Question
Download Solution PDFLet θ be the angle made by the line of regression of Y on X. If σY = 2σX and the correlation coefficient between X and Y is 0.3, the value θ equals
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
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 LYX be line of regression of Y on X
Let the angle made by Lyx with x – axis be θ.
∴ Tangent of the angle made by Lyx with x – axis is tan θ.
But slope of any line with x – axis is tan θ
⇒ Slope of Lyx = byx
⇒ byx = tan θ
⇒ byx = γ(σy/σx)
⇒ tan θ = 0.3 × 2(σx/σx)
⇒ tan θ = 0.3 × 2
∴ The value of θ is tan-1(0.6)
Last updated on Jul 8, 2025
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