Data Analysis with Microsoft Excel: Updated for Office 2007

378 Statistical Methods

There does not appear to be a problem with nonconstant variance. At

least, there is not a big change in the vertical spread of the residuals as you

move from left to right. However, there are two points that look question-

able. The one at the top has a residual value near 8,000 (indicating that this

individual is paid $8,000 more than predicted from the regression equa-

tion), and at the bottom of the plot an individual is paid about $6,000 less

than predicted from the regression.

Except for these two, the points have a somewhat curved pattern—high

on the ends and low in the middle—of the kind that is sometimes helped by

a log transformation. As it turns out, the log transformation would straighten

out the plot, but the regression results would not change much. For example,

if log(salary) is used in place of salary, the R^2 value changes only from

0.732 to 0.733. When the results are unaffected by a transformation, it is

best not to bother because it is much easier to interpret the untransformed

regression.

Normal Plot of Residuals

What about the normality assumption? Are the residuals reasonably in

accord with what is expected for normal data?

Figure 9-15
Residuals
versus
predicted
values for the
male salary
data