12-28, 2021

本文是金融专业的Essay范例，题目是“Factors for High Alumni Giving Rates in Universities（大学高校友捐赠率的因素）”，捐款和捐赠是大学能够发展优秀教育项目、投资库存、建设新校园、提供奖学金等的重要途径之一。为了不断地从校友那里得到捐赠，大学必须为他们的学生提供良好的体验。这些因素包括师生比例、毕业率、新生留校率和学生在教室的百分比。根据123所商学院的数据排名和线性回归模型，新上任的校友关系主管约瑟夫•兰德尔(Joseph Randal)将确定哪些因素在获得高校友捐赠率方面发挥关键作用。

**Abstract****摘要**

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.

**Introduction****介绍**

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

校友捐赠是一个机构获得资金的方式之一，这对大学和学院来说是至关重要的，因为它有助于为新生创造和提供更多的机会，比如助学金、奖学金、新校区、不同系的新项目。Joseph Randal被任命为一所大学的校友关系负责人，这是一个非常困难的职位，伴随着很多问题和任务。在他的新职位上，最主要的关注点之一是校友的贡献以及每位校友个人的贡献。约瑟夫•兰德尔(Joseph Randal)的任务是找出导致校友捐款增加的基本因素/政策。为了让校友有向他们的大学捐款的愿望，他们必须在学生时代有一个积极的经历。约瑟夫发现，有很多因素需要考虑，但在学校获得积极体验的主要原因可能是:毕业率、班级规模、新生留校率和师生比例。为了找到最准确的原因，约瑟夫•兰德尔参考了《美国新闻与世界报道》(u.s. News & World Report)的一份报告，该报告描绘了123所大学和学院的排名数据

**Summarize the Data总结数据**

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)

为了分析和总结123所大学的数据，必须应用描述性统计。描述性统计的一些关键因素是:平均值、标准差、最大值、中值和最小值。根据以上描述性统计，平均毕业率为0.6452，毕业率标准差为0.1698;学生对教师的均值是17.77，学生对教师的标准差是4.52。学生人数在50人以上的班级百分比，均值为0.14，标准差为0.06，学生人数在20人以下的班级百分比，均值为0.40，标准差为0.13。校友捐赠率均值为0.142，标准差为0.1700;新生保留率均值为0.8411，标准差为0.0839。由这一数据可以得到一个相关关系，毕业率与校友出资率和新生留校率正相关。校友捐赠率与新生留校率呈正相关。20人以下班级比例与校友出资率、毕业率、新生留校率呈正相关。而师生比例与新生留任率、毕业率、校友捐献率呈负相关。(修补pg.34)

**Linear Regression Model线性回归模型**

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)

毕业率是影响平均校友捐赠率的主要因素之一。为了预测校友捐赠率，毕业率必须纳入线性回归模型的计算。这个计算需要一个线性回归方程，即，校友捐赠率= -0.06718 + 0.3239(毕业率)。式中，b1为估计斜率，斜率为0.32，为正斜率，表示毕业率每增加1，校友捐献率增加0.32%。在此信息下，R平方值为0.4647，意味着46%的校友贡献率受到毕业率的影响。(修补pg。503)

**Multiple Linear Regression多元线性回归**

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)

为了预测校友捐赠率、师生比例、少于20名学生的班级百分比和毕业率，Joseph Randal开发了一个多元线性回归模型。可以确定，校友出资率为-0.06 + 0.248(毕业率)+ 0.144(20人以下班级的%)- 0.01(学生教员)。在这个方程中有几件事需要注意，0.249是b1的正斜率，它表明随着毕业率增加1，校友捐赠率增加了0.249个百分点;0.144是估计的b2的正斜率。这意味着，如果20人以下班级的比率每增加1人，学生出资率就会增加0.144%。斜率b3为负，其值为-0.001，表示随着师生率下降1，校友出资率将下降0.001个百分点。根据这个信息，R平方的值是0.5235或52.35%。这说明52.35%的校友贡献受到毕业率、师生比例、学生人数少于20人的班级比例的影响。(修补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.

根据这个图表可以得出这样高的校友捐献率是由于他们的新生保留率为98%，毕业率为96%，学生与教师的比率为12:1。我们可以有把握地得出这样的结论:班级规模越小，留校率就越高，因此毕业率也就越高。圣地亚哥州立大学、圣何塞州立大学和南阿拉巴马大学这三所大学的校友捐赠率并列最低，均为2%。这些大学的新生留校率从68%到83%不等，毕业率从37%到66%不等，师生比为25:1。我们可以有把握地得出这样的结论:学生与教师的比例越高，新生留任率越低，毕业率就越低。低毕业率导致校友的贡献率更弱更小。

**Similar School类似的学校**

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.

约瑟夫·兰德尔得知他所在的大学的师生比例为19:1，毕业率为65%，37%的班级学生少于20人，新生留校率为80%，23%的班级学生超过50人。拥有类似数据的最接近的大学是俄亥俄大学，它的师生比例为19:1，毕业率为65%，43%的班级学生少于20人，新生保留率为80%，11%的班级学生超过50人。一旦这个数据匹配，可以得到捐赠率，是8%，这意味着Randal的大学捐赠率也应该是8%。

**Conclusion****结论**

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..

综上所述，这一数据表明，高毕业率、高新生留校率、低师生比例、学生人数少于20人的班级比例高，校友捐赠率就高。为了获得高贡献率,应该提高毕业率高于89%,新生保有率利率应该提高95%以上,类的比例只有不到20个学生应该提高45%以上,学生faculty-ratios-should降到至少15:1,学生人数在50人以上的班级比例应降低到20%以下。所有这些因素都是非常重要的，对结果有很大的影响;因此，必须彻底、仔细、准确地考虑和处理……

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