Given data
[tex]\bar{x}=11,\text{ S}_y=106,\text{ S}_X=1,\bar{\text{ y}}=306,r=-0.62[/tex]
Let us solve for a and b
Solving for b
The formula to use is,
[tex]b=r\frac{S_y}{S_x}[/tex][tex]\begin{gathered} b=-0.62\times\frac{106}{1}=-0.62\times106=-65.72 \\ \therefore b=-65.72 \end{gathered}[/tex]
Solving for a
The formula to solve for a is,
[tex]a=\bar{y}-b\bar{x}[/tex]
Therefore,
[tex]\begin{gathered} a=306-(-65.72)\times11 \\ a=306-(-722.92)=306+722.92=1028.92 \\ \therefore a=1028.92 \end{gathered}[/tex]
The formula for the regression line is,
[tex]\hat{y}=bx+a[/tex]
Substituting the values of a and b
[tex]\hat{y}=-65.72+1028.92[/tex]
Hence, the regression line is
[tex]\hat{y}=-65.72x+1028.92[/tex]
