Forward Stepwise Regression Output

Here, we will show the output from the model we used to illustrate running a forward stepwise linear regression analysis on the "Perform" page.  The general overview of aspatial regression output also applies to forward stepwise regression, and descriptions of output from "Full model" runs of linear, logistic, and Poisson aspatial regression will also be important pages to review when you run stepwise models.

Summary of the model run

After clicking to the run method page and then selecting "Run", we see the following output in the log view, beginning with the summary of the model run.

Summary of entries and removals from the model

The first data table in output from forward stepwise regression shows the order in which variables entered the model, and related measures of model fit.  See pages on implementation of linear, logistic, and Poisson regression to review the measures shown in the table.  C(p) is described here.

From this table, you can see that five of our seven variables were selected to be in the final model, with per capita income having the highest contribution to model fit (selected first, highest partial R-squared and lowest p-value).  Interestingly, the smoking-related variable did not make it into this model of lung cancer, which shows the importance of scale (level of data aggregation).  The next table (shown below) describes the properties of this "best" model, and this model is the one for which the three output datasets appear in the Data view (in an output folder below the response variable, RWM_LUNG).

Significance of individual model parameters

The next table in the output for forward stepwise regression provides the parameter estimates, standard errors, and p-values for each parameter in the model.  See the implementation page for the particular form of regression that you used (linear, logistic, and Poisson) for a description of how the p-values are derived.  Recall that significance values in regression output are reported as "0.0" if they are smaller than 0.000001, and, as described on the categorical variables in regression analyses page, a parameter is estimated for each level of a categorical variable, except for the level that is chosen as the reference value (we chose "2").

  

To compare this output to output from the other model selection approaches, click here for Best Subset, and here for Backward Stepwise.