x | 1 | 4 | 9 | 16 | 26 | 36 |
y | 39 | 46 | 76 | 100 | 150 | 200 |
Complete parts, given Σx = 92, Σy = 611, Σx^{2} = 2326, Σy^{2} = 81,913, Σxy = 13,607, and r ≈ 0.998.
a) Verify the given sums Σx, Σy, Σx^{2}, Σy^{2}, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)
Σx = | |
Σy = | |
Σx^{2} = | |
Σy^{2} = | |
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 r^{2}. 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 r^{2} to three decimal places. Round your answers for the percentages to one decimal place.)
r^{2} = | |
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
a)
ΣX = | 92.000 |
ΣY= | 611.000 |
ΣX^{2} = | 2326.000 |
ΣY^{2} = | 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 r^{2} = | 0.997 | |||
explained = | 99.7% | |||
unexplained= | 0.3% |
d)
predicted value =30.834+4.63*19= | 118.80 |
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