ECONOMICS AND QUANTITATIVE ANALYSIS LINEAR REGRESSION REPORT DUE DATE: 11 February 2019 WORD LIMIT: 1200 words WEIGHTING: 40% Instructions Background One of the biggest challenges in the higher...

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I. Purpose:
The report is written for the clear purpose of estimating the relation between the two key variables of education sector: retention rate and the graduation rate. With the help of simple linear regression technique, the study estimates the association between two major variables of the model. The current research is based on the data available for 29 online colleges. The study puts an attempt to design the research methodology, deliberate the observation, sum up the key findings and the interpretations of the results. The study also provides some recommendations based on the key findings in order to improve the results in future.
II. Background:
Today online education is one of the major industries of the world that not only generates knowledge but also provides employment to a wide segment of world population. Despite the fact that the online colleges are booming in the education industry, they are also facing vast challenges. A high dropout rate is a growing concern for the institutions, instructors and also the policymakers. Several empirical studies have observed that retention rate has positive impact on the graduation rate of the college. (Leeds, et al., 2013)
In United States, higher education institutions are facing key challenges to deliver the quality education under the growing demand from students as well as the financial, social and political pressure. Poor retention rate is undoubtedly a major challenge particularly for the online institutions. Thus it is crucial to find out the association between the two variables and correctly address the issue while considering the policy formulations and resource allocation in the education sector. Policymakers, educators and even the prospective students provide greater emphasis on the retention rate while selecting the programmes in online colleges. (Uplanner, 2019)
III. Methods:
III.A The key variables:
Rate of retention and rate of graduation are the two major variables in the study. While the rate of retention shows the percentage of the students stay in the college, rate of graduation exhibits the total percentage of students completed the degree. The study considers the rate of graduation as dependent variable and the rate of retention as the independent variable.
III.B Methodology:
As far as the methodology is concerned, the study considers the simple linear regression model. III.C Data:
The research study has used the secondary data. The data for both the variables for 29 major institutions are collected from a major online site for education database.
III.D Model specification:
1.The model has 29 observations and two variables that include both the dependent and independent variable.
2.Thus the degrees of freedom is calculated as (29-2)=27.
III.E Empirical form of the model:
The empirical form of the model is
Gr= α0+ βRr
Where Gr represents the graduation rate
α0 is the intercept of the equation
β is the coefficient of the rate of retention, Rr
III.F Theoretical prediction of the model:
Several factors influence the graduation rate of a college and retention rate is one of them. Studies indicate that higher rate of retention is likely to increase the rate of graduation. The primary factors that affect the retention rate is the family crisis, illness, financial constraint, preparation for the study and the failure of the institution to live up as per expectations of the students. (Unigo, n.d.)
IV. Results:
Iv A. Descriptive analysis:
The descriptive analysis is illustrated in the following table. The calculations are shown in the attached excel.
    Mean
    57.41379
    41.75862
    Median
    60
    39
    max
    100
    61
    Min
    4
    25
    Stadard deviation
    23.24023
    9.865724
IV.B Scatter plot:
Scatter plot is nothing the diagrammatic representation of two quantitative variable. In order to have a clear understanding of the degree of association, we need to draw a trend line. The trend line suggests a positive associated between the rate of gradation and the rate of retention in the colleges.
IV.C Estimating the equation:
The estimated equation can be formulated from the summary output of the regression.
    SUMMARY OUTPUT
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    Regression Statistics
    
    
    
    
    
    
    
    Multiple R
    0.670245
    
    
    
    
    
    
    
    R Square
    0.449228
    
    
    
    
    
    
    
    Adjusted R Square
    0.428829
    
    
    
    
    
    
    
    Standard...