374 Statistical Methods
Focus on the last row because it shows the relationships of the other
variables to salary. Years employed is a good predictor because the range
of salary is fairly narrow for each value of years employed (although the
relationship is not perfectly linear). Age at which the employee was hired is
not a very good predictor because there is a wide range of salary values for
each value of age hired. There is not a signifi cant relationship between the
two predictors years employed and age hired. What about the other two
predictors? Looking at the plots of salary against degree and MS hired
makes it clear that neither of them is closely related to salary. The peo-
ple with higher degrees do not seem to be making higher salaries. Those
with a Master’s degree when hired do not seem to be making much more
either. Therefore, the correlations of degree and MS hired with salary
should be low.
You might have some misgivings about using Degree as a predictor.
After all, it is only an ordinal variable. There is a natural order to the four
levels, but it is arbitrary to assign the values 1, 2, 3, and 4. This says that
the spacing from Bachelor’s to Master’s (1 to 2) is the same as the spacing
from Master’s plus 30 hours to PhD (3 to 4). You could instead assign the
values 1, 2, 3, and 5, which would mean greater space from Master’s plus
30 hours to the PhD. In spite of this arbitrary assignment, ordinal variables
are frequently used as regression predictors. Usually, it does not make a
signifi cant difference whether the numbers are 1, 2, 3, and 4 or 1, 2, 3,
and 5. In the present situation, you can see from Figure 9-12 that salaries
are about the same in all four degree categories, which implies that the
correlation of salary and degree is close to 0. This is true no matter what
spacing is used.Correlation Matrix of Variables
The SPLOM shows the relationships between salary and the other vari-
ables. To quantify this relationship, create a correlation matrix of the
variables.To form the correlation matrix:1 Click the Male Faculty sheet tab.
2 Click Multivariate Analysis from the StatPlus menu and then click
Correlation Matrix.
3 Click the Data Values button, click the Use Range References option
button, select the range B1:F45, and click OK.