Problem 7 [20 points = 10 + 5 - 5] Used car sales managers intend to project a trade-in value of a car Y measured in $ using the recorded mileage X in miles. They believe that the linear model may be used. The data set (based on a large number of cars already sold) has shown the following summaries: Means: X - 32,500 miles and Y = $6, 200. Sample-based standard deviations were found as follows: S(X) = 400 miles and S(Y) = $2, 500 The correlation based on collected data was R(X,Y) - -0.64 Answer questions below and show detailed explanations, please! 1. Derive the fitted line equation, Y = bo + b1 . X and identify slope and intercept in this model. 2. One car has X = 30, 000 miles and its owner got the trade-in price of Y = $17, 000. How is the observation, (X - 30,000, Y - 17,000) located relative to the fitted line, above or below? 3. Another car deal operate with the mileage X - 28, 500 miles and the price offered by car dealership was Y = $21, 800. How would this observation, (X -28,500, Y - 21,800) be located relative to the fitted line, above or below? Solution