If the regression coefficient of x on y and y on x are -(1)/(2) and -(1)/(8) respectively, then what is the correlation coefficient between x and y ?

Correct answer: A. -(1)/(4) Correlation coefficient = (-1)/(2) × (-1)/(8) = (1)/(16) =-(1)/(4) Since, both the regression coefficients are negative, correlation coefficient is negative.

NDA 2017

Exam: NDA
Year: 2017
Subject: Mathematics
Chapter: Statistics

NDA 2017 · Mathematics · Statistics

If the regression coefficient of x on y and y on x are -(1)/(2) and...

If the regression coefficient of x on y and y on x are

-\frac{1}{2}

and

-\frac{1}{8}

respectively, then what is the correlation coefficient between x and y ?

Options

A $-\frac{1}{4}$
B $-\frac{1}{16}$
C $\frac{1}{16}$
D $\frac{1}{4}$

Correct answer

A. $-\frac{1}{4}$

Step-by-step solution

Correlation coefficient

=\sqrt{\frac{-1}{2} \times \frac{-1}{8}}=\sqrt{\frac{1}{16}}=-\frac{1}{4}

Since, both the regression coefficients are negative, correlation coefficient is negative.

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