Lecture 14: Covariance, correlation, and linear regression with one variable¶

Learning objectives¶

Introduce the concept of covariance.
Introduce the concept of correlation.
Demonstrate that correlation is not causation.
Demonstrate the non-linear relationships may be missed by the correlation coefficient.
Introduce the supervised learning problem.
Introduce the regression and the classification problems.
Introduce the linear model.
Develop the least squares formulation for fitting linear models.
Develop the mathematical solution of the least squares problem.
Introduce diagnostics for validating a regression model.