Partition of sums of squares

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Related lectures (21)

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Least-squares Approximation

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

DOE Qualitative factors III

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

Nested Model Selection

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

Experimental Design: Strategies and Analysis

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

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.

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.

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.

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