Simple Linear Regression Analysis

This report focuses on identifying the association between the retention rate (RR) and the graduation rate (GR) to assist students in selecting the best institution to attend. The analysis entailed a sample data obtained from the Online Educational database. Results show a strong positive correlation between the RR and the GR.

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Simple Linear Regression Analysis
Institution Name
Student Name

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Simple Linear Regression Analysis
Purpose
In this report the focus will be identifying the association between the retention rate
(RR) and the graduation rate (GR). The two ratios can be used by prospecting students to
gauge the quality of education offered by an institution prior to enrolling in one. (Morris
2018). By comparing the ratios, a student is able to have a criterion for favouring one college
against the other.
Background
Internet coverage is quickly spreading across the globe, moreover individuals are in
need of flexible schedules due to hectic lifestyles. This have combined to make online studies
more and more attractive to many students. Most people especially those undertaking higher
education themselves with tight routines and often have minimal time to travel to colleges so
as to attend classes. Online programmes are defined as courses that students undertake
through computers rather than physically attending classes. The programmes can be taken
while at home or even in offices (Craig 2015). To meet the demand for online courses a
number of institutions have opened up their branches to offer these programmes. In addition
to this, others have cropped up just to avail online educational services. The widely spreading
online learning has left students with a hard choice when it comes to the best institution to
enrol to for the purpose of higher learning.
To assist students with a way of selecting the best institution to attend, economics can
apply the two rates to rank institutions based on quality provision (Sabbah 2011). First the
RR is the percentage of first year first time students who enrol in the school for their second-
year programme. The graduation rate on the other hand is the percentage of the students
admitted in the school in first year who goes ahead and completes their studies within 150%
of the recommended time needed to finalise a course (Anstine 2013).
Method
In this report the analysis entailed a sample data obtained from the Online Educational
database. Out of the secondary data that the organisation collects from accredited universities
to offer online courses, a sample of 29 colleges were selected at random and their RR and GR
noted for the analysis. The use of secondary data is vital for the study as it is more reliable
(Long 2009). As a way of determining the correlation between the two variables a scatter plot

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was drawn in addition to estimating a linear regression equation. Furthermore, the reliability
of the, model was gauged by modelling a simple linear regression. The analysis was done
using the Microsoft Excel.
Results
a. When the descriptive statistics of the two variables are derived the tables below is
obtained.
Descriptive Statistics
RR(%) GR(%)
Mean 57.4138 Mean 41.7586
Standard Error 4.3156 Standard Error 1.8320
Median 60 Median 39
Mode 51 Mode 36
Standard Deviation 23.2402 Standard Deviation 9.8657
Sample Variance 540.1084 Sample Variance 97.3325
Kurtosis 0.4618 Kurtosis -0.8824
Skewness -0.3099 Skewness 0.1764
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
b. A scatter plot assists have a visual outlay of the relationship between the two variables
as represented in the chart.

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The position of the dots in the plot can be interpreted as a sign of a positive
correlation between the two rates (Malakooti 2013).
c. From the scatter plot diagram, it’s possible to derive the line of best fit. When excel is
used to obtain this line. A line explained by an equation y=0.2845 x +25.423 is found
to best explain the relationship between the two rates. In this linear equation the RR is
represented by x while GR by y.
d. The equation that is estimated from the scatter plot is y=0.2845 x +25.423 this linear
equation has agradient of 0.2845 which explains the association between the retention and
graduation rates (Stephanie 2019). An increase (decrease) in the retention rate by 1%
increases (decreases) the graduation rate by 0.2845%. being that the equation has a positive
slope we can use the same to conclude that the two rates have a positive correlation.
e. Statistical significance of the correlation between RR and GR is obtained by modelling the
simple linear regression. The model is summarised by the table below.
SUMMARY OUTPUT
Simple linear regression model
Multiple R 0.6702
R Square 0.4492
Adjusted R Square 0.4288
Standard Error 7.4561
Observations 29
ANOVA
df SS MS F Significance F
Regression 1 1224.2860 1224.2860 22.0221 0.0001
Residual 27 1501.0244 55.5935
Total 28 2725.3103
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 25.4229 3.7463 6.7862 0.0000 17.7362 33.1096 17.7362 33.1096
RR(%) 0.2845 0.0606 4.6928 0.0001 0.1601 0.4089 0.1601 0.4089

