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Forward information criteria procedure
- The procedure does not find an improvement in the criterion for 8 consecutive steps.
- The procedure fits the full model.
- The procedure fits a model that leaves 1 degree of freedom for error.
Forward selection procedure
A method for determining which terms to retain in a model. Forward selection adds variables to the model using the same method as the stepwise procedure. Once added, a variable is never removed. The default forward selection procedure ends when none of the candidate variables have a p-value smaller than the value specified in Alpha to enter.
Backward elimination procedure
A method for determining which variables to retain in a model. Backward elimination starts with the model that contains all the terms and then removes terms, one at a time, using the same method as the stepwise procedure. No variable can re-enter the model. The default backward elimination procedure ends when none of the variables included in the model have a p-value greater than the value specified in Alpha to remove.
If the initial model uses all of the degrees of freedom, the analysis for factorial designs does not stop as other analyses in Minitab do. Instead, with Analyze Factorial Design and Analyze Variability, Minitab removes ¼ of the terms to obtain sufficient degrees of freedom to begin. The number of terms to remove is rounded to the nearest integer and has a maximum of 9. From the saturated model, Minitab removes the terms with the smallest adjusted sums of squares while maintaining model hierarchy. Minitab does not reconsider these terms at later steps. The table of model selection details lists the terms that Minitab removed.
Stepwise method
Performs variable selection by adding or deleting predictors from the existing model based on the F-test. Stepwise is a combination of forward selection and backward elimination procedures.
If the initial model uses all of the degrees of freedom, the analysis for factorial designs does not stop as other analyses in Minitab do. Instead, with Analyze Factorial Design and Analyze Variability, Minitab removes ¼ of the terms to obtain sufficient degrees of freedom to begin. The number of terms to remove is rounded to the nearest integer and has a maximum of 9. From the saturated model, Minitab removes the terms with the smallest adjusted sums of squares while maintaining model hierarchy. Minitab does not reconsider these terms at later steps. The table of model selection details lists the terms that Minitab removed.
Variables to remove
Minitab calculates an F-statistic and p-value for each variable in the model. If the model contains j variables, then F for any variable, xr , is this formula:
Notation
| Term | Description |
|---|---|
| SSE(j – Xr ) | SS Error for the model that does not contain xr |
| SSE j | SS Error for the model that contains xr |
| MSE j | MS Error for the model that contains xr |
If the p-value for any variable is greater than the value specified in Alpha to remove, then Minitab removes the variable with the largest p-value from the model, calculates the regression equation, displays the results, and initiates the next step.
Variables to add
If Minitab cannot remove a variable, the procedure attempts to add a variable. Minitab calculates an F-statistic and p-value for each variable that is not in the model. If the model contains j variables, then F for any variable, xa, is this formula:
Notation
| Term | Description |
|---|---|
| SSE j | SS Error before xa is added to the model |
| SSE(j + Xa ) | SS Error after xa is added to the model |
 | Degrees of freedom for variable Xa |
| MSE(j + Xa ) | MS Error after xa is added to the model |
If the p-value corresponding to the F-statistic for any variable is smaller than the value specified in Alpha to enter, Minitab adds the variable with the smallest p-value to the model, calculates the regression equation, displays the results, then goes to a new step. When no more variables can be entered into or removed from the model, the stepwise procedure ends.
