Question

If $\mathrm{var}\left(x\right)=\frac{21}{4}$ and $\mathrm{var}\left(y\right)=21$ and $r=1$, the standard error of $y$ is

• A. $0$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $1$

Answer 1

The correct option is A

$0$

Explanation for the correct option.

Find the standard error of $y$.

The standard error of $y$ is given as $S_y=\sqrt{1-r^2}$.

Here, $r=1$ so,

$\begin{array}{rcl}{S}_y& =& \sqrt{1-1^2}\\ & =& \sqrt{1-1}\\ & =& 0\end{array}$

So the standard error of $y$ is $0$.

Hence, the correct option is A.