OVERVIEW

Regression models are the workhorses of data analysts in a wide range of fields in the social sciences. We begin this chapter with a discussion of fitting a line to a scatter plot of data, and then we discuss the additional inferences that can be made when we move from a correlation coefficient to a two-variable regression model. We include discussions of measures of goodness-of-fit and on the nature of hypothesis testing and statistical significance in regression models. Throughout this chapter, we present important concepts in text, mathematical formulae, and graphical illustrations. This chapter concludes with a discussion of the assumptions of the regression model and minimal mathematical requirements for estimation.

TWO-VARIABLE REGRESSION

In Chapter 7 we introduced three different bivariate hypothesis tests. In this chapter we add a fourth, two-variable regression. This is an important first step toward the multiple regression model – which is the topic of Chapter9–in which we are able to “control for” another variable (Z)as we measure the relationship between our independent variable of interest (X) and our dependent variable (Y). It is crucial to develop an in-depth understanding of two-variable regression before moving to multiple regression. In the sections that follow, we begin with an overview of the two-variable regression model, in which a line is fit to a scatter plot of data. We then discuss the uncertainty associated with the line and how we use various measures of this uncertainty to make inferences about the underlying population. This chapter concludes with a discussion of the assumptions of the regression model and the minimal mathematical requirements for model estimation.