Economics and Statistical Quantitative Analysis

Question: Discuss about the Economics and Statistical Quantitative Analysis. Answer: Introduction: The current report is concerned with the growing trend of online mode of education throughout the University of United States. The report highlights that in the current years, higher education sector has experienced a sharp surge in recent years. Several universities in United States has offered the privilege to impart online mode of learnings. The existing report consists of the brief discussion of the analysis performed by using the statistical tools. The data takes into the consideration the rate of graduation and the rate of students retained in the university. The main purpose of this study is evaluating the quality of education imparted by the universities located in United States. Background of the study: Studies suggest that a large number of universities in united states is facing numerous challenges. Currently, online mode is considered as one of the highly sought after mode of education. Ever since the expansion of internet, studies has suggested that there has been a vast expansion in the online mode of learning since numerous industries have adopted the trend of imparting internet based learning. A large number of students are offered with the facilities of online mode of education and programme and utilises adequate instrument to implement such facilities. Students generally dwelling in far-away places can have the opportunity of gaining access to their study material and materials imperative for study by using the internet. The existing study focuses on the quality of online education provided by the universities in united states. The study also provides the notion regarding the methods of collecting data through making data analysis. The understanding of the outcomes derived from the study lays down an in depth assessment of the methods used. Methods used for analysis: The report considers the data derived from the 29 universities of United States. In order to assess the data numerous statistical instruments are used to derive the desired outcomes such as measures of central tendency and measures of dispersion. A comparative study is used to evaluate the two variables derived which helps in laying down the notion of superiority of practice concerning the online mode of learning in these universities. The report emphases on the equation of liner regression in order to assure the sum of association amid the two variables. The relationship between the two variables is generally characterised in the form of rate of retention and graduation rate. This is examined by putting into the use tool of scatter diagram. The statistical assessment undertaken enables in better understanding of the association between the rate of graduation and rate retention in the universities (Afifi and Azen 2014). The statistical measures helps in evaluating the quality of education imparted in these universities. Outcomes: The extent of dispersion and central tendency has been calculated with respect to the variables GR and RR. In addition to this, the mean value, maximum and minimum value and standard deviation have been measured for these variables (Zhouet al. 2014). The measurement of mean value provides the location parameters related to the variables. Around twenty-nine universities are served with the average value of the variable with respect to the mean value. In contrast with these facts, the standard deviation is nothing but the measurement of dispersion. The standard deviation provides the scatterness of allocation. On the other hand, the minimum and maximum values provide understanding of allocation. The following table shows the measures: RR(%) Mean 57.41 Standard Error 4.32 Median 60 Mode 51 Standard Deviation 23.24 Sample Variance 540.11 Kurtosis 0.46 Skewness -0.31 Range 96 Minimum 4 Maximum 100 Sum 1665 Count 29 Inter-quartile range 24 CoV 40.48% Table 1: Measures of descriptive statistics (Source: Created by author) GR(%) Mean 41.76 Standard Error 1.83 Median 39 Mode 36 Standard Deviation 9.87 Sample Variance 97.33 Kurtosis -0.88 Skewness 0.18 Range 36 Minimum 25 Maximum 61 Sum 1211 Count 29 Inter-quartile range 14 CoV 23.63% From the below stated computation it is found that the inter-quartile range for rate of retention stands 24 while the coefficient variation for the rate of retention is 40.48%. The inter-quartile range for the graduation rate is 14% while the coefficient variation is 23.63% for the graduation rate. The mean value for the graduation rate is 41.76 and standard error represented as 1.83. The above figure is obtained by putting the retention rate in the x axis and the graduation rate along the y axis. The pattern of the graph shows the incremental pattern. Therefore, this can be argued that the variables have positive and direct relationship among each other. Therefore, the graduation rate and retention rate has proportional to each other. A regression equation is formed by putting GR along x axis and RR