Questions to be answered in your report:

Use methods of descriptive statistics to summarize the data.

Develop and estimated simple linear regression model that can be used to predict the alumni giving rate, given the graduation rate. Discuss your findings.

Develop an estimated multiple linear regression model that could be used to predict the alumni giving rate using the graduation, % of Classes Under 20, and Student/Faculty Ratio as independent variables. Discuss your findings.

Which of the 123 schools has the most (least) impressive giving rate? Discuss your findings.

Consider a school that similar to Joseph’s university. Joseph’s university has 65% graduation rate and a student-faculty ration of 19:1, 37% of the classes have fewer than 20 students, 23% of the classes have more than 50 students, and have a freshman retention rate of 80%. Should Joseph’s university giving rate be greater or less than 8%?

What conclusions and recommendations can you derive from your analysis?

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**SAMPLE SOLUTION**

Business Statistics Project

**Introduction**

The alumni giving rate is a significant concern for most university amidst emerging budget cuts and financial constraints. Most universities are beginning to devise ways of increasing alumni giving rates to address the financial challenges (Anderson, Sweeney & Williams, 2014). However, it is vital to understand the association between the giving rates and other factors such as graduation rates, student-faculty ratio, freshman retention rate, percentage of classes with less than 20 students, and percentage of classes with more than | PLACE YOUR ORDER NOW AT writtask.com | of the factors is essential in understanding the extent to which the variables include alumni giving. The report presents linear and multiple regression models to predict the alumni giving

**Data Summary Using Descriptive Statistics**

The descriptive statistics in Table 1 shows the mean, variance, standard deviation, skewness, median, mode, minimum values for the various variables under analysis. According to the dataset, the average student-to-faculty ratio is 17.77:1, while the percentage of classes with fewer than 20 students | PLACE YOUR ORDER NOW AT writtask.com | of classes with more than 50 | PLACE YOUR ORDER NOW AT writtask.com | alumni is 14.179%, which is relatively lower despite the high average graduation rate of 64.52% over the past six years. The standard deviation and variance give deviation of the data from average values. It shows the level of concentration of the data around the mean. Based on the summary statistics, the standard deviation for alumni giving is at 0.08607, while the student-faculty ratio…

*Table 1: *Descriptive statistics

**Simple Linear Regression Model**

The simple linear regression model shows the relationship between two variables and explains the extent to which one variable depends on the other. A regression of giving rate as the outcome variable and graduation rate as an independent variable shows a positive linkage between the variables. The regression output shows a positive coefficient of 0.3239 for graduation rates and an intercept of -0.06718. The scatter plot and trend line also…

Figure 1: Scatter plot for alumni giving rate (GIVE) and graduation rates (GRAD)

**Multiple Linear Regression Model**

Multiple linear regression, on the other hand, shows the relationship between one outcome variable and more than one independent variable. For the graduation rates, the percentage of classes under 20 students, and the student-faculty ratio as independent variables, the regression model can be generated as | PLACE YOUR ORDER NOW AT writtask.com | output, the coefficients for student-faculty ratio, percentage of classes with less than 20 students, and graduation rates are -0.00102, 0.130197, and 0.257705, respectively. The multiple regression model for the variables can be expressed as Y = 0.2577GRAD + 0.1302LT20 – 0.00102SFR. It shows a negative relationship between giving rate ….

*Table 2: *Multiple linear regression output

**Findings on Giving Rates**

The descriptive statistics summary in Table 1 shows that the University of Notre Dame has the most impressive giving rate at 41%. The high giving rate is supported by the university’s high graduation and freshman retention rates (FRR) of 96% and 98%, respectively. Only a smaller portion of the classes have more than 50 students estimated at 10%, while 55% of the classes have less | PLACE YOUR ORDER NOW AT writtask.com | ratio is also low at 12:1. The indicators support high giving since the university retains most of its freshmen and achieves the highest average graduation rates over the last six months. The descriptive statistics in Table 1 also show that the University of South Alabama had the least impressive giving rate of 2%. It is the least impressive because of the low graduation rate of 37%…

**Comparison of Giving Rates**

The multiple regression model for all the variables under investigation is given as Y = 0.2569FRR + 0.1298GRAD + 0.1507LT20 – 0.0322GT50 – 0.0011SFR. Assuming that Joseph’s university has a graduation rate of 65%, student-faculty ratio of 19:1, percentage of classes with less than 20 students at 37%, 23% with more than 50 students, and freshman retention rate of 80%, the giving rate would be calculated as presented below.

Y = 0.2569FRR + 0.1298GRAD + 0.1507LT20 – 0.0322GT50 – 0.0011SFR

Graduation rate (GRAD) = 65%, Student-faculty ratio = 19:1, percentage of classes with fewer than 20 students = 37%, percentage of classes with more than 50 students at 23%, and freshman retention rate = 80%.

Giving rate (Y) = (0.2569 × 80%) + (0.1298 × 65%) + (0.1507 × 37%) – (0.0322 × 23%) – (0.0011 × 19)

Giving rate = 20.55% + 8.40% + 5.58% – 0.74% – 0.02% = 33.77%

Joseph’s university would have a giving rate of 33.77%. The analysis shows that Joseph’s giving rate should be more than 8% given the average values for the variables.

**Conclusion and Recommendations**

The analysis shows the relationships between the giving rates and other independent variables. The alumni giving rate is expected to be affected by several factors, including graduation rates, student-faculty ratio, freshman retention rate, percentage of classes with less than 20 students, and classes with more than 50 students. A positive nexus exists between alumni giving rates, graduation rate, freshman retention rates, and percentage of classes with less than 50 students. It implies that the university is likely to increase alumni giving rate is they retain most of the freshmen and reduce class size such that there is high student performance. However, a negative linkage exists between the percentage of classes with more than 50 students and the student-faculty ratio. The lower the rates…