Economics and Quantitative Analysis Economy Statistics

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? Answers: 1. Purpose of the research The education sector of USA is growing at a faster pace due to the emergence of the new online universities who are providing easy access to the students. However Goodman (2011) opined that these universities face problems relating to fluctuation in graduation and retention rate of the students. The report will provide an analysis by using the different statistical methods. 2. Background of the research The report is prepared by considering the statistical data of 29 online universities of USA. The data of these 29 universities will help the researcher to analyze the fluctuations of the retention and the graduation rates of the students in the university. The research has also been conducted to analyze whether the co relation between the retention and the graduation rate influences the graduation rate or not (Hanke, 2010). 3. Methods used The use of technical and appropriate methods is essential for carrying out of the statistical analysis (De Maio, 2013).The researcher after considering the overall situation of the study selected the following methods as appropriate for conducting of the research. Microsoft excel SPSS Descriptive statistical analysis including calculation of mean, Standard deviation, minimum and maximum Scatter diagram presentation Preparation of regression equation 4. Results 4.1 Calculation of descriptive statistical analysis Discussion of results The results which are derived in the above three steps shows the relation between the graduation and the retention rates. Analysis of Descriptive statistics: The mean of graduation and the retention rate shows 57.41% and 41.76% respectively. Since the retention rate is higher hence it can be understood that the online universities are able to retain more than half of the students who took admission in the universities. However the low graduation rate indicates that the students could be retained but only half of them graduated. The standard deviation of the two variables shows that the retention rate is comparatively higher than the graduation rate. The minimum ad the maximum of the variables shows that retention rate is more variable in accordance to the graduation rate. Analysis of the scatter plot: The analysis of the scatter plot shows the factors namely the direction, form, strength and outliers. in this case the researcher found to experience a positive direction in the scatter diagram since the larger values are seen in case of retention and graduation rates. According to Zhang (2011), form in a scatter diagram are of different types namely no association, no linear association system, linear association and perfect linear association. The present research shows the results to be linear association. The analysis also shows that the strength is a moderate correlation which ranges between (0.35 r -0.55, 0.35 r 0.55). Hence it can be rightly deduced that the scatter plot between retention and graduation rates are moderate positively linear association. Regression equation analysis: The regression equation is: Graduation rate (G.R) = Intercept Coefficient+ Coefficient of retention rate * Retention rate Considering the values of intercept coefficient 25.42 and retention coefficient 0.2845 the regression will be as below: Graduation rate = 25.423 + 0.2845 * Retention Rate In this case the retention rate is considered to be zero and calculation shows that the co efficient of determination value is 0.449. This information shows that the use of regression model is fitted for the study. Gatignon (2014) has defined the goodness of fit of regression model as the appropriateness of the model for estimation of the variables. In this context it has been proved that any value near to 1is a confident estimation and value deviating from 1 is not a good estimation. The result of this case shows the coefficient to be 0.449 or 44.9% and the moderate estimation standard is 55% . Now since the value is below the moderate estimation hence the regression equation failed to deliver a good result and is not fit for the study. However the nature of the regression analysis shows a moderate relationship between the graduation and retention rates for the universities hence the use of the multiple regression analysis is necessary to get an in-depth knowledge and understanding of the situation, problems and relation. The result shows that the South University has a graduation rate of 25% with a retention rate of 51%. This result shows that among all the universities only South University has a good performance and the educational quality as well as the other factors provided by the university seems to be effective and efficient (Hilbe, 2011). In case of University of Phoenix the graduation rate is 28% and retention rate is 4%. This shows that this university needs to have concerns about the quality of education and quality of service provided beacau4 the retention rate is very low in case of this university. However since all the results are obtained from the relation of only two variables hence the results may deviate on actual calculation. Recommendations Since the study reveals a positive association between the graduation and the retention rate hence it can be recommended that the regression equation is not the best fitted method in this case. It can be ascertained that there are several external variables that influence the retention rate hence it is advisable to analyze the problems with the help of multiple regression analysis. The use of this method will help the researcher will get a deep rooted view of the problem. Reference list Books Fitzmaurice, G., Laird, N. and Ware, J. (2011).Applied longitudinal analysis. Hoboken, N.J.: Wiley. Gatignon, H. (2014). Statistical Analysis of Management Data. Boston, MA: Imprint: Springer. Hilbe, J. (2011).Negative binomial regression. Cambridge, UK: Cambridge University Press. Quick, J. (2010).Statistical analysis with R. Birmingham, UK: Packt Pub. Journals De Maio, F. (2013). Regression Analysis and the Sociological Imagination.TEST, 36(2), pp.52-57. Goodman, A. (2011). Emerging topics and challenges for statistical analysis and data mining.Statistical Analy Data Mining, 4(1), pp.3-8. Hanke, M. (2010). Statistical learning analysis in neuroscience: aiming for transparency.Frontiers in Neuroscience. Zhang, H. (2011). Statistical Analysis in Genetic Studies of Mental Illnesses.Statist. Sci., 26(1), pp.116-129.