Regression and Other Stories

As discussed in Chapter 1, regression is fundamentally a technology for predicting an outcome y from inputs x1, x2, . . . . In this chapter we introduce regression in the simple (but not trivial) case of a linear model predicting a continuous y from a single continuous x, thus fitting the model yi = a+bxi +errortodata(xi,yi), i=1, ..., n. We demonstrate with an applied example that includes the steps of fitting the model, displaying the data and fitted line, and interpreting the fit. We then show how to check the fitting procedure using fake-data simulation, and the chapter concludes with an explanation of how linear regression includes simple comparison as a special case.