Syllabus

## ​​Module 1. Classical Linear Regression

• Ordinary Least Squares (OLS)
• Estimation
• BLUE, Gauss-Markov Theorem
• Confidence
• Confidence Interval for a single Linear Parametric Function (LPF)
• Confidence Regions for multiple LPFs
• Simultaneous Confidence Intervals for multiple LPFs
• Prediction Interval
• Hypothesis Testing
• Testing for the significance of a single LPF
• Testing for the significance of individual predictors: t-test
• ANOVA Table and testing hypothesis involving several LPFs
• Testing for the significance of the entire model/testing for lack of fit: F-test
• Categorical Predictors, Interaction models
• Least Squares in Heteroskedastic Models
• Generalized Least Squares
• Weighted Least Squares
• Residual Diagnostics

• Read chapter 12 of PRA by J. Faraway for a complete linear regression example
• tidyverse from ModernDive for reducing unstructured data to a regression framework.

## ​​Module 2. Beyond Least Squares

• Non-Linear Regression
• Transforming the Response: Box-Cox method
• Transforming the Predictors
• Polynomial Regression
• Regression Splines*
• Local Regression