Lecture 13 – Ordinary Least Squares
Content by Joey Gonzalez, Andrew Bray, Suraj Rampure, Ani Adhikari, Deb Nolan
A reminder – the right column of the table below contains Quick Checks. These are not required but suggested to help you check your understanding.
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.
A case study demonstrating the descriptive capacity of a MLR model.