Do heavier cars really use more gasoline? Suppose a car ischosen at random. Let x be the weight of the car (in hundreds ofpounds), and let y be the miles per gallon (mpg).
x 27 42 31 47 23 40 34 52
y 33 21 24 13 29 17 21 14
Complete parts (a) through (e), given ?x = 296, ?y = 172, ?x2 =11,652, ?y2 = 4042, ?xy = 5917, and r ? ?0.911. (a) Draw a scatterdiagram displaying the data.
(b) Verify the given sums ?x, ?y, ?x2, ?y2, ?xy, and the valueof the sample correlation coefficient r. (Round your value for r tothree decimal places.)
?x =2 ?y =3 ?x2 =4 ?y2 =5 ?xy =6 r =7
(c) Find x, and y. Then find the equation of the least-squaresline = a + bx. (Round your answers for x and y to two decimalplaces. Round your answers for a and b to three decimal places.) x= ___ y = ___ = y____ + ____x
(d) Graph the least-squares line. Be sure to plot the point (x,y) as a point on the line.
(e) Find the value of the coefficient of determination r2. Whatpercentage of the variation in y can be explained by thecorresponding variation in x and the least-squares line? Whatpercentage is unexplained? (Round your answer for r2 to threedecimal places. Round your answers for the percentages to onedecimal place.)
r2 = _______ explained _____ % unexplained ______ %
(f) Suppose a car weighs x = 39 (hundred pounds). What does theleast-squares line forecast for y = miles per gallon? (Round youranswer to two decimal places.) ________mpg
