Question

If the correlation between $x$ and $y$ is $r$, then between $y$ and $x$ correlation will be:

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

Answer 1

The correct option is C

$r$

Explanation for the correct option

The correlation coefficient, $r$, is a measure that describes the extent of the statistical relationship between two interval or ratio level variables.

The correlation for the linear relationship of is given by ${\mathrm{r}}_{\mathrm{xy}}=\frac{\sum \left({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)\left({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}}\right)}{\sqrt{\sum {\left({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)}^2\sum {\left({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}}\right)}^2}}$.

So, the relationship between $y\&x$is nothing but ${\mathrm{r}}_{\mathrm{xy}}=\frac{\sum \left({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}}\right)\left({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)}{\sqrt{\sum {\left({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)}^2\sum {\left({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}}\right)}^2}}$.

Notice that both are the same.

So, if the correlation between $x$ and $y$ is $r$ then the correlation between $y$ and $x$ is $r.$

Hence, option C is correct.