368 Statistical Methods
find that it helps to make the variance more constant, but the regression
results are about the same. Calc HS and Alg Place are still the only signifi cant
coeffi cients, and the R^2 value is almost the same as before. Of course, it is
much harder to interpret the coeffi cients after transformation. Who would
understand if you said that each point in the algebra placement score is worth
0.012 point in the arcsine of the square root of the calculus score divided by
100? From this perspective, the transformed regression is useful mainly to
validate the original regression. If it is valid and it gives essentially the same
results as the original regression, then the original results are valid.Plotting Residuals versus Predictor Variables
It is also useful to look at the plot of the residuals against each of the predic-
tor variables because a curve might show up on only one of those plots or
there might be an indication of nonconstant variance. Such plots are created
automatically with the Analysis ToolPak Add-Ins.To view one of these plots:1 Click the Multiple Regression sheet tab to return to the regression
output.The plots generated by the add-in start in cell J1 and extend to cell Z32.
Two types of plots are generated: scatter plots of the regression residuals ver-
sus each of the regression variables, and the observed and predicted values of
the response variable (calculus score) against each of the regression variables.
See Figure 9-9. (You might have to scroll up and right to see the charts.)Figure 9-9
Plots
created
with the
Regression
command