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The model gives the value of multiple R as 0.6702 which is a proof of a strong
positive correlation between the two variables under study (Tofallis 2009). The P-
value of the intercept is 0 which is lower than 0.05, hence, at a 95% confidence
interval it can be concluded that there is a statistically significant association between
the retention and the graduation rates.
f. To check the fitness of the model we use the significance F value. Being lower than
0.05 proves that the model can be relied upon to estimate the GR values given the RR.
g. The RR for South University is 51% while the GR is 25%. All these falls below the
industry rates of 57.41% for RR and 41.76% for GR. The president of the South
university should therefore be concerned by the performance of the institution. When
the university is ranked by either of the two rates it falls way below the other
institutions. This is a sign of poor service delivery.
h. The Phoenix University’s retention rate is 4%. Comparing this rate to the average rate
of over 57% is a clear evidence that the university administration is failing. There
seems to be no strategy to retain students at all. At only 4% there is sufficient evident
to prove that students who join this college end up disappointed as their expectations
are far from what the university is offering.
Discussion
Average industry mean for the RR is 57.41% with a deviation of 23.24%. On the
other hand, the GR has a mean of 41.75% with a standard deviation of 9.87%. This shows
that the RR fluctuates more compared to the GR. Modelling the simple linear regression
gives the correlation coefficient of the two variables to be 0.6702 which is interpreted as a
strong positive association. By observing the scatter plot the dots are increasing from left
moving to the right a sign of positive correlation. A conclusion can therefore be made that
there is a strong positive correlation between the RR and the GR. In addition, the linear
equation y=0.2845 x +25.423 can best be used to estimate the values of the GR given the RR.
The use of secondary data means the results are more reliable as the data has been collected
and verified prior to publication by the Online Education database. This though does not mean the
study has no weakness. The task entails identifying a correlation between the RR and the GR which
might not be accurately gauged by the small sample space applied. The findings in this study is in line
with findings of other researchers for instance the study done by Meek (2018).
Recommendations

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As a response to the study findings, the following actions need to be put in place.
 Phoenix University should review their curriculum and teaching strategies to meet the
demand of the students.
 The education ministry needs to conduct a farther study so as to identify the issues
ailing online programmes.
 The south University administration should establish student’s assistance centre to
assist students with non-academic issues as a way of bolstering the institution’s
graduation rate.

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References
Anstine, J 2013, Graduation Rates at U.S. Colleges and Universities: A Large Data Set
Analysis. Business Education & Accreditation, 5(2), pp. 2-8.
Craig, R 2015, A Brief History (And Future) Of Online Degrees. [Online]
Available at: https://www.forbes.com/sites/ryancraig/2015/06/23/a-brief-history-and-future-
of-online-degrees/#1519378348d9
[Accessed 1 February 2018].
Long, Y 2009, Human age estimation by metric learning for regression problems, Leipzig,
Germany: Inselstrasse.
Malakooti, B 2013, Operations and Production Systems with Multiple Objectives, s.l.: John
Wiley & Sons.
Meek, K 2018, Why Graduation and Retention Rates Matter. [Online]
Available at: https://www.northcentral.edu/news/why-graduation-and-retention-rates-matter/
[Accessed 1 February 2019].
Morris, C 2018, Why School Graduation and Retention Rates Are Important to Consider.
[Online]
Available at: https://www.earnest.com/blog/graduation-and-retention-rates/
[Accessed 1 February 2019].
Sabbah, J 2011, Retention and graduation rates affect students, university. [Online]
Available at: https://northernstar.info/campus/retention-and-graduation-rates-affect-students-
university/article_61eef84a-7551-11e0-9185-001a4bcf6878.html
[Accessed 1 February 2019].
Stephanie 2019, Regression Equation: What it is and How to use it. [Online]
Available at: https://www.statisticshowto.datasciencecentral.com/what-is-a-regression-
equation/
[Accessed 1 February 2019].
Tofallis, C 2009, Least Squares Percentage Regression. Journal of Modern Applied
Statistical Methods, Volume 7, p. 526–534.
Further Maths Tutorials 2011, Maths Tutorial: Interpreting Scatterplots (statistics). [Online]

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Available at: https://www.youtube.com/watch?v=PE_BpXTyKCE
[Accessed 1 February 2019]