Math 158: Linear Models

Linear models is a second course in statistics which extends a basic statistical linear model in many ways. The mathematics in the course moves quickly, and there will also be extended focus on good modeling practices and interpretation.

The Course

Linear Models is a second course in statistics that builds on introductory statistics using mathematical tools (including calculus and linear algebra). The simple linear regression model will be expanded to multiple linear regression which will see an in-depth analysis. We will investigate the impact of residuals, and we will use graphical tools to enhance both understanding and communication of the models. For data with many explanatory variables, we will use ridge regression and Lasso for predictive modeling. The statistical software R will be used for all analyses, homework, and projects. Focus will be on understanding the methods and interpreting results; we will discuss good modeling practices, ideas of which extend beyond linear models to any types of inference or prediction.

Student Learning Outcomes.

By the end of the semester, students will be able to do the following:

understand the structure of a linear model, including: simple linear regression, multiple linear regression, ridge regression, Lasso, and splines.
know when a linear model is appropriate and what conclusions can be drawn given a particular dataset, including: when are p-values appropriate to use? when is prediction more appropriate? when can or cannot causation be implied?
use graphical tools to investigate models associated with the data at hand, including: exploring data graphically, using graphics to understand leverage and influence values, visualizing smooth models.
communicate results effectively.

Course website

Linear Models was last taught in Spring 2022, materials can be found on the course website.