# Correlation and Covariance

### Correlation

• 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. ### Covariance

It is a measure that quantifies the strength and direction of a relationship between a pair of variables.
$cov(x,y)=\frac{1}{n}\sum_i^n(x_i-\overline{x})(y_i-\overline{y})$

### Correlation Coefficient

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 Causation which says that a correlation does not mean that one thing causes the other.