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Correlation

What is Correlation?

Correlation measures how closely two random variables shift together. It scales the two variables' covariance between -1 and 1 by multiplying the two variables' standard deviations and then dividing the covariance by the result.

The correlation coefficient implies how positively or negatively correlated the two variables are, with numbers between 0 and 1 being positively correlated and -1 and 0 being negatively correlated. Coefficients of 1 and -1 imply a perfect positive or negative correlation.

$$\rho_{xy}=\frac1 n\underset{i=0}{\overset{n}{\sum}}(\frac{x_i-\mu_x}{\sigma_x})(\frac{y_i-\mu_y}{\sigma_y})$$

$$Positive\; Correlation\;$$

A graph demonstrating positive correlation.

$$Negative\; Correlation\;$$

A graph demonstrating negative correlation.

$$No\; Correlation\;$$

A graph demonstrating no correlation.