366 Statistical Methods
Does it appear that the range of values is narrower for large values of pre-
dicted calculus score? If the error variance were lower for students with high
predicted values, it would be a violation of the third regression assumption,
which requires a constant error variance. Consider the students predicted to
have a grade of 80 in calculus. These students have actual grades of around
65 to around 95, a wide range. Notice that the variation is lower for students
predicted to have a grade of 90. Their actual scores are all in the 80s and 90s.
There is a barrier at the top—no score can be above 100—and this limits the
possible range. In general, when a barrier limits the range of the dependent
variable, it can cause nonconstant error variance. This issue is considered
further in the next section.Plotting Residuals versus Predicted Values
The plot of the residuals versus the predicted values shows another view
of the variation in Figure 9-7 because the residuals are the differences be-
tween the actual calculus scores and the predicted values.To make the plot:1 Click the Multiple Regression sheet tab to return to the regression
output.
2 Create a scatter plot of the Residuals in the cell range C29:C109 ver-
sus Predicted Values in the cell range B29:B109 using either the
StatPlus Fast Scatterplot command or using Excel’s built-in com-
mands to create a scatter plot.
3 Specify a chart title of Residual Plot, and label the x axis Predicted
Calculus Scores and the y axis Residuals. Save the scatter plot to a
chart sheet named Residuals vs. Predicted.
4 Change the scale of the x axis from 0–100 to 60–100. Your chart
sheet should look like Figure 9-8.