"In this document we reperform some of the analysis provided in \n",
"*Risk Analysis of the Space Shuttle: Pre-Challenger Prediction of Failure* by *Siddhartha R. Dalal, Edward B. Fowlkes, Bruce Hoadley* published in *Journal of the American Statistical Association*, Vol. 84, No. 408 (Dec., 1989), pp. 945-957 and available at http://www.jstor.org/stable/2290069. \n",
"\n",
"On the fourth page of this article, they indicate that the maximum likelihood estimates of the logistic regression using only temperature are: $\\hat{\\alpha}=5.085$ and $\\hat{\\beta}=-0.1156$ and their asymptotic standard errors are $s_{\\hat{\\alpha}}=3.052$ and $s_{\\hat{\\beta}}=0.047$. The Goodness of fit indicated for this model was $G^2=18.086$ with 21 degrees of freedom. Our goal is to reproduce the computation behind these values and the Figure 4 of this article, possibly in a nicer looking way."
"On the fourth page of this article, they indicate that the maximum likelihood estimates of the logistic regression using only temperature are: $\\hat{\\alpha}$ = **5.085** and $\\hat{\\beta}$ = **-0.1156** and their asymptotic standard errors are $s_{\\hat{\\alpha}}$ = **3.052** and $s_{\\hat{\\beta}}$ = **0.047**. The Goodness of fit indicated for this model was $G^2$ = **18.086** with **21** degrees of freedom. Our goal is to reproduce the computation behind these values and the Figure 4 of this article, possibly in a nicer looking way."
]
},
{
...
...
@@ -484,7 +484,7 @@
"source": [
"## Logistic regression\n",
"\n",
"Let's assume O-rings indpendently fail with the same probability which solely depends on temperature. A logistic regression should allow us to estimate the influence of temperature."
"Let's assume O-rings independently fail with the same probability which solely depends on temperature. A logistic regression should allow us to estimate the influence of temperature."
]
},
{
...
...
@@ -576,8 +576,8 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"The maximum likelyhood estimator of the intercept and of Temperature are thus $\\hat{\\alpha}=5.0849$ and $\\hat{\\beta}=-0.1156$. This **corresponds** to the values from the article of Dalal et al. The standard errors are $s_{\\hat{\\alpha}} = 7.477$ and $s_{\\hat{\\beta}} = 0.115$, which is **different** from the $3.052$ and $0.04702$ reported by Dallal et al. The deviance is $3.01444$ with 21 degrees of freedom. I cannot find any value similar to the Goodness of fit ($G^2=18.086$) reported by Dalal et al.\n",
"**I have therefore managed to partially replicate the results of the Dalal et al. article**."
"The maximum likelyhood estimator of the intercept and of Temperature are thus $\\hat{\\alpha}$ = **5.0849** and $\\hat{\\beta}$ = **-0.1156**. This **corresponds** to the values from the article of Dalal *et al.* The standard errors are $s_{\\hat{\\alpha}}$ = **7.477** and $s_{\\hat{\\beta}}$ = **0.115**, which is **different** from the ***3.052*** and ***0.04702*** reported by Dallal *et al.* The deviance is **3.01444** with **21** degrees of freedom. I cannot find any value similar to the Goodness of fit ($G^2$ = ***18.086***) reported by Dalal *et al.*\n",
"**I have therefore managed to partially replicate the results of the Dalal *et al.* article**."
]
},
{
...
...
@@ -585,7 +585,7 @@
"metadata": {},
"source": [
"## Predicting failure probability\n",
"The temperature when launching the shuttle was 31°F. Let's try to estimate the failure probability for such temperature using our model.:"
"The temperature when launching the shuttle was 31°F. Let's try to estimate the failure probability for such temperature using our model:"
]
},
{
...
...
@@ -621,7 +621,7 @@
"scrolled": true
},
"source": [
"This figure is very similar to the Figure 4 of Dalal et al. **I have managed to replicate the Figure 4 of the Dalal et al. article.**"
"This figure is very similar to the Figure 4 of Dalal *et al.* **I have managed to replicate the Figure 4 of the Dalal *et al.* article.**"
