Question

Drew is undecided about whether to go back to school and get his master’s degree. He is trying to perform a cost-benefit analysis to determine whether the cost of attending the school of his choice will be outweighed by the increase in salary he will receive after he attains his degree. He does research and complies data on annual salaries in the industry he currently works in (he has been working for 10 years), along with the years of experience for each employee and whether or not the employee has a master’s degree. Earning his master’s degree will require him to take out approximately $20,000 worth of student loans. He has decided that if the multiple regression model shows, with 95% confidence, that earning a master’s degree is significant in predicting annual salary, and the estimated increase in salary is at least $10,000, he will enroll in a degree program. Here are the data:

Salary ($)	Years of Experience	Master’s Degree	Dummy variable	Dummy variable
37,620	23	No
67,180	26	Yes
31,280	16	No
20,500	3	No
75,120	27	Yes
59,820	24	Yes
40,180	16	Yes
81,360	31	Yes
36,080	20	No
36,080	11	Yes
36,680	23	No
29,200	12	Yes
34,040	17	No
30,060	13	No
53,300	22	Yes
22,820	6	No
72,900	33	Yes
55,920	20	Yes
18,280	0	No
27,000	9	No
59,600	24	Yes
40,000	16	Yes
81,500	31	Yes
36,000	20	No
36,500	11	Yes
37,020	23	No
29,000	12	Yes

PS. Make sure to first assign the 0 and 1 to the levels of the IV and then be consistent with it. Fill in the dummy variable(s) column(s). Make sure to use appropriate number of variables calculated by the formula (c-1).

A. Is the regression model effective in predicting the DV at alpha of 0.025? Make sure to show which values you use to make the decision.

B. Write down the multiple regression equation using actual names of IVs and DVs. Remember, you need an equation for each level of the qualitative IV.

C. What is the value of the estimated intercept? Interpret the value in terms of years of experience, master’s degree, and salary.

D. What is the values of the estimated slope for the variable “Master’s degree”? Interpret each value in terms of actual IVs and the DV. Do not forget to take into consideration the way you converted categorical variable into the dummy variable.

E. What is the average difference between the salaries of people with and without Master’s degree (holding years of experience constant)?

F. Does the master’s degree significantly influence the salary of the employees at the alpha level of 0.01? Make sure to show which values you use to make the decision.

G. Do the years of experience significantly influence the salary of the employees at the alpha level of 0.01? Make sure to show which values you use to make the decision.

H. Remember, Drew has decided that if the multiple regression model shows that earning a master’s degree is significant in predicting annual salary (at alpha of 0.05), and the estimated increase in salary is at least $10,000, he will enroll in a degree program. Should he? Use the actual numbers from regression model to prove your answer. Hint, there should be two set of values/numbers used.

Answer 1

Let's run the linear regression where Salary is the dependent variable and Master's degree & Experience are the independent variables. We will run the regression in SPSS or you could run on your choice of your software. The output is:

A. Is the regression model effective in predicting the DV at an alpha of 0.025? Make sure to show which values you use to make the decision.

We will use the ANOVA table to see that if the model is effective in predicting the salary or not. The F-ratio is 82.380 and the p-value associated to it is 0.000 which is significant at the level of alpha = 0.025. Hence, we can conclude that the model is effective.

B. Write down the multiple regression equation using actual names of IVs and DVs. You need an equation for each level of the qualitative IV.

Multiple regression equation is:

Salary = 7127.599 + 1629.184*(Experience) + 13061.593*(Degree)

When the employee has a master’s degree, Degree = 1,

Salary = 7127.599 + 1629.184*(Experience) + 13061.593*(1)

Salary = 20189.192 + 1629.184*(Experience)

When Degree = 0,

Salary = 7127.599 + 1629.184*(Experience)

C. What is the value of the estimated intercept? Interpret the value in terms of years of experience, master’s degree, and salary.

Intercept = 7127.599

The intercept value tells us the salary of an employee with zero years of experience and no master’s degree.

D. What are the values of the estimated slope for the variable “Master’s degree”? Interpret each value in terms of actual IVs and the DV.

Slope for the variable Master’s degree = 13061.593

This tells us the expected change in salary of an employee when the employee gains a master’s degree keeping the years of experience constant.

Slope for Years of Experience = 1629.184

This tells us the expected change in salary of an employee when there is a one year increase in experience keeping the status of the degree constant.