Jack is undecided about whethe
Jack is undecided about whether to go back to school and get hismaster’s degree. He is trying to perform a cost-benefit analysis todetermine whether the cost of attending the school of his choicewill be outweighed by the increase in salary he will receive afterhe attains his degree. He does research and compiles data on annualsalaries in the industry he currently works in (he has been workingfor 10 years), along with the years of experience for each employeeand whether or not the employee has a master’s degree. Earning hismaster’s degree will require him to take out approximately $20,000worth of student loans. He has decided that if the multipleregression model shows, with 95% confidence, that earning amaster’s degree is significant in predicting annual salary, and theestimated increase in salary is at least $10,000, he will enroll ina degree program.
| Salary ($) | Years of Experience | Master’s Degree |
| 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 |
1. Is the regression model effective in predicting theDV at an alpha of 0.025? Make sure to show which values you use tomake the decision.
2. Write down the multiple regression equation usingactual names of IVs and DVs. You need an equation for each level ofthe qualitative IV.
3. What is the value of the estimated intercept?Interpret the value in terms of years of experience, master’sdegree, and salary.
4. What are the values of the estimated slope for thevariable “Master’s degree”? Interpret each value in terms of actualIVs and the DV.
Answer:
Let’s run the linear regression where Salary is the dependentvariable and Master’s degree & Experience are the independentvariables. We will run the regression in SPSS or you could run onyour choice of your software. The output is:
1. Is the regression model effective in predicting theDV at an alpha of 0.025? Make sure to show which values you use tomake the decision.
We will use the ANOVA table to see that if the model iseffective in predicting the salary or not. The F-ratio is 82.380and the p-value associated to it is 0.000 which is significant atthe level of alpha = 0.025. Hence, we can conclude that the modelis effective.
2. Write down the multiple regression equation usingactual names of IVs and DVs. You need an equation for each level ofthe 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)
3. What is the value of the estimated intercept?Interpret the value in terms of years of experience, master’sdegree, and salary.
Intercept = 7127.599
The intercept value tells us the salary of an employee with zeroyears of experience and no master’s degree.
4. What are the values of the estimated slope for thevariable “Master’s degree”? Interpret each value in terms of actualIVs and the DV.
Slope for the variable Master’s degree = 13061.593
This tells us the expected change in salary of an employee whenthe employee gains a master’s degree keeping the years ofexperience constant.
Slope for Years of Experience = 1629.184
This tells us the expected change in salary of an employee whenthere is a one year increase in experience keeping the status ofthe degree constant.
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