Multilinear Regression: Design Optimization

In course

Description

This lecture covers the concept of multilinear regression, focusing on design optimization and orthogonality. It explains the algebraic form of ANOVA, the consequences of parting the model, and the cocktail effect of sugar substitutes in causing diabetes. The instructor presents cases, such as designing experiments with available products, analyzing toxicity combinations, and measuring enzyme production. The lecture also delves into methods like fitlm and stepwiselm in MATLAB, the Wilkinson Notation for model terms, and different types of sum of squares. It concludes with a discussion on model fit, including estimated coefficients and statistical measures.

Instructor

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https://mediaspace.epfl.ch/media/0_q6c5cwt3

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Related concepts (32)

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In statistics, a sum of squares due to lack of fit, or more tersely a lack-of-fit sum of squares, is one of the components of a partition of the sum of squares of residuals in an analysis of variance, used in the numerator in an F-test of the null hypothesis that says that a proposed model fits well. The other component is the pure-error sum of squares. The pure-error sum of squares is the sum of squared deviations of each value of the dependent variable from the average value over all observations sharing its independent variable value(s).

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In statistical data analysis the total sum of squares (TSS or SST) is a quantity that appears as part of a standard way of presenting results of such analyses. For a set of observations, , it is defined as the sum over all squared differences between the observations and their overall mean .: For wide classes of linear models, the total sum of squares equals the explained sum of squares plus the residual sum of squares. For proof of this in the multivariate OLS case, see partitioning in the general OLS model.

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