Chapter 1 Prediction

The race is not always to the swift nor the battle to the strong — but that’s the way to lay your bets. – Damon Runyon The attempt to predict the values on some dependent variable by a function of independent variables is typically approached by simple or multiple regression, for one and more than one predictor, respectively. The most common combination rule is a linear function of the independent variables obtained by least-squares, i.e., the linear combination that minimizes the sum of the squared residuals between the actual values on the dependent variable and those predicted from the linear combination. In the case of simple regression, scatterplots again play a major role in assessing linearity of the relationship, the possible effects of outliers on the slope of the least-squares line, and the influence of individual objects in its calculation. Regression slopes, in contrast to the correlation, are neither scale invariant nor symmetric in the dependent and independent variables. One usually interprets the least-squares line as one of expecting, for each unit change in the independent variable, a regression slope change in the dependent variable.1 There are several topics in prediction that arise continually when we attempt to reason ethically with fallible multivariable data. We discuss five such areas in the subsections to follow: regression toward the mean; methods involved in using regression for prediction that incorporate corrections for unreliability; differential prediction effects in selection based on tests; interpreting and making inferences from regression weights; and the distinction between actuarial (statistical) and clinical prediction.