Correlations

• Covariance
  • the joint variability of two random variables
  • calculated by $\frac{\Sigma(x_i-\bar{x})(y_i-\bar{y})}{N-1}$
    • which is kind of like MSE/variance calculation but on two variables instead of squaring it
  • if the covariance is positive and large, then the two variables tend to have a linear relationship
  • if the covariance is 0 then they are not correlated
• Pearson's correlation coefficient
  • essentially a normalized measurement of covariance
  • calculated by the covariance divided by the product of the variables' standard deviations
  • thus the value will range from -1 to 1
  • where 1 or -1 is perfectly linearly correlated and 0 is not