Question

A linear statistical relationship between two variables?

• A. cov (x, y) / 𝜎 _x 𝜎_y
• B. cov (x, y) / 𝜎 _y²
• C. cov (x, y) / 𝜎 _x²
• D. None of these

Answer 1

The correct option is C

cov (x, y) / 𝜎 _x²

Explanation for correct option:

Step- Find the relation between covariance (cov) and standard deviation ($\sigma$) of two variables x, y.

Let cov(x, y) = covariance between the variables x and y.

${\sigma }_x=$The standard deviation of x variable.

${\sigma }_{y=}$The standard deviation of y variable.

cov = Covariance is the inner product also called scalar or dot product of two vectors in that space.

$\chi .y=cov(\chi ,y)$

It forms the following relationship between $cov(x,y)and{\sigma }_{x_{}}$.

$\frac{cov(x,y)}{{{\sigma }_x}^2}=\rho (x,y)$ Where $\rho (x,y)$ is the correlation of $xandy$.

$\rho (x,y)$ is a normalized version of their cov(x, y)

Therefore option (C) $\raisebox{1ex}{$cov(x,y)$}\!\left/ \!\raisebox{-1ex}{${{\sigma }^2}_x$}\right.$ is the correct option