Lecture 13 – Ordinary Least Squares
by Suraj Rampure (Summer 2020)
Make sure to complete the Quick Check questions in between each video. These are ungraded, but it’s in your best interest to do them.
A quick recap of the modeling process, and a roadmap for lecture.
Defining the multiple linear regression model using linear algebra (dot products and matrix multiplication). Introducing the idea of a design matrix.
Defining the mean squared error of the multiple linear regression model as the (scaled) norm of the residual vector.
Using a geometric argument to determine the optimal model parameter.
Residual plots. Properties of residuals, with and without an intercept term in our model.
Discussing the conditions in which there isn't a unique solution for the optimal model parameter. A summary, and outline of what is to come.