Lecture 13 – Ordinary Least Squares
Presented by Anthony D. Joseph and Suraj Rampure
Content by Suraj Rampure, Ani Adhikari, Deb Nolan, Joseph Gonzalez
The Quick Check for this lecture is due Monday, October 12th at 11:59PM. In order to get the Gradescope submission code, you will have to follow the instructions at the end of one of these Google Forms; the instructions for this lecture are more involved as we will have you access the exam platform that we are using for the Midterm exam next week.
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.