Descriptive Analysis and Scatter Diagram of RR and GR

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? Answers: Purpose The purpose behind this study to analyze the data and find the correlation among the retention rate (%) and the graduation rate (%) for 29 online colleges in the United States. This correlation can be seen via use of methodologies like regression analysis and the scatter diagram formation. In this task we have used descriptive analysis along with these methodologies so as to find out the performance of web-based universities / colleges. Background The Online Education System is at its central part what provoked technical developments in e-books, knowledge Management and knowledge Record administration (Dweck, 1990). These arrangements facilitate students to utilize the substance from everywhere with access to the internet. Online system of teaching is a alike way used by the institutes and colleges, which assists in understanding and attaining understanding exclusive of presence in the classes. This education system needs no physical classes attendance and so saves time. These way students can use their time and study as per their convenience. The aim of online education system is to make the students self-sufficient with the web-based journals and articles. This kind of education approach was initiated by U.S with the emergence of internet and has been adopted all over the World (Phipps and Merisotis, 1999, April). Graduation rate It is defined as the grouping of the institutes where initially, 1st year student who productively were able to complete their courses in 150 % of the whole agreed time granted for the selected course. Retention rate It is termed as the category of the institutions where 1st time, 1st year undergraduate students who are interested in proceedind with their studies at the university for the coming session. Method Variables As discussed above, we have considered 2 variables for the study, namely- retention rate (RR) graduation rate (GR). These variables have been used for 29 universities in US for the online courses. These variables are based on the survey to find out the value and contribution of a particular college/ institute. Statistical Analysis:- We can find out the mean (average), standard deviation for the two variables (RR and GR). This would enhance the value of the analysis we have performed. The scatter diagram has been utilized to reflect the correlation among the 2 variables, and also the estimated value of regression equation has been applied. The P value is on 0.05% level of significance to settle on the correlation among Retention rate (RR) with Graduation Rate (GR). The variables relationship can be depicted by use of excel sheets as well. Results a). Descriptive Analysis We have the data for 29 universities offering online courses. This data is w.r.t Retention rate and the Graduation rate. In the first step, we have assessed the mean and Standard Deviation for the data given. Table (i) Variables Mean (Average) Standard Deviation Minimum Maximum Retention Rate 57.41% 23.24% 4% 100% Graduation Rate 41.76% 9.87% 25% 61% Retention rate (RR) In the table (i) above, Mean has been 57.41 for Retention rate (RR) which means that approx 57% students have been part of the online education system .e. are enrolled and are students in the given 29 online universities in USA. The standard deviation for Retention rate is 23.84 % with the highest level of RR as 100% and the lowest of RR as 4% that means there has been a broad range of data distribution. Graduation Rate (GR) The mean has been 41.76 for the Graduation Rate (GR), which reflects that approximately 42% of the students were able to finish the graduation within the 150% of the allotted time. The standard deviation for Graduation rate (GR) is approx 10 % with the highest level of GR as 61% and the lowest of GR as 25% that means there has been an intermediate range of data distribution. b). Scatter Diagram of Retention Rate and Graduation Rate: In the Diagram (a) below i.e. Scatter diagram for RR and GR, there is a robust positive correlation among these 2 variables. There has been an increase in the two variables simultaneously, reflecting a positive relation among them. It means Retention Rate has a positive impact on the Growth Rate. Diagram (a)- Scatter Diagram for RR and GR Source: Own study (c) Simple linear regression equation is utilised to articulate the value of Y on specified value of X. consistent with diagram (a), we attain the equation in scatter chart that makes clear that the slope coefficient is depicted prior to intercept. With the intention of settling on the value of (Y) on (X), the equation specified underneath can be utilized: ÃÅ'‚Yi = bo + b1Xi Where, Yi= Predicted GR b0= Intercept b1Xi=Slope Coefficient Here, with the above equation the Y value is capable of being determined by the specific value of X. For instance if the X value is 85 % in that case the expected Graduation Rate(GR) will be: Y = 25.423 + 0.2845 X = 25.423 + 0.2845 (85) = 25.423 + 24.18 = ~49.6% The forecasted Y value demonstrates that in case the Retention rate (RR) will be 85 % in that case the Graduation Rate(GR) will be approximately 50%. That depicts, if 85 % undergraduates study with the graduation grade only 50 % students will attain/finish the degree in the duration of the course i.e. 3-4 years or within 150% of the duration i.e. 5-6 years. (d) Estimation of regression equation and interpretation of slope coefficient Table (ii) Regression Statistics Multiple R 0.67 R Square 0.45 Adjusted R Square 0.43 Standard Error 7.46 Observations 29 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 25.42 3.75 6.79 0.00 17.74 33.11 RR(%) 28% 6% 4.69 0% 16% 41% Regression equation is Y = o + 1 x + r