# Multiple Regression

The problem with bivariate regression—indeed, with all bivariate hypothesis tests—is that social phenomena are usually the product of many factors, not just one. There is not just one single reason why a person commits a crime, a police officer uses excessive force, or a prison experiences a riot or other major disturbance. Bivariate analyses risk overlooking variables that might be important predictors of the DV. For instance, in the bivariate context, we could test for whether having a parent incarcerated increases an individual’s propensity for crime commission. This is probably a significant factor, but it is certainly not the only one. We can add other factors, such as having experienced violence as a child, suffering from a substance-abuse disorder, and being unemployed, too. Each of these IVs might help improve our ability to understand (i.e., predict) a person’s involvement in crime. The use of only one IV virtually guarantees that important predictors have been erroneously excluded and that the results of the analysis are therefore suspect, and it prevents us from conducting comprehensive, in-depth examinations of social phenomena.

Multiple regression is the answer to this problem. Multiple regression is an extension of bivariate regression and takes the form

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Revisit Formula 14(1) and compare it to Formula 14(9) to see how 14(9) expands on the original equation by including multiple IVs instead of just one. The subscripts show that each IV has its own slope coefficient. With k IVs in a given study, ŷ is the sum of each bkxk term and the intercept.

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