Example 2: Stepwise
Data File. This
example is based on the examples data file Job_prof.sta
(from Neter, Wasserman, and Kutner, 1989, page 473). Open this data file
by selecting Open
Examples from the File menu (classic
menus) or by selecting Open Examples
from the Open menu on the Home tab (ribbon
bar); it is in the Datasets
folder. The first four variables
represent four different aptitude tests that were administered to each
of the 25 applicants for entry-level clerical positions in a company.
Regardless of their test scores, all 25 applicants were hired. Once their
probationary period had expired, each of these employees was evaluated
and given a job proficiency rating (variable Job_prof).
Using stepwise regression, the variables (or subset of variables) that
best predict job proficiency will be analyzed. Thus, the dependent variable
will be Job_prof and variables
will be the independent or predictor variables.
Starting the analysis.
Select Multiple Regression from the Statistics menu. In the Multiple Linear Regression Startup Panel,
click the Variables button and
specify variable Job_prof as
the Dependent variable and variables
from the Independent variable list;
then click the OK button. Next
click the Advanced tab, and select the Advanced options (stepwise or ridge regression)
check box. Then click the OK
button to display the Model Definition dialog box.
Specifying the Stepwise
Regression. You can choose to analyze the data using a Standard,
Forward stepwise, or Backward
stepwise regression method. The popular Forward
stepwise method evaluates the independent variables at each step,
adding or deleting them from the model based on user-specified criteria
(for more information, see Neter, Wasserman, and Kutner, 1989, and Regression
Notes). Therefore, the forward stepwise regression will be used to
analyze the data for this example.
On the Model Definition dialog
box - Quick tab, click
the Method drop-down box and
select Forward stepwise. Next,
on the Stepwise tab you can change the
F to enter and F
to remove values; however, for this example, accept the default
values of 1 and 0,
respectively. In order to view the results at each step of the analysis,
select At each step in the Display results drop-down box.
Now, accept all other defaults in this dialog box and click the OK button to begin the forward stepwise
Step 0. First,
dialog box will be displayed for step 0, when no variables have been entered
in the model.
Step 1. Click
the Next button to proceed to
the next step in the analysis. In the first step, each of the independent
variables are evaluated individually and the variable that has the largest
F value greater than or equal
to the F to enter value is entered
into the regression equation.
Here, variable Test3 met the
F to enter criteria (F>1.
0) and was added to the model. Select the Advanced tab, and then click the
Stepwise regression summary button
to produce a spreadsheet with a summary of the steps so far in the analysis.
Click the Next button in the
Regression Results dialog box to proceed to the next step.
Step 2. Now,
in subsequent steps when a variable is added to the model (based on the
F to enter criteria), the forward
stepwise regression method will examine the variables included in the
model, and, based on the F to remove
criteria, will determine whether any variables already in the model should
be removed. In the second step, variable Test1
is entered into the model. Clicking the Stepwise
regression summary button will produce the following results spreadsheet.
Once again, click the Next
button in the Multiple
Regression Results dialog box to proceed to step 3 in the forward
Step 3 (Final Solution).
There are two variables remaining to evaluate (Test2
and Test4). For this step, the
largest F value was given by
Test4, therefore, it was added
to the model. When Test2 was
evaluated, the F value was less
than the F to enter value of
1.0, therefore, it was not entered
into the model.
The Stepwise regression summary
results spreadsheet now summarizes the variables that were entered into
and kept in the model.
Now, according to the Forward stepwise
regression procedure, the subset of aptitude tests (independent
variables) that best predicts the job proficiency score (dependent variable)
contains Test3, Test1,
and Test4. Therefore, the regression
equation appears as follows:
y = B0 +
To obtain the regression coefficients from the regression summary spreadsheet,
click the Summary: Regression results
The final regression equation is:
y = -124.200 + 1.357*X3
+ 0. 296*X1 + 0. 517*X4