Analysis Of Retention Rate And Growth Rate Of Online Universities In USA

Statistical Analysis of Retention Rate and Growth Rate

Question:

Background One of the biggest challenges in the higher education sector has been the recent growth of online universities. The Online Education Database is an independent organisation whose mission is to build a comprehensive list of accredited online colleges. The Excel spreadsheet (OnlineEdu.xlsx) contains data on the retention rate (%) and the graduation rate (%) for 29 online colleges in the United States.

Instructions

(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?

Your report needs to be structured as follows:

(1) Purpose

(2) Background

(3) Method

(4) Results

(5) Discussion

(6) Recommendations.

Online colleges or universities are made to offer training to the understudies who can’t be display physically in the customary setting, for example, classroom. It has a point of a substantial scale intelligent interest and open access through or through web and other system innovations. Presently a day this methodology of learning or instruction is expanding. The broad utilization of machines and web has made the methodology of learning or instruction through online college quicker and less demanding. These are putting forth a full educational program as same as a typical college, yet as of late there is disaffirm between online college and the ordinary college. The online training database is an autonomous association whose mission is to construct a complete rundown certifies online universities (Welfens and Walther-Klaus, 2007). The motivation behind Retention rate is to screen or see in drawing in and holding understudies for the colleges. Retention rate is ascertained by net wage of the college less profits isolated by Net Pay or Income. Development Rate is the rate of increment of the quantity of understudies of the colleges. Presently I am going to investigate between the retention rate and development rate of the online universities in USA.

In higher studies are confronting disaffirm to pick school or colleges. Which school would it be a good idea for them to pick Online College or ordinary University? Lately understudies are picking online college rather than ordinary college. So there is showing up a greatest test in advanced education part has been late development of online colleges. So we need to investigate the development rate and retention rate of the online colleges in USA.

Regression Model and Interpretation of Coefficient

For this examination we are making mean, minimum value, maximum value and standard deviation of the retention rate and advancement rate of the online universities or colleges of USA. Besides we are also using regression scientific explanation through graduation rate and retention rate (Mccraw, 2012). After that we are discovering the backslide co capable and measurably find the centrality between graduation rate and retention rate.

As showed by the giving data set or surpass desires gave, we adequately circles or figure the conclusions. The outcomes are measured by the aid of some acceptable examination like mean, standard deviation, minimum value and maximum value using some item like Microsoft Office (MS- Excel). The giving data set of the syntheses furthermore its retention rate and graduation rate are in rate is shown in underneath by the help of table.

College	Retention Rate in percentage (%)	Graduation Rate in percentage (%)
Western International University	7	25
South University	51	25
University of Phoenix	4	28
American InterContinental University	29	32
Franklin University	33	33
Devry University	47	33
Tiffin University	63	34
Post University	45	36
Peirce College	60	36
Everest University	62	36
Upper Iowa University	67	36
Dickinson State University	65	37
Western Governors University	78	37
Kaplan University	75	38
Salem International University	54	39
Ashford University	45	41
ITT Technical Institute	38	44
Berkeley College	51	45
Grand Canyon University	69	46
Nova Southeastern University	60	47
Westwood College	37	48
Everglades University	63	50
Liberty University	73	51
LeTourneau University	78	52
Rasmussen College	48	53
Keiser University	95	55
Herzing College	68	56
National University	100	57
Florida National College	100	61

From the given information about the retention rate of online schools or colleges in USA we are going to make a scatter graph by tolerating the upkeep rate and advancement rate as free variable. As showed by the giving data set the most maximum value, minimum value, standard deviation and mean are exhibited in underneath by the aid of the table.

Minimum	4	25
Maximum	100	61
Mean	57.41379	41.75862
Standard Deviation	23.24023	9.865724

 The above table is measured or handling by the help of Microsoft Office or MS- Excel and its significant comparison or equation.

Where, mean estimation of the Retention Rate is proportionate to total entire of the Retention Rate in rate (%) separated by the total no of online schools like 57.414 and moreover mean estimation of the Graduation Rate is equal to total aggregate of the Graduation Rate in rate (%) differentiated by the total no of online universities like 41.759

Correspondingly, the standard deviation is measured by σ= √((σ (x-µ)^2)/(N-1)) or

 

Where, σ = the standard deviation

x = each one estimation of the information set

µ = the mean quality

N = the quantity of qualities or size of the information set

By the help of the above comparison or equation we will viably measured or learn the standard deviation of the retention rate is 23.2402 and furthermore the standard deviation of graduation rate is 9.8657

Quickly are making a scatter chart by taking under considered improvement rate and retention rate of the schools or colleges of USA is sown in below.

From the spread diagram or disseminate graph we can see that advancement rate and support rate are bury related. If improvement rate will extend then support rate will moreover assemble. The rate of both retention and advancement are upward climbing.

The method of basic least square is giving guarantee that gage the backslide line which is moreover the best fitting line, has been drawn from the given data (Drennan, 2002). Here in the above scatter plot the plot does not seem to lie close to the line. So we can say that the backslide line or the best fitting line will fit in amazingly well.

Right away we are making an once-over yield or conclusions of regression measurements by an assumption. 

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.621627987
R Square	0.386421354
Adjusted R Square	0.362822175
Standard Error	17.1688846
Observations	28

Scatter Chart Analysis

 In a matter of seconds we are making a normal regression scientific statement proclamation and interpreting the coefficient inclination or incline. To do this we have expect the qualities. In the followings we have survey backslide and remaining. 

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-0.427733114	15.09197951	-0.02834175	0.97760601	-31.44974098	30.59427475	-31.44974098	30.59427475
25	1.408074644	0.34797141	4.046523943	0.000414052	0.692809173	2.123340114	0.692809173	2.123340114

 In the below table we are put on display the different regression and staying of df, SS, MS, F and Significance of F. we are furthermore giving their total. 

