Data Analysis with Microsoft Excel: Updated for Office 2007

332 Statistical Methods

Recall that if the residuals follow a normal distribution, they should

fall evenly along the superimposed line on the normal probability plot.

Although the points in Figure 8-17 do not fall perfectly on the line, the de-

parture is not strong enough to invalidate our assumption of normality.

Testing for Constant Variance in the Residuals

The next assumption you should always investigate is the assumption of

constant variance in the residuals. A commonly used plot to help verify this

assumption is the plot of the residuals versus the predicted values. This plot

will also highlight any problems with the straight-line assumption.

Figure 8-18

Residuals

showing

nonconstant

variance

If the constant variance assumption is violated, you may see a plot like

the one shown in Figure 8-18. In this example, the variance of the residu-

als is larger for larger predicted values. It’s not uncommon for variability to

increase as the value of the response variable increases. If that happens, you

might remove this problem by using the log of the response variable and

performing the regression on the transformed values.

With one predictor variable in the regression equation, the scatter plot

of the residuals versus the predicted values is identical to the scatter plot of

the residuals versus the predictor variable (shown earlier in Figure 8-16). The

scatter plot indicates that there may be a decrease in the variability of the resid-

uals as the predicted values increase. Once again, though, this interpretation

is infl uenced by the presence of the possible outlier in the fi rst observation.

Without this observation, there might be no reason to doubt the assumption of

constant variance.

Testing for the Independence of Residuals

The fi nal regression assumption is that the residuals are independent of

each other. This assumption is of concern only in situations where there

is a defi ned order for the observations. For example, if we do a regression

of a predictor variable versus time, the observations will follow a sequen-

tial order. The assumption of independence can be violated if the value of

one observation infl uences the value of the next observation. For example,