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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.