http://www.mysolutions.tecnico.ulisboa.pt//~mysolutions.daemon/wiki/index.php?title=Regress%C3%A3o_linear_simples_-_estimativa_de_m%C3%ADnimos_quadrados_de_%5C(%5Cbeta_1%5C)&feed=atom&action=history
Regressão linear simples - estimativa de mínimos quadrados de \(\beta 1\) - Histórico de revisões
2024-03-29T01:20:45Z
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Ist178052 em 11h29min de 27 de maio de 2017
2017-05-27T11:29:12Z
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Para obter o zip que contém as instâncias deste exercício clique aqui[https://drive.tecnico.ulisboa.pt/download/<del class="diffchange diffchange-inline">1414448694690106</del>/<del class="diffchange diffchange-inline">instanciasRLSEstBeta1</del>.zip]</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Para obter o zip que contém as instâncias deste exercício clique aqui[https://drive.tecnico.ulisboa.pt/download/<ins class="diffchange diffchange-inline">288548787894521</ins>/<ins class="diffchange diffchange-inline">Ficha6P3RLSBeta1</ins>.zip]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Se deseja obter o código fonte que gera os exercícios contacte miguel.dziergwa@ist.utl.pt</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Se deseja obter o código fonte que gera os exercícios contacte miguel.dziergwa@ist.utl.pt</div></td></tr>
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Ist178052
http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Regress%C3%A3o_linear_simples_-_estimativa_de_m%C3%ADnimos_quadrados_de_%5C(%5Cbeta_1%5C)&diff=3298&oldid=prev
Ist178052 em 11h25min de 27 de maio de 2017
2017-05-27T11:25:25Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></div></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Num processo de fabrico suspeita-se que o número de artigos defeituosos produzidos por uma máquina \(Y\) dependa da velocidade a que essa mesma máquina está a operar \(x\).</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Num processo de fabrico suspeita-se que o número de artigos defeituosos produzidos por uma máquina \(Y\) dependa da velocidade a que essa mesma máquina está a operar \(x\). Abaixo encontram-se \(<ins class="diffchange diffchange-inline">11</ins>\) resultados referentes <ins class="diffchange diffchange-inline">à </ins>velocidade e ao <ins class="diffchange diffchange-inline">número </ins>de associado de defeituosos:</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">%</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Abaixo encontram-se \(<del class="diffchange diffchange-inline">10</del>\) resultados referentes <del class="diffchange diffchange-inline">\`a </del>velocidade e ao <del class="diffchange diffchange-inline">n\'umero </del>de associado de defeituosos:</div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\(\pmb{\sum_{i=1}^{<del class="diffchange diffchange-inline">10</del>}x_i}\) = <del class="diffchange diffchange-inline">2908 </del>, \(\pmb{\sum_{i=1}^{<del class="diffchange diffchange-inline">10</del>}x_i^2}\) = <del class="diffchange diffchange-inline">873570 </del>, \(\pmb{\sum_{i=1}^{<del class="diffchange diffchange-inline">10</del>}y_i}\) = <del class="diffchange diffchange-inline">451 </del>, \(\pmb{\sum_{i=1}^{<del class="diffchange diffchange-inline">10</del>}y_i^2}\) = <del class="diffchange diffchange-inline">23967 </del>, \(\pmb{\sum_{i=1}^{<del class="diffchange diffchange-inline">10</del>}x_i \, y_i}\) = <del class="diffchange diffchange-inline">135777</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\(\pmb{\sum_{i=1}^{<ins class="diffchange diffchange-inline">11</ins>}x_i}\) = <ins class="diffchange diffchange-inline">3563 </ins>, \(\pmb{\sum_{i=1}^{<ins class="diffchange diffchange-inline">11</ins>}x_i^2}\) = <ins class="diffchange diffchange-inline">1184237 </ins>, \(\pmb{\sum_{i=1}^{<ins class="diffchange diffchange-inline">11</ins>}y_i}\) = <ins class="diffchange diffchange-inline">588 </ins>, \(\pmb{\sum_{i=1}^{<ins class="diffchange diffchange-inline">11</ins>}y_i^2}\) = <ins class="diffchange diffchange-inline">33362 </ins>, \(\pmb{\sum_{i=1}^{<ins class="diffchange diffchange-inline">11</ins>}x_i \, y_i}\) = <ins class="diffchange diffchange-inline">194499</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Admitindo a validade do modelo de regressão linear simples, a estimativa de mínimos quadrados de \(\beta_1\), \(\hat\beta_1\), é igual a:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Admitindo a validade do modelo de regressão linear simples, a estimativa de mínimos quadrados de \(\beta_1\), \(\hat\beta_1\), é igual a:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>A) \(0.