Economics and Quantitative Analysis: Linear Regression Analysis Report

This report investigates the correlation between student retention and graduation rates in online colleges using linear regression analysis. The study utilizes data from 29 online colleges in the United States, sourced from the Online Education Database. The methodology involves descriptive statistics, scatter plots, and simple linear regression to determine the relationship between retention and graduation rates. The results reveal a positive linear association, with the regression equation indicating how changes in retention rates affect graduation rates. The report also includes discussions on the statistical significance of the findings, goodness of fit of the regression model, and specific concerns regarding individual universities. The report recommends that institutions of higher learning should work together with all the stakeholders like parents, government and society to understand and identify issues causing students to abandon studies after enrollment into the university.

ECONOMICS AND QUANTITATIVE ANALYSIS
LINEAR REGRESSION REPORT
Student’s Name
Institution Affiliation

1. Introduction
1.1. Purpose
This report is meant to investigate the correlation between the retention rate and graduation rate,
the ability of the student to persist through to graduation. This is meant to explore whether
retention rate of student in the university/college can influence graduation rate, the number of
students graduating after years of study. This has been facilitated by doing simple regression
analysis of the retention and graduation rates data of different universities and colleges.
1.2. Background
Every year in the United States there’s a good number of students who fail to complete their
college degrees.( Fishman et al., 2017) A third of the undergraduates students leave college
after the first year of study and others require more than four complete their studies. This clearly
reveals that retention rate of student in the university has been decreasing across the year,
thereby posing great economic issues. This mean the expected number of graduates by
institutions and government has continually decreases also. Chance of students defaulting the
loans that they obtain form government agencies to fund their education is higher as most
students when they drop out of school they are not able to pay up their Education loan due
their unsatisfying qualification in the labor market. The exploration of the correlation between
graduation rate and the retention of university will be of great economic significance in a
country.
2. Method

This section provides overview and the technique used to analysis data. To investigate the
association between graduation rate and retention rate retention rate and graduation rate data of
29 different universities and colleges was utilized. This date was sourced from Online Education
Database. To explore the association between graduation rate and retention rate various
statistical analysis were done include the following. First is determination of descriptive statistic;
mean, standard deviation, minimum and maximum. Second, developing scatter plot with
retention as independent variable to determine whether the relationship between graduation rate
and retention rate is linear or nonlinear. Finally, simple linear regression analysis of retention
rate and graduation rate data, to determine the equation that can used to estimate graduation rate
using retention rate and correlation coefficient ( R ), that indicates the level of association
between graduation rate and retention rate. The software that was used in analyzing data is
SPSS and Microsoft Excel software.
3. Results
a. Mean, Standard deviation, Minimum and Maximum
The following table shows the descriptive statistics of the retention rate (RR) and graduation rate
(RR) of 29 institutions of higher education.
Descriptive Statistics
N Minimum Maximum Mean Std.
Deviation
RR(%) 29 4 100 57.41 23.240
GR(%) 29 25 61 41.76 9.866
Valid N
(listwise)
29

From the table, it’s clear that RR has a higher mean, standard deviation and maximum than GR.
On the other hands GR has a higher minimum value than RR. A higher standard deviation
standard deviation implies higher dispersion of distribution of data. This suggests that the values
of RR are more disperse than those of GR due it higher standard deviation.
b. Scatter Diagram
Below is chart that shows the scatter diagram of graduation rate against retention rate.
The data most data points are not forming almost linear pattern with left-right upward trend but
few can form it, which depicted a weak positive linear correlation the two variables (Francis,
2004).
c. Estimation of regression equation
The table below shows the results of regression analysis.

