Data Analysis with Microsoft Excel: Updated for Office 2007

Chapter 9 Multiple Regression 367

This plot is useful for verifying the regression assumptions. For example,

the fi rst assumption requires that the form of the model be correct. A viola-

tion of this assumption might be seen in a curved pattern. No curve is ap-

parent here.

If the assumption of constant variance is not satisfi ed, then it should be

apparent in Figure 9-8. Look for a trend in the vertical spread of the data.

For example, the data may widen out as the predicted value increases.

There appears to be a defi nite trend toward a narrower spread on the right,

and it is cause for concern about the validity of the regression—although

regression does have some robustness with respect to the assumption of

constant variance.

For data that range from 0 to 100 (such as percentages), the arcsine–

squareroot transformation sometimes helps fi x problems with nonconstant

variance. The transformation involves creating a new column of trans-

formed calculus scores where

Transformed calc score 5 sin^21 "calculus score/ 100

Using Excel, you would enter the formula

5 ASIN^1 SQRT^1 x/ 10022

where x is the value or cell reference of a value you want to transform.

If you were to apply this transformation here and use the transformed cal-

culus score in the regression in place of the untransformed score, you would

Figure 9-8
Scatter plot
of residuals
and predicted
scores