Relationship between Retention and Graduation Rates

This assignment analyzes the correlation between student retention rates (RR) and graduation rates (GR) across multiple universities. It utilizes statistical methods such as scatter diagrams, regression analysis, and goodness of fit tests to determine the strength of the relationship between these two variables. The results reveal a moderate positive correlation, indicating that higher retention rates tend to be associated with higher graduation rates. Based on these findings, the assignment offers recommendations to universities for improving both retention and graduation rates.

Economics and quantitative analysis

Table of Contents
PURPOSE........................................................................................................................................3
BACKGROUND.............................................................................................................................3
METHODS......................................................................................................................................3
RESULTS........................................................................................................................................4
Calculation of descriptive statistics.............................................................................................4
Scatter plot...................................................................................................................................5
Correlation between GR % and RR %........................................................................................5
Regression equation.....................................................................................................................6
Goodness of fit test......................................................................................................................6
DISCUSSIONS................................................................................................................................6
RECOMMENDATIONS.................................................................................................................8
REFERENCES................................................................................................................................9

PURPOSE
Statistics is the study of large set of data through applying different types of statistical
methods, tools & techniques. More importantly, it aims at gathering data about a selected sample
size from the large population and organizes and arrange it into statistical form, so as, to analyze
and interpret the results in an effective manner. The purpose of this report is to examine and
analyze the growth of education sector in the terms of graduation as well as retention percentage
considering a sample of 29 US-based colleges. On the basis of it, appropriate suggestions will be
recommended to the educational institutions to combat such challenge.
BACKGROUND
Educational institutes aims at delivering exceptional and excellent quality educations to
the students for their career growth and advancement. However, in today’s period, US
educational sector is threatening from the faster and rapid growth of online universities. Online
Education Database (OED) works as an independent organization whose mission is to create a
comprehensive set of accredited online college. Therefore, the report will perform analysis of 29
US college’s retention and graduation rate (%) through using appropriate statistical tools and
methods.
METHODS
The report will approach various statistical techniques such as descriptive statistical tools,
mean, range, standard deviation and regression method for predicting future, described below:
Mean: It refers to the value that has been derived through dividing the sum of values
with the number of items, also arithmetic mean or average (Jaggia and et.al., 2016). It is greatly
used by analysts to define the whole series of data with a single value, computed through
following formula:
A.M. = (∑X)/N
Here, ∑x – Sum of values

N – Number of items
Mode: It indicates value that occurs most frequently as comparison to others.
Median: It indicates middle value of the series that is equal to 50%(1/2th) of given data
set hence, divide series into two equal parts.
Range: It is the simplest technique of finding out spreader of the series, as it just
identifies the difference between maximum and minimum value. Alternatively, the excess of
highest value over lowest is denoted as range.
Range = Maximum/greatest item size - Minimum/lowest item size
Standard deviation: It is the most effective technique of analyzing the spreader or
dispersion of the series, as it is used to compare the deviation between each and every items to
that of mean value (Carter and et.al., 2016).
Scatter diagram: It will be prepared taking retention rate as an independent variable.
Regression: It is used to detect that how change in independent series or variable will
bring change in dependent variable (Anderson and et.al., 2016). Regression equation will be
developed to anticipate future through addressing possible change in independent item.
RESULTS
Calculation of descriptive statistics
Particulars Retention ratio (%) Graduation ration (GR%)
Mean 57.41379 41.75862
Standard Error 4.315603 1.832019
Median 60 39
Mode 51 36
Standard Deviation 23.24023 9.865724
Sample Variance 540.1084 97.33251
Kurtosis 0.461757 -0.8824
Skewness -0.30992 0.176364
Range 96 36
Minimum 4 25
Maximum 100 61

