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Discuss about the Economics and Quantitative Analysis ?

Answer :


An upward rising trend for online mode of education is noticed in United States of America. During the recent years, higher education sector has witnessed a sharp growth in current years. A large number of universities in United States of America provide the facilities of online mode of education. The current report consists of the brief discussion of the analysis performed. The data obtained represents for rate of graduation and rate of students retained in the university.

Objective of the study:

The primary objective of this study is to analyse the quality of the education provided by the universities of United States.

Background of the study:

Over the years, a large number of education institutes in United States are going through several challenges. Online mode of education is regarded as the most popular source of education. Ever since the growth of internet, there has been a vast expansion in online education with large number of universities following the same trend. Several students are facilitated with online education program and universities make the use of effective tools to implement such programmes.

Students living at distant places can gain the access of their study material and other educative materials through the help of internet. The current report takes into the consideration the quality of online education imparted by the universities. The report also lays down the ideas concerning the methods of collecting data and along with the analysis of data. The interpretation of the result derived from this report provides the in depth analysis of the methods used.

Methods used for analysis:

The current study takes into the consideration data, which is obtained from twenty-nine universities of United States. To analyse the data several statistical tools are used such as measures of central tendency and measures of dispersion. A comparison is drawn measuring the two variables obtained and provides an idea concerning the superiority of practices for online study in these universities.

The study also takes into the consideration the liner of regression equation to ascertain the amount of association between the two variables. The relation amid the two variables namely the rate of retention (RR) and the rate of graduation (GR) is also examined with the help of scatter diagram. The statistical measures adopted will help in understanding the association between the rate of graduation and the rate of return in the universities. The measures adopted will help in understanding the quality of education imparted in these universities.


The rate of return and the rate of graduation are obtained from the measures of central tendency and through measures of dispersion. In order to derive the results mean value, standard deviation, a minimum and maximum value has been computed for the variables. The mean value lays down the parameters for the variables. On the other hand, the average values of the variable in the twenty-nine Universities are provided through using the mean value. Standard deviation represents the measure of dispersion. The standard deviation lays down the scatter distribution. The minimum and the maximum values provides the notion concerning the extension of distribution. Below stated tables provides the measurements;


Graduation Rate (GR)

Retention Rate (RR)




Standard deviation









Table 1: Table measuring the descriptive statistics

(Source: As created by author)

Below listed scatter diagram has been obtained by undertaking the rate of retention in the form of independent variable.

                                                    Figure 1: Figure representing the scatter diagram of Rate of retention and Rate of graduation

                                                                                        (Source: As Created by Author)

The above stated scatter diagram is derived by taking into the consideration the rate of retention along the X axis and the rate of graduation along the Y axis. The scatter diagram represents an upward rising trend. The diagram represents a positive but direct relationship among the variables. This represents an increase in the value of retention rate along with the graduation rate.


A regression equation is performed by taking into the consideration the rate of graduation at the X-axis and the rate of retention at the Y variable. Computation of the results is listed below;  

The regression results derived after computing the above stated equation lays down the regression co-efficient rate at 0.284526. The equation of regression is listed below;

  • Y = 25.4229 + 0.284526*x + e.

In the above stated regression equation, Y signifies the graduation rate in universities and X signifies the retention rate. The “E” variable signifies the components of random error. The P-Value of the coefficient slope represents 6.59 * 10^-5. It is understood that the P-Value is lower than the significant level of 0.05. Hence, the coefficient slope is considerably diverse from 0. The P-Value of the intercept test represents 2.47 * 10^-7. This represents that the P-Value is lower than the given level of significance which stood at α = 0.05.

To conclude with the slope of co-efficient is significantly different from zero value. Furthermore, the regression coefficient reflects a positive result in the above stated equation. The results obtained highlight the positive association amid the rate of graduation (GR) and the rate of retention (RR). The results indicate that with an increase in the value of graduation rate, the value of rate of retention also increases.

The graduation rate and the rate of retention represent the continuous variable. By using the tools of correlation co efficient association amid the two variables is studied. The positive value of correlation represents the direct relation whereas the negative value reflects an indirect association. In the below stated table lays down the correlation between the two variables;


Graduation Rate (%)

Rate of Retention (%)

Graduation Rate (%)



Rate of Retention (%)



Table 2: Table representing correlation between graduation rate and rate of return

(Source: As created by author)

The correlation coefficient derived stood as 0.670245. Thus, it is understood that there is a direct relation among the variables. The adjusted R square helps to determine how good the fitted regression model is.

The adjusted R square derived from the regression model stood 0.428829. Thus, the model is not regarded best in terms of lowering the errors.


The objective of the analysis of the data is to develop an idea concerning the two variables namely, graduation rate and the retention rate. From the analysis it is understood that there is significant difference between the mean value derived for the two rates. The maximum value concerning the rate of retention is on the higher side. Thus, retention rate is more than the graduation rate. The results obtained from the regression analysis represents that there is a direct relation between the two variables. It is noteworthy to denote that value of retention rate increases with the graduation rate.

Conclusion and recommendations:

To conclude with, the report analysed the eminence of the online education in the Universities of United States. Results derived from the analysis states that the rate of graduation is on the higher side in comparison to the rate of retention. Following the study, few recommendations is laid down below;

  1. The adjusted R-square represents a smaller value under the regression analysis. Thus, the regression model is not well suited with the fitted model. The results derived from the regression analysis only provide simple measurement of the data set.
  2. The size of sample is relatively small with only 29-sample size. The results could have been more efficient had some other methodologies of sampling would have been adopted.


Afifi, A.A. and Azen, S.P., 2014. Statistical analysis: a computer oriented approach. Academic press.

Castagliola, P., Achouri, A., Taleb, H., Celano, G. and Psarakis, S., 2015. Monitoring the coefficient of variation using a variable sample size control chart. The International Journal of Advanced Manufacturing Technology, 80(9-12), pp.1561-1576.

Diggle, P.J., 2014. Statistical Analysis of Spatial and Spatial and Spatio-Temporal Point Patterns.

Draper, N.R. and Smith, H., 2014. Applied regression analysis. John Wiley & Sons.

Kleinbaum, D.G., Kupper, L.L., Nizam, A. and Rosenberg, E.S., 2013. Applied regression analysis and other multivariable methods. Nelson Education.

Kolaczyk, E.D. and Csárdi, G., 2014. Statistical analysis of network data with R (pp. 1-5). New York: Springer.

Little, R.J. and Rubin, D.B., 2014. Statistical analysis with missing data. John Wiley & Sons.

Mannor, S. and Tsitsiklis, J.N., 2013. Algorithmic aspects of mean–variance optimization in Markov decision processes. European Journal of Operational Research, 231(3), pp.645-653.

McAuliffe, R.E., 2015. Coefficient of variation. Wiley Encyclopedia of Management.

Montgomery, D.C., Peck, E.A. and Vining, G.G., 2015. Introduction to linear regression analysis. John Wiley & Sons.

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