Question

If `vecx = 18, vecy=100,σ<sub>y</sub> =20` , bary` and correlation coefficient xyr 0.8,  find the regression equation of y on x. 

Answer 1

Regression line of y on x is
`y - bary =byx (x - barx)`        .........(1)

Now, `byx = (Sigmaxy)/(Sigmax^2) = r((sigmay)/sigma_x)`

`therefore  byx =(0,8) (20/14)=16/14 = 8/7`

`therefore(y - bary) = 8/7 (x - barx)`           ....(2)

`therefore (y-100)=8/7(x-18)`

`therefore 7y-700 = 8x - 144`

`therefore 7y = 8x +556`

`therefore y = (8/7)x +(556/7)`