Problem

Salaries (continued). Consider again the salary data from Exercise 4.2 and the regression...

Salaries (continued). Consider again the salary data from Exercise 4.2 and the regression results in Figure 4.9. Consider this output to be for ‘the full model:

y = β0 + β1x1 + β2x2 + β3x3 + e

where y, x1, x2, and x3 were defined in Exercise 4.2.

Now consider the reduced model:

y = β0 + β1x1 + e

Conduct the test to compare these two models. State the hypotheses to be tested, the decision rule, the test statistic, and your decision. What conclusion can be drawn from the result of the test? The regression results for the reduced model can be found in Figure 4.16. Use a 5% level of significance.

Exercise 4.2:

The file on the CD named HARRIS4 contains values of the following four variables for 93 employees of Harris Bank Chicago in 1977:

y, beginning salary in dollars (SALARY)
x1, years of schooling at the time of hire (EDUC)
x2, number of months of previous work experience (EXPER)
x3, number of months after January 1, 1969, that the individual was hired (TIME)

The regression results for the regression of SALARY on the three explanatory variables are shown in Figure 4.9. Use the results to help answer the following questions:

a. What is the estimated regression equation relating SALARY to EDUC, EXPER, and TIME?
b. Conduct the F test for overall fit of the regression. Use a 5% level of significance. State the hypotheses to be tested, the decision rule, the test statistic, and your decision. What conclusion can be drawn from the result of the test?
c. Is education linearly related to beginning salary (after taking into account the effect of experience and time)? Perform the hypothesis test necessary to answer this question. State the hypotheses to be tested, the decision rule, the test statistic, and your decision. Use a 5% level of significance.
d. What percentage of the variation in salary has been explained by the regression?

FIGURE 4.9: Regression Results for Cost Salaries Exercise