Economics Report: Association Between Retention and Graduation Rates

This report investigates the association between the percentage of retention rate and the percentage of graduation rate in online universities. The study employs a correlational research design using quantitative secondary data from the online education database. The analysis includes descriptive statistics, scatter diagrams, and a linear regression model to examine the relationship between the two variables. The results reveal a positive correlation, indicating that higher retention rates are associated with higher graduation rates. The regression equation is estimated, and the goodness of fit is assessed. The report further discusses the statistical significance of the association, provides interpretations of the slope coefficient, and addresses potential concerns from university administrators based on the findings. Recommendations are provided for improving retention rates and the accreditation process of online universities. The report concludes that retention rate is a key factor that influences the graduation rate, highlighting the importance of policies that enhance student retention.

ASSOCIATION BETWEEN THE PERCENTAGE OF THE RETENTION RATE AND
THE PERCENTAGE OF THE GRADUATION RATE

Table of Contents
Introduction................................................................................................................................................3
Purpose...................................................................................................................................................3
Background of the study.........................................................................................................................3
RESEARCH METHODOLOGY........................................................................................................................3
Research design......................................................................................................................................3
Data collection........................................................................................................................................3
Data analysis...........................................................................................................................................3
RESULTS......................................................................................................................................................4
Descriptive analysis................................................................................................................................4
Retention and the graduation rate........................................................................................................4
Scatter diagram of the retention rate and the graduation rate..............................................................5
Estimate of the regression equation.......................................................................................................5
Regression equation and interpretation of the slope of the slope coefficient........................................6
Statistical significance of the association between the retention and the graduation rate....................7
Regression equation goodness of fit.......................................................................................................8
Concerns from the South University after result review........................................................................8
Concerns from the University of Phoenix after result review............................................................8
DISCUSSION............................................................................................................................................9
Mean percentage.................................................................................................................................9
Minimum and maximum percentage.................................................................................................9
Regression equation...............................................................................................................................9
Regression model goodness of fit...........................................................................................................9
Correlation...........................................................................................................................................10
Recommendation......................................................................................................................................10
References.................................................................................................................................................11

Introduction
Purpose
This purpose of this study is to investigate the association between the percentage of the
retention rate and the percentage of the graduation rate.
Background of the study
The growth of online universities is increasing tremendously (Gregory, 2013) and it cuts across
the globe presenting challenges, advantages, and disadvantages to the institutions of higher
learning. Studies by (Muuro et al, 2014) reveal that the growth of online universities have pose a
greate challenge to the institution of higher learning and students experience difficulties in
collaborating with the online universities. However, in order for the online accredited
universities to have higher percentage of the graduation rate, the percentage retention rate should
be high (Jodi, 2011) . Jodi further illustrates the advantages of the online accrediteduniversities
on people with disabilities. This study therefore as it focus on the association between the
retention rate and the graduation rate,will be of great healp to economist in formulation of
policies and making recommendation based on the informed judgement.
RESEARCH METHODOLOGY
Research design
Correlational study design was employed for this study.
Data collection
The study utilizes quantitative secondary data that was obtained from the online education
database.
Data analysis
Quantitative techniques were used for analyzing the data. Data was analyzed for both descriptive
and inferential statistics.
Analysis was carried out using Excel.

RESULTS
Descriptive analysis.
Retention and the graduation rate.
Retention rate (%) Graduation rate (%)
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
Confidence Level (95.0%) 8.840111401
Confidence Level
(95.0%) 3.752720754

Scatter diagram of the retention rate and the graduation rate
0 20 40 60 80 100 120
0
10
20
30
40
50
60
70
scatter plot
RR%
GR%
The scatter diagram reveals the Percentage of the graduation rate (dependent variable) and the
percentage of the retention rate (the independent variable) vary together, in the same way,
portraying an existence of a positive association between the two variables.
Estimate of the regression equation
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.621627987
R Square 0.449221354
Adjusted R Square 0.362822175
Standard Error 7.57961179
Observations 28

