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Tabela de conteúdos
CE-071: Análise de Regressão Linear
Detalhes da oferta da disciplina
- Curso: Estatística.
- Período: 2014/1.
- Local: LABEST, LAB C.
- Horário: Segunda, 20h45-22:00h e quarta 19:00-20:30h.
- Atendimento: Segunda, 19:00-20:30h.
Scripts, notas e documentos
Apostilas e textos úteis: ce071_livros.zip (84 MB)
Histórico das Aulas do Curso
Abaixo o histórico de atividades realizadas em classe e atividades extra classe aplicadas.
- 10/02:
- Informação sobre a oferta da disciplina;
- Introdução à regressão linear;
- Panorama do conteúdo previsto.
- 12/02:
- Análise gráfica exploratória visando aplicação de regressão.
- 17/02:
- Representação matricial;
- Interpretação geométrica;
- Estimação pelo método dos mínimos quadrados.
- 19/02:
- Métodos numéricos considerados na estimação: decomposição QR e de Cholesky.
- 24/02:
- Estimação baseada na verossimilhança.
- 26/02:
- Esperança e variância dos estimadores;
- Teorema de Gauss-Markov;
- Análise de variância.
- 10/03:
- Regressão linear múltipla, resultados representados matricialmente;
- Quadro de análise de variância;
- 12/03:
- Propriedades distribucionais dos estimadores;
- Teste F de uma função linear para inferência sobre \beta;
- Teste F do quadro de análise de variância.
- 17/03:
- Teste de hipótese para \beta e subconjuntos de \beta;
- Teste da soma de quadrados extra;
- Intervalos de confiança para \beta_j e funções lineares de \beta;
- Intervalos de confiança para o valor predito e para observação futura.
- 19/03:
- Prática de regressão linear múltipla com o R;
- Estudo sobre o preço de imóveis em função da área.
- 24/03:
- Fórmulas e matrizes correspondentes ao declarar modelos;
- Tipos de parametrizações em modelos lineares para variáveis categóricas;
- Prática de regressão linear múltipla com o R.
- 26/03:
- Prática de regressão linear múltipla com o R;
- Estudo sobre o preço de veículos em função da quilometragem e tipo de câmbio;
- Especificação e testes de hipóteses entre modelos aninhados.
- 31/03
- 02/04
- 07/04
- 09/04
- 14/04
- 16/04
- 21/04
- 23/04
- 28/04
- 30/04
- 05/05
- 07/05
- 12/05
- 14/05
- 19/05
- 21/05
- 26/05
- 28/05
- 02/06
- 04/06
- 09/06
- 11/06
- 16/06
- 18/06
- 23/06
- 25/06
Links úteis
Avaliações
Trabalho 1
- Função para estimação de beta a partir de X e y. Implementar o método de estimação literal, decomposição de Cholesky e decomposição QR.
- Função para calcular o quadro de análise de variância.
- Função para tabela de estimativas com erro-padrão e IC.
- Função para quadro de anova particionado.
- Função para calcular o valor predito com IC.
- Entregar o código impresso das funções programadas no dia 24/03/14.
## Estima o vetor de parâmetros \beta mycoef <- function(X, y, method){ ... } ## Retorna o quadro de análise de variância corrigido para a média myanova <- function(X, y){ ... } ## Retorna a tabela com erros padrões, t-valor, p-valor e IC para \betas mycoeftable <- function(X, y, conf=0.95){ ... } ## Retorna o quadro de análise de variância particionado para X1 myanovapart <- function(X, y, X1){ ... } ## Retorna o valor predito com IC mypredict <- function(x0, betas, vcov, conf){ ... }
Trabalho 2
- Fazer estudo de simulação para estudar a distribuição amostral dos estimadores e das estatísticas do testes.
- Verificar que
,
, e que
têm distribuição Normal.
- Verificar que
e que
têm distribuição F sob H0 que
.
- Estudar a distribuição da estatística F = QMReg/QMres e comparar com o F anterior.
- Entregar código impresso com gráficos e tabelas que sobre os resultados solicitados no dia 24/03/14.
## Função que retorna estimativas de parâmetros e estatísticas sob uma ## amostra aleatória simulada ao ser executada. mysimula <- function(X, beta, sigma, A, m=beta){ ... } results <- replicate(10000, mysimula)
Trabalho 3
- Programar funções para obter:
- Resíduos ordinários, padronizados e studentizados;
- Valores de alavancagem;
- Distância de Cook;
- DFfits, DFbetas;
- As funções devem receber como argumentos as matrizes X e y e retornas as respectivas medidas;
- Alavancagem
- Resíduos crus
- Resíduos padronizados (ou internamente studentizados)
- Resíduos studentizados (ou externamente studentizados)
- Distância de Cook
- DFfits
- DFbetas
##----------------------------------------------------------------------------- require(car) ##----------------------------------------------------------------------------- ## Dados sobre o preço de leitão (price) de relógios antigos (do avô) em ## função da idade do relógio (age) e do número de potenciais ## compradores (bidders). da <- read.table("http://www.leg.ufpr.br/~walmes/data/business_economics_dataset/EXAMPLES/GFCLOCKA.DAT", header=FALSE) str(da) ## Essa coluna removida é o produto de age*bidders da <- da[,-4] names(da) <- c("age", "bidders", "price") str(da) ##----------------------------------------------------------------------------- ## Dados sobre o salário em função dos anos de experiência de uma ## amostra de trabalhadores sociais. db <- read.table("http://www.leg.ufpr.br/~walmes/data/business_economics_dataset/EXAMPLES/SOCWORK.DAT", header=FALSE) names(db) <- c("yrsexp", "salary") ##-----------------------------------------------------------------------------
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Arquivo em pdf da última avaliação.
