# Stat 542: Lectures

Contents for Stat542 may vary from semester to semester, subject to change/revision at the instructor’s discretion. The contents below are from Spring 2019. UIUC students can access lecture videos [Here]. Please send your comments to liangf AT illinois DOT edu.

ESL = Elements of Statistical Learning; ISLR = An Introduction to Statistical Learning

• Week 2: Linear Regression
• Reading: chap 3 (ISLR); chap 3.1-3.2 (ESL)
• Notes:
[W2.1_LinearRegression_MLR.pdf]
[W2.2_LinearRegression_Geometry.pdf]
[W2.3_LinearRegression_Practice.pdf]
• Code: W2_LinearRegression [Rcode] [Python_1] [Python_2]
• Contents:
• 1. Multiple linear regression
• 1.1 LS setup
• 1.2 LS principle
• 1.3 LS estimate
• 1.4 LS output
• 2. Geometric interpretation
• 2.1 Basic concepts in vector spaces
• 2.2 LS and projection
• 2.3 Properties of LS regression: R-square
• 2.4 Properties of LS regression: linear transformation
• 2.5 Properties of LS regression: rank deficiency
• 3. Practical issues
• 3.1 Analyzing data with R
• 3.2 Interpret LS coefficients
• 3.3 Hypothesis testing
• 3.4 Handle categorical variables
• 3.5 Collinearity
• 3.6 Assumptions and outliers