Economics and Quantitative Analysis: Regression Analysis Report

This report analyzes the performance of online universities in the US using regression analysis, focusing on graduation rates (GR%) and retention rates (RR%). The study examines data from 29 US-based online universities, employing descriptive statistics, scatter plots, and linear regression models to explore the relationship between RR% and GR%. The results indicate a directly proportional relationship, with a regression equation of GR% = 25.423 + 0.285*RR%. The slope coefficient is statistically significant, and the model explains 44.92% of the variation in GR% through RR%. Specific universities like South University and University of Phoenix are discussed in terms of their performance relative to the regression model's predictions. The report concludes with recommendations for improving online university performance, including stricter entry qualifications, addressing factors affecting retention rates, and increased regulatory oversight to ensure quality and relevance. Desklib provides this and many other solved assignments to help students.

ECONOMICS AND QUANTITATIVE ANALYSIS
Regression Analysis
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Purpose
The online courses have witnessed a sizable growth in popularity in the US and such courses
tend to complement the offline university education. With regards to fulfilling future
manpower demand, it is imperative that the intended educational outcomes must be achieved.
Hence, the performance of the online universities in US needs analysis so that any
improvements required may be introduced in a timely manner. For the given analysis, the
performance of online universities has been captured using two key variables namely
graduation rate (GR%) and retention rate (RR%). The graduation rate captures the percentage
of candidates from the retained candidates who are able to graduate. The retention rate
highlights the percentage of candidates who do not drop out of the respective course before
completion. Useful information is conveyed using these indicators in relation to online
university performance which has served as the basis for improvement measures.
Background
Owing to increased penetration of internet, the delivery mechanism of key services and
products has altered fundamentally. One of the services in this regards is education whereby
online delivery provides significant flexibility to students both in terms of location and
timing. Also, the cost associated with online courses is usually only a fraction of the
traditional offline courses. It therefore does not come as a surprise that the popularity and
proponents of online courses has been on a rise (Lederman, 2018). A key aspect which
cannot be ignored in this backdrop is the high drop-out rates which are experienced in the
online courses (Wellman, 2018). Considering this concern, the analysis of performance of
the providers of this course becomes vital as increasingly a larger proportion of student is
seeking online university education in US.
Method
Considering that objective is to offer recommendations derived from statistical analysis,
hence the sample data plays a crucial role. This essentially represents information with
regards to GR% and RR% in relation of 29 US based online universities. For the two
variables under consideration, descriptive statistics summarising central tendency and
dispersion have been computed. Further, in order to explore the extent and nature of
association between RR% and GR%, scatter plot has been drawn. Additionally, linear
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regression analysis model has also been obtained to perform the relevance of slope along with
determining fit. The performance of the selected sample universities has been analysed using
the equation of regression line and suitable recommendations for performance improvement
have been indicated.
Results
a) Excel based descriptive statistics
.
b) Excel based Scatter Plot
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The scatter plot derived above highlights directly proportional relationship between retention
rate and graduation rate. This is reflected from the arrangement of points which are inclined
upwards and hence hint at a positive slope value. The best fit line seems to be indicative of
the pattern as the scatter points do not deviate significantly. This would hint at high strength
of association which is also confirmed from the correlation coefficient value which is higher
than 0.5 (Hillier, 2016).
c) Excel Based Regression Output
d) The regression model obtained above indicates at the following regression line equation.
GR% = 25.423 +0.285*RR%
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In the equation shown above, 25.423 is the intercept value while 0.285 serves as the slope.
When RR% changes by 1 unit, it would be fair to expect that GR% would alter by 0.285 unit.
The fact that the slope for this equation is positive would reflect that the movement in both
variables occurs in the same direction only (Lieberman et. al., 2013).
e) For testing statistically significance of slope coefficient, the following hypotheses would
be used.
For the hypothesis testing, α or significance level is 5%.
The test statistic is T whose value is computed as 4.69 from the regression model.
Additionally, the p value for the t statistic has been derived as 0.00.
