Given the following: rv X = Amount of caffeine consumed daily, in mg rv Y = Number of hours of sleep each night Y - 7.83 - 0.007(X), for X between 29mg and 447mg a) Interpret the numeric value of the slope in context. b) Why does it not make sense on this problem to interpret the Y-intercept? c) Estimate the number of hours of sleep for a person that consumes 300mg of caffeine each day. d) Suppose that your Statistics instructor actually gets about 5.75 hours of sleep each night, after consuming 423mg of caffeine. What is the residual associated with this data point?e) Why should the regression equation NOT be used to predict the amount of sleep for a person that consumes 600mg of caffeine each day