# Conduct Best Subsets Regression

Conduct Best Subsets Regression##
Minitab^{®}
– Procedure

- Select
**Stat**>>**Regression**>>**Best Subsets...** - In the box labeled
**Response**, specify the response. - In the box labeled
**Free predictors**, specify the predictors that you want considered for the model. (Do not include predictors that you specify in the following**Predictors in all models**box.) - (Optional) In the box labeled
**Predictors in all models**, specify all of the predictors that must be included in every model considered. - 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 a best subsets regression. In doing so, require that the predictor *x*_{2} be included in all models considered.

## Minitab Dialog Box

### Sample Output

### Best Subsets Regression: y versus x1, x3, x4, x2

Response is y

The following variables are included in all models: x2

Vars | R-Sq | Mallows | x | x | x | ||
---|---|---|---|---|---|---|---|

R-Sq(adj) | Cp | S | 1 | 3 | 4 | ||

1 | 97.9 | 97.4 | 2.7 | 2.4063 | x | ||

1 | 84.7 | 81.6 | 62.4 | 6.4455 | x | ||

2 | 98.2 | 97.6 | 3.0 | 2.3087 | x | x | |

2 | 98.2 | 97.6 | 3.0 | 2.3121 | x | x | |

3 | 98.2 | 97.4 | 5.0 | 2.4460 | x | x | x |