Question: Drug designed to reduce smoking. A pharmaceutical company has developed a new drug designed to reduce a smoker's reliance on tobacco. Since certain dosages of the drug may reduce one's pulse rate to dangerously low levels, the product-testing division of the pharmaceutical company wants to model the relationship between decrease in pulse rate, y (beats/minute), and dosage, x (cubic centimeters). Different dosages of the drug were administered to eight randomly selected patients, and 30 minutes later the decrease in each patient's pulse rate was recorded. The results are given in the accompanying table. Initially, the company considered the model y = β1x + ε since, in theory, a patient who receives a dosage of x = 0 should show no decrease in pulse rate (y = 0).
(a) Fit a straight-line model that passes through the origin.
(b) Is there evidence of a linear relationship between drug dosage and decrease in pulse rate? Test at α = .10.
(c) Find a 99% prediction interval for the decrease in pulse rate corresponding to a dosage of 3.5 cubic centimeters.