This course covers the fundamentals of General Linear Models and Regression, teaching students how to analyze data using linear models. By the end of the course, learners will be able to understand and apply simple linear regression, multiple linear regression, weighted least squares regression, ridge regression, and various diagnostic tools for model evaluation. The course uses a combination of theoretical explanations, mathematical derivations, and practical examples to help students grasp the concepts effectively. This course is intended for individuals interested in statistics, data analysis, and regression modeling.
Overview
Syllabus
Introduction to Linear Models.
Simple Linear Regression.
Simple Linear Regression: Properties of Least Squares Estimators.
Simple Linear Regression: Estimating the Residual Variance.
Simple Linear regression: Matrix Notation.
Simple Linear Regression: Maximum Likelihood Estimation.
Simple Linear Regression: Partitioning Total Variability.
Simple Linear Regression: Matrix Notation for Sum of Squares.
Simple Linear Regression: ANOVA Table.
Simple Linear Regression: Testing the Model is Useful.
Simple Linear Regression: LSEs are Normally Distributed.
Simple Linear Regression: Confidence intervals for Beta Parameters.
Simple Linear Regression: Coefficient of Determination.
Simple Linear Regression:Confidence and Prediction Intervals on the Mean and Individual Response.
Simple Linear Regression: Simultaneous Inference on B0 and B1.
Simple Linear Regression: Bonferroni and Working-Hotelling Adjustments.
Simple Linear Regression: Residuals and their Properties.
Simple Linear Regression: X and Y Random.
Simple Linear Regression: Test for the Correlation Coefficient.
Simple Linear Regression: Fixed Zero Intercept Model.
Multiple Linear Regression: Introduction.
Multiple Linear Regression: Least Squares Estimates.
Multiple Linear Regression: The Hat Matrix.
Multiple Linear Regression: Estimating the Error Variance.
Multiple Linear Regression: Projection and Idempotent Matrices.
Multiple Linear Regression: Gauss Markov Theorem.
Multiple Linear Regression: Partitioning Total Variability.
Multiple Linear Regression: Type I Sum of Squares.
Multiple Linear Regression: Type II Sum of Squares.
Multiple Linear Regression: Global F Test.
Multiple Linear Regression: Partial F Tests.
Multiple Linear Regression: t Tests for a Single Beta Parameter.
Multiple Linear Regression: General Linear Hypotheses.
Using R: Simple Linear Regression from Scratch.
Multiple Linear Regression: CI/PI on the Mean and Individual Response.
Multiple Linear Regression: Simultaneous Inference of B'=(B0,B1, ... ,Bk).
Multiple Linear Regression: Partitioning the Residual Sum of Squares.
Multiple Linear Regression: Repeated Observations and Lack of Fit Test.
Multiple Linear Regression: Centering and Scaling the Design Matrix.
Multiple Linear Regression: Condition Number / Multicollinearity.
Multiple Linear Regression: Variance Inflation Factor (VIF) / Multicollinearity.
Multiple Linear Regression: Variance Proportions / Multicollinearity.
Multiple Linear Regression: Indicator / Dummy Variables.
Multiple Linear Regression: AIC (Akaike Information Criterion).
Multiple Linear Regression: Choosing a model with R2, Adjusted R2, and MSE.
Multiple Linear Regression: Mallow's Cp.
Multiple Linear Regression: Impact of Under or Over Fitting a Model.
Multiple Linear Regression: The PRESS Prediction SS Statistic.
Multiple Linear Regression: Residual Properties.
Weighted Least Squares Regression: Mahalanobis Distance.
Weighted Least Squares Regression: Hat Matrix.
Weighted Least Squares Regression: Estimability / BLUE.
Weighted Least Squares Regression: Estimating the Error Variance.
Weighted Least Squares Regression: Testing for Estimable Functions.
Weighted Least Squares Regression: Partial F Tests.
Multiple Linear Regression: Canonical Form.
Multiple Linear Regression: Canonical Form and Multicollinearity.
Multiple Linear Regression: Principal Components Model.
Ridge Regression (part 1 of 4): Variance Reduction.
Ridge Regression (part 2 of 4): Deriving the Bias.
Ridge Regression (part 3 of 4): Deriving from 1st principles..
Ridge Regression (part 4 of 4): Canonical Form.
Multiple Linear Regression: Box-Cox Transformation.
Multiple Linear Regression: Box - Tidwell Transformation.
Multiple Linear Regression: Studentized Residuals (Part 1 of 2).
Multiple Linear Regression: Studentized Residuals (Part 2 of 2).
Multiple Linear Regression: Partial Regression Plots (Added Variable Plots).
Multiple Linear Regression: Influence Measures (Part 1 of 2).
Multiple Linear Regression: Influence Measures (Part 2 of 2).
Best quadratic unbiased estimator of variance in a MLR model using Lagrange Multipliers.
Taught by
statisticsmatt
