In Minitab’s best-subsets regression, which criterion is used to determine the best regression equations?

In Minitab’s best-subsets regression, the best regression equations are typically determined using the Adjusted R² criterion. Adjusted R² is an essential measure in regression analysis because it accounts for the number of predictors in the model and adjusts the R² value accordingly, giving a more accurate representation of the model's explanatory power when comparing models with different numbers of predictors. This helps in avoiding the overfitting problem that can occur when simply using R², as R² always increases with the addition of more predictors, regardless of whether they contribute meaningfully to the model.

While R² itself measures the proportion of variance in the dependent variable that can be explained by the independent variables, it does not penalize for the addition of unnecessary predictors. Thus, in the context of best-subsets regression, the focus is on finding the model that achieves a good balance between complexity and explanatory power, which is where adjusted R² prevails.

The other measures, such as p-value, AIC, and R², also provide valuable information but do not serve as the primary criterion for determining the best subset in this specific context. Adjusted R² is preferred as it better reflects the real-world performance of the model when making predictions or interpretations based