Regression Analysis

If there is a correlation between two metric (interval or ratio) variables, this relationship can be used for the prediction of values of one variable (the criterion variable) from values of the other vari able (the predictor variable). Simple linear regression is the prediction of one criterion variable from a single predictor variable. An example would be the prediction of grade point average (GPA) at the end of the freshman year of college from a score on the SAT (formerly called the Scholastic Aptitude Test).

If more than one predictor variable is used, this is referred to as multiple regression. An example would be the use of the variables of SAT score, rank in high school class, average grade on selected high school courses, and high school quality score to predict GPA at the end of the freshman year. In multiple regression, each partial regression coefficient (one for each predictor variable), expresses the relationship between that predictor variable and the criterion variable, controlling for the other predictor variables in the regression equation.

Determination of the best prediction equation is usually based on the criterion of least squares, which involves minimizing the squared deviations of the observed and predicted values of the criterion variable. Once the best regression equation has been determined, it can be used to predict a value on the criterion variable, and confidence intervals can be placed around the predicted criterion score based on an estimate of the standard error of the regression. Most of the time, regression analysis is based on the linear relationships between variables, but curvilinear regression also is possible.