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 Mean values of 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)

The mean values of X and Y are the point of intersection of `bar x`  and `bar y` 

Solving (i) and (ii) 

8x- 10y = - 66  multiply by 5 

`40x - 50y = - 330`

`(40 x - 18 y = 214)/(-32 y = - 544)`

`therefore  "y" = 544/32 = 17`

y = 17

Substituting in (i) 

8x - 170 = - 66

8x = 170 - 66

x = `104/8 = 13`

∴ x = 13 

∴ Mean of x = 13 ,

mean of y = 17