Linear Regression Report on Retention and Graduation Rates

Economics and Quantitative Analysis 1
ECONOMICS AND QUANTITAIVE ANALYSIS: LINEAR REGRESSION REPORT
by Students Name
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Professor’s Name
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Economics and Quantitative Analysis 2
Purpose
The study will on the development of a linear regression line and apply the same in
studying the correlation between the variable’s RR and the GR.
Background
currently several universities have emerged offering various studies. One of the most
challenging task parents and students face is selecting the right school for a course.
Graduation rate (GR) can be defined as the proportion of the college’s first year students
joining the institution for the first time who goes ahead to complete their studies within 150%
of the programs established period (Callahan & Belcheir 2017). On the other hand, rate of
retention (RR) is defined as the proportion of the students joining the college for the first time
who continue to study in the school the following year. Students transfer from a school have
a negative impact on their previous school retention rate (Dunlap & Lowenthal 2010).
Retention and graduation rates are two vital statistics that students and parents need to
consider when choosing a prospective college. They are indicators of the level of student’s
happiness in the college (Rubin 2012). In addition, the two ratios provide an idea of the
school’s support to the students as well as the likelihood that the tuition money is well
utilised. The two rates are simple standard of measure that are easy to interpret as its straight
forward (University of Arkansas, 2014).
Method
As away of gauging quality of education the retention and the graduation rates are
some of the statistics that can assist parents and potential students make a choice. The data to
be used in the analysis is a sample from the online educational database. This is an
organisation that is independently mandated to generate a list of accredited online colleges in
the United States. The sample consist of 29 colleges. Using the Microsoft excel we drew a
scatter plot and modelled a linear regression. Thereafter a line of best fit was developed
(Berg, 2009). Having derived the regression coefficient and the slope of coefficient, the
information was applied in determining the regression between the retention and the
graduation rates.
Results

Economics and Quantitative Analysis 3
a. Descriptive analysis
The table below gives a summary statistic on the rate of graduation and the rate of
retention of the 29 sampled colleges across the US.
RR (%) GR (%)
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
Largest (1) 100 Largest (1) 61
Smallest (1) 4 Smallest (1) 25
Confidence Level
(95.0%) 8.840111401
Confidence Level
(95.0%) 3.752720754
b. Scatter diagram
When a scatter diagram of retention rate verses the graduation, rate is drawn the
figure below is obtained.