Chapter 9 Multiple Regression 377Interpreting the Regression Output
The R^2 of 0.732 shows that the regression explains 73.2% of the variance in
salary. However, when this is adjusted for the number of predictors (four),
the adjusted R^2 is about 0.705=70.5%. The standard error is 3,168.434, so
salaries vary roughly plus or minus $3,000 from their predictions. The over-
all F ratio is about 26.67, with a p value in cell F12 of 1.063 310210 , which
rules out the hypothesis that all four population coeffi cients are 0. Looking
at the coeffi cient values and their standard errors, you see that the coeffi -
cients for the variables Degree and MS Hired have values that are not much
more than 1 times their standard errors. Their t statistics are much less than
2, and their p values are much more than .05; therefore, they are not sig-
nifi cant at the 5% level. On the other hand, Years employed and Age Hired
do have coeffi cients that are much larger than their standard errors, with t
values of 9.39 and 4.49, respectively. The corresponding p values are signifi -
cant at the 0.1% level.
The coeffi cient estimate of 606 for years employed indicates that each
year on the job is worth $606 in annual salary if the other predictors are
held fi xed. Correspondingly, because the coeffi cient for Age Hired is about
$374, all other factors being equal, an employee who was hired at an age
1 year older than another employee will be paid an additional $374.Residual Analysis of Discrimination Data
Now check the assumptions under which you performed the regression.To create a plot of residuals versus predicted salary values:1 Using either the StatPlus Fast Scatterplot command or the Excel’s
Scatter button on the Insert menu, create a scatter plot of the
Residual values in the cell range C27:C71 versus Predicted Val-
ues in the range B27:B71.
2 Enter a chart title of Residual Plot, and label the x axis Predicted
Salaries and the y axis Residuals. Save the scatter plot to a chart
sheet named Residuals vs. Predicted.
3 Change the scale of the x axis from 0–45,000 to 20,000–45,000. Your
chart sheet should look like Figure 9-15.