The slope the regression line of y on x is . Substituting, we have . This is easier than the procedure in the last chapters. Spreadsheets will do all of this work for us. However, I think it's important that you understand the process, which is why this textbook has you work examples by hand.
Most regression equations come from data in observational studies.
In that case, you cannot say that a change in x causes a corresponding change in y , because you cannot infer causality from an observational study. Rather, you must say that the changes are associated . With observational studies, the slope and intercept of the regression line are only descriptive statistics. Read carefully the examples on page 194 to make sure that you understand this point. You might wonder why we use the regression line instead of some other line for prediction.