Linear Regression Report on RR and GR Relationship in Online Education

This report is aimed at modelling a simple linear regression line and apply the techniques to evaluate the nature of relationship between the RR and the GR in online education. The data sample used in the analysis was derived from the Online Education Database which is an independent institution responsible for generating a list of accredited universities cleared to offer online courses. The results of the analysis was thereafter applied in making recommendations to the online institutions.

ECONOMICS AND QUANTITAIVE ANALYSIS 1
Economics and Quantitative Analysis
by Students Name
Course
Professor’s Name
Institution
City
Date

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Linear Regression Report
Purpose
This report is aimed at modelling a simple linear regression line and apply the
techniques to evaluate the nature of relationship between the RR and the GR.
Background
As the use of internet spreads globally educational institutions offering online services
have gone up as well. The present of a number of colleges availing online study opportunities
have increased access to education though it has also come with the challenge of knowing the
right institution to opt for a course. As a way of assisting stakeholders make this crucial
choice in life, two rates have emerged into the limelight that is the RR and the GR (Callahan
& Belcheir 2017). GR by definition is the percentage of freshmen joining an institution who
goes ahead to graduate from the institution within 150% of the time set to normally complete
the course (Dunlap & Lowenthal 2010). On the other hand, RR is the percentage of the
students who join a college as first year and came back to continue on the same institution
during second year of study.
RR and GR are important statistics that make the selection struggle an easy one by
giving students away of ranking the institutions (Rubin 2012). They indicate the level of
education quality that a college offer in addition to proving university’s ability to maintain
the standard set during students’ recruitments (University of Arkansas, 2014).
Method
The data sample used in the analysis was derived from the Online Education Database
which is an independent institution responsible for generating a list of accredited universities
cleared to offer online courses (Berg, 2009). The data sample of 29 colleges was applied to
draw a scatter plot, model a simple regression as well as draw descriptive statistics. The
results of the analysis was thereafter applied in making recommendations to the online
institutions.
Results
a. Descriptive statistics
The table presents a descriptive analysis of the sample data.

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Descprtive Analysis
RR(%) GR(%)
Mean 57.4138 Mean 41.7586
Standard Error 4.3156 Standard Error 1.8320
Median 60 Median 39
Mode 51 Mode 36
Standard Deviation 23.2402 Standard Deviation 9.8657
Sample Variance 540.1084 Sample Variance 97.3325
Kurtosis 0.4618 Kurtosis -0.8824
Skewness -0.3099 Skewness 0.1764
Range 96 Range 36
Minimum 4 Minimum 25
Maximum 100 Maximum 61
Sum 1665 Sum 1211
Count 29 Count 29
Largest(1) 100 Largest(1) 61
Smallest(1) 4 Smallest(1) 25
b. Plotting the scatter diagram
A scatter plot is a graph which represents the values of two variables plotted
along two exes. The pattern of the plot is meant to reveal the association between the
two values. In the diagram below the RR is the independent variable (x axis) while the
GR is the dependent variable (y axis). The diagram below gives the scatter plot of RR
and GR (Emerson, et al. 2013). A reference to the table can be used to conclude that
the retention as well as graduation rate have a positive correlation. That is any
positive change in the RR will affect the graduation rate in the same direction.

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c. Regression equation estimation
From the scatter plot above it can be observed that the line of best fit is
represented by the equation y=0.2845 x +25.423. Given the retention rates this linear
equation can be applied to estimate the graduation rate with the minimal errors
possible.
d. Stating the regression equation
The equation y=0.2845 x +25.423 has been estimated to best describe the
relation between RR and the GR. The slope coefficient describes how the GR values
change when the RR changes by 1% (Tofallis 2009). In this scenario an increase or a
decrease in RR by 1% will lead to an increase or a decrease in the GR value by
0.2845%
e. Explanation of the correlation
To evaluate the nature of association between the RR and the GR a simple
linear regression model is developed as presented in the table below. The 0.6702
obtained as the correlation coefficient indicates a strong positive correlation. The R
square value of 0.4492 mans at least 44.92% of the changes on the GR are explainable
by the RR.

