Question

Please show formulas in excel 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 29 46 33 47 23 40 34 52 y 29 22 24 13 29 17 21 14 Complete parts (a) through (e), given Σx = 304, Σy = 169, Σx2 = 12,244, Σy2 = 3837, Σxy = 6045, and r ≈ −0.877. (a) Draw a scatter diagram displaying the data. Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola Point No Solution Help 510152025303540455055605101520253035 Clear Graph Delete Layer Fill WebAssign Graphing Tool Graph LayersToggle Open/Closed Point 1 Remove This Layer Point 2 Remove This Layer Point 3 Remove This Layer Point 4 Remove This Layer Point 5 Remove This Layer Point 6 Remove This Layer Point 7 Remove This Layer Point 8 Remove This Layer Point 9 Remove This Layer Point 10 Remove This Layer (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 y hat = 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 = y hat = + x (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (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 = 34 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.)

Answer 1

a)

b)

ΣX =	304.000
ΣY=	169.000
ΣX2 =	12244.000
ΣY2 =	3837.000
ΣXY =	6045.000
r =	-0.877

c)

X̅=ΣX/n =	38.00
Y̅=ΣY/n =	21.13
ŷ =	41.827+-0.545x

e)

coefficient of determination r2 =				0.770
explained =				77.0%
unexplained=				23.0%

f)

predicted value =41.827+-0.545*34=

23.30