Question

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).

x2544344723403452

y3017271329172114

Complete parts (a) through (e), given Σx = 299, Σy = 168, Σx2 = 11,915, Σy2 = 3854, Σxy = 5816, and

r ≈ −0.943.

(a) Draw a scatter diagram displaying the data.

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Submission Data

(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

Σx =

Σy =

Σx2 =

Σy2 =

Σxy =

r =

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

x=

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. 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 r2 to three decimal places. Round your answers for the percentages to one decimal place.)

r2 =

explained     %

unexplained     %

(f) Suppose a car weighs x = 39 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.)
mpg

Answer 1

(a) Draw a scatter diagram displaying the data.

(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

Σx = 299

Σy = 168

Σx2 = 11,915

Σy2 = 3854

Σxy = 5816

r = −0.943

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

x=37.375

y=21

= 44.389 - 0.626*x

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) r² = 0.889

explained 88.9 %

unexplained 11.1 %

(f) 19.98