Economic and Quantitative Analysis

Question: Instructions Prepare a 2,000 word report that addresses the following questions: (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? Answer: Introduction: This report aims at highlighting the two key variables in the industry of education, namely graduation rate as well as retention rate. This report includes a detailed analysis that is helpful in establishing a stable relationship amidst the two mentioned variables(FOLSOM et al., 2005). This report emphasizes upon representing the level of relationship amidst graduation as well as retention rate for around twenty nine institutes that are based in the United States of America. Also, this report provides a vivid recommendations depending upon the findings of the research analysis conducted in this report. Background Overview: On analyzing the prevailing economic conditions of the world, it may be identified that the extent of the global competition has been on a tremendous rise across all nations. In almost every industry, business firms have been facing increased rivalry as well as emphasizing upon adopting innovative strategies and techniques for achieving competitive advantage and staying ahead of all competitions. Microeconomic studies have been demonstrating that several factors are there that impact considerably upon the customers, and are said to control the overall market demands. Technological enhancement and development have impacted upon the extent of global competition within the market since it is impacting on the consumer tastes as well as preferences. The current prevailing educational trend reflects that the growing demands for online academic studies and that of educational programs have been extensive because of its convenience and feasibility. The increased evolution of the concept of o nline education has been threatening the age-old system of education(The Low College Graduation Rate of Black Students Is Not Due to Racial Factors, 2005). It is reported that the sector higher education has been facing certain key challenges since online educational programs have been gaining increased popularity. The main target of the Online Education Database is to create a preferred list of the mentioned accredited online institutes. The knowledge about the graduation as well as retention rate for all 29 colleges in the United States has been mentioned in this report. The collected information are analyzed economically and this provided a notion to the current situation of the online educational industry followed by recommendations. Methodology: Some of the effective methods are taken up to analyze the connection between the two mentioned variables. A detailed analysis of these variables may be carried on with the support of statistical functions as well as techniques (Almeida, 2007). The excel program along with its various functions have been used to provide scatter images of the variables. In the report, independent variable is the retention rate. The relationship amidst the two variables, graduation rate and that of retention rate may be clearly demonstrated with the help of regression equation that can be utilized to predict the rate of graduation while the retention rate is constant. The link between the mentioned variables may be depicted in support of some statistical tools. In addition, the report also identifies if the regression is appropriate or not. Results: This part of the report depicts the outcomes achieved from the analysis of the variables with consideration of the relevant statistical tools. It highlights the retention rate as well as the graduation rate of all twenty nine online colleges of the US. To explain the two variables it can be referred that graduation rate is the percentage of overall undergraduate students enrolling in the institute and also graduated from the very institute (De Vos, 2007). The rate of retention refers to the percentage of the students who are likely to continue with the program in the next year as well. The link between these two variables may be indicated. The outcomes derived with the help of various statistical tools are depicted and interpreted within this part. Descriptive Analysis: The descriptive analysis of both graduation rate as well as retention rate involves the estimation of standard deviation, mean, minimum, and maximum. The following table representation shows the required calculation of the statistical measures. As depicted from the above table, it is identified that mean retention rate of all twenty nine online colleges of the nation is approximately 57.41379. On the other side, average of graduation rate is lesser that that of the retention rate which is 41.75862. Here, standard deviation is needed to be identified (Dorn, n.d.). The standard deviation of the retention is calculated around 23.24023 and the same for the graduation rate of all 29 institutes is quite less that is 9.865724. For identifying the range, it is important to identify the minimum as well as maximum values of the two variables. It has been identified that the minimum as well as maximum retention rate is supposedly 4 and 100 respectively. For graduation rate, minimum as well as maximum is estimated approx 25 and 61 respectively. Scatter Diagram: This diagram is represented in this part of the report to demonstrate the extent of dependence as well as nature of correlation amidst the two mentioned variables graduation rate as well as retention rate. In this report, rate of retention is taken on X axis and that of the graduation rate on vertical Y axis. All plotted values reflect the data given for all of the colleges of the United States. From this, the direction of the plot shows that increased values of the rate of retention are associated with greater value of the rate of graduation(Dropouts in America: confronting the graduation rate crisis, 2005). Thus, it may be stated that these variables have a favorable correlation. The pattern of the scatter diagram depicts that a linear link exists between the mentioned variables. If the potential strength of the scatter figure is analyzed it may be inferred that a moderate correlation exists amidst the both graduation rate as well as retention rate. Regression Analysis: The regression equation of both graduation rate and that of the retention rate of all 29 colleges of the country is depicted within this part. This would aid in analyzing the link amidst retention as well as graduation rate. The table below shows the outcomes of the regression analysis: The rate of retention is independent and that of the graduation rate is a dependent variable. So, the equation of regression is shown below: Y = Intercept (Coefficient) + X (Variable Coefficient) Y = 25.4229 + X * 0.2845 Y = 25.4229 + 0.2845X Coefficient of Slope: As reflected in the equation of regression, the coefficient of slope may be suitably estimated. It is identified that the result for this slope coefficient is around 0.2845. This variable shows the slope of the best fitted line upon the scatter diagram. Link amidst both the variables: The table representing regression analysis distinctly reflects the existence of a significant link amidst the two variables, retention rate and graduation rate of the selected colleges of the nation. The value for R square is estimated approx 0.44922. This refers that the two mentioned variables are correlated positively(FOLSOM et al., 2005). The magnitude of this value R is greater and this shows that the extent of dependence amidst the two variables, graduation rate as well as retention rate of online colleges is considerably high. Goodness of Fit: This concept of goodness of fit supports explanation of the level of correctness of the statistical model that fits properly to observational sets. Generally, it supports to summarize the inconsistency amidst the observed as well as expected value of the model. The R square value enables determination of the goodness of fit here. This value R square is estimated approx 0.44922. Thus, it is reflected that equation of regression is not most effective for the link between graduation rate as well as retention rate of all the online institutes(Heckman and LaFontaine, 2010). It is witnessed from the analysis that equation of regression is fit to certain extent if not completely. The diagram below shows the trend line. Discussion: From the statistical analysis, the findings regarding both retention rate and that of the graduation rate is reflected and also highlights upon the significant link between the two. Firstly, as per the given descriptive analysis, standard deviation, mean, minimum and maximum values are calculated. Mean aids in identifying the central tendency of the prescribed distribution values. It is identified that the average of retention rate is greater than that of the graduation rate. Additionally, it is essential to measure dispersion of the particular value set from the mean that supports assessment of the consistency of distribution(Izumi, Shen and Xia, 2013). For retention rate, the standard deviation is considerably greater than the standard deviation of rate of graduation. It distinctly shows that variation or even inconsistency is greater in case of retention rate as compared to that of the rate of graduation of all online institutes in US. Maximum as well as minimum values show the ra nge which is quite broader in case of retention rate as compared to that of the graduation rate. This also reflects increased inconsistency of retention rate values. As referred to the scatter diagram, the firm, direction and that of the strength has been analyzed that helps to understand the form of link amidst the given two variables. It is identified that a positive, linear, and moderate correlation exists amidst graduation as well as retention rate. As per the regression analysis, the value of the R square is approx 0.44922 and this equation is fit in a moderate way. Besides, it has also been identified that the slope of the line is considerably low. After analysis of the correlation it is identified that a positive favorable correlation exists amidst the two variables (Miller, 2014). Therefore, it may be inferred that on increasing the retention rate, the rate of graduation would also get enhanced. But the interdependence amidst the given two variables is quite low. Thus, certain other factors besides retention rate are hence responsible to influence the rate of graduation. With context to South University, it is identified that the rate of retention is around 51% and so as the graduation rate to be 25%. This reflects that the rate of retention is higher but rate of graduation is quite low. As per the outcomes of all 29 colleges of the United States, it has been found that trend is alike. Thus, no such concern is related to the performance of the South University. With respect to Phoenix, rate of retention is 4% whereas the rate of graduation is 28%. This does not favor the findings of all 29 colleges. A positive favorable link has been identified amidst both the variables. Thus, after reviewing of the results it is concluded that a significant concern exists about performance of the university. Recommendations: This part of the report provides the recommendations. It is identified that on increasing the rate of retention, the rate of graduation also gets enhanced. These online colleges must take certain measures to increase the rate of retention. Distinctly, with increase in retention rate the rate of graduation would also enhance(When Transfer Students Are Included in the Count, the College Graduation Rate Gap between Blacks and Whites Gets Worse, 2003). The regression analysis identifies a moderate fit amidst both the variables. It has also been identified that certain factors exist that impact upon the variables. Thus, further study and analysis may be conducted for identifying those factors apart from the retention rate that influence the rate of graduation. References Almeida, R. (2007). Local Economic Structure and Growth.Spatial Economic Analysis, 2(1), pp.65-90. De Vos, M. (2007). Everybody Happy in Graduate School: Empowering Graduate Students, Supporting Their Advisers, and Increasing the Graduation Rate for PhDs in the Humanities at Utrecht University.ADE, pp.24-31. Dorn, S. (n.d.). Quasicohort and Period Measures are Weak Proxies for the New Federal Graduation Rate: Florida Data, 2003-2009 Graduation Years.SSRN Journal. Dropouts in America: confronting the graduation rate crisis. (2005).Choice Reviews Online, 43(01), pp.43-0450-43-0450. FOLSOM, B., PETERSON, G., REARDON, R. and MANN, B. (2005). IMPACT OF A CAREER PLANNING COURSE ON ACADEMIC PERFORMANCE AND GRADUATION RATE.Journal of College Student Retention: Research, Theory and Practice, 6(4), pp.461-473. Heckman, J. and LaFontaine, P. (2010). The American High School Graduation Rate: Trends and Levels.Review of Economics and Statistics, 92(2), pp.244-262. Izumi, M., Shen, J. and Xia, J. (2013). Determinants of Graduation Rate of Public Alternative Schools.Education and Urban Society. Miller, N. (2014). Nontraditional Student Graduation Rate Benchmarks.The Journal of Continuing Higher Education, 62(3), pp.141-151. Surprise: When Transfer Students Are Included in the Count, the College Graduation Rate Gap between Blacks and Whites Gets Worse. (2003).The Journal of Blacks in Higher Education, (39), p.50. The Low College Graduation Rate of Black Students Is Not Due to Racial Factors. (2005).The Journal of Blacks in Higher Education, (48), p.9.