Answer
$y ̂=-1.8x+3.6$
Work Step by Step
$x ̅ =\frac{-2+(-1)+0+1+2}{5}=0$
$s_x=\sqrt {\frac{(-2-0)^2+(-1-0)^2+(0-0)^2+(1-0)^2+(2-0)^2}{5-1}}=1.581$
$y ̅=\frac{7+6+3+2+0}{5}=3.6$
$s_y=\sqrt {\frac{(7-3.6)^2+(6-3.6)^2+(3-3.6)^2+(2-3.6)^2+(0-3.6)^2}{5-1}}=2.881$
$r=\frac{Σ(\frac{x_i-x ̅}{s_x})(\frac{y_i-y ̅}{s_y})}{n-1}=\frac{(\frac{-2-0}{1.581})(\frac{7-3.6}{2.881})+(\frac{-1-0}{1.581})(\frac{6-3.6}{2.881})+(\frac{0-0}{1.581})(\frac{3-3.6}{2.881})+(\frac{1-0}{1.581})(\frac{2-3.6}{2.881})+(\frac{2-0}{1.581})(\frac{0-3.6}{2.881})+}{5-1}=-0.988$
The least-squares regression line:
$y ̂=b_1x+b_0$
$b_1=r\frac{s_y}{s_x}=-0.988\times\frac{2.881}{1.581}=-1.800$
$b_0=y ̅-b_1x ̅ =3.6-1.800\times0=3.6$
So:
$y ̂=-1.8x+3.6$