<del class="diffchange diffchange-inline">1657</del>\)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>A) \(0.<ins class="diffchange diffchange-inline">1340</ins>\)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>B) \(<del class="diffchange diffchange-inline">1</del>.<del class="diffchange diffchange-inline">7705</del>\)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>B) \(<ins class="diffchange diffchange-inline">0</ins>.<ins class="diffchange diffchange-inline">4813</ins>\)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>C) \(<del class="diffchange diffchange-inline">2</del>.<del class="diffchange diffchange-inline">2402</del>\)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>C) \(<ins class="diffchange diffchange-inline">-0</ins>.<ins class="diffchange diffchange-inline">1058</ins>\)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>D) \(<del class="diffchange diffchange-inline">2</del>.<del class="diffchange diffchange-inline">2884</del>\)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>D) \(<ins class="diffchange diffchange-inline">-0</ins>.<ins class="diffchange diffchange-inline">2729</ins>\)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
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Ist178052
http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Regress%C3%A3o_linear_simples_-_estimativa_de_m%C3%ADnimos_quadrados_de_%5C(%5Cbeta_1%5C)&diff=3294&oldid=prev
Ist178052: Criou a página com "<div class="toccolours mw-collapsible mw-collapsed" style="width:420px"> '''Metadata''' <div class="mw-collapsible-content"> *CONTEXTO : Primeiro ciclo universitário *AREA:..."
2017-05-27T11:19:55Z
<p>Criou a página com "<div class="toccolours mw-collapsible mw-collapsed" style="width:420px"> '''Metadata''' <div class="mw-collapsible-content"> *CONTEXTO : Primeiro ciclo universitário *AREA:..."</p>
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'''Metadata'''<br />
<div class="mw-collapsible-content"><br />
*CONTEXTO : Primeiro ciclo universitário<br />
*AREA: Matemática<br />
*DISCIPLINA: Probabilidades e Estatística<br />
*ANO: 2<br />
*LINGUA: pt<br />
*AUTOR: Equipa de Probabilidades e Estatística<br />
*MATERIA PRINCIPAL: Introdução à regressão linear simples<br />
*DESCRICAO: Regressão linear simples - estimativa de mínimos quadrados de \(\beta_1\)<br />
*DIFICULDADE: *<br />
*TEMPO MEDIO DE RESOLUCAO: 5 min<br />
*TEMPO MAXIMO DE RESOLUCAO: 10 min<br />
*PALAVRAS CHAVE: regressão linear simples, estimativa de mínimos quadrados de \(\beta_1\) <br />
</div><br />
</div><br />
<br />
Num processo de fabrico suspeita-se que o número de artigos defeituosos produzidos por uma máquina \(Y\) dependa da velocidade a que essa mesma máquina está a operar \(x\).<br />
%<br />
Abaixo encontram-se \(10\) resultados referentes \`a velocidade e ao n\'umero de associado de defeituosos:<br />
<br />
\(\pmb{\sum_{i=1}^{10}x_i}\) = 2908 , \(\pmb{\sum_{i=1}^{10}x_i^2}\) = 873570 , \(\pmb{\sum_{i=1}^{10}y_i}\) = 451 , \(\pmb{\sum_{i=1}^{10}y_i^2}\) = 23967 , \(\pmb{\sum_{i=1}^{10}x_i \, y_i}\) = 135777<br />
<br />
Admitindo a validade do modelo de regressão linear simples, a estimativa de mínimos quadrados de \(\beta_1\), \(\hat\beta_1\), é igual a:<br />
<br />
A) \(0.1657\)<br />
<br />
B) \(1.7705\)<br />
<br />
C) \(2.2402\)<br />
<br />
D) \(2.2884\)<br />
<br />
<br />
Para obter o zip que contém as instâncias deste exercício clique aqui[https://drive.tecnico.ulisboa.pt/download/1414448694690106/instanciasRLSEstBeta1.zip]<br />
<br />
Se deseja obter o código fonte que gera os exercícios contacte miguel.dziergwa@ist.utl.pt</div>
Ist178052