Impact of Retention on Graduation Rates

This assignment analyzes the relationship between student retention rates and graduation percentages. It involves building a regression model to predict graduation rates based on retention data and evaluating the model's fit. The analysis also considers specific universities, such as South University and the University of Phoenix, comparing predicted and actual graduation rates to identify areas of concern and potential improvement.

ECONOMICS

TABLE OF CONTENTS
ECONOMICS..................................................................................................................................1
Purpose............................................................................................................................................3
Background......................................................................................................................................3
Research method..............................................................................................................................3
Results..............................................................................................................................................4
Discussion........................................................................................................................................5
Descriptive statistics....................................................................................................................5
Scatter diagram............................................................................................................................5
Regression equation for prediction..............................................................................................5
Stating regression equation and explaining slope coefficient......................................................6
Statistical relationship among the dependent and independent variable.....................................6
Regression equation and good fit................................................................................................6
South university...........................................................................................................................6
University of Phoenix..................................................................................................................7
Recommendation.............................................................................................................................7
REFERENCES................................................................................................................................8
Table 1Calcualtion of descriptive statistics.....................................................................................4
Table 2Regression tables.................................................................................................................4
Figure 1Scatter diagram...................................................................................................................4

Purpose
The main purpose of the current research study is to identify the relationship between the
graduation rate and retention rate. Online education is the new segment in education industry and
it became very difficult for existing firms to retain students. The results that will be generated in
the research study will help one in identifying the impact that retention of students has on the
graduation percentage. In this regard regression analysis of the variables will be done.
Background
With passage of time online education trend is increasing consistently. It is assumed that
those educational institutes that will retain graduates for further studies will be able to attract
more students for graduation programs. Current research study is testing this assumption.
Completion is increasing in the education industry as many new colleges are opened that are
providing facility of online study to the students (Webber and Ehrenberg, 2010). It becomes very
important for the educational institutes to retain students that are currently doing a graduation in
college for master’s degree. If in the college retention rate of relevant students will be high more
students would like to take admission in the college for graduation program. It is important to
study the relationship between retention percentage and graduation rate. Thus, for this regression
analysis model is used to explore the relationship among the variables.
Research method
In order to conduct current research secondary data is taken in to account that is related to
different colleges that are providing online education to the students. in order to identify and
understand relationship among the retention rate and graduation percentage regression model is
used in the present research study. By using regression model output forecast about specific
variable will be done in the report. Thus, it can be said that statistical tools are basically used to
analyze the data. Apart from inference statistics descriptive statistics is also used to analyze the
data in better way. On the basis of results of descriptive statistics mean value of the variable will
be identified. Moreover, the extent to which results deviate from mean value will also be found
out. This will reflect whether most of colleges are giving same results or there is difference in
same. Maximum and minimum value of the variable will also be discovered. In this way in
varied ways data set will be analyzed in better way in the current research study.

Results
Table 1Calcualtion of descriptive statistics
RR% GR%
Mean 57.41379 41.75862
STDEV 23.24023 9.865724
Maximum 100 61
Minimum 4 25
Figure 1Scatter diagram
Table 2Regression tables
Regression Statistics
Multiple R 0.670245
R Square 0.449228
Adjusted R
Square 0.428829
Standard Error 7.456105
Observations 29
ANOVA
df SS MS F Significance

F
Regression 1 1224.285956 1224.286 22.02211
6.95491E-
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 25.4229 3.746283822
6.78616
6
2.74E-
07
17.7361641
6 33.10964 17.73616 33.10964
X Variable
1 0.284526 0.060630691
4.69277
2
6.95E-
05 0.1601221 0.40893 0.160122 0.40893
Discussion
Descriptive statistics
Mean value of retention percentage is 57.41% and same for graduation percentage is
41.75%. Standard deviation value for retention percentage is 23 and same for graduation
percentage is 9. This means that with big change in retention rate graduation percentage is
changing slightly or moderately. Minimum retention percentage is 4% and maximum is 100%.
Minimum value for graduation percentage is 25% and maximum value of same variable is 61%.
Thus, it is clear that maximum graduation percentage is only 61% for sample units.
Scatter diagram
Scatter diagram reflects that there are few values of the retention and graduation percentage
which have relationship with each other. Hence, it can be said that there is no big relationship
between both variables values. Thus, colleges must not assume that if there retention rate is high
then graduation percentage will also increase. It can be said that scatter diagram is the one of the
most important method that explains a lot about the studied variables.
Regression equation for prediction
Regression equation for the current research study is given below.
Y=A+BX
Y=25.42+0.28*X
In the above equation Y is the dependent variable which is graduation percentage. A refers
to the alpha which is the mean value of the dependent variable when value of independent

variable is zero. X is the any value of independent variable that is used to make prediction of the
variable.
Stating regression equation and explaining slope coefficient
It can be seen from the above regression equation that mean value of dependent variable is
25.42 when independent variable which is retention percentage value is zero. B refers to the beta
which reflects the change that comes in the dependent variable value with change in the
independent variable. In the equation beta value is 0.28 which is also slope coefficient.
Mentioned value is reflecting that with small change in the retention percentage by 0.28 points
graduation percentage get changed. It can be said that big variation does not come in the
dependent variable with change in the independent variable.
Statistical relationship among the dependent and independent variable
Value of multiple R is 0.67 which reflects that there is a moderate relationship among the
dependent and independent variables which are graduation percentage and retention percentage.
Value of level of significance is 6.67 which mean that there is statistical difference between
mean value of the variables. It can be said that with change in retention rate big variation does
not come in the graduation percentage. Intercept value is 25 which as mentioned above is mean
value of graduation percentage when value of independent variable is zero. Means that in every
condition at least value of graduation percentage will be 25. Slope is also reflecting that big
variation does not come in the dependent variable due to change in independent variable.
Regression equation and good fit
Value of R square is 0.44 which reflects that model is not good fit. This is because value of
R square is very small. Good fit is the one of the most important concept which reflects the
difference that is between expected and actual value of the variable.
South university
Yes, there is a matter of concern because regression equation is revealing the predicted value
of graduation percentage is only 39.7. Maximum value of same variable is 61. Hence, there is
huge difference between both variables and due to this reason there is a matter of concern for
performance of university.
Y=25.42+0.28*51

University of Phoenix
For University of Phoenix predicated value of graduation percentage is 26.54%. Maximum
value is 61 and in comparison to same predicted value is very small. For mention University
predicted value is matter of concern and it needs to improve this percentage. Maximum
Recommendation
It is recommended that colleges must try to increase graduation percentage. They must not
think that by increasing retention percentage graduation percentage can be increased. This is
because there is no significant relationship between both variables. Hence, colleges must try to
identify factors that heavily influence the graduation percentage of college.

REFERENCES
Books and journals
Webber, D.A. and Ehrenberg, R.G., 2010. Do expenditures other than instructional expenditures
affect graduation and persistence rates in American higher education?. Economics of
Education Review 29(6). pp.947-958.