Linear Regression Report on RR and GR Relationship in Online Education

ECONOMICS AND QUANTITAIVE ANALYSIS 1
Economics and Quantitative Analysis
by Students Name
Course
Professor’s Name
Institution
City
Date

ECONOMICS AND QUANTITAIVE ANALYSIS 2
Linear Regression Report
Purpose
This report is aimed at modelling a simple linear regression line and apply the
techniques to evaluate the nature of relationship between the RR and the GR.
Background
As the use of internet spreads globally educational institutions offering online services
have gone up as well. The present of a number of colleges availing online study opportunities
have increased access to education though it has also come with the challenge of knowing the
right institution to opt for a course. As a way of assisting stakeholders make this crucial
choice in life, two rates have emerged into the limelight that is the RR and the GR (Callahan
& Belcheir 2017). GR by definition is the percentage of freshmen joining an institution who
goes ahead to graduate from the institution within 150% of the time set to normally complete
the course (Dunlap & Lowenthal 2010). On the other hand, RR is the percentage of the
students who join a college as first year and came back to continue on the same institution
during second year of study.
RR and GR are important statistics that make the selection struggle an easy one by
giving students away of ranking the institutions (Rubin 2012). They indicate the level of
education quality that a college offer in addition to proving university’s ability to maintain
the standard set during students’ recruitments (University of Arkansas, 2014).
Method
The data sample used in the analysis was derived from the Online Education Database
which is an independent institution responsible for generating a list of accredited universities
cleared to offer online courses (Berg, 2009). The data sample of 29 colleges was applied to
draw a scatter plot, model a simple regression as well as draw descriptive statistics. The
results of the analysis was thereafter applied in making recommendations to the online
institutions.
Results
a. Descriptive statistics
The table presents a descriptive analysis of the sample data.

ECONOMICS AND QUANTITAIVE ANALYSIS 3
Descprtive Analysis
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. Plotting the scatter diagram
A scatter plot is a graph which represents the values of two variables plotted
along two exes. The pattern of the plot is meant to reveal the association between the
two values. In the diagram below the RR is the independent variable (x axis) while the
GR is the dependent variable (y axis). The diagram below gives the scatter plot of RR
and GR (Emerson, et al. 2013). A reference to the table can be used to conclude that
the retention as well as graduation rate have a positive correlation. That is any
positive change in the RR will affect the graduation rate in the same direction.