Class 6 (Module II)

30 Março 2022, 15:00 • Jorge Filipe Campinos Landerset Cadima

[Slides 154-188] 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 of confidence intervals for the expected value of Y, in both simple and multiple linear regressions. Visual interpretation of confidence intervals for E[Y] in simple linear regressions and the confidence bands for the population regression line. Prediction intervals for individual value of Y, given the predictor values. Examples for both simple and multiple linear regressions. Visual interpretation of prediction intervals for E[Y] in simple linear regressions and the prediction bands for individual observations. 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. 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. Relations between the partial F test and the goodness-of-fit F test. Relation between a partial F test with a submodel that has a single predictor less than the full model and the Student's t-test for the significance of the beta_j for that single predictor in the full model.
Nota: Esta aula foi leccionada na quarta-feira, dia 6.4.22, das 15h às 17h35, na Sala S3, simultaneamente presencial e por zoom.