http://www.datafilehost.com/d/2817fcc0
Alunas: Isadora, Michele e Renata
Dados e apresentação (Paula, Jessica e Wagner)
http://www.datafilehost.com/d/b19884e6
Slides utilizados no seminário. 03/06/2014 - Daniel; Eduardo; Gabriel
download dos slides em: http://www.datafilehost.com/d/220d8b44
Apresentação do Trabalho Final de Regressão Ana Flávia, Cintia e Damiane
http://www.datafilehost.com/d/75c6f4a8
Trabalho 6 - Isadora, Michele e Renata
http://www.datafilehost.com/d/de417215
Trabalho Eduardo, Daniel , Gabriel http://www.datafilehost.com/d/30690446 http://www.datafilehost.com/d/f5b3addd
trabalho 6
Trabalho 6 - Exercícios do capitulo 35 do livro Statistics for Environmental Engineers
Ana Flávia, Cintia e Damiane
http://www.datafilehost.com/d/28b2c412
Alunos: Jessica Inoue Paula Alessandra Zeizer Dimas Wagner Lopes do Nascimento TRABALHO 5: http://www.datafilehost.com/d/e130f4bb
Trabalho 5 - Exercıcio 6.6 do livro Applied Linear Regression - Isadora Nascimento, Michele Mottin e Renata Ferreira
http://www.datafilehost.com/d/7c6d34ce
Trabalho 4 http://www.datafilehost.com/d/106084c0
Trabalho 5 - Exercıcio 6.13 do livro Applied Linear Regression
Ana Flávia, Cintia e Damiane
http://www.datafilehost.com/d/1acbdc68
Trabalho 4. Exerccicio 6.4 data "twins"
http://www.datafilehost.com/d/f8756d1f
Trabalho 4 - parte 2 Alunos: Paula, Jessica, Wagner http://www.datafilehost.com/d/20fa4b01
TRABALHO 3
http://www.datafilehost.com/d/067d846b
Medidas de Influencia.
http://www.datafilehost.com/d/a99a7cfe
Trabalho 4 http://www.datafilehost.com/d/12da85d5
Trabalho 4 (baseado no trabalho 3) http://www.datafilehost.com/d/e41a9bd5
Trabalho 3
http://www.datafilehost.com/d/ddc7e402
Trabalho 3 - Programar funções
http://www.datafilehost.com/d/9a419c25 arquivo R
http://www.datafilehost.com/d/6972c21e
Trabalho 03 http://www.datafilehost.com/d/c13cab08
Trabalho sobre funções de medidas de influência. http://bit.ly/1iqRiob
Trabalho 3
http://www.datafilehost.com/d/9b1535ac
Trabalho 4 - http://www.datafilehost.com/d/2b2d3e53
Trabalho 04 - Analise de Regressao Linear http://www.datafilehost.com/d/a81681e1
Trabalho 3 - Regressão Linear. ex.: 12.76 Conjunto de dados EBI
http://www.datafilehost.com/d/97703512
Trabalho Regressão
http://www.datafilehost.com/d/fd640c63
http://www.datafilehost.com/d/e24acc98 http://www.datafilehost.com/d/049bbe0a
Trabalho de Regressão 3
http://www.datafilehost.com/d/f9be4272
http://www.datafilehost.com/d/9877f6cb
http://www.datafilehost.com/d/ff544e8d
Trabalho 3 - Regressão
Trabalho 3 - Análise de Regressão Linear http://www.datafilehost.com/d/a021e242
Trabalho 2 - http://www.datafilehost.com/d/1834d01f
http://www.datafilehost.com/d/d02f2da6
Trabalho http://www.datafilehost.com/d/b393c124
Exercício 12.86
[http://bit.ly/1pNGbYC Download]
Trabalho 2 - Análise de Regressão
http://www.datafilehost.com/d/6d29a80a
http://www.datafilehost.com/d/5da1cb38
Trabalho com os dados em arquivo ZIP. http://www.datafilehost.com/d/fb9f01c7
Material não muito extenso mais útil para declaração de modelos no R, entre outros funcionalidades do R para regressão.
http://www.datafilehost.com/d/ae7eb389