Sum 1665 1211
Count 29 29
Scatter plot
Correlation between GR % and RR %
Particulars Graduation rate Retention rate
Graduation rate 1 .67
Retention rate .67 1
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 1224.286 1224.286 22.02211 6.95E-05
Residual 27 1501.024 55.5935
Total 28 2725.31
Coefficient
s
Standar
d Error t Stat P-value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 25.4229
3.74628
4
6.78616
6
2.74E-
07
17.7361
6
33.1096
4
17.7361
6
33.1096
4
X
Variable
1 0.284526
0.06063
1
4.69277
2
6.95E-
05
0.16012
2 0.40893
0.16012
2 0.40893
Regression equation
Y = a + bx
Y: Dependent/predicted variable: GR %
X: Independent variable: RR%
Y = 25.423 + 0.2845x
Goodness of fit test
H0: Regression line does not capture any significant relationship between GR % and RR %
H1: Regression line does not capture any significant relationship between GR % and RR %
F 22.02210775
alpha 0.05
F-crit 4.210008372
P-value 6.95491086E-05
Sig. Yes
DISCUSSIONS
Mean: As per the results founded, it can be seen that on an average, US educational
institutional retention rate is 57.41% whilst average graduation rate is 40.75% for each
university. Thus, it can be seen that graduation percentage is comparatively greater than retention
%age.

Mode: Majority of the universities has RR and GR % to 51 & 36 as it occurs highest
times.
Median: 50% or half of the RR and GR are equal to 60% and 30% respectively denoted
by median.
Range: Moreover, dispersion result through range for both RR & GR has been founded
to 96% & 36% respectively. Thus, excessive percentage difference in RR shows that this series
data are highly spreader or scatter from the mean 57.41%. However, as the method considers
only the top and lowest value only and ignores other set of data, it can be said that results are
greatly affected by the extreme values and may provide misleading results therefore standard
deviation is considered more appropriate method.
Standard deviation: It is founded greater to 24.57 for RR whilst for GR, it is
comparatively lower to 10.24 only. Thus, the results revealed that RR data are highly spreaded
from the derived average or mean of 57%. It reveals that some universities and college’s RR is
very less than mean i.e. Phoneix & Western International whilst some of the educational
institutions have high RR i.e. National and Florida University.
Scatter diagram: Rising trend from left to upper indicates positive relationship between
dependent & independent variable (Delgado-Friedrich and et.al., 2017). The results of
correlation to 0.67 demonstrated that both the series are moderately related to each other and
100% increase/decrease in one data set will bring change in other data set by 67% in same
direction.
Regression equation: In accordance with the results, 0.67 value of R reflects favorable
& moderate level of relations as it comes under the range of 0.25 to 0.75. However, 0.44 value of
r square presents that change or movement in RR% will bring change by 44% in GR %.
Slope coefficient: In the regression equation, y-intercept is founded 25.423 whilst slope
coefficient is 0.2845 demonstrate that for every retention %, average increase in GR % is 0.2845.
Goodness of fit test: Finding the results, it is founded that 4.21<22.02, thus, null
hypothesis can be rejected and alternative accepted. Thus, it is clear that regression equation is a
good fit for the data set.

RECOMMENDATIONS
Considering the statistical results, it can be interpreted that South University’s RR is just
equal to mode and near to the mean %age of 57.41%. However, its GR is 25% lower than
average performance. However, if we consider Phoneix University’s performance, then it can be
seen that its RR% is very lower than average performance of 57.41% whilst its GR is more near
to the average relatively to South Universities. Both the universities president must look towards
the issues and challenges and make policies to enhance their performance. In such respect,
quality education policy needs to be framed to deliver excellent quality education offerings to the
students. Moreover, coursework must be designed keeping in mind their professional growth and
brighter career requirement for the future growth. Learning through advanced & upgraded
software also help to deliver best quality education to the students and satisfy their educational
need. Along with this, Phoneix University has to recruit talented, skilled & experienced staff to
render quality educations to the students in their interested field. In addition to this, extra
activities, affordable fees, scholarship & other educational services can be offered to attract
prospective consumers and retain existing as well for achieving growth.

REFERENCES
Books and Journals
Anderson, D. R. and et.al., 2016. Statistics for business & economics. Nelson Education.
Carter, R. M. and et.al., 2016. Dispersion measurement of microstructured negative curvature
hollow core fiber. Optical Engineering. 55(11). pp. 116106-116106.
Delgado-Friedrichs, O. and et.al., 2017. Crystal structures as periodic graphs: the topological
genome and graph databases. Structural Chemistry. 28(1). pp. 39-44.
Jaggia, S. and et.al., 2016. Essentials of business statistics: communicating with numbers.
McGraw-Hill Education.