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Case Problem 1 Alumni Giving Alumni donations are an important source of revenue for colleges and universities. If administrators could determine the factors that could lead to increases in the percentage of alumni who make a donation, they might be able to implement policies that could lead to increased revenues. Research shows that students who are more satisfied with their contact with teachers are more likely to graduate. As a result, one might suspect that smaller class sizes and lower student/faculty ratios might lead to a higher percentage of satisfied graduates, which in turn might lead to increases in the percentage of alumni who make a donation. The following table shows data for 48 national universities. The Graduation Rate column is the percentage of students who initially enrolled at the university and graduated. The % of Classes Under 20 column shows the percentages of classes with fewer than 20 students that are offered. The Student/Faculty Ratio column is the number of students enrolled divided by the total number of faculty. Finally, the Alumni Giving Rate column is the percentage of alumni who made a donation to the university. LO 1 - Construct an estimated simple linear regression model that estimates how a dependent variable is related to an independent variable., 2 - Construct an estimated multiple linear regression model that estimates how a dependent variable is related to multiple independent variables., 3 - Compute and interpret the estimated coefficient of determination for a linear regression model., 4 - Assess whether the conditions necessary for valid inference in a least squares linear regression model are satisfied and test hypotheses about the parameters., 5 - Test hypotheses about the parameters of a linear regression model and interpret the results of these hypotheses tests., 9 - Use an estimated linear regression model to predict the value of the dependent variable given values of the independent variables.

Case Problem 1 Alumni Giving Alumni donations are an important source of revenue for colleges and universities. If administrators could determine the factors that could lead to increases in the percentage of alumni who make a donation, they might be able to implement policies that could lead to increased revenues. Research shows that students who are more satisfied with their contact with teachers are more likely to graduate. As a result, one might suspect that smaller class sizes and lower student/faculty ratios might lead to a higher percentage of satisfied graduates, which in turn might lead to increases in the percentage of alumni who make a donation. The following table shows data for 48 national universities. The Graduation Rate column is the percentage of students who initially enrolled at the university and graduated. The % of Classes Under 20 column shows the percentages of classes with fewer than 20 students that are offered. The Student/Faculty Ratio column is the number of students enrolled divided by the total number of faculty. Finally, the Alumni Giving Rate column is the percentage of alumni who made a donation to the university. LO 1 - Construct an estimated simple linear regression model that estimates how a dependent variable is related to an independent variable., 2 - Construct an estimated multiple linear regression model that estimates how a dependent variable is related to multiple independent variables., 3 - Compute and interpret the estimated coefficient of determination for a linear regression model., 4 - Assess whether the conditions necessary for valid inference in a least squares linear regression model are satisfied and test hypotheses about the parameters., 5 - Test hypotheses about the parameters of a linear regression model and interpret the results of these hypotheses tests., 9 - Use an estimated linear regression model to predict the value of the dependent variable given values of the independent variables.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Chapter Review Case Problem 1 Alumni Giving Alumni donations are an important source of revenue for colleges and universities. If administrators could determine the factors that could lead to increases in the percentage of alumni who make a donation, they might be able to implement policies that could lead to increased revenues. Research shows that students who are more satisfied with their contact with teachers are more likely to graduate. As a result, one might suspect that smaller class sizes and lower student/faculty ratios might lead to a higher percentage of satisfied graduates, which in turn might lead to increases in the percentage of alumni who make a donation. The following table shows data for 48 national universities. The Graduation Rate column is the percentage of students who initially enrolled at the university and graduated. The % of Classes Under 20 column shows the percentages of classes with fewer than 20 students that are offered. The Student/Faculty Ratio column is the number of students enrolled divided by the total number of faculty. Finally, the Alumni Giving Rate column is the percentage of alumni who made a donation to the university. LO 1 - Construct an estimated simple linear regression model that estimates how a dependent variable is related to an independent variable., 2 - Construct an estimated multiple linear regression model that estimates how a dependent variable is related to multiple independent variables., 3 - Compute and interpret the estimated coefficient of determination for a linear regression model., 4 - Assess whether the conditions necessary for valid inference in a least squares linear regression model are satisfied and test hypotheses about the parameters., 5 - Test hypotheses about the parameters of a linear regression model and interpret the results of these hypotheses tests., 9 - Use an estimated linear regression model to predict the value of the dependent variable given values of the independent variables.
