-Value 2.29 3.54 4.00 4.44
euro 2.01 2.57 2.80
T-Value 3.47 4.12 4.44
displace 0.0132 0.0195
T-Value 2.32 3.04
hp -0.025
T-Value -2.08
S 4.39 3.48 3.46 3.40 3.38 3.36
R-Sq 69.37 80.84 81.14 81.81 82.11 82.35