As α (0.05)> p value (0.00), hence the evidence presented would lead to H0 rejection and H1
acceptance (Hair et. al., 2015). Hence, it is correct to conclude that slope coefficient is
significant and cannot be assumed to be zero. This implies statistical significance of the lienar
relationship exhibited between the two variables.
f) The R2 value for the regression model has been indicated in the excel output as 0.4492.
Hence, 44.92% of the variations observed in the GR% would be offered explanation by
alternations in the RR%. The regression model also has a non-zero slope which is
considered significant. The model clearly represents a good fit despite the moderate R2
which can be increased by introducing relevant independent variables (Medhi, 2016).
g) The RR% for the South University is higher than 50% and is therefore does not present
any concern. But the issue for the university is that GR% is significantly lower than the
expected value derived from the regression equation taking the input as the actual RR% of
51%. As a result, this aspect needs to be looked into so that measures to improve the GR%
can be undertaken.
h) The GR% for the University of Phoenix is low but still does not pose much concern as the
RR% is only 4%. For this RR%, the GR% expected from the regression model is much
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lower than the current GR% witnessed for the university. Hence, the key area of concern is
the 4% RR% which needs to be addressed on priority basis which also would lead to
improvement in GR%.
Discussion
The average performance for these universities does not seem too problematic but the key
issue is the underlying dispersion amongst the universities. Based on the various measures of
dispersion, it is apparent that GR% has lower dispersion in comparison to RR%. It has been
seen that the performance of majority of sample universities lacks in one aspect which results
in inferior performance. The scatter plot based on the sample data indicates that the linear
association between the given performance variables is strong and positive in nature.
Further, the analysis of the linear regression model hints at the statistical significance of the
slope coefficient.
The key positive aspect about the analysis lies in the fact that conclusions have been derived
backed by statistical analysis. A concerning issue is the potential of the sample data being
biased and thereby lacking in reliability. This could arises owing to use fo improper sampling
technique which does not provide a random sample and hence incorporates various bias
(Flick, 2015). Some mitigation in this regards may be derived from the fact that the results
are comparable with other empirical studies in the recent past in the US context. Considering
the gaps in performance, the analysis has significant implications for the policymakers as
some intervention from regulators may be desirable.
Recommendations
Recommendations aimed towards performance improvement are listed as follows.
1) A key concern that has emerged is with regards to non-serious students. To resolve this
issue, minimum qualifications or marks may be decided by the online universities
collectively. Further, a standardised entry test should be required to be cleared if the
student lacks minimum qualifications or marks.
2) By referring to the available literature and student feedback, the universities provided
online courses must aim to find lapses and introduce rectifying measures for improvement
in retention rate.
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3) Considering the pivotal role that online university courses are gaining in the US
educational system, some degree of regulation with regards to quality and processes is
desirable. This would ensure that the relevance of these courses and related facilities do
not become irrelevant to the current needs of student and industry.
References
Flick, U. (2015) Introducing research methodology: A beginner's guide to doing a research
project. 4th ed. New York: Sage Publications, pp. 65-67
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015) Essentials
of business research methods. 2nd ed. New York: Routledge, pp. 87-89
Hillier, F. (2016) Introduction to Operations Research.6th ed.New York: McGraw Hill
Publications, pp. 134-135
Lederman, D. (2018) Who Is Studying Online (and Where), Available [online] at
https://www.insidehighered.com/digital-learning/article/2018/01/05/new-us-data-show-
continued-growth-college-students-studying [Assessed February 10, 2019]
Lieberman, F. J., Nag, B., Hiller, F.S. and Basu, P. (2013) Introduction To Operations
Research. 5th ed. New Delhi: Tata McGraw Hill Publishers, pp. 78-79
Medhi, J. (2016) Statistical Methods: An Introductory Text. 4th ed. Sydney: New Age
International, pp. 114
Wellman, R. (2018) How to Avoid Dropping Out of an Online College Available [online] at
https://www.usnews.com/education/online-learning-lessons/articles/2018-06-01/how-to-
avoid-dropping-out-of-an-online-college [Assessed February 10, 2019]
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