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).

x	25	46	33	47	23	40	34	52
y	33	22	23	13	29	17	21	14

Complete parts (a) through (e), given Σx = 300, Σy = 172, Σx² = 12,028, Σy² = 4038, Σxy = 5996, and

r ≈ −0.883.

(a) Draw a scatter diagram displaying the data.

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(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 =	2
Σy =	3
Σx2 =	4
Σy2 =	5
Σxy =	6
r =	7

(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	= 8
y	= 9
	= 10	+ 11 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 =	13
explained	14 %
unexplained	15 %

(f) Suppose a car weighs x = 41 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.)
16 mpg

Answer 1

x = 25,   46   ,33   ,47   ,23   ,40,   34,   52

y = 33,   22,   23,   13   ,29,   17,   21,   14

(a)

Scatter diagram is,

b)

Verified the values as below,

Σx = 300

Σy = 172

Σx2 = 12028

Σy2 = 4038

Σxy = 5996

r = -0.883

c)

= 37.5

= 21.5

b = SSxy / SSxx = -454 / 778 = -0.5835476 -0.584

a = = 21.5 - (-0.5835476) * 37.5 =  43.383

y = 43.383 + -0.584 x

(d)

(e)

coefficient of determination r2. =

= 0.779

percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line

= 77.9 %

Percentage is unexplained = 100 - 77.9 = 22.1 %

(f)

For x = 41,

y = 43.383 - 0.584 * 41 =  19.44 mpg