# Correlation and Covariance

**Positive**correlation exists when larger values of$x$correspond to larger values of$y$and vice versa.**Negative**correlation exists when larger values of$x$correspond to smaller values of$y$and vice versa.**Weak or no**correlation exists if there is no such apparent relationship.

It is a measure that quantifies the strength and direction of a relationship between a pair of variables.

$cov(x,y)=\frac{1}{n}\sum_i^n(x_i-\overline{x})(y_i-\overline{y})$

The correlation coefficient, or

**Pearson**product-moment correlation coefficient is another measure of the correlation between data. You can think of it as a**standardized covariance**.$r_{xy}=\frac{cov(x,y)}{\sigma(x)\sigma(y)}=\frac{\sum_i^n(x_i-\overline{x})(y_i-\overline{y})}{\sqrt{\sum_i^n(x_i-\overline{x})^2\sum_i^n(y_i-\overline{y})^2}}$

Make a Scatter Plot, and look at it! You may see a correlation that the calculation does not.Correlation Is Not Causationwhich says that a correlation does not mean that one thing causes the other.

Last modified 2yr ago