Given the following information with an emphasis on the University of Virginia:

Your company was hired to study the costs that universities face and to help your university in question to examine how their expenditures relate to similar competitors. Using least-squared regressions, you estimated the fixed and variable costs for all universities together. However, your boss thinks that private and public firms might have different business models, which could lead to different cost behaviors. 1. Based on this conjecture, calculate the cost behavior based on whether the universities are public or private. a. Are the fixed costs and variable cost per unit the same for private and public universities? Include in your answer the equation for both the private and public universities. (2 points) b. How much variation is explained by your models? Which model has the highest explanatory power (R-squared)? (1 point) B D E F G H Private No Yes No No 10161 7629 1 Name 2 Arizona State University Main campus 3 Brigham Young University at Provo 4 Florida State University 5 University of Central Florida 6 Baylor University 7 Iowa State University 8 Ohio University 9 Santa Clara University 10 Michigan State University 11 University of Miami 12 Columbia University 13 University of Rochester 14 University of Chicago 15 University of California at Irvine 16 Emory University 17 Boston University 18 University of Florida 19 New York University 20 Johns Hopkins University 21 George Washington University 22 University of Virginia Yes No No Yes No Yes Yes Yes Yes No Yes Yes No total_underg Total_Expend 26385.5 $ 151,426,071.00 28004.5 $ 227,683,622.00 20527 $ 178,820,750.00 15906 $ 137,238,252.00 $ 82,237,983.00 19533.5 $ 194,472,070.00 15516 $ 166,711,476.00 3955 $ 48,998,760.00 28700 $ 331,924,000.00 8198 $ 149,465,000.00 3403.5 $ 110,279,836.50 5290 $ 143,735,730.00 3359.5 $ 129,811,013.00 13109 $ 238,878,806.00 5640 $ 166,497,480.00 16527.5 $ 284,256,990.00 26113 $ 414,827,281.00 13815 $ 299,251,005.00 4350.5 $ 250,641,666.50 6206 $ 97,507,470.00 11335 $ 184,121,995.00 Outstate Room.Board Books Personal PhD Terminal S.F.Ratio perc.alumni E 7434 4850 700 2100 88 93 18.9 5 2340 3580 860 1220 76 76 20.5 40 6680 4060 600 1020 80 89 23.1 15 6618 4234 700 1600 80 98 22.2 9 6450 3920 600 1346 71 76 18.5 38 7550 3224 640 2055 81 88 19.2 22 4095 550 2300 79 87 20.4 13 13584 5928 630 1278 88 92 13.9 19 10658 3734 504 600 93 95 14 9 16500 6526 630 1985 82 94 5.9 17 18624 6664 550 300 97 98 5.9 21 17840 6582 500 882 93 99 5.9 23 18930 6380 500 1254 99 99 5.3 36 12024 5302 790 1818 96 96 16.1 11 17600 6000 600 870 97 98 5 28 18420 6810 475 1025 80 81 11.9 16 7090 4180 63 1530 88 97 13.4 20 17748 7262 450 1000 87 98 7.8 16 18800 6740 500 1040 96 97 3.3 38 17450 6328 700 950 92 93 7.6 15 12212 3792 500 1000 90 92 9.5 22 Yes Yes Yes INo - 20.5 23.1 22.2 4234 20.4 2779 888 F G H . L M N 0 P Q R S T U 1 le Room.Board Books Personal PhD Terminal S.F. Ratio perc.alumni Expend Grad.Rate Apps Accept Enroll