Linear Regression Report on Retention Rate and Graduation Rate in Online Education

ECONOMICS AND QUANTITATIVE
ANALYSIS
LINEAR REGRESSION REPORT

Purpose
To find out the relation between the retention rate and the association of different universities which
provides online education
Background
Graduation rates and retention rates are the criteria which is used to determine which college is best fit
foe the students. It also looks in to the decision which the students are going to take by looking in to
both these variables. The retention rate can be defined as the percentage of full-time students who
continue as a student after the graduation year. The students intends to get in to a college and gets the
graduation degree on the year they are supposed to graduate. Before spending the time and money on
a university if they get a relation between the graduation rate and the retention rate then it would be
easy for them to take the decision. Here comes the function of the economists who by their analysis
can decide in which college the students should enrol if there is an association between the graduation
rate which is the dependent variable and the retention rate which is the independent variable. To make
a substantial investment of both time and money this information are required by the economists.
What percentage of students stay with the college is determined by the retention rate and what
percentage of student finish their degree and leave the college is given by the graduation rate.
(Engelmyer, 2019)
Method
In the analysis we are first going to find out the summary statistics of both retention rate and the
graduation rate. Then we are going to fit a regression on the dataset provided i.e. to find out the
relation between graduation rate and the retention rate. The slopes or the coefficients which we
obtained from the data we are going to check significance of the coefficients of them. The sample data
which we have obtained is continuous in nature and it is not categorical also the sample taken is a
random sample which is one of the criteria for applying the linear regression model.
So there are few assumptions which we should consider while applying the linear regression:
 We assume that the relationship between the dependent and independent variable is linear in
nature. To check this we draw the scatter plot between the two data sets and see the linearity
dependence. The residual plot is also plotted once the regression line is fit in to the data to see
that the data taken is random in nature.
 we will get almost equal number of points about the line x = 0 when we are going to draw the
residual plot
 The observations provided are independent to each other.
 For any value of x the value of y varies according to a normal distribution.
 The errors are normally distributed ε ~ N (0, σ2).
 Linear relationship exists between them in a linear regression
 Multivariate normality is one of the assumptions for the model
 As there is only 1 independent variable multi collinearity won’t be a problem
 No auto-correlation or the lag term exists between the errors of the regression line
 Homoscedasticity (Prabhakaran, n.d.)
Results

a)
RR(%) GR(%)
Mean 57.4137931 Mean
41.7586
2
Standard Error 4.315602704 Standard Error
1.83201
9
Median 60 Median 39
Mode 51 Mode 36
Standard Deviation 23.24023181 Standard Deviation
9.86572
4
Sample Variance 540.1083744 Sample Variance
97.3325
1
Kurtosis 0.461757455 Kurtosis -0.8824
Skewness
-
0.309920645 Skewness
0.17636
4
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%)
3.75272
1
b)
0 20 40 60 80 100 120
0
10
20
30
40
50
60
70
GR(%) vs RR(%)
With the help of the scatter plot we can infer that the relationship is quite linear in nature and most of
the retention rate lies within 40% to 80% marks and the corresponding graduation rate lies within
35% to 55%.