Multiple Regression: Standardized and Raw Coefficients

Applying Ordinary Least Squares Regression

Forms of regression (simple linear and multiple) are among the most commonly used statistical techniques in communication research and the social sciences. This is illustrated by the following example. A researcher may be interested in understanding how income, exposure to television violence, and number of friends predict antisocial tendencies. In this particular case, there are three independent variables (income, exposure to violence, and number of friends) that are theorized to influence or predict the dependent variable (antisocial tendencies). To answer this question, a researcher could collect data using survey techniques. Once the data has been collected, the next logical step is to analyze and interpret the data. In this example, OLS multiple regression can be employed to understand the relationship between these variables. In OLS multiple regression, the relationship between the set of predictor (independent) variables and the dependent variable is expressed in terms of the following mathematical formula:

$$Y_i=\mathrm{a}+b_1{X}_{1i}+b_2{X}_{2i}+b_3{X}_{3i}+e_i.$$

Looking at this formula, Y represents the dependent variable (antisocial tendencies) and each X case represents each predictor or independent variable (income, exposure to violence, and number of friends). The regression constant is represented by a and error is denoted by e. Each b represents the “beta” weight for each predictor variable. Even though the above equation reflects one dependent variable and three predictor variables, it is important to remember that multiple regression equations can include more than three predictor variables. In any regression model that contains multiple variables, the relative influence of one predictor variable is computed in light of the other predictor variables that are held constant in the model. In other words, each predictor variable and its relative influence on the dependent variable represents a combination of unique, shared, and error variance.[Page 1054] While it is important to understand the mathematical formula behind the statistical test that is used, in practice, most people conduct their statistical tests with software and focus on interpreting the output.

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