Coefficients
Model Unstandardized
Coefficients
Standardized
Coefficients
t Sig. 95.0%
Confidence
Interval for B
B Std.
Error
Beta Lower
Bound
Upper
Bound
1 (Constant) 25.42
3
3.746 6.78
6
.000 17.736 33.110
RR(%) .285 .061 .670 4.69
3
.000 .160 .409
a. Dependent Variable: GR(%)
The following table shows the value of correlation coefficient ( R=0.670 of GR and RR and
coefficient of determination ( R2=0.449 obtained during regression analysis. The correlation of
0.67 is close to +1 than to 0, implying that there a positive linear association between GR and RR
(Hassett and Stewart, 2006, p. 341). The coefficient determinations (0.449) indicate that there’s
44.9% variability of GR in relation to RR.
Model Summary
Mode
l
R R
Square
Adjusted
R Square
Std. Error
of the
Estimate
1 .670a .449 .429 7.456
a. Predictors: (Constant), RR(%)
d. Stating the estimated regression equation and interpretation of slope coefficient

The intercept coefficient and slope coefficient of the regression model of GR and RR are 25.423
and 0.285, therefore the regression equation will be written as:
Y =0.285 X +25.423 , w h ereY =GraduationRateandX =Rententi onRate
The slope coefficient (0.285) indicates that when retention rate change by one 1% the
graduation rate will change by 0.285%.
e. Statistical Significance of the Simple Regression Equation
There’s statistical significant association between Graduation rate and Retention rate as the p-
values of both the intercept and slope coefficient (RR) are 0.000 which are less than 0.05.
According to Moyé (2006), a p-value less than 0.05 indicates that the null hypothesis that states
that there’s no relationship between the two rejected, thereby adopting the hypothesis that
indicates there’s relationship.
f. Goodness fit of the simple linear regression model
The following is a residual plot to identify whether the above regression is a good fit for the data.
0 20 40 60 80 100 120
-20
-10
0
10
20
RR(%) Residual Plot
RR(%)
Residuals

From the residual plot it’s clear that the simple linear regression model provide a good fit for the
as the data point are on both sides of the x-axis and they do not form a regular pattern (Pardoe,
2012).
g. Concern of South University
South university has 51% retention rate and 25% graduation rate. Its retention rate is not much
far away from the sample mean RR (57.41%) but its graduation rate far away from the sample
mean (41.76).
The great concern of south university is the big disparity between the retention rate and
graduation rate, they differ by 26%. This implies that though south university retains 51%
students within the preliminaries years 26% of these students do not graduate after the stipulated
years of studies.
h. Concern of University of Phoenix
The retention rate and graduation rate of University of Phoenix are 4% and 28% respectively.
These two measures are below the sample means, 57.41% and 41.76% respectively. The great
concern of this university will be the retention rate (4%) which is the lowest among all
universities. Retention of student after enrolment is a big issue facing the university, about 96%
of student who join the university do not complete their studies
4. Discussion

This section focus on key results that explain the association between Graduation rate and
Retention rate, they include scatter diagram and regression analysis.
The data points on the scatter plot do not show a linear pattern but portray a left- right upward
trend with some few points forming a linear pattern. This depicts a weak positive linear
relationship. This contradicts the results of correlation coefficient (R=0.670 from regression
analysis, which indicates high and positive association between graduation and retention rate.
One of the strength of this study is that one is able to understand well the relationship between
the GR and RR of different learning institutions. The limitation of the analysis is that it the
simple model does not show other factors that can affect retention and graduation rate, therefore
this model will not be efficient in some case as it will not display whole image of the institution.
5. Recommendations
The following are recommendation from the results and discussion.
First, there’s association between the graduation are retention rate of students in the colleges and
universities after enrollment. This suggests that simple linear regression model for the two
variables can be used to predict the number of students that are likely to be retained and graduate
after enrollment to a given school.
Second, the simple linear regression model determined in the analysis does not include other key
factors that can influence retention and graduation rate. In order, for this model to be more
inclusive and efficient more factors (variables) (for example, difficult courses and financial
struggles of students) should be included.

Third, institutions of higher learning should work together with all the stakeholders like parents,
government and society to understand and identify issues causing students to abandon studies
after enrollment into the university. They can come up with policies through the government that
help in maintaining higher retention of student among the institutions of higher learning.
Reference
Fishman, T., Ludgate, A., & Tutak, J. (2017) Success by design: Improving outcomes in
American higher education.
Francis, A. (2004) Business mathematics and statistics. Cengage Learning EMEA.
Hassett, M. J., & Stewart, D. (2006) Probability for risk management. Actex Publications.
Moyé, L. A. (2006) Statistical reasoning in medicine: the intuitive P-value primer. Springer
Science & Business Media.
Pardoe, I. (2012) Applied regression modeling: A business approach. John Wiley & Sons.