II. Linear models and polynomial interpolation
Given by Sven Laur
Brief summary: What is a linear model? How to detect linear trends in the data. Mean square error and normalised mean square error of a given linear model. Ordinary least squares estimation and its geometrical interpretation.Polynomial interpolation as a linear regression problem. How does the experiment design influence the reconstruction of linear dependencies. Influence and leverage of various data points. Linear regression for categorical data. One-way and two-way analysis of variance. Methods for regression diagnostics and outlier detection. Model selection and regularisation. No free lunch theorem for interpretation.
Slides: PDF
Video: UTTV(2016) UTTV(2013)
Literature
- Germán Rodríguez: Generalized Linear Models Chapter 2
- Kaare Brandt Petersen and Michael Syskind Pedersen:The Matrix Cookbook: Derivatives
- Russell Davidson and James G. MacKinnon: Econometric Theory and Methods: Chapter 2: The Geometry of Linear Regression
Complementary exercises
- Sanford Weisberg: Applied Linear Regression (3rd edition) pages 18 - 19, 38 - 46, 65 - 68, 92 - 95, 137 - 146, 191 - 193, 206 - 210
- Various datasets used in the examples of Applied Linear Regression
- Various datasets for fitting linear models in Princeton lectures
Free implementations
- Built-in stats package in R:
anova,glm,lm,residuals - Diagnostics for linear model fitting in R
- Example datasets for linear model fitting in R