If the lines of regression of ${Y}$ on ${X}$ and ${X}$ on ${Y}$ are respectively $y={K} x+4$ and $x=4 y+5$, then

JEE MATHEMATICS MCQ: STATISTICS

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If the lines of regression of

{Y}

{X}

and

{X}

{Y}

are respectively

y={K} x+4

and

x=4 y+5

, then

View answer and explanation

Correct option: B

0 \leq {K} \leq \frac{1}{4}

Option B (

0 \leq {K} \leq \frac{1}{4}

) is correct because the product of the regression coefficients must be less than or equal to 1, ensuring that the correlation coefficient's square is within the valid range.

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