forward selection

1. Begin with the null model (\(M_0: y = \bar{y}\)), which contains no predictors.
2. In step 1, fit all \(p\) simple regressions (\(y = \beta_0 + \beta_j x_j\)) and select the predictor that provides the greatest improvement in fit, indicated by the largest reduction in Residual Sum of Squares (RSS).
3. In step \(k\) (where \(k \geq 2\)), based on the current model, evaluate each remaining predictor one at a time and choose the one that yields the most significant improvement in fit.
4. Update the model by incorporating this new predictor and continue to step 3.
5. Terminate the process when no remaining predictor offers a meaningful enhancement.