Suppose you are trying to explain variations in salaries for technicians in a particular field of work. The file P11_71.xlsx contains annual salaries for 200 technicians. It also shows how many years of experience each technician has, as well as his or her education level. There are four education levels, as explained in the comment in cell D1. Three suggestions are put forth for the relationship between Salary and these two explanatory variables:
You should regress Salary linearly versus the two given variables, YrsExper and EducLev.
All that really matters in terms of education is whether the person got a college degree or not. Therefore, you should regress Salary linearly versus YrsExper and a dummy variable indicating whether he or she got a college degree.
Each level of education might result in different jumps in salary. Therefore, you should regress Salary linearly versus YrsExper and dummy variables for the different education levels.
a. Run the indicated regressions for each of these three suggestions. Then (1) explain what each equation is saying and how the three are different (focus here on the coefficients), (2) which you prefer, and (3) whether (or how) the regression results in your preferred equation contradict the average salary results shown in the Pivot Table sheet of the file.
b. Consider the four workers shown on the Prediction sheet of the file. (These are four new workers, not among the original 200.) Using your preferred equation, calculate a predicted salary and a 95% prediction interval for each of these four workers.
c. It turns out (you don’t have to check this) that the interaction between years of experience and education level is not significant for this data set. In general, however, argue why you might expect an interaction between them for salary data of technical workers. What form of interaction would you suspect? (There is not necessarily one right answer, but argue convincingly one way or the other for a positive or a negative interaction.)