Top10perc Top25perc F.Undergrad P.Undergrad 2 34 4850 700 2100 88 93 18.9 5 4602 48 12809 10308 3761 24 49 22593 7585 3 $40 3580 860 1220 76 76 40 7916 33 7365 5402 4615 48 82 27378 1253 4 680 4060 600 1020 80 89 15 7250 58 11651 8683 3023 50 90 18906 3242 5 518 700 1600 80 98 9 6742 46 6986 2959 1918 25 60 12330 7152 6 50 3920 600 1346 71 76 18.5 38 7503 72 6075 5349 2367 34 66 9919 484 7 $50 3224 640 2055 81 88 19.2 22 8420 65 8427 7424 3441 26 59 18676 1715 8 529 4095 550 2300 79 87 13 8811 64 11023 8298 3183 21 54 14861 1310 9 184 5928 630 1278 88 92 13.9 19 10872 100 4019 40 73 3891 128 10 558 3734 504 600 93 95 14 9 10520 71 18114 15096 6180 23 57 26640 4120 11 600 6526 630 1985 82 94 5.9 17 17500 59 7122 5386 1643 42 69 7760 876 12 24 6664 550 97 98 5.9 21 30639 99 6756 1930 871 78 96 3376 55 13 340 6582 500 93 99 5.9 23 26037 80 8766 5498 1243 56 75 5071 438 14 30 6380 500 1254 99 99 5.3 36 36854 90 2999 68 94 3340 39 15 24 5302 790 1818 96 96 16.1 11 15934 66 15698 10775 2478 85 100 12677 864 16 500 6000 600 870 97 98 5 28 28457 96 8506 4168 1236 76 97 5544 17 20 6810 475 1025 80 81 11.9 16 16836 72 20192 13007 3810 45 80 14971 3113 18 190 4180 630 1530 88 97 13.4 20 14737 66 12445 8836 3623 54 85 24470 3286 19 48 7262 450 1000 87 98 7.8 16 21227 71 13594 7244 2505 70 86 12408 2814 20 300 6740 500 1040 96 97 3.3 38 56233 90 8474 3446 911 75 94 3566 1569 21 50 6328 700 950 92 93 7.6 15 14745 72 7875 5062 1492 38 71 5471 1470 22 12 3792 500 1000 90 92 9.5 22 13597 95 15849 5384 2678 74 95 11278 114 300 882 6348 922 192 Your company was hired to study the costs that universities face and to help your university in question to examine how their expenditures relate to similar competitors. Using least-squared regressions, you estimated the fixed and variable costs for all universities together. However, your boss thinks that private and public firms might have different business models, which could lead to different cost behaviors. 1. Based on this conjecture, calculate the cost behavior based on whether the universities are public or private. a. Are the fixed costs and variable cost per unit the same for private and public universities? Include in your answer the equation for both the private and public universities. (2 points) b. How much variation is explained by your models? Which model has the highest explanatory power (R-squared)? (1 point) B D E F G H Private No Yes No No 10161 7629 1 Name 2 Arizona State University Main campus 3 Brigham Young University at Provo 4 Florida State University 5 University of Central Florida 6 Baylor University 7 Iowa State University 8 Ohio University 9 Santa Clara University 10 Michigan State University 11 University of Miami 12 Columbia University 13 University of Rochester 14 University of Chicago 15 University of California at Irvine 16 Emory University 17 Boston University 18 University of Florida 19 New York University 20 Johns Hopkins University 21 George Washington University 22 University of Virginia Yes No No Yes No