Example of stepwise regressionmain topic interpreting results session command see also
Example of stepwise regressionStudents in an introductory statistics course participated in a simple experiment. Each student recorded his or her height, weight, gender, smoking preference, usual activity level, and resting pulse. They all flipped coins, and those whose coins came up heads ran in place for one minute. Afterward, the entire class recorded their pulses once more. You wish to find the best predictors for the second pulse rate.
1 Open the worksheet PULSE.MTW.
2 Choose Stat > Regression > Regression > Fit Regression Model.
3 In Responses, enter Pulse2.
4 In Continuous predictors, enter Pulse1 Ran-Weight.
5 Click Stepwise.
6 Under Method, choose Stepwise.
7 Check Display the table of model selection details and choose Include details for each step.
8 Click OK in each dialog box.
Session window output
Regression Analysis: Pulse2 versus Pulse1, Ran, Smokes, Sex, Height, Weight
Stepwise Selection of Terms
Candidate terms: Pulse1, Ran, Smokes, Sex, Height, Weight
----Step 1---- -----Step 2---- -----Step 3---- Coef P Coef P Coef P Constant 10.28 44.48 42.62 Pulse1 0.957 0.000 0.9125 0.000 0.8122 0.000 Ran -19.12 0.000 -20.07 0.000 Sex 7.75 0.000
S 13.5375 9.82193 9.17509 R-sq 37.97% 67.71% 72.14% R-sq(adj) 37.28% 66.98% 71.19% R-sq(pred) 35.12% 65.01% 69.18% Mallows’ Cp 103.22 13.54 1.88
α to enter = 0.15, α to remove = 0.15
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value Regression 3 19182.0 6393.98 75.95 0.000 Pulse1 1 6631.7 6631.66 78.78 0.000 Ran 1 8569.0 8568.95 101.79 0.000 Sex 1 1177.8 1177.80 13.99 0.000 Error 88 7408.0 84.18 Lack-of-Fit 87 7400.0 85.06 10.63 0.240 Pure Error 1 8.0 8.00 Total 91 26590.0
Model Summary
S R-sq R-sq(adj) R-sq(pred) 9.17509 72.14% 71.19% 69.18%
Coefficients
Term Coef SE Coef T-Value P-Value VIF Constant 42.62 7.36 5.79 0.000 Pulse1 0.8122 0.0915 8.88 0.000 1.10 Ran -20.07 1.99 -10.09 0.000 1.02 Sex 7.75 2.07 3.74 0.000 1.11
Regression Equation
Pulse2 = 42.62 + 0.8122 Pulse1 - 20.07 Ran + 7.75 Sex
Fits and Diagnostics for Unusual Observations
Obs Pulse2 Fit Resid Std Resid 10 118.00 92.03 25.97 2.88 R 13 84.00 105.02 -21.02 -2.38 R 16 58.00 80.66 -22.66 -2.52 R 21 106.00 87.15 18.85 2.09 R 23 102.00 83.91 18.09 2.01 R 25 140.00 116.02 23.98 2.73 R 30 112.00 93.28 18.72 2.11 R 35 128.00 103.03 24.97 2.79 R
R Large residual |
This example uses six predictors. In step 1, the variable Pulse1 entered the model. In step 2, the variable Ran entered. Finally, for step 3, the variable Sex entered the model. No variables were removed during any of the steps. At this point, no more variables could enter or leave, so the automatic procedure stopped.
For each model, Minitab displays the constant term, the coefficient
and its p-value for each variable in the model, S
(square root of MSE), and R
,
adjusted R,
predicted R,
and Mallows' Cp.
The stepwise model selection output is designed to present a concise summary of a number of fitted models. This table is followed by the full regression output for the procedure's final model. For this example, the full regression output corresponds to the model in step 3.
If you want more information on interpreting a regression model, see the other regression examples.