Go to www.pearsonhighered.com/ sullivanstats to obtain the data file 12_3_17. The variable “Cost” represents the four-year 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) In Problem 49 from Section 4.1, a scatter diagram between “Cost” and “Grad Rate” treating “Cost” as the explanatory variable suggested a positive association between the two variables. Treating “Cost” as the explanatory variable, x, tests whether a negative association exists between the cost and annual ROI for graduates of four-year schools at the a = 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 cost is $180,000?