Contributions and donations are one of the essential ways that the universities are able to develop great educational programs, invest in inventory, build new campuses, provide scholarships and many more. In order to receive donations from alumni consistently, the universities must provide a great experience for their students. Some of these factors are student-to-faculty ratio, graduation rate, freshman retention rate and percentage of students in classrooms. The new head of alumni relations Joseph Randal will identify which factor plays a key role in acquiring high alumni giving rates, given data rankings of 123 schools and linear regression model.
Keywords: Donations, Linear Regression, Giving Rates, Ratio
Alumni giving is one of the ways that an institution gets funded, this is essential to the universities and colleges because it helps create and give more opportunities to new students such as grants, scholarships, new campuses, new programs for different departments. Joseph Randal has been assigned to be the head of alumni relations at a university, it is a very difficult position that comes with a lot of issues and tasks. One of the main concerns at his new position is related to the contributions that the alumni make and the contributions each alumnus makes individually. Joseph Randal’s task is to pinpoint the essential factors/policies that cause alumni donations to increase. In order for alumni to have the desire to donate to their university, they must have had a positive experience during their student years. Joseph found out that there are many things to take into consideration, but some of the main reasons for a positive experience at an institution could be: graduation rate, class size, freshman retention rates and student to faculty ratios. In order to find the most accurate reason Joseph Randal turned to a U.S News & World Report that portrays data of 123 universities and colleges ranked
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Summarize the Data
In order to analyze and summarize the data from 123 universities descriptive statistics must be applied. Some of the key factors of descriptive statistics are: mean, standard deviation, maximum, median and minimum. According to the descriptive statistics above, the mean graduation rate is 0.6452, whereas the graduation rate standard deviation is 0.1698; the student-to-faculty mean is 17.77, and the student-to-faculty standard deviation is 4.52. The percentage of classes containing more than 50 students has a mean of 0.14, and the standard deviation of 0.06, the percentage of classes with less than 20 students has a mean of 0.40 and the standard deviation of 0.13. The alumni giving rate has a mean of 0.142 and the standard deviation of 0.1700; the freshman retention rate has a mean of 0.8411 and the standard deviation of 0.0839. From this data, a correlation can be obtained, the graduation rate is positively related with the alumni giving rate and the freshman retention rate. The alumni giving rate and the freshman retention rate are positively related. The percentage of classes with less than 20 students has a positive correlation with the alumni giving rate, graduation rate and the freshman retention rate. However, the student to faculty ratio has a negative correlation with the freshman retention rate, graduation rate and alumni giving rate. (Mend pg.34)
Linear Regression Model
The graduation rate is one of the main factors that affects the average alumni giving rate. In order to predict the alumni giving rate, the graduation rate has to be taken into the calculation of the linear regression model. For this calculation a linear regression equation is needed ,
, the alumni giving rate is = -0.06718 + 0.3239 (Graduation rate). Where, the b1is the estimated slope which is 0.32, it is a positive slope and signifies that as the graduation rate increases by 1, the alumni giving rate will increase by 0.32 percent. Given this information, the R square value is 0.4647, meaning that 46% of the alumni contribution rate is affected by the graduation rate. (Mend pg. 503)
Multiple Linear Regression
In order to predict the alumni giving rate given, the student-to-faculty ratio, percent of classes with less than 20 students, and the graduation rate, Joseph Randal develops a multiple linear regression model. It can be determined that the alumni giving rate is -0.06 + 0.248 (graduation rate) + 0.144 (% of classes with less than 20 students) - 0.01 (student faculty). There are a couple of things in this equation that should be noted, 0.249 is a positive slope for b1 , and it demonstrated that as the graduation rate increases by 1, the alumni giving rate increases by 0.249 percent; 0.144 is an estimated positive slope for b2 . This slope signifies that as the percentage of classes with less than 20 students increases by 1, the alumni giving rate will increase by 0.144 percent. Slope b3 is negative and has a value of -0.001, it signifies that as the student faculty rate decreases by 1, the alumni giving rate will decrease by 0.001 percent. Given this information, the value of the R square is 0.5235 or 52.35%. This demonstrates that 52.35% of the alumni contribution is affected by the following: graduation rate, student-to faculty ratio, percentage of classes with less than 20 students. (Mend pg.531)
Most/Least Impressive Giving Rate
Given the data it can be easily established that most impressive giving rate of a university is the University of Notre Dame, having a 41% alumni giving rate.
Based on this chart, it can be concluded that such a high alumni giving rate is achieved due to their 98 % retention rate of freshman, 96% graduation rate and the student-to faculty rate of 12:1 . It is safe to conclude that the smaller the size of the class, the higher will be the rate of retention, thus higher graduation rates. There are 3 colleges that tied for the least impressive giving rate: San Diego State University, San Jose State University and University of South Alabama, they all have a 2% alumni giving rate. The freshman retention rates of these universities vary from 68% to 83%, graduation rates vary from 37% to 66%, student-to-faculty ratio is 25:1. It is safe to conclude that the higher student-to-faculty ratios, and the lower freshman retention rates are, the lower graduation rates will be. Low graduation rates lead to weaker and smaller contribution rates from the alumni.
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Joseph Randal is given information that his university has a student- to-faculty ratio of 19:1, a graduation rate of 65%, 37% of classes have less than 20 students, freshman retention rate is 80%, and 23% of classes have more than 50 students in their classroom. The closest university with such similar data is Ohio University, it has a student- to-faculty ratio of 19:1, graduation rate of 65%, 43% of classes have less than 20 students, freshman retention rate is 80%, 11% of classes have more than 50 students in their classroom. Once this data has been matched, the giving rate can be obtained, it is 8%, meaning that Randal’s university giving rate should be 8% as well.
In conclusion, this data demonstrates that high graduation rates, high freshman retention rates, low student-to-faculty ratios, high percentages of classes with less than 20 students, have high alumni giving rates. In order to obtain high contribution rates, the graduation rate should be raised above 89%, the freshman retention rates should be raised above 95%, the percentage of classes with less than 20 students should be raised above 45%, the student to faculty-ratios-should be brought down to at least 15:1, and the percentage of classes with more than 50 students should be brought down to less than 20%. All of these factors are very essential and have a great impact on the outcome; therefore, must be considered and approached thoroughly, carefully and precisely..
- Mendenhall, W., Beaver, R. J., & Beaver, B. M. (2013). Introduction to probability and statistics. Boston, MA: Cengage.
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