ABSTRACT
This chapter begins by describing what a regression model does and what the four main objectives of regression analysis are: estimating causal effects, forecasting an outcome, determining predictors of an outcome, and adjusting an outcome for certain factors. The chapter then presents the nuts and bolts of regression analysis (using Ordinary Least Squares), starting with a breakdown of the components of the Simple Regression Model, in which there is just one explanatory variable. It describes the calculations and meanings of the predicted value, the residual, and the R-squared (the explanatory power of the regression). The chapter then discusses correlation vs. causation, which leads into the Multiple Regression Model. This is where the concept of “holding other factors constant” (ceteris paribus) is introduced, although a deeper discussion of its meaning is held off until Chapter 4. The chapter emphasizes that regressions just indicate how variables move with each other, with or without holding other factors constant. One must then assess whether the regression is producing an unbiased estimate of a causal effect (if that is the goal of the regression).
