# Methods and formulas for stepwise in Analyze Binary Response for Response Surface Design

## Forward information criteria procedure

A method for determining which variables to retain in a model. The forward information criteria procedure adds the term with the lowest p-value to the model at each step. Additional terms can enter the model in 1 step if the settings for the analysis allow consideration of non-hierarchical terms but require each model to be hierarchical. Minitab calculates the information criteria for each step. Minitab displays the results of the analysis for the model with the minimum value of the selected information criterion, either AICc or BIC. In most cases, the procedure continues until one of the following conditions occurs:
• The procedure does not find a new minimum of 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.
If you specify settings for the procedure that require a hierarchical model at each step and allow only one term to enter at a time, then the procedure continues until it either fits the full model or fits a model that leaves 1 degree of freedom for error. Minitab displays the results of the analysis for the model with the minimum value of the selected information criterion, either AICc or BIC.

## 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.

## Stepwise method

Performs variable selection by adding or deleting predictors from the existing model based on a chi-square test. Stepwise is a combination of forward selection and backward elimination procedures.

Go to Analysis of Deviance for the calculations of chi-square statistics for a term.

### Variables to remove

Minitab calculates a chi-square statistic and p-value for each variable in the model.

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.