# Methods and formulas for stepwise in Analyze Definitive Screening Design

## 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. Backward elimination does not proceed if the initial model uses all of the degrees of freedom.

## 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. Stepwise selection does not proceed if the initial model uses all of the degrees of freedom.

### 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

TermDescription
SSE(jXr ) 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.

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

TermDescription
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.

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