# Conduct Stepwise Regression

Conduct Stepwise Regression##
Minitab^{®}
– Procedure

- Select
**Stat**>>**Regression**>>**Regression**>>**Fit Regression Model...** - In the box labeled
**Response**, specify the response. - In the box labeled
**Continuous Predictors**, specify all the predictors that you want to be considered for the model. - Click on the Stepwise button.
- Choose 'Stepwise' from among the Method pull-down options.
- (Optional) Use the buttons below the box labeled
**Potential terms**to indicate**terms to include in every model**, specify all of the predictors that must be included in every model considered. - (Optional) Specify the
**Alpha to enter**and**Alpha to remove**significance levels. The default for both is 0.15. - Check the box labeled 'Display the table of model selection details using the pull-down to select '
**Include details for each step**'. - Select
**OK**. - Select
**OK**. The output will appear in the session window.

##
Example

Researchers were interested in learning how the composition of cement affected the heat evolved during the hardening of the cement. Therefore, they measured and recorded the following data (cement.txt) on 13 batches of cement:

- Response
*y*: heat evolved in calories during hardening of cement on a per gram basis - Predictor
*x*_{1}: % of tricalcium aluminate - Predictor
*x*_{2}: % of tricalcium silicate - Predictor
*x*_{3}: % of tetracalcium alumino ferrite - Predictor
*x*_{4}: % of dicalcium silicate

Perform stepwise regression on the data set. Let *α*_{E} = *α*_{R} = 0.15. In doing so, require that the predictor *x*_{2} be included in all models considered.

## Minitab Dialog Boxes

### Sample Output

### Regression analysis: y versus x1, x2, x3, x4

Stepwise Selection of Terms

Candidate terms: x1, x2, x3, x4

Terms | --------Step 1-------- | --------Step 2-------- | ||
---|---|---|---|---|

Coef | P | Coef | P | |

Constant | 57.42 | 52.58 | ||

x2 | 0.789 | 0.001 | 0.6623 | 0.000 |

x1 | 1.468 | 0.000 | ||

S | 9.07713 | 2.40634 | ||

R-sq | 66.63% | 97.87% | ||

R-sq(adj) | 63.59% | 97.44% | ||

R-sq(pred) | 55.74% | 96.54% | ||

Mallows' Cp | 142.49 | 2.68 |

\(\alpha\) to enter = 0.15, \(\alpha\) to remove = 0.15 At your request, the stepwise procedure included these terms in every module: x2