Question

x 1 4 9 16 26 36 y 39 46 76 100 150 200 Complete parts,...

x 1 4 9 16 26 36
y 39 46 76 100 150 200

Complete parts, given Σx = 92, Σy = 611, Σx2 = 2326, Σy2 = 81,913, Σxy = 13,607, and r ≈ 0.998.

a) 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 =

b) 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

c) 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     = %


d) The calves you want to buy are 19 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)
=_____ kg

Homework Answers

Answer #1

a)

ΣX = 92.000
ΣY= 611.000
ΣX2 = 2326.000
ΣY2 = 81913.000
ΣXY = 13607.000
r = 0.998

b)

X̅=ΣX/n = 15.33
Y̅=ΣY/n = 101.83
ŷ = 30.834+4.63x

c)

coefficient of determination r2 = 0.997
explained = 99.7%
unexplained= 0.3%

d)

predicted value =30.834+4.63*19= 118.80
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