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SUMMARY OUTPUT
Regression Statistics
Multiple R 0.670244797
R Square 0.449228088
Adjusted R Square 0.428829129
Standard Error 7.456104604
Observations 29
ANOVA
df SS MS F Significance F
Regression 1 1224.285956 1224.285956 22.02210775 6.95491E-05
Residual 27 1501.024388 55.59349587
Total 28 2725.310345
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 25.42290363 3.746283822 6.786165928 2.7441E-07 17.73616416 33.1096431 17.73616416 33.1096431
RR(%) 0.284526003 0.060630691 4.692771862 6.95491E-05 0.1601221 0.408929906 0.1601221 0.408929906
f. Fitness of the model
The fitness of a regression model is evaluated by the significance F statistics
test. In the model above the value is below 0.05. At a 95% confidence interval the
model is fit and can be used to predict the values of the GR given the RR (Malakooti
2013).
g. South University
South university’s graduation rate is 25%. When this value is compared to the
industry’s average rate of 41.76%, then its clear that the South University
performance is very poor and need management intervention. Similarly, the RR is
51% slightly falling below the industry rate of 57%. This information indicates that
competitively South University is offering poor quality services.
h. Phoenix university
The retention rate at Phoenix university is 4% which is way below the average
of 57%. In addition, the graduation rate stands at 28% also below average. Phoenix
University administration should be concerned as the institution’s performance is
extremely below per.
Discussion
The education’s sector average graduation rate stands at 41.76% while the RR is
57.41%. the institution with the least retention rate has 4% with the highest being 100%.
Also, the graduation range is minimal at 25% with a range of 36%.
Upon developing the simple linear regression model, the findings indicate that there is
a strong positive correlation between the two variables with a regression coefficient of 0.6702
supporting the argument. This same finding is visible in the scatter plot drawn above.

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The research by Jewell (2015) found out that the RR and the GR are affected by
similar aspects of the university. This gives an insight into the possibility of correlation
between the two variables.
The small sample size that has been analysed to arrive at the conclusion limits the
authenticity of the study. This is because the size may not represent the actual population
thereby leading to formulation of misleading recommendations (Sidle & McReynolds 2009).
Recommendations
From the findings derived from the data analysis above the following aspects need to
be taken in to account.
i. The South and Phoenix university need to set student centre department to
deal with issues affecting students while at the school.
ii. The universities need to review their curriculum to ensure the quality if
education in the institutions is as per the expectations if the students
iii. Farther research ought to be conducted to determine the main issues behind
the low RR and GR in the two school

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References
Berg, B 2009, Qualitative Research Methods for the Social Sciences. Seventh ed. Boston:
Pearson Education Inc.
Callahan, J & Belcheir, M 2017, Testing Our Assumptions. Journal of College Student
Retention: Research, Theory \& Practice, Volume 19, pp. 161–175.
Dunlap, J & Lowenthal, P 2010, Defeating the Kobayashi Maru: Supporting Student
Retention by Balancing the Needs of the Many and the One. Educause Quarterly,vol. 33, no.
3, pp. 33.
Emerson, J, Green, W, Schoerke, B & Crowley, J 2013, The Generalized Pairs Plot". ..
Journal of Computational and Graphical Statistics, 22(1), p. 79–91.
Jewell, S 2015, Retention and Graduation Rates at Public Research Universities: Do
Medical Centers Affect Rates?. [Online]
Available at: http://martin.uky.edu/sites/martin.uky.edu/files/Capstone_Projects/
Capstones_2015/Jewell.pdf
[Accessed 29 January 2018].
Malakooti, B 2013, Operations and Production Systems with Multiple Objectives, New
Jersey: John Wiley & Sons.
Rubin, M 2012, Social class differences in social integration among students in higher
education: A meta-analysis and recommendations for future research. Journal of Diversity in
Higher Education, Volume 5, p. 22–38.
Sidle, M. & McReynolds, J 2009, The freshman year experience: Student retention
andstudent success. NASPA Journal, 46(3), pp. 434-446.
Tofallis, C 2009, Least Squares Percentage Regression. Journal of Modern Applied
Statistical Methods, Volume 7 , p. 526–534.
University of Arkansas 2014, Increasing Graduation Rates, University of Arkansas Quality
Initiative Proposal. [Online]
Available at: https://provost.uark.edu/accreditation.php
[Accessed 30 January 2018].

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