The U.S. News & World Report website provides rankings of the best colleges and universities in the United States. The free version of Best Colleges gives information such as number of students enrolled, tuition rates, and so forth. Among the data provided are the percentage acceptance rate (at the time of this writing the data is for the fall semester of 2008) and the average freshman retention rate (at the time of this writing, the average percentage of freshman entering starting in 2005 through 2008 who returned to school the following fall is given).
One might wonder if there is a statistically significant relationship between average freshman percentage retention rate and the percentage acceptance rate at colleges and universities in the United States. To investigate this possible relationship, go to the U.S. News & World Report website (www.usnews.com). Then make selections as follows: Education; Best Colleges; National Universities; View National Universities Rankings. From the rankings, compile a list of the ranked universities and their most recent acceptance rates. Following the list of ranked universities is a list of unranked schools. Omit these unranked schools from your analysis. Next, return to the National Universities page and select Freshman Retention Rate from the National Universities Quick Comparison list. Compile a list of average retention rates for the schools in your list of ranked universities. Finally, enter the ranked universities and their corresponding acceptance rates and average freshman retention rates into a spreadsheet.
Using Excel or MINITAB, construct a scatter plot of average freshman retention rate versus acceptance rate. Describe any apparent relationship between these variables. Develop a simple linear regression model expressing average freshman retention rate as a linear function of acceptance rate. Then use Excel or MINITAB to fit the model. Using the computer output, identify the key summary measures-r2, the standard error, and the F-statistic from the ANOVA table. Identify and interpret the estimated regression coefficients. Suppose that a university has an acceptance rate of 90 percent. Use your regression model to predict the average freshman retention rate for this school. Prepare a brief report summarizing your analysis and conclusions.