Multiple Regression

Multiple regression is a prediction equation that determines the correlation between a combination of two or more predictor variables and a criterion variable. For example, we might use undergraduate GPA, graduate GPA, and GRE scores (verbal, quantitative, and analytical) to predict success in graduate school. Multiple regression is one of the most widely used statistical techniques in the social sciences, because of its versatility and precision. It can be used to analyze data from any of the major quantitative research designs: experimental, causal-comparative, and correlational. It can handle nominal, ordinal, interval, and ratio data. And it provides not only the relationship between variables but also the magnitude of the relationships.

Example

The use of multiple regression is illustrated in a relationship study conducted by Lunenburg and Columba (1992). The purpose of their study was to identify personality factors and education level that distinguish high performing urban principals from average performing urban principals (n = 179). Four independent criteria were used to measure principal performance (dependent variable): supervisor’s ratings, paired comparison ratings, peer nomination ratings, and teacher ratings, resulting in an overall performance score. Sixteen personality factors (measured by the 16PF) and education level (master’s or doctorate) were the predictors (independent variables). Stepwise multiple regression analysis revealed that factors E (dominant), M (imaginative), Q2 (self-sufficient), A (warm), and doctoral education level were consistent predictors of superior performance of urban principals (see Table 4.3). Because multiple regression is one of the most widely used statistical techniques in the social sciences, we will explain the procedure in some detail using the example as a model.

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