1. (5) Given a data set below. X 2 3 5 6 6 Y 10 9 7 4 2 a. Draw a scatter diagram of the data. b. Find the linear correlation coefficient (you may use the calculator function). c. Determine whether there is a linear relation between x and y (Compare r with the critical value to make a decision). 2. (5) The following data represent the price of a random sample of used Chevy Camaros, by age. Age, x (year) 2 5 2 5 4 1 6 1 3 Price, y, (dollars) 15,900 10,988 16,980 9,995 11,995 20,365 10,824 18,650 11,488 a. Draw a scatter diagram treating the age of the car as the explanatory variable and price as the response variable. b. Find the correlation coefficient between age and price. Based on the correlation coefficient, is there a linear relation between age and price.

1. An engineer wants to determine how the weight of a car, x, affects gas mileage, y. The following data represent the weights of various domestic cars and their miles per gallon in the city for the 2015 model year. Car/ Weight (lb)/ Miles per Gallon Buick LaCrosse/ 4724/ 17 Cadillac XTS/ 4006/ 18 Chevrolet/ 3097/ 22 Chevrolet Impala/ 3555/ 19 Chrysler 300/ 4029/ 19 Dodge Charger/ 3934/ 19 Dodge Dart/ 3242/ 24 Ford Focus/ 2960/ 26 Ford Mustang/ 3530/ 19 Lincoln MKZ/ 3823/ 18 (a) Find the correlation coefficient, and determine whether there is a linear relation between the weight and miles per gallon. (b) Find the least-squares regression equation treating weight as the explanatory variable and miles per gallon as the response variable. (c) Interpret the slope and y-intercept, if appropriate. (d) A Cadillac CTS weighs 3649 pounds and gets 20 miles per gallon. Is the miles per gallon of a CTS above average or below average for cars of this weight? (e) Would it be reasonable to use the least-squares regression line to predict the miles per gallon of a Toyota Prius, a hybrid gas and electric car? Why or why not?