Answer
$y ̂=1.1x-3.7$
Work Step by Step
$x ̅ =\frac{3+5+7+9+11}{5}=7$
$s_x=\sqrt {\frac{(3-7)^2+(5-7)^2+(7-7)^2+(9-7)^2+(11-7)^2}{5-1}}=3.162$
$y ̅=\frac{0+2+3+6+9}{5}=4$
$s_y=\sqrt {\frac{(0-4)^2+(2-4)^2+(3-4)^2+(6-4)^2+(9-4)^2}{5-1}}=3.536$
$r=\frac{Σ(\frac{x_i-x ̅}{s_x})(\frac{y_i-y ̅}{s_y})}{n-1}=\frac{(\frac{3-7}{3.162})(\frac{0-4}{3.536})+(\frac{5-7}{3.162})(\frac{2-4}{3.536})+(\frac{7-7}{3.162})(\frac{3-4}{3.536})+(\frac{9-7}{3.162})(\frac{6-4}{3.536})+(\frac{11-7}{3.162})(\frac{9-4}{3.536})}{5-1}=0.984$
The least-squares regression line:
$y ̂=b_1x+b_0$
$b_1=r\frac{s_y}{s_x}=0.984\times\frac{3.536}{3.162}=1.100$
$b_0=y ̅-b_1x ̅ =4-1.100\times7=-3.7$
So:
$y ̂=1.1x-3.7$