Transcribed Image Text:Chapter Review Case Problem 1 Alumni Giving Alumni donations are an important source of revenue for colleges and universities. If administrators could determine the factors that could lead to increases in the percentage of alumni who make a donation, they might be able to implement policies that could lead to increased revenues. Research shows that students who are more satisfied with their contact with teachers are more likely to graduate. As a result, one might suspect that smaller class sizes and lower student/faculty ratios might lead to a higher percentage of satisfied graduates, which in turn might lead to increases in the percentage of alumni who make a donation. The following table shows data for 48 national universities. The Graduation Rate column is the percentage of students who initially enrolled at the university and graduated. The % of Classes Under 20 column shows the percentages of classes with fewer than 20 students that are offered. The Student/Faculty Ratio column is the number of students enrolled divided by the total number of faculty. Finally, the Alumni Giving Rate column is the percentage of alumni who made a donation to the university. LO 1 - Construct an estimated simple linear regression model that estimates how a dependent variable is related to an independent variable., 2 - Construct an estimated multiple linear regression model that estimates how a dependent variable is related to multiple independent variables., 3 - Compute and interpret the estimated coefficient of determination for a linear regression model., 4 - Assess whether the conditions necessary for valid inference in a least squares linear regression model are satisfied and test hypotheses about the parameters., 5 - Test hypotheses about the parameters of a linear regression model and interpret the results of these hypotheses tests., 9 - Use an estimated linear regression model to predict the value of the dependent variable given values of the independent variables.
University A 1 2 Boston College 3 Brandeis University 4 Brown University 5 California Institute of Technology 6 Carnegie Mellon University 7 Case Western Reserve Univ. 8 College of William and Mary 9 Columbia University 10 Cornell University 11 Dartmouth College 12 Duke University 13 Emory University 14 Georgetown University 15 Harvard University 16 Johns Hopkins University 17 Lehigh University 18 Massachusetts Inst. of Technology 19 New York University 20 Northwestern University 21 Pennsylvania State Univ. 22 Princeton University 23 Rice University 24 Stanford University 25 Tufts University 26 Tulane University 27 U. of California-Berkeley 28 U. of California-Davis 29 U. of California-Irvine 30 U. of California-Los Angeles 31 U. of California-San Diego 32 U. of California-Santa Barbara 33 U. of Chicago 34 U. of Florida 35 U. of Illinois-Urbana Champaign 36 U. of Michigan-Ann Arbor 37 U. of North Carolina-Chapel Hill 38 U. of Notre Dame 39 U. of Pennsylvania 40 U. of Rochester 41 U. of Southern California 42 U. of Texas-Austin 43 U. of Virginia 44 U. of Washington 45 U. of Wisconsin-Madison 46 Vanderbilt University 47 Wake