ABSTRACT
Multiple regression (MR) has been described as a general data analytic system (e.g., Cohen, 1968) because many commonly used statistical models can be regarded as its special cases. Furthermore, many advanced models have MR as a special case. The ubiquity of MR makes this model one of the most important and widely used statistical methods in social science research. In general, the idea of the MR model is to relate a set of regressor (independent or predictor) variables to a criterion (dependent or outcome) variable, for purposes of explanation and/or prediction, with an equation linear in its parameters. More formally, the MR model is given as
Y i = β
0 + β
1 X
1i + ... + β
k X
ki + ε
i (1)
where β 0 is the population intercept, β
k is the population regression coefficient for the kth regressor (k
= 1, ..., K), X ki
is the kth regressor for the ith individual (i = 1, ..., N), and ε i is the error for the ith indi-
vidual, generally assumed to be normally distributed with mean 0 and population variance σ ε
2. For contemporary treatments of MR applied to a wide variety of examples, we recommend Cohen, Cohen, West, and Aiken (2003), Pedhazur (1997), Harrell (2001), Fox (2008), Rencher and Schaalje (2008), and Muller and Fetterman (2002). Specific desiderata for applied studies that utilize MR are presented in Table 21.1 and explicated subsequently.
