ABSTRACT
Correlation models differ from regression models in that each variable (yis and xis) plays a symmetrical role, with neither variable designated as a response or predictor variable. They are viewed as relational, instead of predictive in this
process. Correlation models can be very useful for making inferences about
any one variable relative to another, or to a group of variables. We use the
correlation models in terms of y and single or multiple xis. Multiple regression’s use of the correlation coefficient, r, and the coeffi-
cient of determination r2 are direct extensions of simple linear regression correlation models already discussed. The difference is, in multiple regres-
sion, that multiple xi predictor variables, as a group, are correlated with the response variable, y. Recall that the correlation coefficient, r, by itself, has no exact interpretation, except that the closer the value of r is to 0, weaker the linear relationship between y and xis, whereas the closer to 1, stronger the linear relationship. On the other hand, r2 can be interpreted more directly. The coefficient of determination, say r2 ¼ 0.80, means the multiple xi predictor variables in the model explain 80% of the y term’s variability. As given in Equation 5.1, r and r2 are very much related to the sum of squares in the analysis of variance (ANOVA) models that were used to evaluate the rela-
tionship of SSR to SSE in Chapter 4:
r2 ¼ SST SSE SST
¼ SSR SST
: (5:1)
For example, let
SSR ¼ 5000, SSE ¼ 200, SST ¼ 5200.
