###### G. Multiple Regression

# About Multiple Regression

The other statistical tests included in these lessons focus on a comparison of two factors - yet most questions we want to examine in the social world involve the influence of many factors. For example, say we are interested in learning about the effectiveness of a program to help high school students get into college. To evaluate the program, we want a statistical tool to determine whether students who were involved in the program were more likely to get to college than those who were not. However, there are many factors beyond participation in a program that influence the likelihood of a student attending college: high school grades, career aspirations, family income, and parental education level are all likely to have some influence as well. What would help assess the effectiveness of the program is a tool that would somehow account for these factors in examining the program's effects.

Multiple regression is such a tool. Multiple regression (or, more generally, "regression") allows researchers to examine the effect of many different factors on some outcome at the same time. The general purpose of multiple regression is to learn more about the relationship between several independent or predictor variables and a dependent variable. For some kinds of research questions, regression can be used to examine how much a particular set of predictors explains differences in some outcome. In other cases, regression is used to examine the effect of some specific factor while accounting for other factors that influence the outcome.

In this latter use of regression analysis, the researcher uses algebraic methods to "hold constant" a group of factors involved in some social phenomenon except one, in order to see how much of the net result that one factor accounts for. In the example of the college program for high school students, we could use regression to examine the effects of the program while accounting for differences in grades, aspirations, income and parental education level that might also influence college attendance. By mathematically holding constant all factors but one at a time, the researcher can measure the part a particular factor played in some outcome.