Purpose

One of the biggest challenges in the higher education sector has been the recent growth of online universities. The Online Education Database is an independent organisation whose mission is to build a comprehensive list of accredited online colleges. The Excel spreadsheet (OnlineEdu.xlsx) contains data on the retention rate (%) and the graduation rate (%) for 29 online colleges in the United States.

(a) Provide a descriptive analysis of the two variables (e.g., mean, standard deviation, minimum and maximum).
(b) Develop a scatter diagram with retention rate as the independent variable. What does the scatter diagram indicate about the relationship between the two variables?
(c) Develop and estimate a regression equation that can be used to predict the graduation rate (%) given the retention rate (%).
(d) State the estimated regression equation and interpret the meaning of the slope coefficient.
(e) Is there a statistically significant association between graduation rate (%) and retention rate (%). What is your conclusion?
(f) Did the regression equation provide a good fit? Explain.
(g) Suppose you were the president of South University. After reviewing the results, would you have any concerns about the performance of your university compared to other online universities?
(h) Suppose you were the president of the University of Phoenix. After reviewing the results, would you have any concerns about the performance of your university compared to other online universities?

Report needs to be structured as follows:
1. Purpose
2. Background
3. Method
4. Results
5. Discussion
6. Recommendations.

Purpose of this study is to find the relation between retention rate (%) and graduation rate (%). Through this study we also try to find whether retention rate can predict the graduation rate significantly.

Retention rate is defined as the number of students (converted to percentage) who continue the school next year. Graduation rate is defined as the number of students (converted to percentage) who complete their course within 150 % of the time of course. (What are graduation, retention, and transfer rates?)

Graduation rates and Retention rates have gained much attention recently. Recently institutes providing higher education are focusing on getting better retention rates and graduation rates. One research paper recognized the key points by which retention rates and graduation rates at an institute can be improved (Hanover Research).

IPEDS data was analysed and concluded not to find a significant correlation between graduation rate and institute retention plans (Ronald Anthony Milon, 2006).

Published literature cited tried to find relation between various environmental and social factors with retention rates and graduation rates. We were unable to cite any study which examined the relation between retention rate (%) and graduation rate (%).

This study try to find whether any relation exist between retention rate and graduation rate.

29 online education institutes of USAs data regarding retention rate (%) and graduation rate(%) was included for the analysis in this study. So, there are 2 variables and29 observations. Retention rates and graduation rates are continuous variables. So were summarized descriptively as mean and standard deviation. Minimum and maximum were also calculated. Correlation technique was used to find association between the variables. To find association Pearson correlation coefficient was calculated. Scatter plot was plotted to visually examine the trend of relation between retention rate and gradation rate.

Background

Regression technique was used to examine the relation between retention rate (%) (the independent variable) and graduation rate (%) (the dependent variable). ANOVA for the model, Goodness of fit for the model and hypothesis testing for slope was also carried out.

Pearson correlation coefficient value should lie between 0 to 1. Correlation coefficient value near to 0 indicates there is no correlation and value near to 1 indicates there is strong correlation. R-squared (Goodness of fit) will also lie between 0 to 1. R-squared value near to 0 indicates poor fit and near to 1 indicates good fit.

All the hypothesis testing and comparisons will be carried out at 5% significance level.

Hypothesis for Analysis of Variance –

Ho: The model is not significant

Ha: The model is significant

Hypothesis for slope –

Ho: β (slope) = 0

Ha: β (slope) ≠ 0

The analysis was performed on MS Excel. Correlation and regression was carried out using Excel Data Analysis Toolpak.

Analysis was performed on the data of 29 online colleges of USA for the two variables, retention rate and graduation rate. Retention rate and graduation rate were described as mean, standard deviation, minimum and maximum and is presented below.

Table 1: Descriptive Statistics

	Retention Rate (%)	Graduation Rate (%)
Mean	57.41	41.76
SD	23.24	9.87
Min	4	25
Max	100	61

Mean retention rate is 57.41 % and mean graduation rate is 41.76 %. Standard deviation for the retention rate is 23.24 % and standard deviation for Graduation rate is 9.87 %.

Scatter plot presented below was plotted to visually examine the relation between retention rate as independent variable and graduation rate.

Figure 1: Scatter plot

A slight positive linear relationship can be observed between retention rate and graduation rate. The line is not exactly parallel to x axis. Also, we can observe that as there is increase in retention rate graduation rate also increases.

Excel Data Analysis Toolpak was used to carry out correlation. Pearson correlation coefficient of 0.67 was obtained. So, a moderately positive linear relationship was found between retention rate and graduation rate. This was also supported by the scatter plot.

