Question

In a partially destroyed laboratory record of an analysis of regression data, the following data are legible : 

Variable of X = 9 

Regression equations : 8x - 10g + 66 = 0 and  40x- 18g = 214

Find Correlation coefficient between X and Y on the basis of the above information.

Answer 1

Given variance of x   `sigma _x^2 = 9 => sigma_x = 3`

Regression equations : 

8x - 10 y  + 66 = 0       ....(i)

40 x - 18 y = 214        ....(ii)

Correlation coefficient between x and y 

Y = `4/5 "x" - 33/5`                     `therefore "b"_"yx" = 4/5`

X = `18/40 "y" - 214/40`             `therefore "b"_"xy" = 9/20`

r = `sqrt ("b"_"xy" xx "b"_"yx")`

r = `sqrt (4/5 xx 9/20)`

`= sqrt (36/100)`

`= 6/10 = 0.6`

∴ r = 0.6