Question

After ten years on the job, Drew is trying to decide whether to go back to school and get a masters degree. He performs a cost-benefit analysis to determine whether the cost of attending school will be covered by the increase in salary he will received after he attains his degree. He does research and compiles data on annual salaries in his industry, health care, along with the years of experience for each employee and whether the employee has a master’s degree. Earning his master’s degree will require him to take out about $20,000 in student loans. He has decided that if his analysis show that the degree will increase his salary by at least $10,000, he will enroll in the program.

The data used in his analysis are the following:

Salary ($)	Years of Experience	Master's Degree	Master’s Dummy
37620	22	No	0
67080	27	Yes	1
31280	15	No	0
21500	2	No	0
75120	28	Yes	1
59820	25	Yes	1
40180	15	Yes	1
81360	32	Yes	1
35080	19	No	0
36080	12	Yes	1
36680	22	No	0
29200	1	Yes	1
33040	18	No	0
30060	14	No	0
53300	21	Yes	1
22820	7	No	0
72900	31	Yes	1
55920	22	Yes	1
19280	0	No	0
26000	7	No	0

Drew added a dummy variable to indicate whether the employee had a master’s degree. The variable “Master’s dummy” took the value 1 if the employee had a master’s degree, 0 if not. He then regressed Salary on Years of Experience and the Master’s degree dummy. What results does he find? Show in JMP or Excel.

1. Conduct an F-test for the overall significance of the model.

2. Conduct a t-test to determine whether there is a statistically significant relationship between years of experience and salary, holding master’s degree constant.

3. Conduct a t-test to determine whether there is strong evidence that a Master’s degree increases salary by $10,000 or more, holding years of experience constant.

4. Based on the regression results, would you recommend that Drew pursue a Master’s degree? Why or why not?

Answer 1

Using Excel, go to Data, select Data Analysis, choose Regression. Put Salary in Y input range and Years of Experience and Master's Dummy in X input range.

Regression Statistics
Multiple R	0.961266541
R Square	0.924033362
Adjusted R Square	0.91509611
Standard Error	5606.872279
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	6500623195	3.25E+09	103.3912	3.05699E-10
Residual	17	534429284.9	31437017
Total	19	7035052480
	Coefficients	Standard Error	t Stat	P-value
Intercept	12172.34146	2577.149149	4.723181	0.000196
Years of Experience	1362.195122	148.4359557	9.176989	5.37E-08
Master’s Dummy	15772.68293	2827.305592	5.578698	3.33E-05

1. H0: β1 = β2 = 0

H1: At least one βi ≠ 0

p-value = 0.000

Since p-value is less than 0.05, we reject null hypothesis and conclude that at least one βi ≠ 0. The model is significant.

2. H0: β1 = 0

H1: β1 ≠ 0

p-value = 0.000 (5.37E-08)

Since p-value is less than 0.05, we reject null hypothesis and conclude that β1 ≠ 0.

There is a statistically significant relationship between years of experience and salary, holding master’s degree constant.

3. H0: β2 = 0

H1: β2 ≠ 0

p-value = 0.000 (3.33E-05)

Since p-value is less than 0.05, we reject null hypothesis and conclude that β2 ≠ 0.

There is a strong evidence that a Master’s degree increases salary by $10,000 or more, holding years of experience constant.

4. Slope of Master's dummy = 15772.683

This means that if employee has Master's degree, salary increases by 15722.683.

So, Drew should pursue a Master’s degree.