Develop and estimated simple linear regression model that can be used to predict the alumni giving rate, given the graduation rate. Discuss your findings.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
*Help with what variables are needed for regression please!*
Chadwick has just been named the director of alumni relationships at a local university. 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 ration might lead to a higher percentage of satisfied graduates, which in turn might lead to increases in percentage of alumni who make a donation.
Chadwick is feeling an extra pressure to increase total giving to the university because of recent budget cuts. Chadwick is also feeling pressured to increase the percentage of alumni to give. Chadwick found this new metric called average alumni giving rate U.S. News & World Report.
To investigate further, Chadwick needs to assemble the data on classes, graduation rates, and most important, alumni giving rates for top 123 colleges and universities based on alumni giving.
The attached data base shows data of the top 123 colleges ranked by U.S. News & World Report.
- Develop and estimated simple linear regression model that can be used to predict the alumni giving rate, given the graduation rate. Discuss your findings.
| School | SFR | LT20 | GT50 | GRAD | FRR | GIVE |
| Arizona State | 24 | 42% | 16% | 59% | 81% | 8% |
| Arkansas State—Jonesboro | 19 | 49% | 4% | 37% | 69% | 11% |
| Auburn | 18 | 24% | 17% | 66% | 87% | 31% |
| Air Force | 8 | 74% | 0.10% | 81% | 88% | 11% |
| Military Academy | 8 | 95% | 0% | 86% | 92% | 28% |
| Akron | 20 | 39% | 6% | 35% | 69% | 15% |
| Arizona | 20 | 35% | 17% | 60% | 79% | 5% |
| Arkansas | 18 | 28% | 18% | 58% | 83% | 23% |
| Ball State | 18 | 34% | 12% | 57% | 78% | 11% |
| Baylor | 14 | 49% | 9% | 71% | 85% | 14% |
| Boise State | 21 | 33% | 11% | 27% | 67% | 8% |
| Boston College | 14 | 47% | 6% | 91% | 96% | 27% |
| Bowling Green State | 19 | 33% | 7% | 61% | 75% | 8% |
| BYU | 21 | 46% | 12% | 78% | 84% | 17% |
| SUNY | 16 | 36% | 21% | 67% | 88% | 9% |
| Alabama | 19 | 46% | 16% | 67% | 85% | 34% |
| Central Michigan | 22 | 32% | 11% | 54% | 78% | 8% |
| Clemson | 16 | 51% | 13% | 76% | 91% | 28% |
| Colorado State | 18 | 34% | 19% | 64% | 83% | 7% |
| Berkley | 17 | 62% | 15% | 91% | 97% | 12% |
| Cincinnati | 17 | 38% | 11% | 56% | 84% | 11% |
| Boulder | 18 | 38% | 16% | 68% | 84% | 8% |
| Fresno | 20 | 18% | 10% | 49% | 83% | 4% |
| Duke | 8 | 71% | 6% | 94% | 97% | 36% |
| East Carolina | 17 | 33% | 14% | 57% | 78% | 5% |
| Eastern Michigan | 18 | 39% | 5% | 38% | 72% | 3% |
| Florida Atlantic | 21 | 27% | 15% | 42% | 77% | 4% |
| Florida International | 28 | 23% | 22% | 46% | 81% | 6% |
| Florida State | 22 | 35% | 16% | 74% | 90% | 19% |
| Connecticut | 18 | 44% | 17% | 81% | 93% | 17% |
| Florida | 21 | 41% | 16% | 84% | 96% | 15% |
| Georgia IoT | 19 | 40% | 23% | 80% | 93% | 28% |
| Georgia State | 20 | 14% | 16% | 48% | 83% | 6% |
| Georgia | 19 | 35% | 12% | 82% | 94% | 14% |
| Hawaii | 14 | 45% | 10% | 50% | 78% | 8% |
| Houston | 23 | 28% | 22% | 46% | 79% | 13% |
| Indiana | 19 | 34% | 18% | 71% | 90% | 16% |
| Iowa State | 17 | 30% | 20% | 70% | 85% | 15% |
| Kansas State | 21 | 49% | 11% | 60% | 79% | 19% |
| Kent State | 20 | 45% | 8% | 50% | 76% | 4% |
| Idaho | 18 | 45% | 10% | 55% | 78% | 11% |
| Illinois—Urbana-Champaign | 16 | 34% | 21% | 84% | 94% | 13% |
| Iowa | 16 | 49% | 12% | 70% | 84% | 12% |
| Kansas | 20 | 42% | 12% | 61% | 79% | 18% |
| Kentucky | 18 | 30% | 16% | 58% | 80% | 12% |
| Louisiana State—Baton Rouge | 22 | 34% | 19% | 61% | 85% | 14% |
| Louisiana Tech | 22 | 48% | 9% | 49% | 73% | 13% |
| Louisiana—Lafayette | 23 | 30% | 7% | 40% | 74% | 7% |
| Louisiana—Monroe | 18 | 30% | 13% | 30% | 72% | 5% |
