Question

If two regression lines are: y = 4 + kx and x = 5+4y, then the range of k is?

Answer 1

Given:

Thetwo regression lines are: y = 4 + kx and x = 5+4y

To find:

The range of k is?

Solution:

From given, we have,

The two regression lines are: y = 4 + kx and x = 5+4y

The given regression line of y on x is y = kx + 4 .  

And regression line of x on y is x = 4y + 5 .  

Therefore regression coefficient of y on x = b(y, x) = k .  

Similarly regression coefficient of x on y = b(x, y) = 4 .  

as, we know that ,

b(y, x).b(x, y) = r²

⇒ r² = 4k and as

0 ≤ (r²) ≤ 1  

⇒ 0 ≤ (4k) ≤ 1 or

0 ≤ k ≤ (1/4)

Therefore, the range of k is 0 ≤ k ≤ (1/4)