Answer
$y ̂=-3.84x+145.48$
Work Step by Step
$x ̅ =\frac{10+14+17+18+21}{5}=16$
$s_x=\sqrt {\frac{(10-16)^2+(14-16)^2+(17-16)^2+(18-16)^2+(21-16)^2}{5-1}}=4.183$
$y ̅=\frac{105+94+82+76+63}{5}=84$
$s_y=\sqrt {\frac{(105-84)^2+(94-84)^2+(82-84)^2+(76-84)^2+(63-84)^2}{5-1}}=16.202$
$r=\frac{Σ(\frac{x_i-x ̅}{s_x})(\frac{y_i-y ̅}{s_y})}{n-1}=\frac{(\frac{10-16}{4.183})(\frac{105-84}{16.202})+(\frac{14-16}{4.183})(\frac{94-84}{16.202})+(\frac{17-16}{4.183})(\frac{82-84}{16.202})+(\frac{18-16}{4.183})(\frac{76-84}{16.202})+(\frac{21-16}{4.183})(\frac{63-84}{16.202})}{5-1}=-0.992$
The least-squares regression line:
$y ̂=b_1x+b_0$
$b_1=r\frac{s_y}{s_x}=-0.992\times\frac{16.202}{4.183}=-3.84231$
$b_0=y ̅-b_1x ̅ =84-(-3.84231)\times16=145.47696$
So:
$y ̂=-3.84x+145.48$
