The two lines of regression are 8x - 10y = 66 and 40x - 18y = 214, and variance of x series is 9. What is the standard deviation of y series?

Concept:

Coefficient of correlation = 

Where, b_yx and b_xy are regression coefficients

or the slopes of the equation y on x and x on y are denoted as b_yx and b_xy

Standard deviation = 

,  and are the standard deviation of y and x series respectively.

Calculation:

Here, The two lines of regression are 8x - 10y = 66 and 40x - 18y = 214

⇒ 10y = 8x - 66

⇒ byx = 8/10 = 4/5

And, 

40x - 18y = 214

⇒ 40x =18y + 214

⇒ bxy = 18/40 = 9/20

Now, Coefficient of correlation = 

= 

bxy  > 0 and byx > 0.

So, r = 3/5

Here, variance of x series is 9

⇒ Standard deviation of x series is

 = √9 = 3

We know, 

So, 

= 4

Hence, option (2) is correct.