ANOVA
df SS MS F
Significance
F
Regression 1 940.7152 940.7152 16.37436 0.000414
Residual 26 1493.713 57.45051
Total 27 2434.429
Coefficients
Standard
Error t Stat P-value
Lower
95%
Upper
95%
Intercept 25.42302221 4.263687 6.123062 1.79E-06 17.34269 34.87096
7 0.284532436 0.067819 4.046524 0.000414 0.135028 0.413837
From the above output, our regression equation to be used for estimation of the percentage
graduation rate given the percentage of the retention rate is estimated as follows;
The regression equation that estimates the graduation rate is Graduation rate = 25.423 + 0.2845 *
retention rate. This implies that an increase of the percentage of the retention rate by one unit
will result to an increase in the percentage of the graduation rate by 0.2845 units (Jesper , 2010).
Regression equation and interpretation of the slope of the slope coefficient
0 20 40 60 80 100 120
0
10
20
30
40
50
60
70
f(x) = 0.284526002809143 x + 25.4229036318199
R² = 0.449228088348509
GR% Aganst RR%
Series2
Linear (Series2)
Linear (Series2)
RR%
GR%

The estimated equation is
y = 0.2845 x + 25.423 where y represents the percentage of the graduation rate and x represent
the percentage of the retention rate.
Graduation rate = 25.423 + 0.2845 * retention rate
This is interpreted as follows;
There is a positive relationship between the two variables. An increase in one unit of the
percentage of the retention rate will result in the corresponding increase of the percentage of the
graduation rate by 0.2845 units
Statistical significance of the association between the retention and the graduation rate
We postulate a hypothesis as follows;
Null hypothesis: There is no association between the percentage of graduation rate and the
percentage of the retention rate
Alternative hypothesis: There is an association between the percentage of graduation rate and the
percentage of the retention rate
Correlations
GR RR
GR Pearson
Correlation 1 .670**
Sig. (2-tailed) .000
N 29 29
RR Pearson
Correlation .670** 1
Sig. (2-tailed) .000
N 29 29
**. Correlation is significant at the 0.01 level
(2-tailed).
The correlation is 0.670

Since the p-value 0.01, is less than the α = 0.05, we reject the null hypothesis and conclude that
there is enough evidence for the existence of an association between the percentage of graduation
rate and the percentage of the retention rate.
Regression equation goodness of fit
From the excel output, R- Square is 0.449221354 which shows an average good fit.
The model is, therefore, fit for predicting the percentage of the graduation rate as shown by the R
square which is 44.92%. This implies that about 44.92% of the variation in the percentage of the
graduation rate (dependent variable) is being explained by the percentage of the retention rate
(independent variable) (Simonetti et al, 2016).
Concerns from the South University after result review
Graduation rate = 25.423 + 0.2845 * retention rate
In the South University the percentage of the retention rate is 51 and the percentage of the
Graduation rate is 25
Graduation rate= 25.423 + 0.2845 * 51
= 39.9325
As the president, I would not have any concerns regarding the performance of the University
compared to other online universities because of the continuous increase of the percentage of the
percentage of graduation rate from 25 to 39.93
Concerns from the University of Phoenix after result review
In the University, the percentage of the retention rate is 4 and the percentage of the graduation
rate is 28
Graduation rate = 25.423 + 0.2845 * retention rate
Graduation rate= 25.423 + 0.2845 * 4
= 26.561
As the president, I would have concerns regarding the performance of the University compared
to other online university because of the decrease of the percentage of the percentage of
graduation rate from 28 to 36.56 due to the decrease of the percentage of the retention rate.

