Regression Analysis & Confidence Interval

1. You may recall that at our first class we discussed a data file collected from a graduate survey. At that time we were concerned most with descriptive statistics. The file is GRADSURVEY (attached). An interesting question is whether there are some variables in that data file that can explain or predict anticipated salary in five years. Four potential variables are Graduate GPA, GMAT, Spending, and Number of Jobs.

a) Using only Graduate GPA as a variable, determine the regression model used to predict anticipated salary in 5 years. Even if it is not a "good" model, it is all you have to address the following situation: You interview for a job and your Graduate GPA is 3.85. You receive a job offer that guarantees you a salary of $95,000 in 5 years. Having studied past data, what should you do if your decision is based only on salary?

b) Using all the four variables listed above, carry out the required analysis to see if you can develop a regression model that is significant at the 5% level. Are all independent variables needed in your model? Interpret your findings.

c) What happens if you add another variable "Expected Salary"? Why does it increase the prediction ability of the model?

Data set

ID Num Gender Age Height Major Graduate GPA Undergrad Specialization Undergrad GPA GMAT Employment Status Number of Jobs Expected Salary Anticipated Salary in 5 Years Satisfaction Advisement Spending
ID01 M 22 69 IS 3.90 CM 3.30 600 PT 0 45 75 5 200
ID02 M 35 67 A 3.92 O 3.34 480 FT 2 120 250 4 150
ID03 M 31 67 MR 3.77 BU 3.04 550 FT 2 85 120 5 65
ID04 M 28 73 M 3.43 BI 3.41 530 FT 4 100 150 5 150
ID05 M 36 70 EF 3.51 BU 3.12 610 FT 3 80 90 4 300
ID06 F 27 60 A 3.00 SS 3.50 460 FT 3 100 150 4 250
ID07 M 30 68 EF 3.65 CM 3.02 580 FT 5 100 125 4 400
ID08 M 28 66 A 3.00 CM 2.84 590 FT 1 60 100 6 60
ID09 F 24 65 UN 3.22 CM 3.13 570 FT 4 50 60 4 180
ID10 M 33 70 A 3.90 SS 3.24 530 PT 5 50 80 4 700
ID11 M 26 71 A 4.00 BU 3.89 550 FT 3 60 100 5 100
ID12 M 24 74 M 3.20 BU 3.22 500 FT 2 65 100 4 200
ID13 M 31 69 A 3.53 CM 3.33 540 FT 3 80 110 6 300
ID14 M 39 71 EF 3.42 CM 3.04 570 FT 2 100 150 1 100
ID15 F 29 63 MR 3.12 BU 3.14 480 UN 1 50 100 4 1000
ID16 M 26 74 MR 3.43 EN 2.56 600 FT 4 40 65 4 300
ID17 F 23 64 IS 3.75 CM 3.00 580 FT 1 70 100 5 200
ID18 F 26 63 A 3.30 HU 3.23 520 FT 3 60 75 4 150
ID19 M 30 63 EF 4.00 O 3.75 580 FT 3 105 120 6 150
ID20 F 25 63 MR 4.00 BU 3.72 650 FT 1 60 100 4 130
ID21 F 27 62 MR 3.25 ED 3.77 480 UN 2 45 65 4 300
ID22 F 25 63 EF 3.51 BU 3.64 500 FT 2 60 80 4 200
ID23 M 32 73 A 3.35 BU 2.87 580 FT 1 80 140 5 90
ID24 F 31 65 MR 3.22 BU 2.95 540 FT 3 65 85 6 170
ID25 M 25 68 EF 3.47 BU 3.18 590 PT 1 60 150 4 320
ID26 M 29 73 IB 3.67 HU 3.56 620 FT 2 65 135 4 200
ID27 F 25 64 MR 3.40 SS 3.26 600 FT 2 55 90 4 600
ID28 M 37 68 M 3.65 EN 3.41 530 FT 2 90 130 2 200
ID29 M 34 66 A 3.54 BI 3.38 540 FT 1 70 100 3 100
ID30 F 33 61 M 3.64 ED 2.79 570 FT 2 45 80 4 160
ID31 F 38 65 EF 4.00 BU 3.78 570 PT 1 80 110 4 230
ID32 M 30 72 EF 3.70 PS 3.55 550 FT 2 75 150 5 500
ID33 M 32 73 M 3.24 PA 3.17 580 FT 2 60 85 6 250
ID34 F 28 61 A 3.37 SS 3.68 610 FT 1 75 95 3 150
ID35 F 27 66 IS 3.56 CM 3.27 560 FT 1 65 90 4 120
ID36 M 41 74 IB 3.28 SS 3.65 490 FT 1 50 85 1 160
ID37 F 35 65 M 3.16 PS 3.29 510 FT 3 75 100 2 100
ID38 F 25 63 IS 3.59 CM 3.45 560 FT 1 60 90 3 160
ID39 M 32 70 EF 3.80 EN 3.03 600 FT 2 90 160 7 130
ID40 M 30 69 M 3.15 O 3.22 540 PT 1 55 85 6 110

2. An auditor for a government agency needs to evaluate payments for doctors' office visits paid by Medicare in a particular zip code during the month of June. A total of 25,056 visits occurred during June in this area. The auditor selects a sample of 138 visit claims for the audit. It is determined that the average amount of reimbursement was $93.40 and the standard deviation was $34.55. In 12 of the office visits, an incorrect amount of reimbursement was provided. For the 12 office visits in which there was an incorrect reimbursement, the differences between the amount reimbursed and the amount that the auditor determined should have been reimbursed are in the data file Medicare.

a) What information would you give the agency if it wants to know the total amount of reimbursement it incurred for this geographic area in June? The agency is satisfied with a maximum error of 5% in any estimates it receives.

b) What information would you give the agency if it wants to know the total difference between the amount reimbursed and the amount the auditor determined should have been reimbursed? Again a maximum 5% error is allowed.

Data set

Difference
17
25
14
-10
20
40
35
30
28
22
15
5

Please see attached files.