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Chapter 6: One Step Forward and Two Steps Back: Regression Model Selection
Best Subsets Regression: Distance versus Hang, R_Strength . . .
R L
F F
R L 1 1 O
e e
S S x x S
t t i i t
r r b b r
e e i i e
a g g i i g
n t t t t t
g h h y y h
R-Sq(adj)
C-p
Vars R-Sq
S
1
X
67.1
64.1
1.7
Figure 6-5:
1
2.3
16.043
61.8
65.0
X
74.1
13.206
−0.0
78.5
X
2
X
Best
13.294
X
73.8
78.2
X
0.1
2
subsets
74.1
1.3
3
X
X
X
80.6
13.214
procedure Response is Distance Mallows 15.570 H n n 1 1 n 125
X X
13.581
X
79.5
3
1.6
72.7
results for 4 81.4 72.1 3.0 13.724 X X X X
the punt 4 80.7 72.0 3.3 13.977 X X X X
5 81.5 68.2 5.0 14.643 X X X X X
distance
5 81.4 68.2 5.0 14.650 X X X X X
example. 6 81.5 62.9 7.0 15.812 X X X X X X
Looking at the first two rows of Figure 6-5, the top one-variable model is the
one including hang time only. The second-best one-variable model includes
only right foot flexibility. The right foot flexibility model has a lower value of
2
R and a higher Mallow’s C-p than the hang time model, which is why it’s the
second best.
Row three shows that the best two-variable model for estimating punt dis-
tance is the model containing right leg strength and overall leg strength. The
best three-variable model is in row five. It shows that the best three-variable
model includes right foot strength, right foot flexibility, and overall leg
strength. The best four-variable model is found in row seven, and includes
right foot strength, right and left foot flexibility, and overall foot strength.
The best five-variable model is found in row nine and includes every variable
except left foot strength. The only six-variable model is listed in the last row.
2
Choosing the best model by using R adjusted and Mallow’s C-p
Now among the best one-variable, two-variable, three-variable, four-variable,
and five-variable models, which one should you choose for your final multi-
ple regression model? That is, which model is the best of the best? With all