Given the information in the image The least-squares regression equation is: Σx-24, Σy-16 Σ-180, Σν-90 ,...

Question

Question

Given the information in the image

Σx-24, Σy-16 Σ-180, Σν-90 , Σν-15, η 10

The least-squares regression equation is:

Answer 1

Answer #1

Ʃx = 24, Ʃy = 16, Ʃxy = 75, Ʃx² = 180, Ʃy² = 90, n = 10

x̅ = Ʃx/n = 24/10 = 2.4

y̅ = Ʃy/n = 16/10 = 1.6

SSxx = Ʃx² - (Ʃx)²/n = 180 - (24)²/10 = 122.4

SSyy = Ʃy² - (Ʃy)²/n = 90 - (16)²/10 = 64.4

SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 75 - (24)(16)/10 = 36.6

Slope, b = SSxy/SSxx = 36.6/122.4 = 0.29902

y-intercept, a = y̅ -b* x̅ = 1.6 - (0.29902)*2.4 = 0.88235

Least-squares regression equation:

ŷ = 0.8824 + 0.2990 x

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Answer 2

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