Question

The variables collected for this sample are average starting salary upon graduation ($), the percentage of applicants to the full-time program who were accepted, the average GMAT test score of students entering the program, program per-year tuition ($), and percent of students with job offers at time of graduation.

Build at least five different multiple regression models with different combinations of predictors and transformations. Provide the regression equation for each model and its Adjusted R2 and F statistic.

University	Tuition per year ($)	Average GMAT score	Acceptance Rate (%)	Graduates employed at graduation (%)	Average starting salary and bonus ($)
1	61875	732	7.1	73.6	142834
2	58875	726	11.0	76.9	144750
3	62424	728	20.7	84.3	142574
4	61520	724	23.5	87.4	137615
5	63454	713	13.8	79.6	142936
6	61596	713	23.2	80.7	136357
7	63148	716	18.2	75.7	139006
8	61605	716	22.1	83.8	142489
9	60744	721	18.1	74.9	135933
10	58000	690	25.1	81.8	137154
11	58975	719	23.7	69.4	126871
12	58192	692	30.0	79.6	132316
13	51500	699	26.7	84.5	111974
14	58300	687	31.2	75.5	131865
15	48100	678	30.7	81.7	128347
16	52200	691	47.4	70.3	118938
17	46800	686	34.8	71.7	115694
18	51786	684	31.6	64.4	114129
19	47950	688	41.3	77.1	113830

Answer 1

At first , enter the data correctly in the Worksheet

1. Here we are interested to see whether average starting salary and bonus($) depend on all the other variables or not.

STEPS: Go to stats , click on regression; again select regression and then on fit regression model. Click on average starting salary and bonus($) as response and the other columns as continuous predictors; Click on OK.

Regression Equation:

Average starting salary and bon = 107270 + 1.324 Tuition per year($) - 93 Average GMAT score
- 417 Acceptance Rate(%)
+ 314 Graduates employed at graduatio

Adjusted R2: 77.29%

F statistic: 16.32

2. Here we are interested to see whether acceptance rate(%) depend on the average GMAT score of the students and their per year tuition fees.

STEPS: Go to stats , click on regression; again select regression and then on fit regression model. Click on acceptance rate(%) as response and Tuition per year($) and average GMAT score as continuous predictors; Click on OK.

Regression Equation:

Acceptance Rate(%) = 271.9 - 0.000551 Tuition per year($) - 0.305 Average GMAT score

Adjusted R2: 66.15%

F statistic: 15.64

3. Here we are interested to see whether graduates employed at graduation(%) depend on their average GMAT score of the students and their per year tuition fees.

STEPS: Go to stats , click on regression; again select regression and then on fit regression model. Click on graduates employed at graduation(%) as response and Tuition per year($) and average GMAT score as continuous predictors; Click on OK.

Regression Equation:

Graduates employed at graduatio = 58.6 + 0.000306 Tuition per year($)
+ 0.002 Average GMAT score

Adjusted R2:   0.00%

F statistic: 0.75

4. Here we are interested to see whether average starting salary and bonus($) depend on average GMAT score of the students and their per year tuition fees.

STEPS: Go to stats , click on regression; again select regression and then on fit regression model. Click on average starting salary and bonus($) as response and Tuition per year($) and average GMAT score as continuous predictors; Click on OK.

Regression Equation:

Average starting salary and bon = 12226 + 1.650 Tuition per year($) + 35 Average GMAT score

Adjusted R2: 71.90%

F statistic: 24.03

5. Here we are interested to see whether average starting salary and bonus($) depend on average GMAT score of the students, whether they are employed at graduation or thei acceptance rate(%).

STEPS: Go to stats , click on regression; again select regression and then on fit regression model. Click on average starting salary and bonus($) as response and average GMAT score, graduates employed at graduation(%),Acceptance Rate(%)  as continuous predictors; Click on OK.

Regression Equation:

Average starting salary and bon = 20604 + 132 Average GMAT score - 638 Acceptance Rate(%)
+ 436 Graduates employed at graduatio

Adjusted R2: 61.78%

F statistic: 10.70

Hopefully this will help you. In case of any query, do comment. If you are satisfied with the answer, give it a like. Thanks.