Linear Regression: MLE for Methods of Estimation

Most of our semester in BIOS 6611 has focused on the ordinary least squares approach to estimation and derivation of our regression coefficients. However, we can also use maximum likelihood estimation to derive our beta coefficients and other quantities of interest (and, spoiler, the beta coefficients are identical to OLS!). The MLE approach is more general, however, and will be useful as you take future classes and learn about generalized linear models (e.g., logistic regression, Poisson regression, etc.). This lecture shows the approach for deriving the maximum likelihood estimators for linear regression and motivates the next step of learning about generalized linear models.

A video for the Biostatistical Methods I (BIOS 6611) course in the Department of Biostatistics and Informatics at the University of Colorado-Anschutz Medical Campus taught by Dr. Alex Kaizer. Slides and additional material available at https://www.alexkaizer.com/bios_6611.

Table of Contents:

00:00 - Intro Song
00:16 - Welcome
00:45 - Methods of Estimation for Regression
02:14 - MLE for Linear Regression
04:20 - Y's PDF
05:34 - The Likelihood Function
07:07 - The Log-Likelihood
08:24 - MLE of Regression Coefficients
09:21 - MLE of Variance
11:48 - Generalized Linear Model Preview