<p>The maximum likelyhood estimator of the intercept and of Temperature are thus <spanclass="math">$\hat{\alpha}=5.085$</span> and <spanclass="math">$\hat{\beta}=-0.116$</span>.</p>
<p>The maximum likelyhood estimator of the intercept and of Temperature are thus <spanclass="math">$\hat{\alpha}=5.085$</span> and <spanclass="math">$\hat{\beta}=-0.116$</span>.</p>
<p>This corresponds to the values from the article of Dalal et al. The standard errors are <spanclass="math">$s_{\hat{\alpha}} = 7.477$</span> and <spanclass="math">$s_{\hat{\beta}} = 0.115$</span>, which is different from the <spanclass="math">$3.052$</span> and <spanclass="math">$0.047$</span> reported by Dallal et al. The deviance is <spanclass="math">$G^2 = 3.014$</span> with 22 degrees of freedom.</p>
<p>This corresponds to the values from the article of Dalal et al. The standard errors are <spanclass="math">$s_{\hat{\alpha}} = 7.477$</span> and <spanclass="math">$s_{\hat{\beta}} = 0.115$</span>, which is different from the <spanclass="math">$3.052$</span> and <spanclass="math">$0.047$</span> reported by Dallal et al.</p>
<p>I cannot find any value similar to the Goodness of fit (<spanclass="math">$G^2=18.086$</span>) reported by Dalal et al. However, the number of degrees of freedom is similar to theirs (21).</p>
<p>The deviance is <spanclass="math">$G^2 = 3.014$</span> with 22 degrees of freedom. I cannot find any value similar to the Goodness of fitreported by Dalal <em>et al.</em>(<spanclass="math">$G^2=18.086$</span>). However, the number of degrees of freedom is different but at least similar to theirs (21).</p>
<p>There seems to be something wrong. Oh I know, I haven't indicated that my observations are actually the result of 6 observations for each rocket launch. The correct way to do this would be to weight the data using the <code>Count</code> column. Since I don't know how to do that with the <ahref="https://github.com/JuliaStats/GLM.jl">GLM</a> package I'm using, I will simply duplicate the data:</p>
<p>There seems to be something wrong. Oh I know, I haven't indicated that my observations are actually the result of 6 observations for each rocket launch. Let's indicate these weights (since the weights are always the same throughout all experiments, it does not change the estimates of the fit but it does influence de variance estimate).</p>
<p>Good, now I have recovered the asymptotic standard errors <spanclass="math">$s_{\hat{\alpha}} = 3.052$</span> and <spanclass="math">$s_{\hat{\beta}} = 0.047$</span>,</p>
<p>Good, now I have recovered the asymptotic standard errors <spanclass="math">$s_{\hat{\alpha}} = 3.052$</span> and <spanclass="math">$s_{\hat{\beta}} = 0.047$</span>,</p>
<p>The Goodness of fit (Deviance) indicated for this model is <spanclass="math">$G^2 = 18.086$</span> with 137 degrees of freedom. Now <spanclass="math">$G^2$</span> is in good accordance to the results of the Dalal <em>et al.</em> article, but the number of degrees of freedom is 6 times larger than i should, due to my tampering of the data to duplicate them instead of weighting them.</p>
<p>The Goodness of fit (Deviance) indicated for this model is <spanclass="math">$G^2 = 18.086$</span> with 137 degrees of freedom. Now <spanclass="math">$G^2$</span> is in good accordance to the results of the Dalal <em>et al.</em> article, but the number of degrees of freedom is approximately 6 times larger than that of Dalal <em>et al</em>. Note that, even removing this factor (which is probably due to the way the number of residual degrees of freedom are defined in both libraries in the presence of weights), the values are similar but still differ by 9%.</p>
<h1>Predicting failure probability</h1>
<h1>Predicting failure probability</h1>
<p>The temperature when launching the shuttle was 31°F. Let's try to estimate the failure probability for such temperature using our model:</p>
<p>The temperature when launching the shuttle was 31°F. Let's try to estimate the failure probability for such temperature using our model:</p>
