Invest in Education Go to the book's website to obtain the data file 14_1_17. The variable "2013 Cost" represents the fouryear cost including tuition, supplies, room and board, the variable "Annual ROI" represents the return on investment for graduates of the school-essentially how much you would earn on the investment of attending the school - the variable "Grad Rate" represents the graduation rate of the school.

(a) We saw that a scatter diagram between "2013 Cost" and "Grad Rate" treating "2013 Cost" as the explanatory variable suggested a positive association between the two variables. Treating "2013 Cost" as the explanatory variable, \(x\), test whether a negative association exists between the 2013 cost and annual ROI for graduates of four-year schools at the \(\alpha=0.01\) level of significance. Normal probability plots suggest the residuals are normally distributed.

(b) Construct a \(90 \%\) confidence interval for the slope of the true least-squares regression line.

(c) What is the mean annual ROI for a four-year school whose 2013 cost is \(\$ 180,000\) ?