Regression analysis

Abstract

When two quantitative variables are measured for a number of individuals we may be not so much interested in a measure of association between the variables (provided by a correlation coefficient) as in predicting the value of one variable from the value of the other variable. For example, if trainee salesmen take a test at the end of their training period, can the test score be used to predict the first-year sales, and how accurate is the prediction? One way to answer such a question is to collect both the test score and the first-year sales of a number of salesmen and from these sample data develop an equation relating these two variables. This equation is an example of a regression equation,† the simplest type of which is a simple‡linear regression equation which can be represented by a straight line on the scatter diagram for the two variables. We should be careful to draw the scatter diagram first, however, to decide whether the relationship between the variables appears to be reasonably linear (this is not the case in Fig. 13.3, for example).