Intercept coefficient In the table (ii) above, there has been a steady transform of 25.42 in the GR which is not as a consequence of RR. Slope coefficient It intricate the type of transform that is to Y due to the changes in values of X. As observed in table (ii) the rate of slope coefficient is 28%. This implies that an average of 28 % of undergraduates finishing the graduation can be assured by the 1 unit augment in the percentage of students getting enrolled. Residual or r It is the variation among recorded value and estimated value of dependent variables. Herein, the observation of standard residual depicts that the score is +3 further lesser than -3 is well thought-out to be outliners although there have been no outliners. (e) The association between GR RR The value of intercept and Retention Rate in regression scrutiny is 0. therefore we can conclude one thing concerning RR-that there is a well-built association among (Retention Rate and Growth Rate. then again augment in students getting enrolled will augment in the number of students turning to graduates as well. (f) Is that Regression Equation provides a good fit? For regression model a good fit is achieved by the value of R2. In the diagram above, for the scatter diagram, Regression analysis depicts the value of R2 as 45% i.e. the variance or difference in regression for Graduation Rate for the 29 online universities. This equation is a good fit, since 45% can be considered as a high value. (g) Performance of South University compared to other online universities and Presidents Concern The Retention Rate for the South University stated is 51%, which means its approximately 6.5% less than the Mean Retention Rate (57.41%) for the 29 web based universities. on the other hand the Graduation Rate of the South universities is barely 25%, this demonstrates that the number of undergraduates finishing their graduation as of south university is negligible. The Retention Rate of south universities is 51% . Consequently this immense variation in the Retention Rate and Graduation Rate of the South universities generates a pitiable representation of the south universities regarding repute and excellence. The assessed Graduation Rate is 40 %, which is extremely small in comparison to other universities. on the other hand, with the intention of developing the Graduation Rate repute of the university admission eligibility standards excellence of schooling have to be paid attention to. (h) Performance of University of Phoenix compared to other online universities and President Concern The University of Pheonix has a extremely small Retention Rate i.e 4 % and smallest Graduation Rate which is 28 %. mutually these values are below standard w.r.t other universities. As I am the President, so the enrolment percentage is a cause of worry for me, since its also the bare minimum. In order to make these 2 variables better I need to consider some well planned strategy as well as improve on the policies for admission of students. The quality of education can be enhanced by employing a good, experienced and knowledgeable faculty. In case there is a need for revision of the content of the courses, it should also be done. The better the marketing strategies, higher will be the number of enrolments, and better the quality of education, higher will be the graduation rate. Discussions The Mean Graduation Rate=42% and Mean Retention Rate= 57%. As the data is broad, so the Retention Rates standard deviation is quite elevated. Graduation Rates deviation is merely 10%. There have been dropouts, leading to lower GR and RR. There have been cases wherein students leave the online courses and join regular institutes, or leave the courses in between. However, The analysis for regression has been depicting intercept at 25% depicting that the movement in Graduation Rate is not standard retention or at the time the retention is null. These variations are owing to diverse causes for instance low cost, first-class students etc. Recommendation: Online System of education gives the freedom to the understudies, yet occasionally understudies exploit the freedom therefore there ought to be a fitting check on the understudies by their professors (Roblyer and Edwards, 2000). All the online colleges ought to keep up their standard regarding training material a framework, superior instruction to the understudies. It has been observed that great and prepared staffs ought to dependably be able to guide students and make them comprehend the real issue, so that inevitably they can discover the arrangement all alone and turn into self-sufficient ones. The charges composition ought to be kept exceptionally moderate and available for all the levels of understudies present in the general public. Students ought to be permitted to view and listen in all the live addresses at some occasions (Newby et al. 2000). The marketing technique also needs to be god, so as to increase the number of enrolments to the university. And the fees structure should be kept very affordable and accessible for all the levels of students present in the society. References Dweck, C. S. (1990). Self-theories and goals: Their role in motivation, personality, and development. Paper presented at the Nebraska Symposium on Motivation, Lincoln Newby, T. J., Stepich, D. A., Lehman, J. D., Russell, J. D. (2000). Instruction technology for teaching and learning. Upper Saddle River, NJ: Merrill. Phipps, R., Merisotis, J. P. (1999, April). Whats the Difference? A review of contemporary research on the effectiveness of distance learning in higher education. Washington, DC: The Institute for Higher Education Policy. Roblyer, M. D., Edwards, J. (2000). Integrating educational technology into teaching (2nd ed.). Upper Saddle River, NJ: Merrill.