Correct Answer - Option 4 : 4
Given
Regression lines
x + 2y - 5 = 0
2x + 3y - 8 = 0
var(x)= σx = 12
Calculation
x + 2y - 5 = 0 ------(i)
Let y = - x/2 + 5/2 be the regression line of y on x [ from equation 1]
2x + 3y - 8
x = -(3/2)y + 8/2 be the regressiopn line of x on y
⇒ bxy = -1/2 and byx = -3/2
bxy = Regression line of y on x
byx = Regression line of x on y
We know that regression coefficient = r = √(byx × bxy)
⇒ r = √(-1/2 × -3/2)
∴ r = √3/2 < 1
σx = 12 = 2√3
We know that byx = γ(σy/σx)
⇒ -1/2 = √3/2 (σy/2√3)
⇒ σy = - 2
∴ var(y) = variance of y =(-2)2 = 4
