Page 137 - Intermediate Statistics for Dummies

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Part II: Making Predictions by Using Regression
The goal of any model selection procedure is to have the smallest number of
2
x variables in the model as possible, with a high enough value of R adjusted
and a small enough Mallow’s C-p to feel good about it.
Applying forward selection
to punt distances
To get a better feel for the forward selection procedure, you can apply it to the
punt distance example. The researchers turn their data over to your capable
hands for model selection. Using Minitab, you decide to apply the forward
selection procedure to the punt distance data shown in Table 6-1, using an
entry level of α = 0.05. You can now examine your results, shown in Figure 6-2.
In this section, you see the step-by-step process Minitab used to come up
with your results; you also see how to interpret those results in a way your
client researchers will appreciate and understand (which is the goal of all
things data analytical). You also get a heads up on how your choice of entry
level can impact your results.
Stepwise Regression: Distance versus Hang, R_Strength . . .
Forward Selection. Alpha-to-Enter: 0.05
Response is Distance on 6 predictors, with N = 13
Figure 6-2: Step 1
Forward Constant −22.33
selection
Hang 43.5
results for
T-Value 4.73
the punt P-Value 0.001
distance
S 15.6
data with
R-Sq 67.05
entry level
R-Sq(adj) 64.06
0.05.
Mallows C-p 1.7
Breaking down the results
You can see in Figure 6-2 that the procedure you asked Minitab to use is
forward selection (line one) and that you set the α level for entering a new
variable to be 0.05. In line two, you can see the response (y) variable is dis-
tance, and you have six predictor (x) variables to start with, all based on a
sample of N = 13 observations.