Definition, estimation, and interpretation of a regression model (Gaussian linear model, Poisson regression, logistic regression). Inference on the model's parameters, model checking, and fit to the data.
Course Prerequisites
Introduction to real analysis: functions, derivatives. Introduction to matrix algebra: vector/matrix operations. Probability: probability, independence; random variables (definition, distribution function, moments. The Gaussian, Poisson, and binomial distributions). Statistics: data representation, descriptive statistics, summary statistics. Inference: point estimation, hypothesis testing, confidence intervals, likelihood-based inference.
Teaching Methods
Lectures and exercises
Assessment Methods
Written exam (exercises)
Texts
Fox, J., 2015. Applied regression analysis and generalized linear models. Sage Publications. Abraham and Ledolter, Introduction to Regression Modeling, Duxbury Press, 2006
Contents
Introduction to regression models, types of regression models (number of variables, parametric/nonparametric).
Linear model via OLS: assumptions, estimation, interpretation. Descriptive properties of OLS regression line; inferential properties of the estimators.
Simple Gaussian linear model: - Assumptions, estimation via likelihood. Exact distribution of the ML estimators. - Inference for the simple Gaussian linear models: inference about the regression coefficients, inference about the mean (prediction), F test. - Decomposition of the total sum of squares, coefficient of determination R^2. - Diagnostics and model checking: analysis of the residuals.
Multiple Gaussian linear model: - Specification, interpretation of the parameters, estimation. Properties of the estimators. - Geometric interpretation. - The Gauss-Markov theorem. - Inference in the multiple linear model: test about an individual coefficient (t-test); test about the significance of the overall model; test about a subset of the regression parameters. - Model comparison and the R^2 coefficient. - Notable examples: ANOVA and ANCOVA
Generalized linear models: - Poisson regression: assumptions, interpretation, estimation, inference. - Logistic and probit regression: assumptions, interpretation, estimation, inference.
