ABSTRACT
Stepwise regression starts by finding the one independent variable of the set that, by itself, explains the greatest amount of variability in the dependent variable. Given a large set of independent variables, stepwise regression is a very handy way to find a subset of independent variables that together predict the dependent variable. One way to approach the problem is to use polynomial regression—that is, use a polynomial in the independent variables as the model. The reason we need to be concerned about the validity of the assumptions of independence, normality, and homogeneity is that violations of the assumptions can lead us to make incorrect inferences about the parameters of the regression model. The idea of weighted least squares is to weight the observations in inverse proportion to their variance. Information on weighted least squares can be found in more advanced books on regression.
