<div dir="ltr"><div>Já que estamos falando de correlações espúrias, recomendo dar uma olhada no pacote datasauRus do R. Pra quem manja do assunto, é como o quarteto de Anscombe, mas com muito mais exemplos esdrúxulos. Todas as imagens abaixo possuem eixos x e y com o mesmo valor para a correlação amostral:<br></div><div><br></div><div><img src="cid:ii_klwbr5tr0" alt="datasauRusPlot-1.png" width="496" height="354"><br></div><div><br></div><div>Um ano e meio atrás escrevi um post no meu blog mostrando como podemos usar esse conjunto de dados em aula, para mostrar para os alunos como é importante fazer uma análise exploratória gráfica em nossas análises: <a href="https://marcusnunes.me/posts/correlacoes-e-graficos-de-dispersao/">https://marcusnunes.me/posts/correlacoes-e-graficos-de-dispersao/</a></div><div><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr">--</div><div dir="ltr"><div dir="ltr">Marcus Nunes</div><div dir="ltr">Professor Adjunto</div><div dir="ltr"><div dir="ltr"><a href="https://marcusnunes.me/" target="_blank">https://marcusnunes.me/</a></div></div><div dir="ltr">Universidade Federal do Rio Grande do Norte</div><div dir="ltr">Departamento de Estatística</div><div dir="ltr">Laboratório de Estatística Aplicada - <a href="http://lea.estatistica.ccet.ufrn.br/" target="_blank">http://lea.estatistica.ccet.ufrn.br</a></div><div>Curso de Big Data - <a href="https://introbigdata.org" target="_blank">https://introbigdata.org</a><br></div><div dir="ltr">Aplicações em Shiny - <a href="http://shiny.estatistica.ccet.ufrn.br" target="_blank">http://shiny.estatistica.ccet.ufrn.br</a></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, Mar 5, 2021 at 10:11 AM Basilio de Bragança Pereira <<a href="mailto:basilio@hucff.ufrj.br">basilio@hucff.ufrj.br</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="auto">Sobre assunto correlato sugiro olhar na Wikipédia os dados e gráficos de <div>Anscombe ‘s quartet<br><br><div id="gmail-m_-2973631257447826909AppleMailSignature" dir="ltr">Enviado do meu iPhone</div><div dir="ltr"><br>Em 5 de mar de 2021, à(s) 10:01, Julio Stern <<a href="mailto:jmstern@hotmail.com" target="_blank">jmstern@hotmail.com</a>> escreveu:<br><br></div><blockquote type="cite"><div dir="ltr">
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<span style="margin:0px;font-size:12pt;background-color:rgb(255,255,255)"><span style="margin:0px;font-size:14pt;font-family:Arial,Helvetica,sans-serif">Caros Redistas </span></span></div>
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<span style="margin:0px;font-size:12pt;background-color:rgb(255,255,255)"><span style="margin:0px;font-size:14pt;font-family:Arial,Helvetica,sans-serif">Conversando com colegas de outras areas sobre a diferenca entre Causalidade e Correlacao, </span></span><span style="color:rgb(0,0,0);font-family:Calibri,Helvetica,sans-serif;font-size:12pt"><span style="font-size:14pt;font-family:Arial,Helvetica,sans-serif">principalmente
no contexto de vacinas, tratamentos medicos para Covid, etc. </span></span><span style="color:rgb(0,0,0);font-family:Calibri,Helvetica,sans-serif;font-size:12pt"><span style="font-size:14pt;font-family:Arial,Helvetica,sans-serif">acabei conhecendo o</span></span><span style="color:rgb(0,0,0);font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR"> livro: </span></div>
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<span style="color:rgb(0,0,0);font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR"> </span><span style="color:rgb(0,0,0);font-family:Calibri,sans-serif;font-size:11pt" lang="PT-BR"><span style="font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></div>
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<span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">>>></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Tyler
Vigen (2015).</span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Spurious Correlations.</span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Hachette
Books.<span> </span></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">que tem gráficos fantasticos, com series temporais totalmente desconexas que exibem altíssima correlacao.<span> </span></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">Nao tenho o livro, mas alguns graficos podem ser vistos em<span> </span></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">>>> <a href="https://www.tylervigen.com/spurious-correlations" target="_blank">https://www.tylervigen.com/spurious-correlations</a></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">>>> <a href="https://tylervigen.com/discover" target="_blank">https://tylervigen.com/discover</a></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">Comecei a fazer umas continhas rapidas sobre a probabilidade, p</span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> , </span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">de
obter, em duas series temporais, x(t) e y(t) ,<span> </span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">com dez pontos de abscissa t={1,2, ... 10}</span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">e
ordenada no intervalo [0,1] , uma alta correlação, i.e.,<span> </span></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">p = Pr ( corr ( x(t) , y(t) )<span> </span></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">>=</span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">(1-alpha)
) , para alpha= 0.1</span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">ou</span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">0.05<span> </span></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">ou</span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">0.01</span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">Assumindo nao haver estrutura alguma nas series x(t) e y(t) , o resultado eh muito baixo.<span> </span></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">Mesmo considerando uma enorme biblioteca de graficos aleatorios, nao da...<span> </span></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">Parece ser necessario assumir "a priori" a existência de alguma "estrutura intrinseca de associacao" entre os pontos de cada uma das series temporais,
por exemplo, alguma estrutura de auto-correlacao.<span> </span></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">Antes de sair por ai tentando reinventar a roda, melhor perguntar a quem sabe...<span> </span></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">Alguem ja deve ter pensado neste problema!<span> </span></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">Alguma
ideia de como modela-lo?<span> </span></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">Abraco a todos e tudo de bom,<span> </span></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif" lang="PT-BR">---Julio Stern<span> </span></span><span style="margin:0px" lang="PT-BR"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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