CHAPTER 17 More of a Good Thing: Multiple Regression 245

»

» ^{The multiple r2 value represents the amount of variability in the dependent}

variable explained by the model, so you want it to be high. As shown in

Figure 17-2, it is 0.52 in this example, indicating a moderately good fit.»

» ^{A statistically significant F statistic indicates that the model predicts the}

outcome significantly better than the null model. As shown in Figure 17-2, the

p value on the F statistic is 0.009, which is statistically significant at α = 0.05.

Figure 17-4 shows another way to judge how well the model predicts the outcome.

It’s a graph of observed and predicted values of the outcome variable, with a

superimposed identity line (Observed Predicted). Your program may offer this

observed versus predicted graph, or you can generate it from the observed and pre-

dicted values of the dependent variable. For a perfect prediction model, the points

would lie exactly on the identity line. The correlation coefficient of these points is

the multiple r value for the regression.

Watching Out for Special Situations

that Arise in Multiple Regression

Here we describe two topics that come up in multiple regression: interactions

(both synergistic and anti-synergistic), and collinearity. Both relate to how the

simultaneous behavior of two predictors can influence an outcome.

FIGURE 17-4:

Observed versus

predicted

outcomes for the

model SBP ~ Age

+ Weight, for the

data in

Table 17-2.

© John Wiley & Sons, Inc.