## Question:

(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 variables upon which the performance of a university is dependent upon are the graduation rate and the retention rate. The graduation rate takes account of the students that attain their degree rather than drop out of the college or graduate from the university, where as retention rate refers to the number of students that intend to continue their education from the particular institute or university rather than switching to the competitors. It should be noted that the graduation rate is directly proportional to the retention rate which means that graduation rate would increase as the retention rate increases because the students that are retained by the university are then graduated from that university however this is not always the case. Number of statistical tools has been used for this particular purpose and this objective. The first method to be utilized is to calculate the mean which then is used to develop second method which is the standard deviation method. Mean is the most observed and most common rate between the graduation rate and the retention rate where as standard deviation rate is volatility from the mean (Altman, 2010). Furthermore min and max amount method can be utilized in which the min amount would provide the minimum rate of retention and graduation where the max amount would provide the maximum rate of retention rate and graduation rate. Accordingly then a scatter diagram would be used to determine the relationship and correlation between the two variable in the given data. The results could provide a positive correlation or a negative correlation. In some cases, it is possible that there might not be any relationship between the variables. Furthermore the report follows with another statistical tool that is the regression model that shapes an equation that provides a relationship between the retention rate and graduation rate.

PURPOSE:

The objective of this report is to analyze the data of 29 online colleges statistically. The tools used in this process are statistical such as standard deviation, mean, min, max, regression analysis and scatter diagram. Regression analysis and scatter diagram would provide the relationship between the two variables which in this case are the retention rate and graduation rate. The mean is the centre figure in the provided data set which means it is the most common figure among the two variables in the data set. Whereas the standard deviation refers to the volatility from the mean calculated. The other method that is min and max would provide the minimum and maximum rate of the variables. Regression analysis and scatter plot would provide the relationship between the two variables, in which one would be independent and other dependent. In this case, retention rate would be independent variable and graduation rate would be dependent upon earlier variable.

BACKGROUND:

The statistical calculation is used upon the data set provided of 29 universities as it would provide a reasonable basis for understanding the relationship between the retention rate and the graduation rate. Such methods are also used by most analysts to determine the relationship among different variables. Among others, regression equation is most commonly used as it provides the relationship between the variables in a linear equation such as the one provided:

Y=mX+C

Where X is the independent variable, Y is the dependent one that depends on the value of X and C is the Y-intercept.

METHOD

Initially the most basic method to be used in this process is the determination of the mean. The mean provides the most common number for the retention rate and graduation rate in the data provided whereas standard deviation provides the volatility from the mean. Accordingly, the other two methods that are the min and max provide the minimum and maximum rate accordingly for the retention rate and graduation rate. The scatter plot would be used to determine the relationship between the two variables that are retention rate and the graduation rate. Relationship can be a positive relationship and it can be a negative relationship (Touchette, 2011). A positive relationship would suggest that the dependent variable is directly proportional to the independent variable which means that the dependent variable would increase if the independent one increases. A negative relationship would suggest that the dependent variable is inversely proportional to the independent variable meaning if the independent variable increases, the dependent variable would supposedly decrease. For example if more electronics are used then more electricity would be consumed. In such case number of electronics would be an independent variable and amount of electricity consumed would be the dependent variable. However it is not necessary that a relationship would always be positive as there could also be a negative relationship meaning both variables behaving in a completely opposite manner. For example, more a student studies, less there would be chance he would fail. Another relevant example would be higher the expenses of a company, lesser the profits earned. Sometimes there is no relationship between the variables for example the relationship between hunger and intake of water or taking a nap. Although there is no point to identify the relationship between the two variables, however some analysts think that the relationship should be further explored using other methods and models (Denis, 2012). Another model that can be used to determine the relationship between the retention rate and graduation rate is the regression analysis. This method would provide an equation that would explain the relationship between the two variables. Supposedly those two variables are graduation rate and retention rate. The graduation rate is X and retention rate would be Y. A positive relationship is found between the two variables i.e. retention rates and graduation rates as it was observed that X increases as Y increases.

