Class 3 (Module II)

21 Março 2022, 09:30 • Jorge Filipe Campinos Landerset Cadima

[Slides 77-111] Multiple linear regressions in a descriptive context. The alternative representation in the space of variables. The column-space of matrix X, C(X). The orthogonal projection matrix H (the 'hat matrix'). Properties of orthogonal projections. The orthogonal projection of the response vector y onto C(X) and the Least Squares formula for the vector of parameters, b. The three Sums of Squares and the Fundamental Formula of Linear Regression as an application of the Pythagorean Theorem to the right triangle defined by the projection of vector y onto C(X). An alternative right triangle defined by the centred vector y^c. The definition of the Coefficient of Determination and its properties in a Multiple Linear Regression, with a geometric interpretation in the space of variables. Multiple Linear Regressions in R: an example with the iris data. Models and submodels. Some properties of submodels. Polynomial regressions as a special case of multiple regressions: general idea and an example with the vineleaves dataset.
Nota: Esta aula foi leccionada na segunda-feira, dia 28.3.22, das 9h45 às 12h25, na Sala S1, simultaneamente presencial e por zoom.