The p-value may be used as an alternative to R2 adj for model selection:
Backward elimination with the p-value approach. In backward elimination, we would iden- tify the predictor corresponding to the largest p-value. If the p-value is above the significance level, usually α = 0.05, then we would drop that variable, refit the model, and repeat the pro- cess. If the largest p-value is less than α = 0.05, then we would not eliminate any predictors and the current model would be our best-fitting model.
Forward selection with the p-value approach. In forward selection with p-values, we reverse the process. We begin with a model that has no predictors, then we fit a model for each possible predictor, identifying the model where the corresponding predictor’s p-value is smallest. If that p-value is smaller than α = 0.05, we add it to the model and repeat the process, considering whether to add more variables one-at-a-time. When none of the remaining predictors can be added to the model and have a p-value less than 0.05, then we stop adding variables and the current model would be our best-fitting model.
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