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The goal of this analysis is to evaluate the connection between the levels of students retained and those graduating in the online institutions of higher learning in the United States and how it is connected with studying over the internet.

The factors that are influencing the changes occurring in education in institutions of higher learning are globalization, changes in employer needs, changing demographics, technology, economy and globalization among others. Each with a significant and entirely transformative impact. This makes online learning a simple, accessible and inexpensive mode of delivering education and hence a disruptive technology as it moves away from the complicated and expensive initial program.

The success of online higher education is a result of a short time spent on courses and a quality curriculum. The correlation between rates of retention and of graduation varies significantly in online courses as opposed to traditional courses. The rate of retention refers to the ratio of students who continue with the program after the completion of their first year. The attainment rate is the proportion of students who accomplish their educational program within 150% of the recommended completion time.

Given the dataset, the variables are the rate of retention which is independent of any factor while the rate of graduation is dependent on several factors. The independent variable is the predictor that is manipulated to comprehend how the dependent variable responds.

Linear regression is expressed as Y= bX + A

Where Y is the reliant variable, b is the gradient of the line, X the selfgoverning variable and A the intercept on the Y-axis. This means that an alteration of the unit of an independent variable directly affects the unit change of the dependent variable and the gradient. The R-squared measures how near the inputs are next to the builtin streak by using a normal probability curve to verify the effectiveness of R2 and the fit model. The regularity of the error term is meant for confirming the viability of the linear regression. Mathematically it is described as

Rsquared = the explained variation/ total variation

Results

a)

b) The scatter plot is a positive representation of the retention rate, and the graduation rate as an increase in the retention rate leads to an increase in graduation rates

c) Using the retention rate as the independent variable, a simple linear regression equation helps calculate and hence envisage valediction rates for online higher learning programs. This comparison is expressed as follows

Graduation rate = α + β*Retention rate

Where α is a constant and β is a parameter.

d)

Standard errors in parentheses *** p<0.01 ** p<0.05

A percentage increase in retention rate would result in a graduation rate increase of 0.285 which is statistically significant at the 0.1% level of significance. The table above indicates a progressive connection between rates of retention and that of graduation.

e) There exists a statistically noteworthy relationship between the rates of graduation and those of retention as shown in the previous question. An upsurge in the retention rates will result in an upsurge in the graduation rates by a factor of 0.285 which is statistically significant as the level of significance is 0.1%.

f) The model did not appropriately meet the coefficient in the determination of the prototype being 0.449 only 50% of the variance in the completion rate can be defined by the holding rate.

g) The calculated results show that the graduation rates are not entirely dependent on retention rates and hence other factors that may increase the graduation rates need to be considered.

h) The University of Phoenix has both a low retention rate and a below average graduation rate. This is an area of concern, and the programs should be reviewed to understand why there is a low retention rate and how to adjust that.

To assess the relationship between retention rate and graduation rates, the evocative statistic scatters plot and simple linear regression among other plot tools for estimation are employed. The results found, therefore, suggest the presence of a positive relationship between the retention rates and the graduation rates. Despite this, it is worth noting that the model does not completely fit and that the retention rate can only explain approximately 50% of the

variation in the graduation rates. This means that there is a possibility that there are numerous other factors that influence the graduation rates. This creates the need to find out what these factors are and how they influence the graduation rates for online higher education programs.

The study carried out above has shown that the model is not providing satisfactory results as other factors are influencing the graduation rates of students rather than retention rates. The recommendation would, therefore, be, to research and analyze other factors that affect graduation rates which can be done using resources from other already available studies. To determine if online learning is costeffective and if the retention rates and graduation rates as factors have an impact on it, does not provide us with a modest response of yes or no. An analyst working in this area of research would, therefore, require a lot of rigorous information regarding effective instructional strategies and the method of enhancing scholarly productivity. This, therefore, means that more attention also needs to be paid to other factors such as subject domain, structure, of course, budget, the role of the educator and the design and outline of the educational platform as it affects the delivery of content among many other factors.

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