Answer to Question #195832 in Statistics and Probability for Victoria

Question

How to find correlation coefficient

Answer 1

The correlation coefficient is a statistical measure of the strength of the relationship between the relative movements of two variables.

To measure the Pearson product-moment correlation, the covariance of the two variables must first be determined. The standard deviation of each variable must then be calculated. The correlation coefficient is calculated by multiplying the covariance by the product of the standard deviations of the two variables.

$\rho _{xy}=\frac{Cov\left(x,\:y\right)}{\sigma _x\sigma _y}$

Where:

$Cov\left(x,\:y\right)$ $=$ Covariance of variables $x$ and $y$.

$\sigma _x=$ Standard deviation of $x$

$\sigma _y=$ Standard deviation of $y$

$\rho _{xy}=$ Pearson product-moment correlation coefficient

The standard deviation is a calculation of how much data deviates from its mean. The covariance of two variables is a measure of how they shift together, but its magnitude is unbounded, making it difficult to interpret. The normalized version of the statistic can be calculated by dividing covariance by the product of the two standard deviations. The correlation coefficient is this number.