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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.  contains data on the retention rate (%) and the graduation rate (%) for 29 online colleges in the United States.

 College RR(%) GR(%) Western International University 7 25 South University 51 25 University of Phoenix 4 28 American InterContinental University 29 32 Franklin University 33 33 Devry University 47 33 Tiffin University 63 34 Post University 45 36 Peirce College 60 36 Everest University 62 36 Upper Iowa University 67 36 Dickinson State University 65 37 Western Governors University 78 37 Kaplan University 75 38 Salem International University 54 39 Ashford University 45 41 ITT Technical Institute 38 44 Berkeley College 51 45 Grand Canyon University 69 46 Nova Southeastern University 60 47 Westwood College 37 48 Everglades University 63 50 Liberty University 73 51 LeTourneau University 78 52 Rasmussen College 48 53 Keiser University 95 55 Herzing College 68 56 National University 100 57 Florida National College 100 61

Instructions

Conduct a simple linear regression analysis to examine the association between the ‘retention rate’ (the independent variable) and the ‘graduation rate’ (the dependent variable). Using the Excel data file, prepare a 1200 word repot using the following structure.

In this section, the purpose of the report need to be clearly and concisely stated.

In this section, write an overview of the association between retention and graduation. Why would economists be interested in this particular issue?

Method

In this section, provide a brief overview of the data and empirical approach used to examine the association between retention and graduation.

1. Provide a descriptive analysis of the two variables (e.g., mean standard deviation, minimum and maximum).

2. Develop a scatter diagram with retention rate as the independent variable. What does the scatter diagram indicate about the relationship between the two variables?

3. Estimate a regression equation that can be used to predict the graduation rate (%) given the retention rate (%)

4. State the estimated regression equation and interpret the meaning of the slope coefficient

5. Is there a statistically significant association between graduation rate (%) and retention rate (%). Explain

6. Did the regression equation provide a good fit? Explain

7. 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?

8. 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?

In this section, provide a brief overview of the key results. What are the key strengths and limitations of this analysis? (e.g., data, method, etc.). How do the results from this analysis compare with other studies? (e.g., are the findings consistent?). Do these findings have clear policy implications?

In this section, you should present three well-considered recommendations.

## Overview of the Online Education Database

In wake of the growing trend of online university education in US, the given report aims to carry out a quantitative analysis based on the data provided so as to present findings in relation to these universities performance. Two key variables that have been used for performance analysis are Retention Rate (RR) and Graduation Rate (GR). The underlying relationship between these two variables would also be analysis. Based on this analysis, prudent recommendations can be offered in order to improve the US online university education so that this can contribute to the economic growth in a significant manner.

In the backdrop of technological revolution leading to developments of communication aids which are internet based, the delivery of product and services has seen a fundamental change. With regards to education, this has resulted in growing popularity of online courses. These courses tend to be flexible and offer a large degree of convenience to the students when compared to the classroom based education system. Also, owing to assess over the internet, the cost of these courses is comparatively a fraction of the offline courses (Craig, 2015). But online courses do have their concerns particularly in the context of dedication of the students which is apparent in higher dropouts of online courses as compared of offline courses (Hill, 2015). As a result, the objective of the given report is to highlight the underlying relationship between RR and GR for US based online universities so that inference can be made with regards to their relevance to the overall education system.

Taking into consideration the sample data of 29 US based online colleges, the underlying analysis is based on applying relevant statistical techniques. The summary statistic for the given variables has been outlined so that an overall picture of the industry (online education) can be gauged from the sample provided. In order to highlight the underlying relationship between RR and GR, scatter plot has been drawn with the former being the independent variable and latter being the dependent variable.  Also, a linear regression model has been worked out based on the sample data so as to obtain estimates of GR based on the different values of RR across online colleges across US.  The regression analysis is used for providing the colleges with useful recommendations in order to boost their overall performance and improve service quality.

1. For the two variables at hand i.e. GR and RR, the relevant summary statistics are reflected below.

1. The requisite scatter plot between RR and GR is indicated below with the former as the independent variable and latter acting as the dependent variable.

The scatter plot above clearly highlights a positive relationship between RR % and GR%. Also, the magnitude of this linear relationship seems to be moderately strong considering that deviations of the scatter points from the line of best fit are not very high (Hair et. al., 2015).

