Relationship between Retention Rate and Graduation Rate in Online Colleges in the US

This report investigates the relationship between retention rate and graduation rate in online colleges in the US. It uses data from 29 online institutions and includes descriptive analysis, correlation analysis, and regression analysis. The findings show a positive association between retention rate and graduation rate.

Economics & QT 1
Economics and Quantitative Analysis
Student’s Name
Student’s Number
University
Module Code
Module Name
Date

Economics & QT 2
Purpose
This report aims at investigating the relationship between retention rate (RR) and graduation
rate (GR) in online colleges in the US. More specifically, the report uses data from Online
Edu with 29 online institutions in the US.
Background
The shifting nature of the American economy, high competition in the employment industry,
and the preference of employers for knowledgeable, skilled employees have influenced the
increase in the desire for higher education. There has been a significant increase in the need
for graduates with postsecondary qualifications over the last five decades. The high demand
for higher education has led to a corresponding increase in the number of organizations to
meet the demand (Baum, Kurose, and McPherson, 2013). This is in addition to the recent
growth of online universities. Despite the increase in the enrolment for higher education, few
students graduate and most of them drop out before completing the required period.
The study on the association between retention and graduation is significant because the
graduation rate gives insight into the number of students that completed their degrees in a
timely manner after enrolling. Additionally, it is a transparent metric useful in the
measurement of the quality of the school (Sanford, and Hunter, 2011).
Method
The research used data obtained from the OnlineEdu.xlsx on 29 online academic institutions
in the US. The total number of observations is 29, and two variables namely retention rate
(independent variable) and graduation rate (dependent rate); all are continuous variables. A
descriptive analysis was carried out in the form of mean, standard deviation, maximum and
minimum. To find out the connection between the studies variables, the researcher adopted a

Economics & QT 3
correlation approach including a Personal correlation coefficient. The report also used a
scatter plot to visually examine the relation between the variables under study (Mukaka,
2012). A regression analysis was also used to ascertain the relation between the RR and GR.
Moreover, analysis of variance (ANOVA), a goodness of fit and hypothesis testing for the
slope was undertaken.
According to Sedgwick (2012), the Pearson correlation coefficient values range between 0
and 1. The nearer the value is to 0 the weaker the association, whereas the nearer the value
approaches 1, the stronger the association. R- Squared is the value of the goodness of fit and
also falls between 0 and 1. Similarly, the closer the value of the goodness of fit, the poor the
fit and a value closer to 1 shows strong goodness of fit. A 5% level of significance was used
in all the tests. All the data analysis was carried out using MS Excel Data Analysis Toolpak.
The hypothesis for the ANOVA is as shown below:
H0: Regression model is not significant
H1: Regression model is significant
The hypothesis testing for the slope is as indicated below:
H0: there is no variation between zero and the slope
H1: There is a variation between zero and the slope.
Results
Descriptive Analysis of RR and GR

Economics & QT 4
Table 1.1 Descriptive Analysis of RR and GR of online colleges in the US
GR (%) RR (%)
Mean 41.76 57.41
Standard
Deviation 9.87 23.24
Max 61 100
Min 25 4
Source: Author
The average RR (%) of all the 29 academic institutions in the US is 57.41% and the GR (%)
is 41.76%. the SD for RR is 23.24% and that of GR is 9.87%. based on these findings, there
is a higher dispersion in the RR from the mean than GR.
Scatter Diagram
Table 1.2 Scatter Diagram with RR as the Independent Variable
0 2 0 4 0 6 0 8 0 1 0 0 1 2 0
0
10
20
30
40
50
60
70
f(x) = 0.284526002809143 x + 25.4229036318199
R² = 0.449228088348509
S catt e r d i ag ram
Retention Rate (%)
Graduation rate (%)

Economics & QT 5
The scatter diagram shows a minor positive association. Any increase in the RR leads to a
corresponding increase in graduation rate. These results in the scatter plot were also
supported by the Pearson correlation coefficient of 0.67calculated using Excel.
Regression Analysis
Regression Statistics
Multiple R
0.670244
797
R Square
0.449228
088
Adjusted R Square
0.428829
129
Standard Error
7.456104
604
Observations 29
ANOVA
df SS MS F
Significanc
e F
Regression 1 1224.285956
1224.28
6
22.0221077
5 6.95E-05
Residual 27 1501.024388 55.5935
Total 28 2725.310345
Coefficient
s
Standard
Error t Stat P-value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept
25.4229036
3
3.74628382
2
6.78616
6
2.7441E-
07
17.7361
6
33.1096
4
17.7361
6
33.1096
4
X
Variable
1
0.28452600
3
0.06063069
1
4.69277
2
6.95491
E-05
0.16012
2 0.40893
0.16012
2 0.40893
Regression Equation
Based on the regression analysis outcomes, the regression equation is estimated as shown
below:

Economics & QT 6
Y =mx + c
Y = 0.28RR + 25.42
The slope value is 0.28 which shows a positive association between RR and GR. This means
that for every increase in the RR by 0.28 units, the GR increases at the same rate.
There was a statistically significant association between RR and GR with a p-value of 6.95.
Therefore, there is a substantially linear relationship between the study variables.
Goodness of fit
R 2 is 0.4492, which indicates that there is the goodness of fit, and is further evidenced also
by the findings of the correlation analysis. It is average because the value is approximately
0.5. In other words, 44.92% of the variance in GR is accounted for by the RR.
South University
The institution has the minimum graduation rate of 25% with a 51% retention rate. As the
president of the institution, I will be concerned about its performance because it has the
poorest GR among other 29 online universities.
University of Phoenix
As the president of the institution, I will seriously be concerned about the institution’s
performance because it has the least RR of 4% among the 29 institutions. This may demand
changes in the school administration because it shows that we do not deliver in order to
attract more students.
Discussion
The mean RR for all the online institutions under study was greater than that of the GR. This
implies that the number of students coming back to the same college the following year or

Economics & QT 7
those being retained is higher than the number of graduates. However, the mean RR and GR
for the study is much lower than those found in other literature. For instance, the RR and GR
for Frostburg State University was 54% and 26% for the fourth year respectively (Frostburg
State University, 2018). Ohio University had an RR and GR of 75% and 70% respectively
(Ohio University, n.d). But the report by the National Student Clearinghouse (2017) found
out that the GR was 45% and the RR of 12%. The fluctuation in the RR is much higher than
in the GR. Maximum RR is 100% while minimum RR is 4%. On the other hand, minimum
GR is 25% and maximum GR is 61%.
There was a positive correlation between the variables under study as is also evidenced in the
goodness of fit value of 44.92%. This means that 55% of the differences are unaccounted for
in the model. This can be attributed to other factors that influence GR such as social factors.
There was a significant statistical association with significant slope based on the analysis of
variance.
The study, therefore, confirmed the existence of the association between GR and RR. The
findings can be used by the administrators of colleges to improve their area of weakness by
determining their RR or GR. However, the study only considered 29 colleges thus limiting its
generalization.
Recommendations
The institutions with poor retention rates should institute measures to improve RR by
increasing resources for academic advising and develop intervention programs (Guillory,
2009). This will create the urge for the students to come back to the institution. The colleges
with the least graduation rates should implement strategies to ensure that the students not
only continue from one year to the next but to completion. This can be accomplished by

Economics & QT 8
increasing access to course material, identify at-risk students, and implement better
undergraduate programmes (Talbert, 2012).
Online colleges should also carry out an analysis of their RR and GR annually in addition to
the students’ views on the possible causes of RR and GR (James and Mathew, 2012). Then
the organization can devise strategies that will address the needs of the students

Economics & QT 9
References
Baum, S., Kurose, C. and McPherson, M., 2013. An overview of American higher
education. The Future of Children, pp.17-39.
Frostburg State University, 2018. Retention and Graduation Rates. [online]. Available from:
https://webcache.googleusercontent.com/search?q=cache:zZ4FKo-SfSUJ:https://
www.frostburg.edu/academics/air/institutional-research/-retention-and-graduation-
rates.php+&cd=6&hl=en&ct=clnk&gl=ke [accessed 05 Feb. 19].
Guillory, R.M., 2009. American Indian/Alaska Native College Student Retention
Strategies. Journal of Developmental Education, 33(2), p.14.
James, L. and Mathew, L., 2012. Employee Retention Strategies: IT Industry. SCMS Journal
of Indian Management, 9(3).
Mukaka, M.M., 2012. A guide to appropriate use of correlation coefficient in medical
research. Malawi Medical Journal, 24(3), pp.69-71.
National Student ClearingHouse, 2017. Completing College – National – 2017. [online[.
Available from: https://nscresearchcenter.org/signaturereport14/ [accessed 05 Feb. 19].
Ohio University, n.d. Office of Institutional Researc. Graduation Rates. [online[. Available
from: https://www.ohio.edu/instres/student/gradrates.html [accessed 05 Feb. 19].
Sanford, T. and Hunter, J.M., 2011. Impact of performance funding on retention and
graduation rates. education policy analysis archives, 19, p.33.
Sedgwick, P., 2012. Pearson’s correlation coefficient. Bmj, 345, p.e4483.
Talbert, P.Y., 2012. Strategies to Increase Enrollment, Retention, and Graduation
Rates. Journal of Developmental Education, 36(1), p.22.