Lectures related to Linear Regression: Absence or Presence of Covariates

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

Explores orthogonal projections and the Gram-Schmidt method for constructing bases.

Explores subspaces, spectra, and projections in linear algebra, including symmetric matrices and orthogonal projections.

Delves into singular value decomposition and its applications in linear algebra.

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

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

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

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

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Explains Singular Value Decomposition, focusing on orthogonal vectors and matrix decomposition.

Explores orthogonal projections, orthonormal bases, and QR factorization in linear algebra.

Explains orthogonal projection in linear algebra, focusing on transforming non-orthogonal bases into orthogonal ones.

Explains the method of least squares in linear regression to find the best-fitting line to a set of data points.

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

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

Explores Gram-Schmidt process, orthogonal projection, QR factorization, and least squares solutions for linear systems.

Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.

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