Yes Yes Yes Yes No Yes Yes No total_underg Total_Expend 26385.5 $ 151,426,071.00 28004.5 $ 227,683,622.00 20527 $ 178,820,750.00 15906 $ 137,238,252.00 $ 82,237,983.00 19533.5 $ 194,472,070.00 15516 $ 166,711,476.00 3955 $ 48,998,760.00 28700 $ 331,924,000.00 8198 $ 149,465,000.00 3403.5 $ 110,279,836.50 5290 $ 143,735,730.00 3359.5 $ 129,811,013.00 13109 $ 238,878,806.00 5640 $ 166,497,480.00 16527.5 $ 284,256,990.00 26113 $ 414,827,281.00 13815 $ 299,251,005.00 4350.5 $ 250,641,666.50 6206 $ 97,507,470.00 11335 $ 184,121,995.00 Outstate Room.Board Books Personal PhD Terminal S.F.Ratio perc.alumni E 7434 4850 700 2100 88 93 18.9 5 2340 3580 860 1220 76 76 20.5 40 6680 4060 600 1020 80 89 23.1 15 6618 4234 700 1600 80 98 22.2 9 6450 3920 600 1346 71 76 18.5 38 7550 3224 640 2055 81 88 19.2 22 4095 550 2300 79 87 20.4 13 13584 5928 630 1278 88 92 13.9 19 10658 3734 504 600 93 95 14 9 16500 6526 630 1985 82 94 5.9 17 18624 6664 550 300 97 98 5.9 21 17840 6582 500 882 93 99 5.9 23 18930 6380 500 1254 99 99 5.3 36 12024 5302 790 1818 96 96 16.1 11 17600 6000 600 870 97 98 5 28 18420 6810 475 1025 80 81 11.9 16 7090 4180 63 1530 88 97 13.4 20 17748 7262 450 1000 87 98 7.8 16 18800 6740 500 1040 96 97 3.3 38 17450 6328 700 950 92 93 7.6 15 12212 3792 500 1000 90 92 9.5 22 Yes Yes Yes INo - 20.5 23.1 22.2 4234 20.4 2779 888 F G H . L M N 0 P Q R S T U 1 le Room.Board Books Personal PhD Terminal S.F. Ratio perc.alumni Expend Grad.Rate Apps Accept Enroll Top10perc Top25perc F.Undergrad P.Undergrad 2 34 4850 700 2100 88 93 18.9 5 4602 48 12809 10308 3761 24 49 22593 7585 3 $40 3580 860 1220 76 76 40 7916 33 7365 5402 4615 48 82 27378 1253 4 680 4060 600 1020 80 89 15 7250 58 11651 8683 3023 50 90 18906 3242 5 518 700 1600 80 98 9 6742 46 6986 2959 1918 25 60 12330 7152 6 50 3920 600 1346 71 76 18.5 38 7503 72 6075 5349 2367 34 66 9919 484 7 $50 3224 640 2055 81 88 19.2 22 8420 65 8427 7424 3441 26 59 18676 1715 8 529 4095 550 2300 79 87 13 8811 64 11023 8298 3183 21 54 14861 1310 9 184 5928 630 1278 88 92 13.9 19 10872 100 4019 40 73 3891 128 10 558 3734 504 600 93 95 14 9 10520 71 18114 15096 6180 23 57 26640 4120 11 600 6526 630 1985 82 94 5.9 17 17500 59 7122 5386 1643 42 69 7760 876 12 24 6664 550 97 98 5.9 21 30639 99 6756 1930 871 78 96 3376 55 13 340 6582 500 93 99 5.9 23 26037 80 8766 5498 1243 56 75 5071 438 14 30 6380 500 1254 99 99 5.3 36 36854 90 2999 68 94 3340 39 15 24 5302 790 1818 96 96 16.1 11 15934 66 15698 10775 2478 85 100 12677 864 16 500 6000 600 870 97 98 5 28 28457 96 8506 4168 1236 76 97 5544 17 20 6810 475 1025 80 81 11.9 16 16836 72 20192 13007 3810 45 80 14971 3113 18 190 4180 630 1530 88 97 13.4 20 14737 66 12445 8836 3623 54 85 24470 3286 19 48 7262 450 1000 87 98 7.8 16 21227 71 13594 7244 2505 70 86 12408 2814 20 300 6740 500 1040 96 97 3.3 38 56233 90 8474 3446 911 75 94 3566 1569 21 50 6328 700 950 92 93 7.6 15 14745 72 7875 5062 1492 38 71 5471 1470 22 12 3792 500 1000 90 92 9.5 22 13597 95 15849 5384 2678 74 95 11278 114 300 882 6348 922 192