ECO82001 Report On Linear Regression

Purpose

The main of analysis is to investigate the empirical relationship of retention rate (%) and graduation rate (%) for 29 colleges of US offering online education. The focus is on examining the direction and strength of association between these variables, along with recognising that whether relationship is significant or not. 

Background

The enhancing attrition rate in online colleges is of great concern for educational sector and focus is on improving the retention rate, such that number overall online graduates can increase (Allen and Seaman  2013).

 It is generally accepted that retention rate in online colleges is low, however researchers are interested in further studying this aspect to identify that whether number of students enrolled in online courses, are showing high likelihood to graduate from online colleges or not     (Herbert  2006). 

Therefore, it is important to recognise the relationship between retention and graduation rate of online colleges to develop policies of higher education. 

Method 

In order to carry out empirical analysis, secondary data of Online Education Database is used for 29 colleges. From empirical analysis methods, descriptive statistics are used to view overall picture of retention and graduation rate. The scatter plot is also drawn to visually depict relationship of underlying variables. Additionally, main reliance is maintained on linear regression analysis with an aim of measuring significance of the association between retention rate (%) and graduation rate (%) of online colleges. 

Results

• Descriptive Analysis 

The results of descriptive analysis are given in table 1. It can be seen that mean value of retention rate is 57.41 while, it is 41.76 for graduation rate. The mean value for retention rate (%) is high, showing that graduation rate (%) is less than retention rate. Additionally, standard deviation indicates spread of values around mean, which is more for retention rate than for graduation rate. Moreover, the values of skewness are -.310 for retention rate and .176 for graduation rate, which are both close to zero and thus it shows normal distribution of both retention and graduation rates.  

• Relationship between RR and GR 

Figure 1 is showing relationship between retention rate and graduation rate, having RR (%) on X-axis and GR (%) on Y-axis. It can be seen that scatter points on graph are showing upward trend which indicates that with rising values of retention rate, there will be increase in graduation rate as well. Therefore, it is evident that retention rate has strong and positive association with graduation rate in given sample. 

Figure 1. Scatter diagram for RR(%) and GR(%) 

• Regression Equation

Regression equation attempts to find the value of graduation rate, based on retention rate, which is given as follows; 

Y= 25.42 + .285X 

In this equation, Y indicates graduation rate which is outcome variable and X denotes retention rate that is predicting vairable.