Question

I ONLY need answers from Question 5 to Question 10 Thank you!

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.

Use the regression results to answer the following questions:

1. Write the estimated regression equation.

2. Interpret the coefficient on the variable “Years of experience.”

3. Write the estimated equation relating salary to years of experience for an employee without a master’s degree.

4. Write the estimated equation relating salary to years of experience for an employee with a master’s degree.

5.   Sketch a graph illustrating your answers to questions 4 and 5 (it need not be to scale). Be sure to label the axes, slopes, and intercepts.

6. Interpret the coefficient on “Master’s Degree.” What exactly does it tell you?

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

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

9. 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.

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

Answer 1

using excel>data>data analysis Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.961267
R Square	0.924033
Adjusted R Square	0.915096
Standard Error	5606.872
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	6.5E+09	3.25E+09	103.3912	3.06E-10
Residual	17	5.34E+08	31437017
Total	19	7.04E+09
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	12172.34	2577.149	4.723181	0.000196	6735.032	17609.65
Years of Experience	1362.195	148.436	9.176989	5.37E-08	1049.023	1675.368
Master's Degree	15772.68	2827.306	5.578698	3.33E-05	9807.59	21737.78

1. the estimated regression equation is

Salary = 12172.34+1362.195*years of experience +15772.68*master's degree

2. Interpretation of the “Years of experience.” : For every one unit increase in year experience, Salary will be increased by $1362.195

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.88598
R Square	0.784961
Adjusted R Square	0.773015
Standard Error	9167.6
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	5.52E+09	5.52E+09	65.7059	2.03E-07
Residual	18	1.51E+09	84044885
Total	19	7.04E+09
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	13554.84	4194.279	3.231746	0.004628	4742.989	22366.7
Years of Experience	1744.774	215.2469	8.105917	2.03E-07	1292.557	2196.991

3.the estimated equation relating salary to years of experience for an employee without a master’s degree is

Salary = 13554.84+1744.774*years of experience

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.740067
R Square	0.547699
Adjusted R Square	0.522571
Standard Error	13295.71
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3.85E+09	3.85E+09	21.79647	0.000191
Residual	18	3.18E+09	1.77E+08
Total	19	7.04E+09
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	29336	4204.471	6.977334	1.62E-06	20502.73	38169.27
Master’s Dummy	27760	5946.021	4.668669	0.000191	15267.87	40252.13

4. the estimated equation relating salary to years of experience for an employee with a master’s degree.

Salary = 29336+27760*master's degree