Linear Regression Report on Retention and Graduation Rates

This report analyzes the correlation between retention rates and graduation rates in 29 US colleges using linear regression. The study finds a strong positive correlation between the two rates and recommends universities to consider both when making selections. The report also provides recommendations for universities to improve their retention and graduation rates.

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ECONOMICS AND QUANTITAIVE ANALYSIS: LINEAR REGRESSION REPORT
by Students Name
Name of the course
Professor’s Name
University
City/State
Date

Economics and Quantitative Analysis 2
Purpose
The study will on the development of a linear regression line and apply the same in
studying the correlation between the variable’s RR and the GR.
Background
currently several universities have emerged offering various studies. One of the most
challenging task parents and students face is selecting the right school for a course.
Graduation rate (GR) can be defined as the proportion of the college’s first year students
joining the institution for the first time who goes ahead to complete their studies within 150%
of the programs established period (Callahan & Belcheir 2017). On the other hand, rate of
retention (RR) is defined as the proportion of the students joining the college for the first time
who continue to study in the school the following year. Students transfer from a school have
a negative impact on their previous school retention rate (Dunlap & Lowenthal 2010).
Retention and graduation rates are two vital statistics that students and parents need to
consider when choosing a prospective college. They are indicators of the level of student’s
happiness in the college (Rubin 2012). In addition, the two ratios provide an idea of the
school’s support to the students as well as the likelihood that the tuition money is well
utilised. The two rates are simple standard of measure that are easy to interpret as its straight
forward (University of Arkansas, 2014).
Method
As away of gauging quality of education the retention and the graduation rates are
some of the statistics that can assist parents and potential students make a choice. The data to
be used in the analysis is a sample from the online educational database. This is an
organisation that is independently mandated to generate a list of accredited online colleges in
the United States. The sample consist of 29 colleges. Using the Microsoft excel we drew a
scatter plot and modelled a linear regression. Thereafter a line of best fit was developed
(Berg, 2009). Having derived the regression coefficient and the slope of coefficient, the
information was applied in determining the regression between the retention and the
graduation rates.
Results

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a. Descriptive analysis
The table below gives a summary statistic on the rate of graduation and the rate of
retention of the 29 sampled colleges across the US.
RR (%) GR (%)
Mean 57.4137931 Mean 41.75862069
Standard Error 4.315602704 Standard Error 1.832018976
Median 60 Median 39
Mode 51 Mode 36
Standard Deviation 23.24023181 Standard Deviation 9.865724115
Sample Variance 540.1083744 Sample Variance 97.33251232
Kurtosis 0.461757455 Kurtosis
-
0.882399313
Skewness
-
0.309920645 Skewness 0.176364432
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
Confidence Level
(95.0%) 8.840111401
Confidence Level
(95.0%) 3.752720754
b. Scatter diagram
When a scatter diagram of retention rate verses the graduation, rate is drawn the
figure below is obtained.

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An observation of the trend of the scatter plots reveals a strong positive
correlation between the RR and the GR. This shows that when a university have a
high RR the rate of graduation is also expected to be high (Emerson, et al. 2013).
c. Estimating regression equation
The equation y=0.2845 x +25.423can be applied in redicting the GR given the
RR o predict the college graduation rate given the retention rate. In this case the x
represents the retention rate while the graduation rate is presented by the y value.
d. Estimating and interpreting the regression equation
The equation y=0.2845 x +25.423 is modelled to predict the correlation
between the RR and the GR. In this model the value of the graduation rate when the
retention rate is zero is 25.423%, a change of the retention rate by 1% changes the GR
by 0.2845%. the value 0.2845 is the slope coefficient, it describes how the graduation
rate changes with a change in the GR (Tofallis 2009).
e. Statistical significant
When a regression model is developed the table below gives a summary of the
findings.

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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
From this table the value of the regression coefficient (r) is obtained as 0.6702.
this shows that the retention rate and the graduation rate have a strong positive
correlation. The R square value is 0.4492. The value means that 44.92% of the
changes in the graduation rates are explainable by the differences in the retention
rates.
f. Regression equation fit
The F statistics is used to evaluate the effectiveness of the model in predicting
the situation. In this case the value of the F statistics is 5%, when the regression is
evaluated at a 95% significance level. This can be used to approve that the regression
model is a significant fit in modelling the relationship between the RR and the GR
(Malakooti 2013).
g. South University
The South University has a retention rate of 51% with a 25% GR. Using the
model developed at 51% retention rate the graduation rate should be
y= ( 0.2845∗51 ) +25.423=39.93 %. From this model, it’s evident that the graduation
rate is lower than expected something that should worry the university president.
h. University of Phoenix
Phoenix has a RR of 4% with GR of 28%. From the model a 4% retention rate
should give a graduation rate of y= ( 0.2845∗4 ) +25.423=26.561 %. As the president
of Phoenix University there should be no concern as the university is performing way
better than other schools at the same retention rate.
Discussion
The college retention rates have a mean of 57% with a deviation of 23%. On the other
hand, the graduation rate has a mean of 41% with a standard deviation of 9%. This shows that

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the graduation rate is more volatile than the retaining rates. When the linear regression is
modelled the coefficient of regression is obtained as 0.6702 proving a strong positive
correlation. This result is consistent with findings from other scholars. For instance,
according to Jewell (2015), the aspects of a university that impact on the retention rate have
the same effect on the graduation rate. For instance, a university that focuses on providing
quality education to its students is likely to retain students beyond the first year. Due to the
quality education this same university will have a higher graduation rate. This proves a strong
positive correlation between the RR and the GR. An increase in one will also go along with
increase with another. Furthermore, as students maintain the college there is a probability of
graduation in time hence positively impacting on the graduation rate (Sidle & McReynolds
2009).
The major limitation of this study is the small sample size that has been applied when
arriving at the conclusions. This may not have an actual representation of the population.
Being that the findings are in line with other past studies on the two ratios, it can be
concluded that the rates need to be accounted for when making university selections.
Recommendations
Based on the analysis and the findings above the following need to be looked at;
The president of the university of Phoenix need to appoint a team to assist investigate the
reason behind the low retention rate being experienced at the university.
Despite the high retention experienced in South University the graduation rate is still
below the expected number, the president therefore needs to have the root of the issue
investigated.
Having concluded that RR has a positive impact on the GR, the online universities
should set a department to assist gather and respond to the students need in a propriate
manner.

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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, p. 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, p. 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/
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Rubin, M 2012, Social class differences in social integration among students in higher education: A
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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].