Online class on Monday, March 15, as on Tuesday March 9 there was the Module I test

Revision of matrix operations and properties. Exercise 11. [Slides 87-115] Again the geometry of the space of variables. An alternative right triangle beginning with the centred vector y^c: the fundamental formula of linear regressions as a direct application of the Pythagorean Theorem; the geometric interpretation of the Coefficient of Determination. Properties of linear regressions (with the intercept). Interpretation and units of measurment of the fitted coefficients b_j and of residuals. The vector of residuals as an orthogonal projection on the orthogonal complement of C(X). An example: a multiple regression on the iris dataset. Multiple regressions in R. Submodels: definition, properties and warning. Example: a simple linear regression with the iris data, as a submodel of the previous example. Polynomial regression: the concept; the trick to fit them as multiple linear regressions; an example (videira dataset). The transition to an inferential context. Initial assumptions and the model equation.