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

Question

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

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Answer 1 · 2017-11-10T09:58:45

$y=-0.552+2.097x$

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

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

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

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

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

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

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

$y=-0.552+2.097x$