Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). 25 46 33 47 23 40 34 52 28 19 24 13 29 17 21 14 LA USE SALT Complete parts (a) through (e), given Ex = 300, Ey = 165, Ex?= 12,028, Ey? = 3657, Exy = 5766, and re -0.9484. (a) Draw a scatter diagram displaying the data. 50 g 25 45 25 40 y (miles per gallon) y (miles per gallon) y (miles per gallon) y (miles per gallon) 20 35 20 30 30 15 15 25 25 30 35 40 45 50 15 20 25 25 30 35 40 45 50 15 20 25 O x (weight of the car (in hundreds of pounds)) x (weight of the car (in hundreds of pounds)) x (weight of the car (in hundreds of pounds)) x (weight of the car (in hundreds of pounds)) (b) Verify the given sums Ex, Zy, Ex?, Ey?, Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex = Ey 3 2 Ey = Exy (c) Find x, and y. Then find the equation of the least-squares line y = a + bx. (Round your answers to four decimal places.) * = (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. 50 45 25 25 y (miles per gallon) y (miles per gallon) y (miles per gallon) y (miles per gallon) 3 20 N 35 30 15 15 25 25 15 20 25 25 30 35 40 45 50 25 30 35 40 45 50 15 20 25 x (weight of the car (in hundreds of pounds)) x (weight of the car (in hundreds of pounds)) AC x (weight of the car (in hundreds of pounds)) AC x (weight of the car (in hundreds of pounds)) (e) Find the value of the coefficient of determination . What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for / to four decimal places. Round your answers for the percentages to two decimal place.)45 25 y (miles per gallon) y (miles per gallon) y (miles per gallon) y (miles per gallon) 35 8 20 30 30 15 15 25 25 30 35 40 45 50 15 20 25 25 30 35 40 45 50 15 20 25 O x (weight of the car (in hundreds of pounds)) x (weight of the car (in hundreds of pounds)) x (weight of the car (in hundreds of pounds)) x (weight of the car (in hundreds of pounds)) (b) Verify the given sums Ex, Ey, Ex?, Ey?, Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex = Ey Ey = EXY = (c) Find x, and y. Then find the equation of the least-squares line y = a + bx. (Round your answers to four decimal places.) * = (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. 50 25 y (miles per gallon) y (miles per gallon) y (miles per gallon) y (miles per gallon) 20 N CO 30 15 15 25 25 15 20 25 25 30 35 40 45 50 25 30 35 40 45 50 15 20 25 x (weight of the car (in hundreds of pounds)) AC x (weight of the car (in hundreds of pounds)) AC x (weight of the car (in hundreds of pounds)) AC x (weight of the car (in hundreds of pounds)) (e) Find the value of the coefficient of determination . What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for * to four decimal places. Round your answers for the percentages to two decimal place.) P= explained unexplained Suppose a car weighs x = 35 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.) mpg Need Help? Read it Master It Submit