# Chapter 4 Review Problem Solution

**Chapter 4 Review Problem Solution**

(a) The best variable to use would be job complexity because it has the highest magnitude (absolute value) of correlation with absenteeism and hence the highest R2

(b) We would predict absenteeism to be 2.322 days for this employee, which we could round to 2 days:

(c) No. The root mean square error for the multiple regression is 1.38. Thus, about 1/3 of the time, the multiple regression’s prediction of absenteeism will be off by more than 1.38 and about 5% of the time, the multiple regression’s prediction of absenteeism will be off by more than 1.38*2=2.76. The multiple regression model is not typically able to forecast an employee’s absenteeism to within 1.

(d) A 95% confidence interval is where n-(5+1)=71, so we round down and use .

(e) We want to test versus where refers to the coefficient on base pay in the multiple regression of absenteeism on base pay, job complexity, seniority, age and dependents. The p-value for this test is shown on the JMP output as 0.7885. Thus, there is not strong evidence that base pay is useful for predicting absenteeism once job complexity, seniority, age and dependents have been taken into account.

(f) To examine whether multicollinearity might be a serious problem, we examine the variance inflation factors. All of the variance inflation factors are below 10, so there is no indication that multicollinearity might be a serious problem.

(g) We want to test versus .

We use the partial F-test. The test statistic is

The critical value for rejecting the test at the 0.05 level is . Rounding to , we see that the test statistic is less than the critical value. Thus, there is not strong evidence that seniority and/or age are useful for predicting absenteeism once job complexity, base pay and dependents have been taken into account.

(h) The coefficient on base pay in the simple regression is a marginal slope and measures not only the direct association between base pay and absenteeism but also the indirect association between other variables not included in the regression (job complexity, seniority, age and dependents) and absenteeism through base pay. For example, base pay is positively correlated with job complexity and job complexity is negatively correlated with absenteeism. The coefficient on base pay in the multiple regression is a partial slope and measures the association between base pay and absenteeism holding fixed job complexity, seniority, age and dependents.