This question was previously asked in

SSC CGL Tier-II ( JSO ) 2019 Official Paper ( Held On : 17 Nov 2020 )

Option 3 : tan^{-1} 0.6

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10 Questions
10 Marks
7 Mins

**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)**