along the y axis. The outcomes of regression analysis are given as follows: Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 25.4229 3.746284 6.786166 2.74E-07 17.73616 33.10964 17.73616 33.10964 RR(%) 0.284526 0.060631 4.692772 6.95E-05 0.160122 0.40893 0.160122 0.40893 Table 2: Results of regression analysis (Source: Created by author) The regression equation formed from the above values shows that the regression coefficient with respect to regression coefficient is 0.284526. The formed regression equation is as follows: In the above equation, the x is representing the retention rate and y is representing the graduation rate in the universities. In addition to this, the variable e represents the erroneous components (McIntosh and Mii? 2013). The p-value of the coefficient is 6.59 * 10^-5. The p-value has less in quantity in comparison with the significance level 0.05. Therefore, coefficient of slope is not 0. The test considered for the intercept is 2.47 * 10^-7. In contrast with this, the p-value has lesser value than the significance level = 0.05. Therefore, coefficient of slope is not 0. In addition to this, the coefficient of regression has positive value in this equation. Therefore, there is positive associative relation within the variables GR and RR. Therefore, this can be argued that the variables have positive and direct relationship among each other. Therefore, the graduation rate and retention rate has proportional to each other. The graduation rate and retention rate are continuous variables. The associative relationships between these two variables are measures with the help of correlation co efficient (Parkset al. 2014). The direct and indirect relations are measures with the help of positive and negative values of this coefficient respectively. The following table is showing the correlation between these two variables: GR(%) RR(%) GR(%) 1 RR(%) 0.670245 1 Table 3: Correlation between retention rate and graduation rate (Source: Created by author) The obtained value for the correlation coefficient is 0.670245. Therefore, it is proven that the variables have direct relationship with each other. In addition to this, the integrity of the regression model is evaluated with the help of adjusted R-Squared for the model. Regression Statistics Multiple R 0.670245 R Square 0.449228 Adjusted R Square 0.428829 Standard Error 7.456105 Observations 29 Table: Adjusted R squared for the regression model (Source: Created by author) The value of adjusted R- Squared in this model is 0.428829. In contrast with this fact, this model is perfect in reducing the errors. Discussion: The major objective of the analysis of data is to generate an idea of variables such as graduation rate and rate of retention. Upon conducting the analysis, it is found that there is large degree of difference between the mean values obtained from the above mentioned two rates (Heiberger and Holland 2015). The maximum value concerning the rate of retention is based on the higher side. Therefore, the rate of retention is higher than the rate of graduation. The outcome derived from the analysis portrays that there is prevailing circumstances of direct relationship between the two variables. It is worth mentioning that the value of retention rate increases with the rate of graduation. Being the president of South University there are concerns relating to the part time courses. The university should work towards improving the part time education for those students who does not have full time campus facilities. On the other hand, being the president of the Phoenix it is found that student s of distant learners needs to be offered flexibility with certification programme which helps in keeping in stay with the interested course related work and some sometimes even easier to impart learnings under innovative programmes. Conclusion: Upon concluding the report, it is evident from the analysis that online mode of learnings is important in United States. Outcomes of result obtained represent that graduation rate is superior to the rate of retention. The study also lays down few recommendations, which are as follows; The adjusted R-square lays down relatively smaller value under the regression analysis. Thus, the model of regression is not a good fit model. The outcomes of the regression analysis only signifies simple measurement of data. The sample size is very small having only 29 universities. It is recommended that the result would have been effective if other methods of sampling would have been considered for analysis. Reference list: Afifi, A.A. and Azen, S.P., 2014.Statistical analysis: a computer oriented approach. Academic press. Heiberger, R.M. and Holland, B., 2015.Statistical analysis and data display: an intermediate course with examples in R. Springer. McIntosh, A.R. and Mii?, B., 2013. Multivariate statistical analyses for neuroimaging data.Annual review of psychology,64, pp.499-525. Parks, D.H., Tyson, G.W., Hugenholtz, P. and Beiko, R.G., 2014. 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