1. Consider the enrollment data for Business Week’s top 30 U.S. graduate busines
ID: 3330911 • Letter: 1
Question
1. Consider the enrollment data for Business Week’s top 30 U.S. graduate business programs in the file HW_06.xlsx. Use the data to estimate a multiple regression equation to assess whether there is a relationship between the total number of full-time students (Enrollment) and the following explanatory variables: a) the proportion of female students, b) the proportion of minority students, and c) the proportion of international students enrolled at these business schools.
a. Interpret the coefficients of the estimated regression equation. Do any of these results surprise you? Explain.
b. How well does the estimated regression equation fit the given data?
c. If we add another independent variable, type of schools (Column D) in the above-developed multiple regression model, what’s the new appropriate multiple regression equation? How are you going to interpret the difference between private school and public school on average starting base salary from this new regression equation?
Fulltime Business Week Ranking School Name State Type Enrollment Avg GMAT Resident Tuition, Fees Pct International Pct Female Pct Minority Pct with job offers Avg starting base salary 1 University of Chicago Illinois Private 1144 713 97165 35 35 7 92 107091 2 Harvard University Massachusetts Private 1801 720 101660 33 38 9 94 124378 3 Northwestern University Illinois Private 1200 711 93918 34 36 13 95 108064 4 University of Pennsylvania Pennsylvania Private 1651 714 104410 44 36 9 89 112186 5 University of Michigan Michigan Public 898 706 80879 27 34 13 89 103608 6 Stanford University California Private 739 726 97842 43 36 13 94 121171 7 Columbia University New York Private 1234 716 94104 33 32 13 87 107450 8 Duke University North Carolina Private 878 696 95000 40 39 12 92 100136 9 Massachusetts Institute of Technology Massachusetts Private 780 708 46784 36 35 9 92 111184 10 University of California-Berkeley California Private 500 714 66475 39 30 4 90 108967 11 Cornell University New York Public 593 694 93000 27 39 7 84 100700 12 Dartmouth College New Hampshire Private 506 712 91905 31 33 13 94 110305 13 New York University New York Private 832 708 89184 32 41 15 84 101063 14 UCLA California Public 731 711 66590 32 34 6 80 101306 15 Indiana University Indiana Public 473 663 40882 37 26 13 88 92000 16 University of Virginia Virginia Public 644 693 84000 30 29 9 92 103963 17 University of North Carolina-Chapel Hill North Carolina Public 562 678 43503 32 32 10 82 95647 18 Southern Methodist University Texas Private 201 642 81384 18 28 8 80 84828 19 Carnegie Mellon University Pennsylvania Private 392 690 93840 23 21 12 96 103012 20 University of Notre Dame Indiana Private 316 677 77340 28 24 9 80 89660 21 University of Texas -- Austin Texas Public 552 681 48800 24 31 11 88 96537 22 Brigham Young University Utah Private 315 673 18530 10 20 5 78 88958 23 Emory University Georgia Private 373 680 82856 42 39 14 82 93620 24 Yale University Connecticut Private 382 718 93098 28 34 11 89 99562 25 University of Southern California California Private 525 692 88800 34 29 6 88 91863 26 University of Maryland Maryland Public 257 660 60583 35 29 11 81 85225 27 University of Washington Washington Public 225 688 43556 18 36 5 85 86426 28 Washington University Missouri Private 294 681 83172 34 37 12 81 90775 29 Georgia Institute of Technology Georgia Public 156 681 17816 19 27 5 98 93403 30 Vanderbilt University Tennessee Private 382 656 81076 18 25 6 83 89891Explanation / Answer
a)
Pct International coefficient is 16.4085 which shows that keeping all other things constant, enrollment would go up by 16.4085 when pct international goes up by 1.
Pct Female coefficient is 23.57 which shows that keeping all other things constant, enrollment would go up by 23.57 when pct female goes up by 1.
Pct Minority coefficient is -6.0068 which shows that keeping all other things constant, enrollment would go down by -6.0068 when pct minority goes up by 1.
Intercept is -549.9861 which means enrollment is negative keeping all the factors at 0.
The figures for intercept and pct minority are surprising because enrollment cannot be negative at any cost
b)
r^2 is 0.2989 which means 29.89% of the variation in dependent variable is explained for by the independent variable.
c)
Keeping private schools as 1 and public schools as 0, we get the coefficient of type of schools as 151.1855 which means enrollment goes up by 151.1855 when a school is private.
SUMMARY OUTPUT Regression Statistics Multiple R 0.546730308 R Square 0.29891403 Adjusted R Square 0.218019495 Standard Error 364.284345 Observations 30 ANOVA df SS MS F Significance F Regression 3 1471056.615 490352.205 3.695107831 0.024388504 Residual 26 3450280.185 132703.084 Total 29 4921336.8 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -549.986113 409.513046 -1.343024644 0.190871209 -1391.752235 291.7800086 Pct International 16.40850626 10.44911553 1.570324896 0.128431021 -5.069958316 37.88697083 Pct Female 23.57240639 15.02842444 1.56852147 0.12885097 -7.318962451 54.46377524 Pct Minority -6.006829351 23.90420097 -0.251287603 0.803567227 -55.14261815 43.12895944Related Questions
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