LCE5861 - Linear Models I

Credit hours

Instructor
Cesar Goncalves de Lima
Edwin Moises Marcos Ortega
Idemauro Antonio Rodrigues de Lara
Renata Alcarde Sermarini

Objective
The objectives of the course are: (1) Interpret and solve problems involving the Gauss-Markov linear model in its various characterizations. (2) Identify estimable functions and build point, interval and region estimates. (3) Perform analysis of variance and interpret concepts about orthogonal projection and orthogonal decomposition of sums of squares. (4) Discuss the quadratic forms of interest and identify hypothesis with unbalance data or empty cells. (5) Use computational resources.

Content
(1) Matrix algebra review: generalized inverses,inconsistent systems, orthogonal projection. (2) Linear Model of Gauss-Markov: multiple linear regression model; overparametrized models, cell means models, with parametric restrictions and equivalent models. (3) Estimability and pontual estimability. BLUE´s estimated functions. Gauss-Markov´s theorem. Practical rules of estimability. (4) Analysis of variance and sums of squares. Projection and orthogonal decomposition, orthogonal contrasts, R(.) notation. Expectation, distribution and independence of quadratic forms. (5) Interval and region estimation. (6) Hypothesis test: sums of squares of hypothesis, equivalent hypothesis, the likelihood ratio test and other test criteria. (7) Constraints on parameters and constraints on solutions. Reparametrization and equivalent models. (8) Generalized linear model of Gauss-Markov: weighted and generalized least squares, estimation and tests. (9) Unbalanced experiments and with empty cells. Interpretation of hypothesis.

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