The Multiple Regression Model

The past two chapters have introduced most of the major concepts important to the practice of regression analysis. At this point we'll extend the discussion to consider situations in which a response variable Y has simultaneous linear relationships with more than one independent factor. We have been interpreting RSquare as the fraction of the variation in Y associated with variation in X. We've seen examples where a single factor accounts for most of the variation in Y, but we've also seen examples where one X accounts for a small portion of Y's variation. In such cases, we might want to use multiple regression analysis to investigate additional factors.

Multiple regression substantially expands our ability to build models for variation in Y, by enabling us to incorporate the separate effects of more than one factor, and also by enabling us to examine ways in which factors might interact with one another. The multiple regression model accommodates more than one predictive factor: