Introduction

In the previous chapter, we introduced the OLS regression line. This chapter is about interpreting regression in several different senses of the word. Section 5.2 interprets what regression does by exploring the way in which it compresses information about a scatter diagram. We then go on to compare the regression line to the SD line. Another interpretation, in Section 5.3, takes advantage of regression's historical roots. We show how regression was first used and point out that there are in fact two regression lines for summarizing the relationship between two variables. Section 5.4 examines regression from another angle, interpreting the regression slope as a weighted sum of the Y values. This will make clear that regression coefficients are closely related to the sum (and average). Next, Sections 5.5 and 5.6, demonstrate how to interpret the output from a regression, including the residuals and two new statistics called the RMSE and R2. We show how regression output can be used to reveal important characteristics about the underlying data. Finally, Section 5.7, examines some of the limitations of regression analysis as a descriptive tool. Regression is not always appropriate and may mislead the reader.

Regression as Double Compression

Workbooks: Double Compression.xls; East North Central FT Workers.xls

Regression answers a question about the relationship and movement between variables. Given a value of X, the regression line predicts Y.