15.1 INTRODUCTION

In Figure 3.1 (After ANOVA, what?), we noted several procedures that might follow ananalysis of variance when the effects of factors were significant. However, we have not yet treated cases in which the factor levels are quantitative. Figure 3.1 suggests two procedures to follow when significant effects are present: the method of orthogonal polynomials when the factor levels are equispaced, and general methods of curve fitting or regression.

Some experimenters prefer to treat all analyses as regression models because even the ANOVA procedures considered to this point can be cast into a regression model. This is evidenced by the term GLM (general linear model) of most computer packages. If anyone of the independent variables ( X's) is quantitative and its effect is statistically significant, one probably should use regression analysis in an attempt to determine a mathematical model suitable for predicting the magnitude of the response variable from values of the independent variables. This regression procedure will be examined for Y as a function of one X, where the relationship may be linear, quadratic, or a higher order polynomial. The case of multiple regression, where Y is a function of several X's, will also be considered. Our search for an adequate prediction equation relies on computer software because most real problems are too difficult to handle otherwise.