Question

Let θ be the angle made by the line of regression of Y on X. If σ_Y = 2σ_X and the correlation coefficient between X and Y is 0.3, the value θ equals
1. tan^-1 0.3
2. cot^-1 0.3
3. tan^-1 0.6
4. cot^-1 0.6

Answer 1

Correct Answer - Option 3 : tan^-1 0.6

Given

Let θ be the angle made by the line of regression of Y on X.

σY = 2σX and the correlation coefficient between X and Y  = γ =  0.3

Calculation

Let L_YX be line of regression of Y on X

Let the angle made by L_yx with x – axis be θ.

∴ Tangent of the angle made by L_yx with x – axis is tan θ.

But slope of any line with x – axis is tan θ

⇒ Slope of L_yx = b_yx

⇒ b_yx = tan θ

⇒ b_yx = γ(σ_y/σ_x)

⇒ tan θ = 0.3 × 2(σ_x/σ_x)

⇒ tan θ = 0.3 × 2

∴ The value of θ is tan^-1(0.6)