Excel Data Analysis Toolpak was used to carry out simple linear regression. For Regression analysis retention rate was input as independent variable and the dependent variable was graduation rate.

Table 2: Regression Results

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.670245
R Square	0.449228
Adjusted R Square	0.428829
Standard Error	7.456105
Observations	29
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1224.286	1224.286	22.02211	6.95E-05
Residual	27	1501.024	55.5935
Total	28	2725.31
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	25.4229	3.746284	6.786166	2.74E-07	17.73616	33.10964
RR(%)	0.284526	0.060631	4.692772	6.95E-05	0.160122	0.40893

Goodness of fit for the model was obtained to be 0.4492. This means that 44.92 % of variation in graduation rate is accounted for by the retention rate. Remaining 65 % of variation was not accounted for by the model. So, we can say that this model has moderate fit. The significance of the model was concluded based on Analysis of Variance results. The Analysis of Variance was found to be highly significant with p-value of

Regression equation can be given by –

Graduation Rate = 0.28*Retention Rate + 25.42

Regression resulted in the value of slope as 0.28. The value of slope implies that positive relation exist between retention rate and graduation rate. This means that 0.28 unit increase in graduation rate was observed when Retention rate increases by unit. Significance of slope was tested using two sided t-test. t-test resulted in the highly significant p-value of

Method

Retention rates and graduation rates of 29 online colleges of USA were collected and included in this study. Analysis was performed with purpose to examine whether there exist relation between retention rate and graduation rate. In this study we also tried to find whether retention rate can significantly predict graduation rate. Scatter Plot was plotted to visually examine the relation between retention rate and graduation rate.

Mean Retention Rate was greater than mean Graduation Rate. It means number of students retained or who attend the college next year is greater than the number of students who successfully complete their graduation within timeframe.

Florida State University Student Success Team published a paper which states the graduation rate of public institute is 52.4 % which is much higher than the mean retention rate calculated in this study.

Standard deviation for retention rate was greater than standard deviation for graduation rate. Minimum retention rate is less than minimum graduation rate and maximum retention rate is greater than maximum graduation rate.

Moderate positive correlation was found between retention rate and graduation rate. Goodness of fit value also implied moderate fit of the regression model. Only 44.92% of variation in graduation rate was accounted for by retention rate. Thus, about 55% of variation is not explained by this regression model. This means that there must be other social and environmental factors affecting graduation rate. Analysis of Variance model was found significant. Slope of Regression equation was found to be significant. This means that there exist significant linear relationship between retention rate and graduation rate. This is also supported by the trend observed in the scatter plot. Collectively from the above facts, we can also conclude that among many factors retention rate is certainly a factor which significantly predict graduation rate.

Thus, in our study we found mean for retention rate is greater than mean for graduation rate with more variation in retention rate values. We also found moderate positive linear correlation between retention rate and graduation rate based on correlation results and scatter plot. We found that there exist significant linear relationship between retention rate and graduation rate with moderate fit model.

The graduation rate of South University is poorest among other 27 online institutes included in the study. It shares same graduation rate with Western International University. This means that less number of students successfully complete their graduation in South University within timeframe. As a President of South University I should be concerned about lifting the graduation rate and should take some firm steps to boost spirit of students to complete their graduation successfully and within acceptable timeframe.

For the University of Phoenix retention rate is poorest with low graduation rate also. As a President of University of Phoenix, I should execute such strategies not only motivate students to retain or attend the college next year as well but also boost their morale to complete their graduation successfully within acceptable timeframe.

References

1) What are graduation, retention, and transfer rates? Available from: https://fafsa.ed.gov/help/fotw91n.htm (Accessed on 08 Jan 2015)

2) Practical Steps to Improving Retention and Graduation Rates. Florida State University Student Success Team. Available from: www.hawaii.edu/offices/app/hgi/EDI_02-2013/PracticalStepsFinal.pdf (Accessed on 07 Jan 2015)

3) HANOVER RESEARCH (2011). Improving Student Retention and Graduation Rates. Available from: www.mybrcc.edu/intranet/attachments/article/110/Improving%20Student%20Retention%20and%20Graduation%20Rates.pdf (Accessed on 07 Jan 2015)

4) Ronald Anthony Milon (2006). The Relationship Between Institutional Retention Plans and Retention Rates. Chapter 4 Data Collection Analysis (Page 75). Available from : https://books.google.co.in/books?id=3lvGweq5jVgC&printsec=frontcover#v=onepage&q&f=false (Accessed on 07 Jan 2015)