| Louisville | 18 | 25% | 12% | 49% | 78% | 12% |
| Marshall | 20 | 38% | 4% | 44% | 71% | 10% |
| Miami | 17 | 32% | 12% | 80% | 89% | 16% |
| Michigan State | 16 | 23% | 21% | 77% | 91% | 14% |
| Middle Tennessee | 21 | 32% | 7% | 45% | 81% | 6% |
| Mississippi State | 20 | 38% | 14% | 58% | 83% | 17% |
| Maryland—College Park | 18 | 35% | 16% | 81% | 94% | 10% |
| Massachusetts—Amherst | 19 | 45% | 17% | 69% | 87% | 11% |
| Memphis | 15 | 36% | 11% | 40% | 76% | 6% |
| Miami | 11 | 53% | 7% | 80% | 90% | 17% |
| Michigan—Ann Arbor | 15 | 48% | 16% | 90% | 96% | 15% |
| Minnesota—Twin Cities | 21 | 38% | 19% | 70% | 89% | 13% |
| Missouri | 20 | 47% | 15% | 69% | 85% | 16% |
| New Mexico State | 20 | 45% | 10% | 45% | 76% | 6% |
| North Carolina State—Raleigh | 18 | 30% | 20% | 71% | 90% | 11% |
| Northern Illinois | 17 | 44% | 12% | 56% | 75% | 6% |
| Northwestern | 7 | 75% | 6% | 94% | 97% | 30% |
| Naval Academy | 9 | 56% | 0.10% | 89% | 97% | 21% |
| Nebraska—Lincoln | 20 | 38% | 14% | 64% | 84% | 22% |
| Nevada—Reno | 27 | 33% | 16% | 50% | 78% | 9% |
| New Mexico | 22 | 40% | 14% | 44% | 78% | 7% |
| North Carolina—Chapel Hill | 14 | 37% | 13% | 90% | 97% | 22% |
| North Texas | 23 | 29% | 20% | 48% | 76% | 5% |
| Notre Dame | 12 | 55% | 10% | 96% | 98% | 41% |
| Ohio State—Columbus | 19 | 32% | 20% | 78% | 93% | 15% |
| Ohio | 19 | 42% | 11% | 65% | 80% | 8% |
| Oklahoma State | 19 | 39% | 12% | 59% | 79% | 15% |
| Oregon State | 25 | 36% | 20% | 60% | 82% | 12% |
| Mississippi | 18 | 46% | 13% | 59% | 80% | 13% |
| Oklahoma | 17 | 41% | 11% | 64% | 83% | 19% |
| Oregon | 20 | 37% | 17% | 68% | 84% | 13% |
| Penn State | 17 | 39% | 15% | 85% | 93% | 21% |
| Purdue | 14 | 37% | 17% | 69% | 87% | 19% |
| Rice | 6 | 69% | 8% | 92% | 97% | 32% |
| Rutgers | 15 | 41% | 20% | 77% | 91% | 10% |
| SDSU | 21 | 22% | 24% | 66% | 83% | 2% |
| San Jose State | 25 | 25% | 9% | 44% | 82% | 2% |
| Southern Methodist | 12 | 58% | 8% | 74% | 89% | 19% |
| Stanford | 6 | 70% | 13% | 95% | 98% | 34% |
| Pittsburgh | 14 | 42% | 18% | 78% | 92% | 13% |
| South Alabama | 22 | 42% | 8% | 37% | 68% | 2% |
| South Carolina | 19 | 38% | 11% | 68% | 87% | 17% |
| South Florida | 28 | 23% | 16% | 51% | 86% | 15% |
| Southern Mississippi | 18 | 43% | 11% | 47% | 74% | 13% |
| Syracuse | 16 | 61% | 9% | 82% | 91% | 17% |
| Temple | 19 | 33% | 8% | 65% | 87% | 8% |
| Texas A&M | 19 | 21% | 23% | 79% | 92% | 21% |
| Texas Christian | 13 | 40% | 8% | 74% | 86% | 18% |
| Texas State | 19 | 19% | 19% | 55% | 78% | 5% |
| Texas Tech | 23 | 22% | 24% | 63% | 82% | 15% |
| Troy | 20 | 58% | 4% | 40% | 72% | 9% |
| Tulane | 11 | 67% | 6% | 74% | 89% | 19% |
| Tennessee | 15 | 31% | 8% | 60% | 85% | 11% |
| Texas—Austin | 18 | 34% | 25% | 81% | 92% | 14% |
| Toledo | 19 | 34% | 31% | 45% | 68% | 5% |
| Alabama—Birmingham | 17 | 39% | 15% | 41% | 79% | 13% |
| UCLA | 16 | 52% | 22% | 90% | 97% | 13% |
| Central Florida | 31 | 28% | 23% | 63% | 86% | 16% |
| UNLV | 22 | 25% | 18% | 41% | 76% | 5% |
| USC | 9 | 63% | 11% | 89% | 97% | 39% |
| Texas—San Antonio | 23 | 24% | 23% | 26% | 58% | 5% |
| Tulsa | 11 | 70% | 1% | 65% | 88% | 22% |
| Utah | 15 | 42% | 17% | 57% | 83% | 11% |
| Utah State | 19 | 32% | 18% | 56% | 74% | 8% |
| Virginia | 16 | 52% | 16% | 93% | 97% | 22% |
| Washington | 12 | 33% | 21% | 80% | 93% | 15% |
| Wyoming | 14 | 42% | 10% | 53% | 73% | 10% |
| Vanderbilt | 8 | 64% | 9% | 91% | 97% | 23% |
| Virginia Tech | 17 | 25% | 21% | 80% | 92% | 15% |
| Wake Forest | 11 | 54% | 3% | 89% | 94% | 29% |
| Washington State | 15 | 37% | 22% | 69% | 83% | 13% |
| West Virginia | 23 | 32% | 19% | 59% | 80% | 12% |
| Western Kentucky | 19 | 43% | 6% | 49% | 73% | 13% |
| Western Michigan | 19 | 36% | 11% | 52% | 74% | 10% |
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