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Chapter 6: One Step Forward and Two Steps Back: Regression Model Selection
at each step. Note that each type of model selection procedure can produce a
different final model, which is normal. After all, if all the techniques led you
to the same result, why bother having more than one technique?
Using the punt distance data presented in Table 6-1, imagine that you ana-
lyzed the data by using the backward selection procedure with level of
removal α = 0.10. I show your results in Figure 6-4. Each stage in the model
selection process is represented by a column in the results.
Examining the x variables: The Step 1 column
The Step 1 column of Figure 6-4 shows all the x variables in the model.
Looking at the p-values in that first column, you can see that the largest one
turns out to be 0.953. This p-value is associated with the left leg strength vari-
able. (Check out the next section on the Step 2 column to find out what hap-
pens to this variable.)
Stepwise Regression: Distance versus Hang, R_Strength . . . 121
Backward elimination. Alpha-to-Remove: 0.1
Response is Distance on 6 predictors, with N = 13
Step 1 2 3 4 5
Constant −31.26 −33.29 −33.30 −35.25 12.77
Hang 3 4
T-Value 0.10 0.16
P-Value 0.927 0.874
R_Strength 0.28 0.29 0.33 0.39 0.56
T-Value 0.56 0.78 1.08 1.46 2.64
P-Value 0.596 0.461 0.310 0.178 0.025
L_Strength 0.04
T-Value 0.06
P-Value 0.953
R_Flexibility 1.24 1.28 1.34 0.86
T-Value 0.79 0.96 1.10 0.99
P-Value 0.457 0.371 0.303 0.346
L_Flexibility −0.41 −0.42 −0.41
T-Value −0.50 −0.57 −0.59
Figure 6-4: P-Value 0.634 0.588 0.574
Backward O_Strength 0.21 0.21 0.22 0.22 0.27
selection T-Value 1.21 1.50 1.87 2.00 2.71
procedure P-Value 0.271 0.177 0.098 0.077 0.022
for S 15.8 14.6 13.7 13.2 13.2
estimating R-Sq 81.47 81.45 81.38 80.58 78.45
punt R-Sq(adj) 62.93 68.21 72.07 74.11 74.14
distance. Mallows C-p 7.0 5.0 3.0 1.3 −0.0