PayScale is a company that reports statistics on colleges and universities. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 11_3_24 using the file format of your choice for the version of the text you are using. The data contain the four-year cost and graduation rate for over 1300 colleges and universities. Do schools that charge more have higher graduation rates? The variable "2013 Cost" represents the four-year cost of attending the college or university. The variable "Grad Rate" represents the percentage of incoming freshman who graduate within six years.
(a) Draw a scatter diagram treating "2013 Cost" as the explanatory variable and "Grad Rate" as the response variable.
(b) Determine the correlation coefficient between "2013 Cost" and "Grad Rate."
(c) Is there a linear relation between "2013 Cost" and "Grad Rate"?
(d) Find the least-squares regression line.
(e) Is the graduation rate of Harvey Mudd College higher than would be expected among all schools that charge $229,500? Explain.
(f) What proportion of the variability in graduation rates is explain by the 2013 cost of attending?