ABSTRACT
This chapter examines this problem in two important situations, partial correlation and multiple regression. A common problem in multiple regression analysis is to evaluate the effects of one or more predictors in the context of another predictor or set of predictors. These tests are important for several reasons. One reason is practical. Sometimes one has an equation based on one set of predictors and wishes to see whether a second predictor improves ones ability to predict the outcome variable. If so, then one can profitably use the larger equation; if not, then the simpler equation is better. Another reason is theoretical. Suppose that one believes that the relationship between several predictor variables and an outcome variable is obscured by their association with another set of variables. A better picture of the obscured relationship is obtained if one removes the effects of the obscuring set. The intent here is like that underlying partial correlation, but set in a predictor-outcome context.
