LINEAR REGRESSION REPORT
Background One of the biggest challenges in the higher education sector has been the recent growth of online universities. The Online Education Database is an independent organisation whose mission is to build a comprehensive list of accredited online colleges. The Excel spreadsheet (OnlineEdu.xlsx) contains data on the retention rate (%) and the graduation rate (%) for 29 online colleges in the United States.
instructions Conduct a simple linear regression analysis to examine the association between the 'retention rate' (the independent variable) and the 'graduation rate (the dependent variable). Using the Excel data file, prepare a 1200 word repot using the following structure. Purpose (2 marks) In this section. the purpose ofthe report need to be clearly and concisely stated.
Background (4 marks) In this section, write an overview of the association between retention and graduation. Why would economists be interested in this particular issue?
Method (4 marks) In this section, provide a brief overview of the data and empirical approach used to examine the association betiveen retention and graduation.
Results (20 marks)
a) Provide a descriptive analysis of the two variables (e.g., mean standard deviation, minimum and maximum). (2 marks). LI) Develop a scatter diagram with retention rate as the independent variable. What does the scatter diagram indicate about the relationship between the two variables? (3 marks). c) Estimate a regression equation that can be used to predict the graduation rate (%) given the retention rate (%) (2 marks). d) State the estimated regression equation and interpret the meaning of the slope coefficient (2 marks). e) Is there a statistically significant association between graduation rate (%) and retention rate (%). Explain (2 marks). JO Did the regression equation provide a good fit? Explain (3 marks). g) Suppose you were the president ofSouth University. 'Vier revieiving the results, would you have any concerns about the pelf ormance olyour university compared to other online universities? (3 marks). 10 Suppose you li'ere the president of the University of Phoenix. 4/let reviewing the results, would you have any concenis about the performance ()f sour university cotnpared to other online universities? (3 marks)
Discussion (5 marks) In this section, provide a brief overview of the key results. What are the key strengths and limitations oft/us analysis? (e.g., data, method, etc.). How do the results from this analysis compare with other studies? (e.g., are the findings consistent?), Do these findings have clear policy implications? Recommendations (5 marks) In this section, you should present three well-considered recommendations.
LINEAR REGRESSION REPORT
The Purpose of this report is to find relationship between the retention rates achieved by various rates and the graduation rates achieved by the same set of universities and predict the estimated values for a particular university and see if their performance is satisfactory.
Students persisting in an university till completing their graduation over a 3-year period is seen as an vindication of the policies of the university and their ability to provide quality education online. Together both the retention rates and graduation rates can be seen as successful for an university. However retention % is a direct result of the universities policies and graduation % is highly dependent upon retentions. Its thus natural to think that graduation rate % would increase if the universities take appropriate actions to increase retention in later years.
Primary the data collected would be put into use for estimating the correlation between the two variables like the RR% and GR%. The same would be used to estimate the regression equation and with the help of the same the expected GR% can be estimated with reasonable accuracy. A Scatter plot diagram would also be produced to see the visible trend in the GR% (Kothari, 2013).
|Standard Error||4.315603||Standard Error||1.832019|
|Standard Deviation||23.24023||Standard Deviation||9.865724|
|Sample Variance||540.1084||Sample Variance||97.33251|
The Average RR% is found to be 57.41% and the degree of variance is too high as can be seen in the sample variance. The average GR% I s found to be 41% which is much lower than the RR% and the GR% also ahs a fairly high degree of variance as well.
The scatter Diagram for the two chosen variables are presented as follows:
The regression output is presented as follows:
|Adjusted R Square||0.428829|
|Coefficients||Standard Error||t Stat||P-value||Lower 95%||Upper 95%||Lower 95.0%||Upper 95.0%|
|X Variable 1||0.284526||0.060631||4.692772||6.95E-05||0.1601221||0.40893||0.160122||0.40893|
Regression equation between the two variables are presented nd estimated as follows:
Regression Equation: Y = a+ bX
a = Y intercept
b = Slope of the Regression line
X = Retention Rate %
Y = Graduation rate %.
In the above regression output the Y intercept (a) is 25.4229 which means the value of Y would be 25.4229 even when the value of X is kept at zero. Thus, even if no retention is made by the universities concerned the graduation rate % would be approximately 25.43%.
The value of the B or the slope of the line is .2845 and which means with each % of retention by the universities the graduation rate % would be expected to increase by .2845 as shown by the slope of the line.
Regression Equation: Y = a+ bX = 25.4229 + .2845 X.
So, if in a given year the RR% is found to be 70%, the graduation rate is expected to be 48.18125%.
Y = a+ bX = 25.4229 + .2845 X. = 25.4229 + .2845*(80) = 25.4229 + 22.76 = 48.1825%.
Yes. There is a fair degree of statistical significance between the variables concerned. The Multiple R of the two variables are found to be .6702. Which means if the retention rate changes positively then the graduation rate would move forward as well. The correlation is not very strong but there a fairly moderate to high degree of correlation between the two.
The R-squared which has been obtained indicates to us how well the regression line obtained fits the given set of data. It is able to indicate the proportion of the probable variance in the Graduation rate (GR%) explained by the Retention Rate % which is the independent variable.
The correlation coefficient between the dependent variables and other independent variables are .67 and the when the same is squared the value (R Square) is coming to be .4492 or in other words 44.92% of all the variations are automatically explained by the regressors or independent variables which are 2 in number. As the value of the R-squared is fairly high the same presents a case of goof fit and approximately half of the variables are explained by the R-Squared (Cortinhas, 2013).
g) South University concerns from the results
the South University has a RR% of 51 and GR % of 25.
If we apply the regression equation obtained above to the data collected form the university then the GR % is estimated as follows:
Y = a+ bX = 25.4229 + .2845 X. = 25.4229 + .2845*(51) = 25.4229 + 14.51 = 39.94%.
As can be seen as per the given data set the graduation % of the south university was expected to be 40% approx. but the actual % of graduation of the university is quite lower at 25%. This means the graduation rate % is much lower and the president of the university has reasons to feel disappointed and concerned and he must take steps to increase the quality of the study etc. and eventually increase the GR% (Fernandes, 2014).
h) University of Phoenix concerns form the results
If we apply the regression equation obtained above to the data collected from the university then the GR % is estimated as follows:
Y = a+ bX = 25.4229 + .2845 X. = 25.4229 + .2845*(4) = 25.4229 + 1.136 = 26.57%.
As can be seen as per the given data set the graduation % of the university of phoenix was expected to be 26.56% approx. but the actual % of graduation of the university is quite lower at 28%. This means the graduation rate % is much higher than expectation and hence the president of the university has no reasons to feel disappointed.
The Regression model fits well to the data set and it can be observed that the graduation rate is generally showing a tendency of increase. Thus, it can be said that the universities concerned can be increase graduation rates if they try to retain students by rationalizing the fee structure and providing better quality tuition etc. Each f the universities listed can use the regression equation to find if the GR% is below or above the expectation and then take steps to increase the same in the future years (Cortinhas, 2013).