Concept

Explained sum of squares

Related lectures (19)

Covers the estimation of distributions using various methods such as minimum loss and expectation.

Covers ANOVA method, focusing on partitioning total sum of squares into treatment and error components, mean square calculations, Fisher statistic, and F-distribution.

Linear Regression: Simple

Introduces simple linear regression, properties of residuals, variance decomposition, and the coefficient of determination in the context of Okun's law.

Model with Interactions

Explains models with interactions, emphasizing the significance of factors and F-values.

Multilinear Regression: Design Optimization

Explores multilinear regression, design optimization, ANOVA, model fit, and experimental design.

Polynomial Optimization: SOS and Nonnegative Polynomials

Explores polynomial optimization, emphasizing SOS and nonnegative polynomials, including the representation of polynomials as quadratic functions of monomials.

Analysis of Variance: ANOVA

Covers Analysis of Variance (ANOVA) to compare means of multiple groups efficiently.

Least-squares Approximation

Explains the concept of least-squares approximation and its computation in specific and general cases.

Model Comparison in Linear Regression

Explores comparing models in linear regression through residual sum of squares reduction and F-tests.

Experimental Design: Strategies and Analysis

Discusses experimental design strategies, factors, responses, treatment combinations, and degrees of freedom.

Model Diagnostics: Outliers, Leverage, and Influential Observations

Explores outliers, leverage, and influential observations in statistical models, including methods for detection and assessment.

Nested Model Selection

Explores nested model selection in linear models, comparing models through sums of squares and ANOVA, with practical examples.

Regression Methods: Spline Smoothing

Covers regression methods focusing on spline smoothing and penalised fitting to balance data fidelity and smoothness.

Linear Regression: Model Adjustment and Parameter Estimation

Explains the decomposition of total sum of squares, model adjustment, and parameter estimation in linear regression.

Quadratic Forms and Symmetric Bilinear Forms

Explores quadratic forms, symmetric bilinear forms, and their properties.

DOE Qualitative factors III

Explores qualitative factors in Design of Experiments, including Latin squares, factorial designs, and ANOVA tables.

Polynomial Optimization: SOS and SDP

Explores Sum of Squares polynomials and Semidefinite Programming in Polynomial Optimization, enabling the approximation of non-convex polynomials with convex SDP.

Fermat's Theorem: Sums of Squares

Explores Fermat's Theorem, factorization of integers, properties of Z[i], and Hurwitz quaternions.

Linear Regression: Understanding Quantitative Relationships

Covers linear regression, from developing research questions to interpreting R-squared and adding predictors to improve the model.