ANOVA
	df	SS	MS	F	Significance F
Regression	1	4826.678724	4826.678724	16.37435602	0.000414052
Residual	26	7664.035561	294.7705985
Total	27	12490.71429

In the followings there is a graph of coefficients, standard error, t-Stat, P-value, lower and upper rates in percentage. 

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-0.427733114	15.09197951	-0.02834175	0.97760601	-31.44974098	30.59427475	-31.44974098	30.59427475
25	1.408074644	0.34797141	4.046523943	0.000414052	0.692809173	2.123340114	0.692809173	2.123340114

In the going hand in hand with we are showing the observations, predication 7 and leftover/ residual in the below table from 1-28 different variables or components. 

RESIDUAL OUTPUT
Observation	Predicted 7	Residuals
1	34.77413297	16.22586703
2	38.9983569	-34.9983569
3	44.63065548	-15.63065548
4	46.03873012	-13.03873012
5	46.03873012	0.961269879
6	47.44680476	15.55319524
7	50.26295405	-5.262954052
8	50.26295405	9.737045948
9	50.26295405	11.73704595
10	50.26295405	16.73704595
11	51.6710287	13.3289713
12	51.6710287	26.3289713
13	53.07910334	21.92089666
14	54.48717798	-0.487177983
15	57.30332727	-12.30332727
16	61.5275512	-23.5275512
17	62.93562584	-11.93562584
18	64.34370049	4.656299513
19	65.75177513	-5.751775131
20	67.15984977	-30.15984977
21	69.97599906	-6.975999061
22	71.3840737	1.615926295
23	72.79214835	5.207851652
24	74.20022299	-26.20022299
25	77.01637228	17.98362772
26	78.42444692	-10.42444692
27	79.83252157	20.16747843
28	85.46482014	14.53517986

From the given data we have learned the regression scientific explanation. Translation or Interpretation of Coefficient as a change of rate of Y is situated up of as a change in the prohibitive mean of Y. There is no need of taking assurance breaks for coefficients into records. When we evaluate or deciphered a regression coefficient adequately as a rate of advancement of a prohibitive mean which is rather than a change in given two variables. It is all that much crucial to take into under thought the weakness in the estimation of the regression coefficient. As indicated by this procedure I have discovered the backslide numerical proclamation line. Which are y= 1.860x + 29.51 and y= 1.143x + 24.60. Of course I have taken a 95% assurance between time for the inclination or slant. The rate of advancement of the prohibitive mean of Y concerning x is evaluated to be some place around 1.860 and 1.143 is regularly attractive over saying; the rate of advancement of the unforeseen mean of Y with respect to x is close around 2 or more. The understanding of the coefficient of which is not genuinely gigantic. This kind of interpretations is frequently made shockingly (Canadian economy online, 2006). If the regression coefficient of t test is not measurably discriminating, this won’t be the suitable to interpret or evaluate the coefficient. There is no accurately tremendous immediate which dependence of the mean of Y on x was perceived. In the translation or interpretation of coefficients in the various regressions with the same tongue or variable is in a broad sense used as a piece of single immediate regression.

As demonstrated by the giving data set or exceed expectations sheet the retention rate estimation of the South University is much higher than valuation for the graduation rate regard. The retention rate regard in rate of the South University is 51% and the graduation rate estimation of the South College is only 25%. Thusly, the retention rate estimation of the South University is 26% more than the graduation rate regard. This is exhibited that the improvement of the school, which is moreover associated with the advancement of the college furthermore when the retention rate quality is extension than backslide rate estimation of the South University is in like manner augmentation. We unmistakably said that the retention rate estimation of the South University is moreover particularly with respect to the regression rate regarded (Ryan and Others, 2010). Hence backslide examination of the South University is incredible fit furthermore the improvement rate and the advancement of the South University is augmentation. Thusly, the amounts of the understudies are moreover augments and also the school is similarly offered some new stream or learning task for some new understudies. In this manner it is clearly said that the retention rate regard when addition than the arrangement of activity is in advantage.

Conclusion

According to the giving data set or exceed expectations sheet the support rate estimation of the University of Phoenix is much lower than deference of the graduation rate regard. The retention rate regard in rate of the University of Phoenix is only 04% and also the graduation rate estimation of the University of Phoenix is 28%. In like manner, the graduation rate estimation of the University of Phoenix is 24% more than the retention rate regard. The retention rate worth is exhibited that the advancement of the school, which is similarly associated with the improvement of the university or college furthermore when the retention rate quality is development than the regression rate estimation of the University of Phoenix is also increase however in University of Phoenix the graduation rate quality is extensions and more than the retention rate regard. Hence the regression correlation of the University of Phoenix is terrible fit and furthermore the improvement rate and the advancement of the University of Phoenix is reduction. Consequently, the amounts of the understudies are moreover reduces furthermore the school is completed not offered some new stream or learning framework for some new understudies. Likewise it is unmistakably said that the graduation rate regard when addition than the arrangement of activity is in hardship.

As per the above detailed analysis we will effortlessly measure some unmistakable examination like mean, standard deviation, minimum as well as maximum values and also regression estimations of some online colleges, which are additionally talked about in above. The retention rate esteem and the graduation rate estimation of the online colleges are additionally given in rate (%). By the assistance of the retention rate worth and graduation rate esteem we will likewise discover or measures the regression estimations of the online colleges (Levy, 2009). The regression estimations of the online colleges are likewise talks about in above. The regression estimations of the online colleges are likewise demonstrated the development of the online colleges like augmentations of the understudies, expanding the learning project and a few others, which is additionally related to the net benefit of the colleges or plan of action.

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