Multiple Regression analysis: correlating more than two variables

Multiple Regression or Multiple Correlation is a mulivariate statistical analysis that you undertake when you correlate more than two variables. This technique can be used for prediction purposes and has been frequently used to predict college freshmen Grade Point Averages (GPA) with both forms of the SAT (Math and Verbal) and High School Rank in Class (RIC). The formula below shows the prediction equation with the three predictors [x¹ x² and x³ ] and what is predicted [y].

[ x¹(HS GPA) + x² (SATM) + x³ (SATV) + constant = ŷ( College GPA)]

There are two conditions that should exist when you use this multivariate technique.

1. The variables that you are using to predict with should have a low correlation with each other. In this case, HSGPA, SATV and SATM should have low inter-correlations. They are called the predictors.

2. The predictor variables, however, should have a high correlation with the variable that they are trying to predict – in this case College GPA. This is called the criterion variable.

When predictors are entered into a multiple regression equation in a preplanned sequence, it is called a stepwise regression analysis. There must be a theoretical rationale for this and not a random nature.

Return from multiple regression analysis to statistical tests.