1. The regression related output derived from Excel is presented as follows.

## Purpose of the Report

1. Considering the regression output from excel, the regression equation is listed as follows.

From the above regression equation, it is clear that the slope comes out as 0.28 which indicates that a change in the RR by 1 percentage point would lead to corresponding change in the GR by 0.28 percentage point. Also, considering that the magnitude of the slope is positive, it reflects that the direction of change for the two variables would be same (Hillier, 2016).

1. For determining if the association between the above two variables i.e. RR and GR have statistical significance or not, the slope coefficient of the regression model needs to be tested for significance by using hypothesis testing.

Let the significance level for the test be 5% or 0.05.

For the slope coefficient of RR, as indicated in the regression output, the t stat is 4.69 with a corresponding p value of 0.00.

As the computed p value for the slope coefficient (i.e. 0.00) is lower that the level of significance, hence, it would be correct to conclude that the available evidence warrants rejection of null hypothesis and acceptance of alternate hypothesis (Flick, 2015). As a result, it is fair to conclude that the significance of slope coefficient is proven which also implies that RR and GR have a significant linear relationship.

1. The R2value (also called coefficient of determination) for the regression model under review has been derived as 0.4492 which is moderate since 44.92 of the variation in the dependent variable is explained on the basis of independent variable. Also, the significance of the slope coefficient has been established which implies model is a good fit

(Hastie,  Tibshirani and  Friedman, 2014).

1. If I am the president of South University, I would be concerned as despite having an RR of 51%, the GR is only 25%. By putting the value of RR in the regression equation obtained, the GR should have come out as about 40%. Considering that actual GR% is significantly lower than the estimated GR%, hence the reasons responsible for this need to be found and rectified.
2. If I am the president of University of Pheonix, I would be concerned about the abysmal RR% at 4% which is the lowest amongst the given sample data. However, a positive aspects is that despite the RR% being lowest, the GR is 28% which exceeds the estiamte made through regression analysis. Also, the GR% for University of Pheonix is superior in comparison to South University which has retention rate of 51%.

The results highlight that average RR% is about 55% while the average GR% is about 41% which seems reasonable. A higher dispersion is noticed in the RR% considering the wide range for this variable. The scatter plot highlights a positive and strong linear relationship between RR% and GR%. Further, the regression model highlights that 1% change in RR% would change GR% by 0.28% in the same direction. Also, the slope coefficient is found to be significant and the model a good fit (Hair et. al.,2015). Further, low GR% is a matter of concern for South University while low RR% is the concern for University of Phoenix.

A key strength of the analysis is that it is based on statistical analysis which lends credibility and enhances objective analysis. A limitation is that there is no information with regards to the sampling technique deployed to select the 29 colleges and also the market share in online education represented by these. However, the results obtained in the results section are supported from similar studies which enhances the relevance of the results. The results do have policy implications with regards to regulation of content and other measures that tend to have an impact on the quality of these online courses.

Considering the analysis carried out below, following recommendations may be offered to the online colleges in USA.

• Measures need to be taken to improve the retention rate by conducting surveys and feedback from the students. The respective colleges should resolve various issues that the students face to the extent feasible.
• Additionally, considering the issues with regards to the seriousness of the students enrolling for these courses, it makes sense to have some kind of entrance test or minimum academic grades to enrol which would ensure that only the serious candidates are able to enrol.
• Besides, it make sense for these online colleges and universities to offer courses that are relevant considering the changing job dynamics and the demand supply mismatch. This would result in enhanced relevance for these courses which potentially would address the issues of low RR% and GR%.

References

Craig, R.(2015),A Brief History (And Future) Of Online Degrees, [Online] Available at https://www.forbes.com/sites/ryancraig/2015/06/23/a-brief-history-and-future-of-online-degrees/#5be1eb3a7e37 [Accessed January 26, 2019]

Flick, U.(2015), Introducing research methodology: A beginner's guide to doing a research project, New York: Sage Publications, pp. 67-71

Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., & Page, M. J. (2015). Essentials of business research methods, New York: Routledge, pp. 103-106

Hastie, T., Tibshirani, R. and  Friedman, J.(2014), The Elements of Statistical Learning, New York: Springer Publications, pp. 89-93

Hill, P. (2015),No Discernible Growth in US Higher Ed Online Learning, [Online] Available athttps://mfeldstein.com/no-discernible-growth-us-higher-ed-online-learning/ [Accessed January 26, 2019]

Hillier, F. (2016),  Introduction to Operations Research, New York: McGraw Hill Publications, pp. 143-147

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