Covariance and correlation¶

Python notebook: https://github.com/daviskregers/data-science-recap/blob/main/07-covariance-and-correlation.ipynb

Covariance¶

• It measures how two variables vary in tandem for their means.

• Measuring covariance

  • Think of the data sets for the two variables as high dimensional vectors
  • Convert these to vectors of variances from the mean
  • Take the dot product (cosine of the angle between them) of the two vectors
  • Divide by the sample size

• Interpreting covariance is hard

  • We know a small covariance, close to 0, means there isn't much correlation between the two variables.
  • And large covariances - that is, far from 0 (could be negative for inverse relationships) mean there is a correlation.
  • Then the question is - how large does it have to be?

Correltation¶

• Just divide the covariance by the standard deviations of both variables and that normalizes things.
• So a correlation results:
  • 0 means no correlation
  • 1 means perfect correlation
  • -1 means perfect inverse correlation

• Remember that correlation does not imply causation.
  • Only a controlled, randomized experiment can give you insights on causation.
  • Use correlation to decide what experiments to conduct!