Analyzing the Association Between Retention Rate and Graduation Rate

This report investigates the relationship between retention rates and graduation rates in accredited online universities using regression analysis. The study employs descriptive and inferential statistics, including scatter plots, regression equations, and correlation analysis, to determine the association between these two variables. The results indicate a positive correlation, suggesting that an increase in retention rates leads to an increase in graduation rates. The report discusses the implications of these findings for online universities, particularly concerning policy and strategies for improving student outcomes. It also assesses the fitness of the regression model and addresses the limitations of the study, recommending further research into methods for enhancing retention rates to boost graduation rates. The report concludes with the recommendation that the percentage of the retention rate should be improved in the institutions of higher learning to increase the percentage of the graduation rate.

ASSOCIATION BETWEEN THE RETENTION RATE AND THE GRADUATION RATE

Table of Contents
1.0. INTRODUCTION.........................................................................................................................3
1.1. Purpose the study............................................................................................................................3
1.2. Background to the study.................................................................................................................3
2.0. RESEARCH METHODOLOGY............................................................................................................3
2.1. Research design..........................................................................................................................3
2.2. Data collection............................................................................................................................3
2.3. Data analysis...............................................................................................................................4
3.0. RESULTS...........................................................................................................................................4
3.2. INFERENTIAL STATISTICS.............................................................................................................5
3.2.1. Scatter plot of the retention rate and the graduation rate................................................5
3.3. REGRESSION ANALYSIS...................................................................................................................5
3.3.1. Estimation of the regression equation................................................................................5
3.3.2. Regression equation and the slope coefficient...................................................................6
3.4. CORRELATION.............................................................................................................................7
3.4.3. Concerns of the performance of the South University after results review.......................8
3.4.4. Concerns of the performance of the University of Phoenix after results review..............8
4.0. DISCUSSION.................................................................................................................................9
4.1.1. Mean percentage....................................................................................................................9
4.1.2. Minimum and maximum percentage......................................................................................9
4.2. Scatter plot......................................................................................................................................9
4.3. Regression equation........................................................................................................................9
4.4. Correlation....................................................................................................................................10
4.5. Regression model goodness of fit.................................................................................................10
4.6. Strength.....................................................................................................................................10
4.7. Limitation..................................................................................................................................10
4.8. Policy implication.....................................................................................................................11
5.0. RECOMMENDATION...............................................................................................................11
References.................................................................................................................................................12

1.0. INTRODUCTION
1.1. Purpose the study
The purpose of this study is to investigate the association between the percentage of the retention
rate and the percentage of the graduation rate among the accredited online universities.
1.2. Background to the study
The growth of online universities is increasing tremendously (Young, 2011) and this has been a
great challenge to the institution of higher learning majorly on the retention rates and graduation
rates. The association between the graduation rate and the retention rate according to (Anon,
2014) is positive. The study further reveal that the growth of online universities have posed a
greate challenge to the institution of higher learning and students experience difficulties in
collaborating with the online universities. However, online accredited universities are much
concerned with the retention rate and how the factor is associated with the graduation rate. The
study by (Stefano et al, 2012) presents the advantages of online universities on people with
disabilities, but does not show the retention rate and how it is associated with the graduation rate.
Economist are interested in the results of the association between the retention rate and the
graduation rate in order to make informed judgement and come up with the recommendation that
will help boost the percentage of the graduation rate. This study therefore, focuses investigating
the association between the retention rates and the percentage of the graduation rate.
2.0. RESEARCH METHODOLOGY
2.1. Research design
Descriptive and inferential design research was employed for this study.
2.2. Data collection
The study utilizes quantitative secondary data that was obtained from the online education
database.

2.3. 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.
3.0. RESULTS
3.1. Descriptive analysis
3.1.1. Retention rate and the graduation rate
The table below gives the descriptive summary of the retention rate 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

3.2. INFERENTIAL STATISTICS
3.2.1. Scatter plot 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 (REISENBACH,
2011)
3.3. REGRESSION ANALYSIS
3.3.1. Estimation of the regression equation
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 1224.286 1224.286 22.02211 6.95491E-05
Residual 27 1501.024 55.5935

