Module II - Class 2

8 Março 2021, 14:30 • Jorge Filipe Campinos Landerset Cadima

[Slides 48-86] More non-linear relations that can be linearized by suitable transformations: the (2-parameter) logistic relation; the power law; hyperbolic relations; Michaelis-Menten relation (for each, we discussed the linearizing transformations and solved differential equations that gave rise to them). Multiple linear regression: the problem, a motivating example; the difficulties associated with more than one predictor; the least-squares criterion. An alternative representation of the data: the space of variables. The geometric problem in the space of variables that corresponds to a least-squares solution. The model matrix and its column-space, C(X). Orthogonal projections onto C(X) and the matrix of orthogonal projections, the hat-matrix H. The projected vector y-hat and the formula for the model parameters, b. The three sums of squares and the fundamental formula as an application of the Pythagorean Theorem.