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The number of murders and robberies per 100,000 population for a random selection of states are...

The number of murders and robberies per 100,000 population for a random selection of states are shown. Let the x variable be murders and the y variable be robberies. Given that r = 0.8042, Sx = 1.789, Sy = 56.337. Murders 2.4 2.7 5.6 2.6 2.1 3.3 6.6 5.7 Robberies 25.3 14.3 151.6 91.1 80 49 173 95.8 a) Find the equation for the regression line. b) Find the predicted value for the number of robberies when x = 4.

math   Statistics-And-Probability   
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Answer #1

ΣX = 31
ΣY = 680.1
ΣX * Y = 3202.71
ΣX2 = 142.52
ΣY2 = 80033.99

Equation of regression line is Ŷ = a + bX
b = (nΣΧΥ – ΣΧΣΥ)/(ηΣΧ? - (ΣΧ)2)
b = ( 8 * 3202.71 - 31 * 680.1 ) / ( 8 * 142.52 - ( 31 )^{2})
b = 25.333
a =( Σ Y - ( b * Σ X) ) / n
a =( 680.1 - ( 25.3326 * 31 ) ) / 8
a = -13.151
Equation of regression line becomes Ŷ = -13.151 + 25.333 X

When X = 4
Ŷ = -13.151 + 25.333 X
Ŷ = -13.151 + ( 25.333 * 4 )
Ŷ = 88.18

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