Specify the options for the stepwise regression analysis of your response surface design.

Stepwise removes and adds terms to the model for the purpose of identifying a useful subset of the terms. If you choose a stepwise procedure, the terms that you specify in the Terms sub-dialog box are candidates for the final model. For more information, go to Using stepwise regression and best subsets regression.

Specify the method that Minitab uses to fit the model.
###### Note

- None: Fit the model with all of the terms that you specify in the Terms sub-dialog box.
- Forward information
criteria: 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. 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.

- Stepwise: This method starts with an empty model, or includes the terms you specified to include in the initial model or in every model. Then, Minitab adds or removes a term for each step. You can specify terms to include in the initial model or to force into every model. Minitab stops when all variables that are not in the model have p-values that are greater than the specified Alpha to enter value, and when all variables in the model have p-values that are less than or equal to the specified Alpha to remove value.
- Forward selection: This method starts with an empty model, or includes the terms you specified to include in the initial model or in every model. Then, Minitab adds the most significant term for each step. Minitab stops when all variables that are not in the model have p-values that are greater than the specified Alpha to enter value.
- Backward elimination: This method starts with all potential terms in the model and removes the least significant term for each step. Minitab stops when all variables in the model have p-values that are less than or equal to the specified Alpha to remove value.

The terms that are included in the final model can depend on hierarchy restrictions for models. For more information, see the topic on Hierarchy below.

Displays the set of terms that the procedure will assess. Indicators (E or I) next to the term in the list signify how the procedure handles the term. The Method you choose determines the initial settings in this list. You can modify how the procedure handles the terms with the two buttons below. If you don't use these buttons, the procedure can add or remove the term from the model based on its p-value.

- E = Include term in every model: Select a term and click this button to force the term into every model regardless of its p-value. Click the button again to remove this condition.
- I = Include term in the initial model: Select a term and click this button to include the term in the initial model. The procedure can remove these terms if its p-value is too high. Click the button again to remove this condition. This button is only available if you choose Stepwise in Method.

Specify which information criterion to use in forward selection.

Both AICc and BIC assess the likelihood of the model and then apply a penalty for adding terms to the model. The penalty reduces the tendency to overfit the model to the sample data. This reduction can yield a model that performs better in general.

As a general guideline, when the number of parameters is small relative to the sample size, BIC has a larger penalty for the addition of each parameter than AICc. In these cases, the model that minimizes BIC tends to be smaller than the model that minimizes AICc.

In some common cases, such as screening designs, the number of parameters is usually large relative to the sample size. In these cases, the model that minimizes AICc tends to be smaller than the model that minimizes BIC. For example, for a 13-run definitive screening design, the model that minimizes AICc will tend to be smaller than the model that minimizes BIC among the set of models with 6 or more parameters.

For more information on AICc and BIC, see Burnham and Anderson.^{1}

- Alpha to enter
- Enter the alpha value that Minitab uses to determine whether a term can be entered into the model. You can set this value when you choose Stepwise or Forward selection in Method.
- Alpha to remove
- Enter the alpha value that Minitab uses to determine whether a term is removed from the model. You can set this value when you choose the Stepwise or Backward elimination in Method.

You can determine how Minitab enforces model hierarchy during a stepwise procedure. The Hierarchy button is disabled if you specify a non-hierarchical model in the Terms sub-dialog box.

In a hierarchical model, all lower-order terms that comprise the higher-order terms also appear in the model. For example, a model that includes the interaction term A*B*C must also include the terms: A, B, C, A*B, A*C, and B*C to be hierarchical.

Response surface models must be hierarchical if you want to produce an equation in uncoded units. However, weigh that consideration against the fact that models that contain too many terms can be relatively imprecise and can reduce the ability to predict the values of new observations.

Consider the following tips:

- Fit a hierarchical model first. You can remove insignificant terms later.
- If your model contains categorical variables, the results are easier to interpret if the categorical terms, at least, are hierarchical.

- Hierarchical model
- Choose whether the stepwise procedure must produce a hierarchical model.
- Require a hierarchical model at each step: Minitab can only add or remove terms that maintain hierarchy.
- Add terms at the end to make the model hierarchical: Initially, Minitab follows the standard rules of the stepwise procedure. At the final step, Minitab adds the terms that produce a hierarchical model, even if their p-values are greater than the Alpha to enter value. If you select this option when the Method is Forward information criteria, Minitab displays an error. To get a hierarchical model that minimizes the criterion among the models in the steps, select Require a hierarchical model at each step.
- Do not require a hierarchical model: The final model can be non-hierarchical. Minitab will add and remove terms based only on the rules of the stepwise procedure.

- Require hierarchy for the following terms
- If you require a hierarchical model, choose the types of terms that must be hierarchical.
- All terms: Terms that include continuous and/or categorical variables must be hierarchical.
- Terms with categorical predictors: Only terms that include categorical variables must be hierarchical.

- How many terms can enter at each step
- If you require hierarchy at each step, choose the number of terms that Minitab can add at each step in order to maintain hierarchy.
- At most one term can enter at each step: A higher-order term can enter the model only if hierarchy is maintained when adding that single term. All lower-order terms that comprise the higher-order must already be in the model.
- Extra terms can enter to maintain hierarchy: A higher-order term can enter the model even if it produces a non-hierarchical model. However, the terms that are necessary to produce a hierarchical model are also added, even if their p-values are greater than the Alpha to enter value.

Specify the information to display about the stepwise procedure.

- Details about the method: Display the type of stepwise procedure and the alpha values to enter and/or remove a predictor from the model.
- Include details for each step: Display the coefficients, p-values, and model summary statistics for each step of the procedure.