Aula 3 (Módulo II)

20 Março 2023, 08:00 • Elsa Maria Félix Gonçalves

Tools to work with random vectors: the expected vector and its properties; the matrix of (co-) variances and its properties; the MultiNormal distribution and its properties; the Linear Model in matrix/vector notation. First consequences of the model: the distribution of the random vector Y of response variable observations; the distribution of the vector of estimators beta-hat (with proofs and interpretations).

The problem with using the Normal distribution for beta-hat_j: the unknown variance sigma^2 of the random errors. Estimating sigma^2 with the Residual Means Square (QMRE) and its effect on the pivot quantity for inference on the model parameters beta_j. Confidence intervals for individual beta_j. Hypothesis tests for individual beta_j. Examples.

Nota: Esta aula foi leccionada na terça-feira, dia 28/03/2023, das 11h às 13h.