How do you find the equation of the regression line for the given data?

[(x:, -5, -3, 4, 1, -1, -2, 0, 2, 3, -4), (y:, -10, -8, 9, 1, -2, -6, -1, 3, 6, -8)]

1 Answer
Nov 10, 2017

y=-0.552+2.097x

Explanation:

The equation for the regression line is y=a+bx, {[a=\bary-b\barx],[b=(S_(x y))/(S_(x x))]}

\bary=(\Sigmay)/n=-16/10=-1.6

\barx=(\Sigmax)/n=-5/10=-0.5

S_(x x)=\Sigmax^2-((\Sigmax)^2)/n=85-((-5)^2)/10=82.5

S_(x y)=\Sigmaxy-((\Sigmax)(\Sigmay))/n=181-80/10=173

b=(S_(x y))/(S_(x x))=173/82.5=2.097 ("to 2d.p")

a=\bary-b\barx=-1.6-2.097(-0.5)=-0.552 ("to 2d.p"}

y=-0.552+2.097x