The file FTMBA contains data from a sample of full time MBA programs offered by private universities. 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.

Develop the most appropriate multiple regression model to predict the mean starting salary upon graduation. Developing a good regression model is an art as well as a science that requires significant practice. Please answer the following questions in your quest for the most appropriate model.

1. Build a simple linear regression model with each of the predictors and the dependent variable. Provide the R2 for each simple linear regression model. Which predictor has the highest correlation with the dependent variable?
2. 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.
3. From the models considered in the previous questions, what model is the most appropriate one? Justify your selection.
4. Interpret the coefficients in the regression equation of your selected model within the context of the problem.
5. What is the significance (p-value) for overall fit and each predictor in the model? Explain.
6. Conduct a residual analysis for your selected model. Create residual plots for all the predictors and the predicted values. Does your selected model meet the necessary assumptions? Are there any areas of concerns with your model? Include residual plots and comment on the information shown on them
7. 

1 N 4 7 8 9 10 A B D E Tuition per Average Acceptance Graduates employed 1 University year ($) GMAT score Rate(%) at graduation (%) 2 61875 732 7.1 73.6 2 58875 726 11.0 76.9 3 62424 728 20.7 84.3 5 4 61520 724 23.5 87.4 6 5 63454 713 13.8 79.6 6 61596 713 23.2 80.7 8 7 63148 716 18.2 75.7 9 61605 716 22.1 83.8 10 60744 721 18.1 74.9 11 58000 690 25.1 81.8 12 11 58975 719 23.7 69.4 13 12 58192 692 30.0 79.6 14 13 51500 699 26.7 84.5 15 14 58300 687 31.2 75.5 16 15 48100 678 30.7 81.7 17 16 52200 691 47.4 70.3 18 17 46800 686 34.8 71.7 19 18 51786 684 31.6 64.4 20 19 47950 688 41.3 77.1 21 20 50400 676 26.2 74.3 22 21 51667 684 32.1 79.0 23 22 45686 670 30.5 65.3 24 23 43770 664 41.6 67.9 25 24 44200 650 49.0 69.9 26 25 34480 629 37.4 72.2 27 26 47275 649 63.5 67.9 28 27 44940 630 67.9 59.1 29 28 40200 638 48.4 65.8 30 29 54355 563 64.7 50.0 31 30 40230 639 52.7 33.3 32 31 38688 532 49.2 73.3 33 32 36050 594 73.4 43.1 34 33 52820 548 64.0 41.9 35 34 33166 496 54.4 74.1 36 35 46700 625 54.2 33.3 37 36 39238 488 51.1 47.4 Average starting salary and bonus ($) 142834 144750 142574 137615 142936 136357 139006 142489 135933 137154 126871 132316 111974 131865 128347 118938 115694 114129 113830 117074 101961 108558 94963 112071 74421 86925 83465 90117 65563 66648 49753 77779 62320 92653 65888 67800 38 37 36140 587 3.1 36.8 52274 1 N 4 7 8 9 10 A B D E Tuition per Average Acceptance Graduates employed 1 University year ($) GMAT score Rate(%) at graduation (%) 2 61875 732 7.1 73.6 2 58875 726 11.0 76.9 3 62424 728 20.7 84.3 5 4 61520 724 23.5 87.4 6 5 63454 713 13.8 79.6 6 61596 713 23.2 80.7 8 7 63148 716 18.2 75.7 9 61605 716 22.1 83.8 10 60744 721 18.1 74.9 11 58000 690 25.1 81.8 12 11 58975 719 23.7 69.4 13 12 58192 692 30.0 79.6 14 13 51500 699 26.7 84.5 15 14 58300 687 31.2 75.5 16 15 48100 678 30.7 81.7 17 16 52200 691 47.4 70.3 18 17 46800 686 34.8 71.7 19 18 51786 684 31.6 64.4 20 19 47950 688 41.3 77.1 21 20 50400 676 26.2 74.3 22 21 51667 684 32.1 79.0 23 22 45686 670 30.5 65.3 24 23 43770 664 41.6 67.9 25 24 44200 650 49.0 69.9 26 25 34480 629 37.4 72.2 27 26 47275 649 63.5 67.9 28 27 44940 630 67.9 59.1 29 28 40200 638 48.4 65.8 30 29 54355 563 64.7 50.0 31 30 40230 639 52.7 33.3 32 31 38688 532 49.2 73.3 33 32 36050 594 73.4 43.1 34 33 52820 548 64.0 41.9 35 34 33166 496 54.4 74.1 36 35 46700 625 54.2 33.3 37 36 39238 488 51.1 47.4 Average starting salary and bonus ($) 142834 144750 142574 137615 142936 136357 139006 142489 135933 137154 126871 132316 111974 131865 128347 118938 115694 114129 113830 117074 101961 108558 94963 112071 74421 86925 83465 90117 65563 66648 49753 77779 62320 92653 65888 67800 38 37 36140 587 3.1 36.8 52274