RESULTS

The results are explained along with the table of data sets below

DISCUSSION

It can been be said from the above table that the most common number for retention rate i.e. the number that majority of the universities have achieved as retention rate is calculated 57% where as the most common number for graduation rate is 41%. However the standard deviation from such means for retention rate was calculated 23% whereas standard deviation from mean for graduation rate was calculated 9.9%. The max provides the maximum retention rate among the institutes and maximum graduation rate amongst the institutes. The min provides the minimum retention rate among the institutes and minimum graduation rate amongst the institutes. From the above calculations, the maximum graduation rate was determined as 61% where the maximum retention rate determined was 100%. However from the above calculations the minimum graduation rate was determined as 25% and minimum retention rate determined was 4% from the data set provided.

The scatter plot for the analysis is presented below

It is observed that within the range of 40% and 80% the relationship between graduation rate and retention rate cannot be determined accurately however if whole graph is considered, it can be reasonably determined that the relationship is a linear relationship as the graduation rate is increasing as the retention rate is increasing. This is due to the fact that if a student chooses to stay in a university where he was previously studying; there are high chances that he will graduate from the same university in which he was retained (Gulliksen, 2009). There both variables that is graduation rate and retention rate are positively correlated.

Regression analysis statistically determines the relationship between two different variables by producing an equation using the two variables. From the two variables, one is an independent variable where as second variable is dependent of the first one. The equation used in this method is

Y=mX+C

In the above equation, X is the independent variable as it does not depend upon other factors; however Y is the dependent variable which depends upon the changes is X and it is y, we are aiming to determine. And c is the Y intercept.

For the data provided of the 29 online universities, the regression chart is provided as follows

The relation between the graduation rate and retention rate can be observed to be linear one from the above table as it can be seen that universities with higher retention rates provide higher graduation rates. A positive correlation serves that if Y increases if the Y increases. This is due to the fact that y is dependent upon the value of X which is independent of any influences. The above calculation provides 0.28 slope, Y as the graduation rate and X as the retention rate whereas the Y-intercept was calculated as 25.4.

This proves that mostly students are satisfied with the existing standard of education provided to them and are motivated to continue their further education from the same university which effectively increases the graduation rate of the university. Although mostly universities have linear relationship between the graduation rates and retention rates, however there are some universities with higher retention rate and lower graduation rate and there are also some universities with higher graduation rates and lower retention rates suggesting that some of the data provided do not fit in the linear equation. However such figures are immaterial and can be ignored (Lin, 2011). So in conclusion it could be said that the graduation rate is directly proportional to the retention rate suggesting that mostly student prefer to complete their education rather than to drop out which effectively increases the graduation rate.

RECOMMENDATIONS

The retention rates and the graduation rates are most favourable and highest for University Of South but as the president of the university it highly concerns me that there some universities that have high graduation rates but lower retention rates as described earlier it not every but a minor and immaterial number of universities. However in the same way, South University possesses a very favourable retention rate but the graduation rate is very disappointing and not what is expected. The issue should be discussed the senior management or at least with the instructor as he would have knowledge regarding this and would provide guidance regarding this matter. It is possible that such low graduation rate would be due to high dropout rate of students having financial issues and cannot afford further education. The graduation rate of Phoenix University is higher but its retention rate is quite low which suggest that students switch to universities during the final period of their education. Finally it could be said that the issue should be resolves as soon as possible as it would increase the graduation rate of the university which would in turn improve the overall raking of the South University as it would have higher graduation rate then its retention rate. This issue should be the priority of the president and his main concern so that the graduation rate could be increased. It should also be ensured that the issue is discussed with the instructor and the ex-students that have left the university to determine the cause of their departure.

## References

Altman, D.G., 2010. Standard deviations and standard errors. BMJ Journal, pp.52-58.

Denis, D., 2012. THE EARLY ORIGINS AND DEVELOPMENT OF THE SCATTERPLOT. Journal of the History of the Behavioral Sciences, pp.103-30.

Gulliksen, H., 2009. A mechanical model illustrating the scatter diagram with oblique test vectors. Springer Journal, 16(2), pp.223-38.

Lin, D.Y., 2011. Linear regression analysis of censored medical costs. Oxford Journals, 1(1), pp.35-47.

Touchette, P.E., 2011. A scatter plot for identifying stimulus control of problem behavior. US National Library of Medicine , pp.343-51.

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