Answer
$y ̂=-0.72x+116.6$
Work Step by Step
$x ̅ =\frac{20+30+40+50+60}{5}=40$
$s_x=\sqrt {\frac{(20-40)^2+(30-40)^2+(40-40)^2+(50-40)^2+(60-40)^2}{5-1}}=15.811$
$y ̅=\frac{100+95+91+83+70}{5}=87.8$
$s_y=\sqrt {\frac{(100-87.8)^2+(95-87.8)^2+(91-87.8)^2+(83-87.8)^2+(70-87.8)^2}{5-1}}=11.735$
$r=\frac{Σ(\frac{x_i-x ̅}{s_x})(\frac{y_i-y ̅}{s_y})}{n-1}=\frac{(\frac{20-40}{15.811})(\frac{100-87.8}{11.735})+(\frac{30-40}{15.811})(\frac{95-87.8}{11.735})+(\frac{40-40}{15.811})(\frac{91-87.8}{11.735})+(\frac{50-40}{15.811})(\frac{83-87.8}{11.735})+(\frac{60-40}{15.811})(\frac{70-87.8}{11.735})}{5-1}=-0.970$
The least-squares regression line:
$y ̂=b_1x+b_0$
$b_1=r\frac{s_y}{s_x}=-0.970\times\frac{11.735}{15.811}=-0.720$
$b_0=y ̅-b_1x ̅ =87.8-(-0.720)\times40=116.6$
So:
$y ̂=-0.72x+116.6$
