The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. We've recorded bivariate data for a sample of 19 Cadets, each bought new two years ago and each sold used within the past month. For each Cadet in the sample, we've kept track of the mileage x (in thousands of miles) that the Cadet had on its odometer at the time it was sold used and the price y (in thousands of dollars) at which the Cadet was sold used. The least-squares regression equation computed from our data is y =36.52-0.55x. We have in our possession a two-year-old Cadet that has 29.1 thousand miles on it, and we are interested in selling it. We have used the regression equation to predict its selling price, but we also are interested in both a prediction interval for its selling price and a confidence interval for the mean selling price of Cadets with this same mileage. We have already computed the following for our data. . mean square error (MSE) ~ 6.35 (29.1-X) 19 = 0.0836, where X1, X2, ", X19 denote the sample mileages, and x denotes their mean Based on this information, and assuming that the regression assumptions hold, answer the questions below. (If necessary, consult a list of formulas.) (a) What is the 95% prediction interval for an individual value for used selling price (in thousands of dollars) when the mileage is 29.1 thousand miles? (Carry your intermediate computations to at least four decimal places, and round your X ? answer to at least one decimal place.) Lower limit: Upper limit: (b) Consider (but do not actually compute) the 95% confidence interval for the mean used selling price when the mileage is X 15 29.1 thousand miles. How would this confidence interval compare to the prediction interval computed above (assuming ? that both intervals are computed from the same sample data)? O The confidence interval would have the same center as, but would be wider than, the prediction interval. The confidence interval would be positioned to the right of the prediction interval. The confidence interval would be positioned to the left of the prediction interval. The confidence interval would have the same center as, but would be narrower than, the prediction interval. The confidence interval would be identical to the prediction interval. (c) For the mileage values in this sample, 35.4 thousand miles is more extreme than 29.1 thousand miles is, that is, 35.4 is X 5 ? farther from the sample mean mileage than 29.1 is. How would the 95% prediction interval for the mean used selling price when the mileage is 29.1 thousand miles compare to the 95% prediction interval for the mean used selling price when the mileage is 35.4 thousand miles? The intervals would be identical. The interval computed from a mileage of 29.1 thousand miles would be wider but have the same center. The interval computed from a mileage of 29.1 thousand miles would be narrower but have the same center. Pic stitch mileage of 29.1 thousand miles would be wider and have a different center
