Sumários

Aula 6 (Módulo II)

29 Março 2023, 09:00 • Fernanda Maria dos Reis Torroaes Valente

[Pt] Resolução de exercícios de Regressão Linear com o apoio do R, no ambiente RStudio: ex. 1 a) e b) (leitura de ficheiros de dados, txt, csv e xlxs; as funções plot e lm; análise do resultado da função summary aplicada a um objecto lm; testes t e teste F global, cálculo do p-value; as funções fitted e residuals e as três somas de quadrados).

[En] Resolution of Linear Regression exercises with the support of R in RStudio: ex. 1 a) and b) (reading data files, txt, csv and xlxs; the plot and lm functions; analysis of the result of the summary function applied to a lm object; t-test and global F-test, p-value calculation; the fitted and residuals functions and the three sums of squares).

NOTA: Esta aula foi leccionada na quarta-feira, dia 12/04/2023, das 10h-12h.

Aula 5 (Módulo II)

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

The principle of parsimony and the partial F test to compare a model and one of its submodels: the general result; alternative (equivalent) expressions for the hypotheses and the test statistic; justification of the right-tailed rejection region. An example.

Stepwise search algorithms. Akaike Information Criterion and respective Interpretation. The adjusted R^2 and respective Interpretation. The leaps algorithm.

Model validation. The distribution of the residuals, given the Linear Model. Standardized residuals. Residual plots and how to read them. Outliers. Other diagnostics: leverage and Cook distance.

Nota: Esta aula foi leccionada na terça-feira, dia 04/04/2023, das 11h-13h.

Aula 4 (Módulo II)

22 Março 2023, 09:00 • Elsa Maria Félix Gonçalves

Inference for any linear combination of the model parameters: confidence intervals and hypothesis tests for the general result a^t Beta. The specific cases of the sum or difference of two parameters, and of the expected value of Y given the predictor values. Examples.

The goodness-of-fit F test: the general result; alternative (equivalent) expressions for the hypotheses and for the test statistic. The justification for right-tailed rejection regions. Examples of the goodness-of-fit test with R.

Nota: Esta aula foi leccionada na segunda-feira, dia 03/04/2023, das 8h30-11h.

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.

Aula 2 (Módulo II)

15 Março 2023, 09:00 • Elsa Maria Félix Gonçalves

Nonlinear relations that can be linearized with suitable transformations of one or both variables (examples: the exponential relation, the (2-parameter) logistic relation, the power law, hyperbolic-type relations, the Michaelis-Menten curve).

Multiple Linear Regression in a descriptive context. The Least Squares criterion in a multiple regression context. The impossibility of visualization for more than two predictors. The vectors of n observations, the vector of n ones and the vector y-hat of the n fitted values of y, which is a linear combination of the vectors of predictors and the vector of n ones. The model matrix X. Linear combinations of the columns of matrix X. The Linear Model in an inferential context: introduction, additional assumptions, the model in a multiple linear regression context. The matrix/vector notation for the Model: the Model equation and the random vector of estimators of the model parameters (beta-hat).

Nota: Esta aula foi leccionada na segunda-feira, dia 27/03/2023, das 8h30h às 11h.