General Linear Model: Symmetric Matrices

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Covers regression diagnostics for linear models, emphasizing the importance of checking assumptions and identifying outliers and influential observations.

Ridge Regression: Penalised Least Squares

Explores Ridge Regression for handling multicollinearity and the LASSO method for model selection.

Assessing Significance and Fit

Covers confidence intervals, R2, and examples on cement heat evolution and car horsepower-MPG relationships.

Stationary Points and Saddle Points

Explores stationary points, saddle points, symmetric matrices, and orthogonal properties in optimization.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.

Diagonalization of Symmetric Matrices

Explores diagonalization of symmetric matrices and their eigenvalues, emphasizing orthogonal properties.

Linear Models: Ridge, OLS and LASSO

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

Linear Models and Overfitting

Explores linear models, overfitting, and the importance of feature expansion and adding more data to reduce overfitting.

Likelihood Estimation and Least Squares

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

Symmetric Matrices: Eigenvalues and Eigenvectors

Explores the diagonalization of symmetric matrices using eigenvectors and eigenvalues, emphasizing orthogonality and real eigenvalues.