Linear Models: Least Squares and QR Factorization

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Related lectures (38)

QR Factorization: Least Squares System Resolution MOOC: Linear Algebra (Part 3)

Covers the QR factorization method applied to solving a system of linear equations in the least squares sense.

Linear Models: Least Squares

Explores linear models, least squares, Gaussian vectors, and model selection methods.

Linear Models: Ridge, OLS and LASSO

Covers linear models like Ridge, OLS, and LASSO, explaining singular values and regression analysis.

Linear Regression Testing

Explores least squares in linear regression, hypothesis testing, outliers, and model assumptions.

Linear Regression: Estimation and Inference

Explores linear regression estimation, linearity assumptions, and statistical tests in the context of model comparison.

Geometry and Least Squares

Discusses the geometry of least squares, exploring row and column perspectives, hyperplanes, projections, residuals, and unique vectors.

Likelihood Estimation and Least Squares

Introduces simple and multiple normal linear regression, and maximum likelihood estimation with practical examples.

Splines: Fundamentals and Applications

Explores B-splines, natural cubic splines, and smoothing splines in regression problems and their practical applications.

Linear Regression: Statistical Inference and Regularization

Covers the probabilistic model for linear regression and the importance of regularization techniques.

Regression: Linear Models

Explores linear regression, least squares, residuals, and confidence intervals in regression models.

Singular Value Decomposition: Applications and Solutions

Explores Singular Value Decomposition, matrix solutions, and least squares regression in data analysis.

Weighted Least Squares Estimation: IRLS Algorithm

Explores the IRLS algorithm for weighted least squares estimation in GLM.

Least Squares Solutions Log in to Mediaspace to watch this video

Explains the concept of least squares solutions and their application in finding the closest solution to a system of equations.

Least Squares Solutions Log in to Mediaspace to watch this video

Covers least squares solutions for linear systems using matrix operations and normal systems, illustrated with examples.

Linear Regression Basics Log in to Mediaspace to watch this video

Covers the basics of linear regression, instrumental variables, heteroskedasticity, autocorrelation, and Maximum Likelihood Estimation.

Gram-Schmidt Algorithm: Orthogonalization and QR Factorization Log in to Mediaspace to watch this video

Introduces the Gram-Schmidt algorithm, QR factorization, and the method of least squares.

Matrix Equivalence Theorems Log in to Mediaspace to watch this video

Explores matrix equivalence theorems for systems of equations and least squares solutions.

Linear Regression Basics Log in to Mediaspace to watch this video

Covers the basics of linear regression, including OLS, heteroskedasticity, autocorrelation, instrumental variables, Maximum Likelihood Estimation, time series analysis, and practical advice.

Linear Regression: Basics and Estimation Log in to Mediaspace to watch this video

Covers the basics of linear regression and how to solve estimation problems using least squares and matrix notation.

Nonlinear Machine Learning: k-Nearest Neighbors and Feature Expansion Log in to Mediaspace to watch this video

Covers the transition from linear to nonlinear models, focusing on k-NN and feature expansion techniques.

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