In this chapter we introduce the statistical technique of regression analysis. This form of statistical study is more complex than the treatment given here would suggest: excluded are multiple and non-linear regression. Indeed, many second-year statistical courses will cover regression analysis only. As presented here, however, regression techniques will be found to be applicable to many research situations in the social sciences.

Regression analysis is applied to numerical data, usually continuous, although discontinuous data are also amenable to regression. The design of the analysis presents a departure from what we have covered in previous chapters: instead of comparing two or more samples, regression focuses on the relation between two variables. Moreover, there is a stated interest in explaining the behavior of the dependent variable according to the independent variable (in multiple regression, there are several independent variables). As you recall, the dependent or response variable (usually referred to as Y) is the one whose behavior we wish to understand and predict. The independent or predictor variable (usually referred to as X) is the one we use to understand and explain the behavior of the Y. The researcher manipulates or controls the independent variable, in order to observe the response of the dependent one. Thus, the main distinction between the X and Y is that the former can be controlled, or at least measured without error, by the researcher. The latter is free to vary, and is simply recorded (not manipulated).