Forest University 48 Washington University-St. Louis 49 Yale University 50 51 52 53 54 55 B State ΜΑ ΜΑ RI CA PA OH VA NY NY NH NC GA DC ΜΑ MD PA ΜΑ NY IL PA NJ TX CA ΜΑ LA CA CA CA CA CA CA IL FL IL MI NC IN PA NY CA TX VA WA WI TN NC MO CT C Graduation Rate 85 79 93 85 75 72 89 88 90 91 94 92 84 91 97 89 81 92 72 90 80 95 92 92 87 72 83 74 74 78 80 70 84 67 77 83 82 94 90 76 70 66 92 70 73 82 82 86 94 D % of Classes Under 20 39 68 60 65 67 52 45 69 72 61 68 65 54 73 64 55 65 63 66 32 68 62 69 67 56 58 32 42 41 48 45 65 31 29 51 40 53 65 63 53 39 4 44 37 37 68 59 73 77 E Student- Faculty Ratio 13 8 8 3 10 8 12 7 13 10 8 7 10 8 9 11 6 13 8 19 5 8 7 9 2528898 12 17 19 20 18 19 20 4 23 15 15 16 13 7 10 13 21 13 12 13 9 11 7 7 F Alumni Giving Rate 25 33 400 46 28 31 27 31 35 53 45 37 29 46 27 40 44 13 30 21 67 40 34 29 17 18 7 9 13 8 12 36 19 23 13 26 49 41 23 22 13 28 12 13 31 38 33 50 G H I J K L M N O P Q R S T U V W X Y Z AA AB AC AD AE AF AG AH Al AJ
Transcribed Image Text:University A 1 2 Boston College 3 Brandeis University 4 Brown University 5 California Institute of Technology 6 Carnegie Mellon University 7 Case Western Reserve Univ. 8 College of William and Mary 9 Columbia University 10 Cornell University 11 Dartmouth College 12 Duke University 13 Emory University 14 Georgetown University 15 Harvard University 16 Johns Hopkins University 17 Lehigh University 18 Massachusetts Inst. of Technology 19 New York University 20 Northwestern University 21 Pennsylvania State Univ. 22 Princeton University 23 Rice University 24 Stanford University 25 Tufts University 26 Tulane University 27 U. of California-Berkeley 28 U. of California-Davis 29 U. of California-Irvine 30 U. of California-Los Angeles 31 U. of California-San Diego 32 U. of California-Santa Barbara 33 U. of Chicago 34 U. of Florida 35 U. of Illinois-Urbana Champaign 36 U. of Michigan-Ann Arbor 37 U. of North Carolina-Chapel Hill 38 U. of Notre Dame 39 U. of Pennsylvania 40 U. of Rochester 41 U. of Southern California 42 U. of Texas-Austin 43 U. of Virginia 44 U. of Washington 45 U. of Wisconsin-Madison 46 Vanderbilt University 47 Wake Forest University 48 Washington University-St. Louis 49 Yale University 50 51 52 53 54 55 B State ΜΑ ΜΑ RI CA PA OH VA NY NY NH NC GA DC ΜΑ MD PA ΜΑ NY IL PA NJ TX CA ΜΑ LA CA CA CA CA CA CA IL FL IL MI NC IN PA NY CA TX VA WA WI TN NC MO CT C Graduation Rate 85 79 93 85 75 72 89 88 90 91 94 92 84 91 97 89 81 92 72 90 80 95 92 92 87 72 83 74 74 78 80 70 84 67 77 83 82 94 90 76 70 66 92 70 73 82 82 86 94 D % of Classes Under 20 39 68 60 65 67 52 45 69 72 61 68 65 54 73 64 55 65 63 66 32 68 62 69 67 56 58 32 42 41 48 45 65 31 29 51 40 53 65 63 53 39 4 44 37 37 68 59 73 77 E Student- Faculty Ratio 13 8 8 3 10 8 12 7 13 10 8 7 10 8 9 11 6 13 8 19 5 8 7 9 2528898 12 17 19 20 18 19 20 4 23 15 15 16 13 7 10 13 21 13 12 13 9 11 7 7 F Alumni Giving Rate 25 33 400 46 28 31 27 31 35 53 45 37 29 46 27 40 44 13 30 21 67 40 34 29 17 18 7 9 13 8 12 36 19 23 13 26 49 41 23 22 13 28 12 13 31 38 33 50 G H I J K L M N O P Q R S T U V W X Y Z AA AB AC AD AE AF AG AH Al AJ
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