Total 28 2725.31
Coefficients
Standar
d Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Intercept
25.4229036
3 3.746284 6.786166 2.74E-07
17.7361641
6 33.10964 17.73616
X Variable 1
0.28452600
3 0.060631 4.692772 6.95E-05 0.1601221 0.40893 0.160122
The regression equation to be used for estimation of the graduation rate percentage given the
percentage of the retention rate is estimated as follows;
Graduation rate = 25.42290363+ 0.284526003* retention rate
3.3.2. Regression equation and 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
RR(%)
GR(%)
The estimated equation is

y = 0.2845x + 25.423 where y represents the percentage of the graduation rate (dependent
variable) and x represent the percentage of the retention rate (independent variable).
Graduation rate = 25.423 + 0.2845 * retention rate
This is interpreted as;
There is a positive relationship between the two variables. An increase in one unit of the
percentage of the retention rate (independent variable) will result in the corresponding increase
of the percentage of the graduation rate (dependent variable) by 0.2845 units
3.4. CORRELATION
3.4.1. Association between the retention rate 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
At 1% level of significance,
RETENTION RATE (%) GRADUATION RATE (%)
RETENTION RATE (%) 1
GRADUATION RATE (%) 0.670245 1
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. The correlation between the two variables is
0.670245
The percentage of the retention rate and the percentage of the graduation rate have a positive
association. The two variables move in the same way or direction. Therefore, an increase of the
independent variable (percentage of the retention rate) results in an increase of the dependent
variable (percentage of the graduation rate) and vice versa.
3.4.2. Fitness of the regression model
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.670244797
R Square 0.449228088
Adjusted R Square 0.428829129
Standard Error 7.456104604
Observations 29
From the excel output, 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).
3.4.3. Concerns of the performance of the South
University after results review
The equation to predict the percentage of graduation rate is
Graduation rate = 25.423 + 0.2845 * retention rate
In the University the percentage of the retention is 51 and the percentage of the Graduation is 25
Graduation rate = 25.423 + 0.2845 * retention rate

= 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
3.4.4. Concerns of the performance of the University of
Phoenix after results review
In the University, the percentage of the retention is 4 and the percentage of the graduation 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 Universities 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.
4.0. DISCUSSION
4.1.1. Mean percentage
The mean of the percentage of retention rate and graduation rate are 57.41 and 41.76
respectively. This implies that universities mean percentage of graduation is less compared to the
mean percentage of retention. A study that was conducted by (Sneyers, 2017) which focused on
the graduation rates in the universities provide consistent results. It reveals that out 63.78% of
students who graduate; 28% are from online universities. Sneyers further says that the mean
percentage for the online universities is increasing tremendously across the world resenting a
great challenge to the institution of higher learning.
4.1.2. 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

4.2. Scatter plot
The two variables vary together in a similar way. This means that an increase of the percentage
the retention rate results in a corresponding increase in the percentage of the graduation rate
(Einstein, 2013). Therefore, the online universities growth rate is increasing as the retention rate
increases
4.3. Regression equation
The estimated regression equation 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. (Rodenbusch, 2016) Studies on
the ways of increasing graduation rates by employing a course-based research reveal that the
graduation rates increased by 16% from 2015 to 2016. He says that the course-based research,
retention rate is positively correlated with the graduation rate; which is a consistent result to
these study
4.4. 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 (Heiko et al, 2009).
A study conducted by (Murray, 2014) reveals that graduation rate and the retention rate are
positively correlated and they vary in a similar way which supports this study. Murray says that
dropouts in the universities is a great challenge and factor that affect the graduation rate.
The online universities percentage of graduation rate is increasing with the increase of the
percentage of the retention rate (Dagley, 2015). Dagley further says that the retention rate and
graduation rate should be improved through the community stem learning.
4.5. Regression model goodness of fit
R- Square is 0.449221354. Which shows an average good fit. The regression model with the
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).
4.6. Strength
The study utilized two basic statistical tools;
1. Regression model which clearly expressed the linear relationships between the two
variables through an equation.
2. Correlation which measured the strength of the relationship between the two variables.
4.7. Limitation
The study only reveals the relationship, the association and estimate of the equation for
predicting the percentage of the graduation rate but does not give ways of improving the
retention rate in order to increase the percentage of the graduation rate
4.8. Policy implication
The results obtained through regression and correlation analysis have positive implication to
policy making as it provided the relationship framework between the retention and the
graduation rate. The results will see more online universities adopting methods of improving the
retention rate and subsequently increasing graduation rate.
5.0. RECOMMENDATION
i. The percentage of the retention rate should be improved in the institutions of higher
learning to increase the percentage of the graduation rate.
ii. Implementation of tuition-paying classes will see the retention rate increasing, which will
increase the percentage of the graduation rate
iii. 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.

References
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Heiko et al., (2009). Versatile plans with correlation test insights. Insights in Medication, 28(10), pp.
1429-1444.
Murray, M. (2014). Variables influencing graduation and understudy dropout rates at the College of
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