(a) Provide a descriptive analysis of the two variables (e.g., mean, standard deviation, minimum and maximum).
(b) Develop a scatter diagram with retention rate as the independent variable. What does the scatter diagram indicate about the relationship between the two variables? (c) Develop and estimate a regression equation that can be used to predict the graduation rate (%) given the retention rate (%).
(d) State the estimated regression equation and interpret the meaning of the slope coefficient.
(e) Is there a statistically significant association between graduation rate (%) and retention rate (%). What is your conclusion?
(f) Did the regression equation provide a good fit? Explain.
(g) Suppose you were the president of South University. After reviewing the results, would you have any concerns about the performance of your university compared to other online universities?
(h) Suppose you were the president of the University of Phoenix. After reviewing the results, would you have any concerns about the performance of your university compared to other online universities?
The two variables that are used within this report for the performance of several universities are named as the graduation rate and a retention rate. The graduation rate is dependent on the retention rate where the retention rate means the rate at which the students continue their education from the same university. Through it, the graduation rate will likely increase because the retention rate is higher. This would mean that the increase in the retention rate will have a positive increasing effect on the graduation rate which needs to be assessed through scatter plot and regression equation (Beldona, 2010). Other statistical tools will also be used like min and max method, mean and standard deviation. The min method provides us with the most minimum retention rate among the universities and the most minimum graduation rate among the universities. The max method will provide us with the most maximum retention and graduation rate. The mean will provide the analyst with the most common percentage among the universities signifying the retention rate and graduation rate. The standard deviation will provide us the variability from the mean. The scatter plot will facilitate in identifying the relationship between the two variables and the regression equation will help in illustrating the relationship in an equation.
The 29 online universities are to be analyzed in accordance with their performance using statistical tools to statistically analyze the data for it. Those statistical measures would include the min-max method, scatter plot, mean, standard deviation and regression equation. All of the terms are already explained in the previous section. The purpose would notify as to how the two variables are interrelated with each other.
The statisticians use these measures to understand the dataset provided within the study. The statistical tools will help us in understanding the statistical relationship between the two variables and hence, it would be quite effective to apply the statistical tools to determine the exact relationship between the two variables. (Armstrong, 2013) In accordance with the regression equation, this is the most significant statistical tool because the relationship between the two variables is described in to an equation where the relationship provides us with a good analysis of the independent and dependent variable. This is done through an equation below:
Y = m X +c
The retention rates and graduation rates have been a in significant relation between each other which has resulted the retention rate to officially think of it that all such retention rates were increasing and the graduation rates are decreased.
Firstly, mean is determined which would let us know the most common rate among the 29 online universities. The mean would identify the most common rate in accordance with the retention rate and graduation rate. In the same way, then standard deviation method will let the statisticians know as to how much variability is there from the determination of mean. Some other methods like min and max method. The min means the least possible value for the retention rate or graduation rate. However, the scatter plot will also be used which represents the illustration of the graph through which the type of relationship will be evident. There are three types of relationship which can be illustrated through a scatter plot (Kahng, 20010). The first one is known as a positive relationship between the two variables. That means that when X increases, Y also increases. Then there exists a negative relationship. That means that when X increases, Y decreases or when X decreases, Y increases. Therefore, the two variables are then negatively correlated. After that, the third type of relationship is the no relationship (Omran, 2010). This means that there is no resultant increase in Y with an increase in X. Both the variables remain unchanged. Then the regression method is also used to describe the relationship between the two variables in an equation form.
The results for the given data are shown below:
A statistical technique used to explain or predict the behaviour of a dependent variable. Generally, a regression equation takes the form of Y= m X + c , where Y is the dependent variable that the equation tries to predict, X is the independent variable that is being used to predict Y, a is the Y-intercept of the line, and c is a value called the Y intercept (Kahng, 2013). It can be seen that the mean retention rate is 57.4% while the mean graduation rate is 42%. The standard deviation for the retention rate is 23% while the standard deviation for the graduation rate is 9.8%. The max retention rate is 100% while the max graduation rate is 61%. The minimum retention rate is 4% while the minimum graduation rate is 25%. The most common retention rate among the universities is 57.4% emulated by the graduation rate of 42%.
The scatter plot for this data set is shown as under:
The m slope is calculated as the graduation rate = M x retention rate + 25.4%. Hence
According to the author, the scatter diagram shows a positive relationship between the two variables. However, at certain instances, the retention rates are lower and the graduation rates are substantially higher (Murnance, 2013). This is a great concern for the statistical analyst from this point of view. However, to sum up as a whole, the retention rate increases due to which the graduation rate also increases.
The regression equation can be described as the relationship between the two variables being studied or researched. It also makes sense for the dependent of any influence on the subject through these two variables (Abernathy, 2011). The regression equation is as under:
The above regression equation is Y = 0.284 X + 25.423. Y is the graduation rate, X is the retention and 25.423 is the Y intercept. Hence, the positive relationship is quite significant from the above universities. And, this can be proved in this manner:
Y = 0.2845 x 35 + 25.423 = 35%
Y = 0.2845 x 40 + 25.43 = 36%
Therefore, the increase in any positive aspects will prove to be a great source of influence on the graduation rate.
Discussion and Recommendations
The University of South has a favorable graduation rate along with a retention rate. The graduation rate increases because the retention rate increases as it has been discussed above already. But the first and foremost concern is that some of the universities have lower retention rates but their graduation rates increase and that might be due to the fact that the retention rate is decreasing. Apart from this, the Universities of Phoenix has a lower retention rate and the most surprising fact is that the graduation rates also increase (Karafiath, 2014). The graduation rates are solely dependent on the retention rate. With such a lower retention rate, the graduation rates are increasing. This would mean that when the retention rate increases, the graduation would increase more than all this. This is due to the fact that with a lower retention rate, the graduation rate is still more favorable.
Abernathy, J.R., 2011. Smoking as an independent variable in a multiple regression analysis upon birth weight and gestation. BMJ Journal, 56(4), pp.626-33.
Armstrong, J.S., 2013. Illusions in Regression Analysis. International Journal of Forecast, 3(2), pp.689-94.
Beldona, S., 2010. Regression analysis for equipment auditing. Managerial Auditing Journal, 22(8), pp.809-22.
Kahng, S., 20010. TEMPORAL DISTRIBUTIONS OF PROBLEM BEHAVIOR BASED ON SCATTER PLOT ANALYSIS. Journal of Applied Behavior Analysis, 31(4), pp.593-604.
Kahng, S., 2013. TEMPORAL DISTRIBUTIONS OF PROBLEM BEHAVIOR BASED ON SCATTER PLOT ANALYSIS. Journal of Applied Behavior Analysis, 31(4), pp.593-604.
Karafiath, I., 2014. Estimating cross-sectional regressions in event studies with conditional heteroskedasticity and regression designs that have leverage. International Journal of Managerial Finance, 10(4), pp.418-31.
Murnance, J., 2013. U.S. High School Graduation Rates: Patterns and Explanations. Journal of Economic Literature, 51(2), pp.370-422.
Omran, M., 2010. Linear Versus Nonâ€linear Relationships Between Financial Ratios and Stock Returns: Empirical Evidence from Egyptian Firms. Review of Accounting and Finance, 3(2), pp.84-102.