"Running head: ECONOMICS AND QUANTITATIVE ANALYSISEconomics and Quantitative analysisName of the studentName of the UniversityAuthor note:ECONOMICS AND QUANTITATIVE ANALYSIS1Executive Summary:This research study highlights on the interrelationship between the retention rates (%)and the graduation rate (%) of the online universities of US. The recent growth of theseuniversities is a major challenge to the system of higher education in the US. To analyze theeffect, a regression analysis has been performed with the help of excel tool. The regressionanalysis depicts the fact that there is a significant association between the two variables.ECONOMICS AND QUANTITATIVE ANALYSIS2Table of ContentsIntroduction: ............................................................................................................................... 3Purpose:...................................................................................................................................... 3Background: ............................................................................................................................... 3Method: ...................................................................................................................................... 4Results: ....................................................................................................................................... 4Discussion: ................................................................................................................................. 6Conclusion and Recommendations: ........................................................................................... 9Reference List: ......................................................................................................................... 10 ECONOMICS AND QUANTITATIVE ANALYSIS3Introduction:In this research study, the researcher concentrates on the interrelationship between theretention rates with the graduation rate of the online universities of United States. Now, toanalyze the growth of online universities in the higher education sector, the regressionanalysis has been performed. With the help of suitable statistical tools and technique, itseffect on the higher education sector in the US has been evaluated.Purpose:The recent growth of the online universities creates the severe challenges in the highereducational sector. From the twenty-first century, there is a huge growth of the onlineuniversities in the US which changes the values, culture, nature and the control of the highereducation in this country. The public resources and the associated social expectations areundergoing the fundamental shifts in respect of the higher education in the US. Moreover, thecurriculum, students, faculty and its functions need to make a drastic change in the highereducational sector of US due to the growth of online universities. Thus, the purpose of thisresearch is to analyze the effect the external influences by the growth of online universitieson the higher educational sector of US.Background:One of the major issues in the higher educational sector in the US is the recent growthof the online universities. The growth of this type of universities changes the nature, valuesand system of the higher education in the US. In this perspective, the impact of the growth ofthese online universities on the higher education system of US has been evaluated by theOnline Education Database. Hence, the interrelationship between the retention rate and thegraduation rate for 29 online colleges in the US has been analyzed. ECONOMICS AND QUANTITATIVE ANALYSIS4Method:In order to perform the following research, the researcher needs to use the relevantstatistical tools and technique. In this perspective, with the help of excel tool, the descriptiveanalysis, scatter diagram, regression equation, and the goodness of fit have been calculated.Furthermore, the comparative analysis regarding the performance factor of the SouthUniversity and the University of Phoenix with the database of the online universities has beendone by using Excel tool.Results:(a). Mean 41.75862Standard deviation 9.865724Minimum 25Maximum 61Table 1: Descriptive Statistics of Graduation rateSource: (As created by author)Mean 57.41379Standard deviation 23.24023Minimum 4Maximum 100Table 2: Descriptive Statistics of Retention rateSource: (As created by author)(b).ECONOMICS AND QUANTITATIVE ANALYSIS5Scatter Diagram 70 60 50 40 30 20 10 0 0 20 40 60 80 100 120 Retention rate (%) Figure 1: Scatter diagram Source: (As created by author)(c). Coefficients T-Stat P valueIntercept 25.42290363 6.786165928 2.74E-07X variable (retention 0.284526003 4.692771862 6.95E-05rate)Table 3: Regression analysis of the retention rate and the graduation rateSource: (As created by author)(f).Regression StatisticsMultiple R 0.670244797R Square 0.449228088Graduation rate (%)ECONOMICS AND QUANTITATIVE ANALYSIS6Adjusted R Square 0.428829129Standard Error 7.456104604Observations 29Table 4: Regression Statistics of the retention rate and the graduation rateSource: (As created by author)Discussion:In order to perform the research analysis, a regression analysis has been done byconsidering the retention rate as the independent variable and the graduation rate as thedependent variable.(a).Both mean and the standard deviation are high and significant of the retention ratecompared to the graduation rate. Moreover, the range of the variable retention rate or themaximum and minimum are significant compared to the graduation rate.(b).The scatter diagram represents the positive relationship between the two variables inwhich the retention rate is considered as an independent variable, and the graduation rate isconsidered as a dependent variable. It indicates the one-to-one correspondence relationshipbetween them. If there is a change in retention rate, then the graduation rate also changes.(c).According to the given database, the estimated linear regression equation is y = a + bxwhere, y is the independent variable (graduation rate), x is the dependent variable (retention ECONOMICS AND QUANTITATIVE ANALYSIS7rate), “a” is the intercept term and “b” is the slope coefficients of the x variable. Thisregression equation helps to predict the effect of the graduation rate (%) given the retentionrate (%). (d).Now, as the regression results, the estimated regression equation is y = 25.42290363+ 0.284526003 x. This regression equation signifies that if the retention rate is zero, then the value ofthe graduation rate is 25.42290363 which is the intercept term. Moreover, due to the changesin the value of x, y changes simultaneously. If the value of x increases, then the value of ywill be the summation of the increased value of x multiplied by the value of slope coefficients(0.284526003) with the intercept term (25.42290363). It shows the positive relation which isalso shown in the scatter diagram and the graduation rate is fully dependent on the retentionrate. (e).To test whether the regression equation is statistically significant or not, theresearcher needs to assume a hypothesis. H0: There is no significant effect between the two variables the retention rate (%) and thegraduation rate (%).H1:There is a significant effect between the two variables the retention rate (%) and thegraduation rate (%).In the words of Montgomery, Peck and Vining (2015), if the p-value is lower than “a”level of significance, then the null hypothesis is rejected. On the contrary, if the p-value is "