DISCUSSION
Mean percentage
The descriptive analysis reveal that the mean percentage of retention rate and graduation are
57.41 and 41.76 respectively. This implies that universities mean percentage of graduation is less
compared to the mean percentage of retention.
Minimum and maximum percentage
The mean percentage of the retention and graduation rate is 57.4138 and 41.7586 respectively.
The results reveal that the percentage of the minimum and maximum retention rate is 4 and 100
respectively while the minimum and maximum percentage of the graduation rate is 25 and 61
respectively.
Regression equation
The regression equation that estimates the graduation rate is Graduation rate = 25.423 + 0.2845 *
retention rate. This implies that an increase of the percentage of the retention rate by one unit
will result to an increase in the percentage of the graduation rate by 0.2845 units (Jesper , 2010).
The results show that the independent (percentage of the retention rate) and independent
(percentage of the graduation rate) variables are positively correlated. The two variables vary
together in a similar way; an increase of the percentage the retention rate results to a
corresponding increase in the percentage of the graduation rate. This implies that the online
universities growth rate is increasing as the retention rate increases. The findings of (Crawford,
2015) in his study on the retention of the students and the graduation indicates that retention rate
is a major factor that determines the increase or decrease in the percentage of the graduation rate.
Regression model goodness of fit
R- Square is 0.449221354. Which shows an average good fit. The regression model with the
regression equation; Graduation rate = 25.423 + 0.2845 * retention rate is fit for predicting the
percentage of the graduation rate as shown by the R square which is 44.92%. This implies that
about 44.92% of the variation in the percentage of the graduation rate (dependent variable) is
being explained by the percentage of the retention rate (independent variable).

Correlation
The correlation between the independent variable (percentage of the retention rate) and the
dependent variable (percentage of the graduation rate) r =0.670245 justifies the existence of a
positive correlation between the variables
A study conducted by (Dagley et al, 2015) reveals that graduation rate and the retention rate are
positively correlated and they vary in a similar way which supports this study. Dagley further
illustrated that the retention rate in universities should be put into consideration for a better
percentage of the graduation rate. The percentage of the retention rate can be improved through
community stem learning.
The online universities percentage of graduation rate is increasing with the increase of the
percentage of the retention rate (Boden, 2011). Bolden studies support the findings of these
studies
Recommendation
i. The percentage of the retention rate is a key factor that enhances the increase in the
percentage of the graduation rate. Institutions of higher learning should formulate policies
that increase the retention rate because of its positive association with the percentage of
the graduation rate
ii. Higher education sector should set a standard criterion of accrediting online institutions
of higher learning and develop the mechanism of evaluating the potentiality of the
graduates.
iii. The increase or decrease in the percentage of the graduation rate is majorly determined
by the retention rate.

References
Boden, T. (2011). Retention and Graduation Rates: Insights from an Extended Longitudinal View. Journal
of College Student Retention: Research, Theory and Practice, 13(2), pp. 86-94.
Crawford, G. (2015). The Academic Library and Student Graduation: An Exploratory Study. Libraries and
the Academy., 15(1), pp. 6-13.
Dagley et al., (2015). Increasing Retention and Graduation Rates through a STEM Learning Community.
Journal of College Student Retention: Research, Theory & Practice, 1(5), pp. 2-15.
Gregory, J. (2013). Professional development of online university teaching. Distance Education, 34(3),
pp. 35-48.
Jesper, M. (2010). A Model for Positively Correlated Count Variables. International Statistical Review,
78(1), pp. 278-296.
Jodi, B. (2011). Students with disabilities and online learning: A cross-institutional study of perceived
satisfaction with accessibility compliance and services. Journal of Students with disabilities and online
learning, 14(4), pp. 50-62.
Muuro et al., 2014. Students’ perceived challenges in an online collaborative learning environment: A
case of higher learning institutions in Nairobi, Kenya. The International Review of Research in Open and
Distributed Learning, 15(6), pp. 184-193.
Simonetti., (2016). Goodness of fit measures for logistic regression model: an application for students’
evaluations of university teaching. Quality & Quantity, 3(9), pp. 25-33.