Answer
$y ̂=0.780x-3.3$
Work Step by Step
$x ̅ =\frac{5+10+15+20+25}{5}=15$
$s_x=\sqrt {\frac{(5-15)^2+(10-15)^2+(15-15)^2+(20-15)^2+(25-15)^2}{5-1}}=7.906$
$y ̅=\frac{2+4+7+11+18}{5}=8.4$
$s_y=\sqrt {\frac{(2-8.4)^2+(4-8.4)^2+(7-8.4)^2+(11-8.4)^2+(18-8.4)^2}{5-1}}=6.348$
$r=\frac{Σ(\frac{x_i-x ̅}{s_x})(\frac{y_i-y ̅}{s_y})}{n-1}=\frac{(\frac{5-15}{7.906})(\frac{2-8.4}{6.348})+(\frac{10-15}{7.906})(\frac{4-8.4}{6.348})+(\frac{15-15}{7.906})(\frac{7-8.4}{6.348})+(\frac{20-15}{7.906})(\frac{11-8.4}{6.348})+(\frac{25-15}{7.906})(\frac{18-8.4}{6.348})}{5-1}=0.971$
The least-squares regression line:
$y ̂=b_1x+b_0$
$b_1=r\frac{s_y}{s_x}=0.971\times\frac{6.348}{7.906}=0.780$
$b_0=y ̅-b_1x ̅ =8.4-0.780\times15=-3.3$
So:
$y ̂=0.780x-3.3$
