For $$10$$  observations on price $$\left( x \right)$$ and supply $$\left( y \right)$$, the following data was obtained :
$$\sum {x = 130} ,\,\sum {y = 220} ,\,\sum {{x^2} = 2288} ,\,\sum {{y^2} = 5506} {\text{ and }}\,\sum {xy = 3467} .$$
What is line of regression of $$y$$ on $$x\,?$$

Solution :
$$\eqalign{ & {\text{Line of regression of }}y{\text{ on }}x{\text{ is :}} \cr & y - \overline y = {b_{yx}}\left( {x - \overline x } \right) \cr & \overline y = \frac{{\sum y }}{n}\,;\,\overline x = \frac{{\sum x }}{n} \cr & \Rightarrow \overline y = \frac{{220}}{{10}} = 22\,;\,\overline x = \frac{{130}}{{10}} = 13 \cr & {b_{yx}} = r.\frac{{{\sigma _y}}}{{{\sigma _x}}} \cr & \Rightarrow r = \frac{{n\sum {xy} - \left( {\sum x } \right)\left( {\sum y } \right)}}{{\sqrt {\left[ {n\sum {{x^2} - } {{\left( {\sum x } \right)}^2}} \right]\left[ {n\sum {{y^2} - } {{\left( {\sum y } \right)}^2}} \right]} }} \cr & \Rightarrow r = \frac{{10\left( {3467} \right) - \left( {130} \right)\left( {220} \right)}}{{\sqrt {\left[ {\left( {10 \times 2288} \right) - {{130}^2}} \right]\left[ {\left( {10 \times 5506} \right) - {{220}^2}} \right]} }} \cr & \Rightarrow r = 0.962 \cr & {\sigma _y} = \sqrt {\frac{{{{\sum y }^2}}}{n} - {{\left( {\frac{{\sum y }}{n}} \right)}^2}} \cr & \Rightarrow {\sigma _y} = 8.2\,;\,\,{\sigma _x} = 7.73 \cr & \Rightarrow {b_{xy}} = 0.962 \times \frac{{8.2}}{{7.73}} = 1.02 \cr & \Rightarrow {\text{Line of regression of }}y{\text{ on }}x{\text{ is :}} \cr & y - 22 = 1.02\left( {x - 13} \right) \cr & \Rightarrow y = 1.02x + 8.74 \cr} $$