Answer
$y ̂=2.023x-2.324$
Work Step by Step
$x ̅ =\frac{3+4+5+7+8}{5}=5.4$
$s_x=\frac{(3-5.4)^2+(4-5.4)^2+(5-5.4)^2+(7-5.4)^2+(8-5.4)^2}{5-1}=2.073$
$y ̅=\frac{4+6+7+12+14}{5}=8.6$
$s_y=\frac{(4-8.6)^2+(6-8.6)^2+(7-8.6)^2+(12-8.6)^2+(14-8.6)^2}{5-1}=4.219$
$r=\frac{Σ(\frac{x_i-x ̅}{s_x})(\frac{y_i-y ̅}{s_y})}{n-1}=\frac{(\frac{3-5.4}{2.073})(\frac{4-8.6}{4.219})+(\frac{4-5.4}{2.073})(\frac{6-8.6}{4.219})+(\frac{5-5.4}{2.073})(\frac{7-8.6}{4.219})+(\frac{7-5.4}{2.073})(\frac{12-8.6}{4.219})+(\frac{8-5.4}{2.073})(\frac{14-8.6}{4.219})}{5-1}=0.994$
The least-squares regression line:
$y ̂=b_1x+b_0$
$b_1=r\frac{s_y}{s_x}=0.994\times\frac{4.219}{2.073}=2.023$
$b_0=y ̅-b_1x ̅ =8.6-2.023\times5.4=-2.324$
So:
$y ̂=2.023x-2.324$
