Let X and Y represent prices (in Rs) of a commodity in Kolkata and Mumbai respectively. It is given X̅ = 65, Y̅ = 67, σ_X = 2.5, σ_Y = 3.5 and r(X, Y) = 0.8. What is the equation of regression of Y on X ?

Concept:

Equation of regression of Y on X:

The equation of regression of Y on X with given values of \(\rm \bar X, \bar Y,\sigma_{x}\mbox{ and }\sigma_{y}\) is given as follows:

\(\rm \rm \dfrac{y-\bar Y}{\sigma_y} =r_{xy} \dfrac{x-\bar X}{\sigma_x} \)

Calculation:

It is given that X̅ = 65, Y̅ = 67, σX = 2.5, σY = 3.5 and r(X, Y) = 0.8 .

Using the equation of regression of Y on X we write:

\(\rm \rm \rm \frac{y-\bar Y}{\sigma_y} =r_{xy} \frac{x-\bar X}{\sigma_x} \\ \left(\frac{y-67}{3.5}\right) =0.8 \times \left(\frac{x-65}{2.5}\right)\\ y - 67 = 1.12(x-65)\\y-67=1.12x-72.8\\y=1.12x-5.8\)

Therefore, the required equation is y = 1.12x - 5.8