Question

If $2$ random variables $x$ and $y$ of a bivariate distribution are connected by the relationship $3x+2y=4$, then correlation coefficient $r_{xy}=$

• A. $1$
• B. $-1$
• C. $\frac{2}{3}$
• D. $\frac{-2}{3}$

Answer 1

The correct option is B

$-1$

Explanation for the correct option:

Step 1. Find the correlation coefficient:

Rearrange the above equation in terms of $y$

$\Rightarrow$$2y=4-3x$

$\Rightarrow$$2y=-3x+4$

$\Rightarrow$ $y=\frac{-3}{2}x+2$

Step 2. Compare the above equation with the standard linear equation $y=mx+c$

$\Rightarrow$$m=\frac{-3}{2}$

the slope is negative that is the variable are in an inverse relationship

$\therefore$The correlation coefficient is $\mathbf{-}\mathbf{1}$

Hence, Option ‘B’ is Correct.