{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Analysis of the risk of failure of the O-rings on the Challenger shuttle"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On January 27, 1986, the day before the takeoff of the shuttle _Challenger_, had\n",
"a three-hour teleconference was held between \n",
"Morton Thiokol (the manufacturer of one of the engines) and NASA. The\n",
"discussion focused on the consequences of the\n",
"temperature at take-off of 31°F (just below\n",
"0°C) for the success of the flight and in particular on the performance of the\n",
"O-rings used in the engines. Indeed, no test\n",
"had been performed at this temperature.\n",
"\n",
"The following study takes up some of the analyses carried out that\n",
"night with the objective of assessing the potential influence of\n",
"the temperature and pressure to which the O-rings are subjected\n",
"on their probability of malfunction. Our starting point is \n",
"the results of the experiments carried out by NASA engineers\n",
"during the six years preceding the launch of the shuttle\n",
"Challenger."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Loading the data\n",
"We start by loading this data:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Collecting seaborn\n",
" Downloading seaborn-0.11.2-py3-none-any.whl (292 kB)\n",
"\u001b[K |████████████████████████████████| 292 kB 5.6 MB/s eta 0:00:01\n",
"\u001b[?25hCollecting pandas>=0.23\n",
" Downloading pandas-1.1.5-cp36-cp36m-manylinux1_x86_64.whl (9.5 MB)\n",
"\u001b[K |████████████████████████████████| 9.5 MB 46.2 MB/s eta 0:00:01\n",
"\u001b[?25hRequirement already satisfied, skipping upgrade: numpy>=1.15 in /opt/conda/lib/python3.6/site-packages (from seaborn) (1.15.2)\n",
"Requirement already satisfied, skipping upgrade: scipy>=1.0 in /opt/conda/lib/python3.6/site-packages (from seaborn) (1.1.0)\n",
"Requirement already satisfied, skipping upgrade: matplotlib>=2.2 in /opt/conda/lib/python3.6/site-packages (from seaborn) (2.2.3)\n",
"Requirement already satisfied, skipping upgrade: pytz>=2017.2 in /opt/conda/lib/python3.6/site-packages (from pandas>=0.23->seaborn) (2019.3)\n",
"Requirement already satisfied, skipping upgrade: python-dateutil>=2.7.3 in /opt/conda/lib/python3.6/site-packages (from pandas>=0.23->seaborn) (2.8.1)\n",
"Requirement already satisfied, skipping upgrade: cycler>=0.10 in /opt/conda/lib/python3.6/site-packages (from matplotlib>=2.2->seaborn) (0.10.0)\n",
"Requirement already satisfied, skipping upgrade: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /opt/conda/lib/python3.6/site-packages (from matplotlib>=2.2->seaborn) (2.4.6)\n",
"Requirement already satisfied, skipping upgrade: six>=1.10 in /opt/conda/lib/python3.6/site-packages (from matplotlib>=2.2->seaborn) (1.14.0)\n",
"Requirement already satisfied, skipping upgrade: kiwisolver>=1.0.1 in /opt/conda/lib/python3.6/site-packages (from matplotlib>=2.2->seaborn) (1.1.0)\n",
"Requirement already satisfied, skipping upgrade: setuptools in /opt/conda/lib/python3.6/site-packages (from kiwisolver>=1.0.1->matplotlib>=2.2->seaborn) (45.2.0.post20200209)\n",
"\u001b[31mERROR: pandas 1.1.5 has requirement numpy>=1.15.4, but you'll have numpy 1.15.2 which is incompatible.\u001b[0m\n",
"Installing collected packages: pandas, seaborn\n",
" Attempting uninstall: pandas\n",
" Found existing installation: pandas 0.22.0\n",
" Uninstalling pandas-0.22.0:\n",
" Successfully uninstalled pandas-0.22.0\n",
" Attempting uninstall: seaborn\n",
" Found existing installation: seaborn 0.8.1\n",
" Uninstalling seaborn-0.8.1:\n",
" Successfully uninstalled seaborn-0.8.1\n",
"Successfully installed pandas-1.1.5 seaborn-0.11.2\n"
]
}
],
"source": [
"!pip install seaborn --upgrade"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Collecting numpy\n",
" Downloading numpy-1.19.5-cp36-cp36m-manylinux2010_x86_64.whl (14.8 MB)\n",
"\u001b[K |████████████████████████████████| 14.8 MB 5.6 MB/s eta 0:00:01\n",
"\u001b[?25hInstalling collected packages: numpy\n",
" Attempting uninstall: numpy\n",
" Found existing installation: numpy 1.15.2\n",
" Uninstalling numpy-1.15.2:\n",
" Successfully uninstalled numpy-1.15.2\n",
"Successfully installed numpy-1.19.5\n"
]
}
],
"source": [
"!pip install numpy --upgrade"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import pandas as pd\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"\n",
"# Read data from CSV file into a Pandas DataFrame\n",
"df = pd.read_csv(\"shuttle.csv\")\n",
"\n",
"# Extracting data for plotting\n",
"x = df['Temperature']\n",
"y = df['Pressure']\n",
"z = df['Malfunction']\n",
"\n",
"# Create a figure and a 3D Axes\n",
"fig = plt.figure(figsize=(10, 8))\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"\n",
"# Scatter plot\n",
"sc = ax.scatter(x, y, z, c=z, cmap='viridis', s=100, alpha=0.7)\n",
"\n",
"# Labeling axes\n",
"ax.set_xlabel('Temperature')\n",
"ax.set_ylabel('Pressure')\n",
"ax.set_zlabel('Malfunction')\n",
"\n",
"# Adding color bar which maps malfunction values to colors\n",
"cbar = fig.colorbar(sc, orientation='vertical')\n",
"cbar.set_label('Malfunction')\n",
"\n",
"# Title\n",
"plt.title('3D Scatter Plot of Temperature, Pressure, and Malfunction')\n",
"\n",
"# Show plot\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Requirement already satisfied: statsmodels in /opt/conda/lib/python3.6/site-packages (0.9.0)\n",
"Note: you may need to restart the kernel to use updated packages.\n"
]
}
],
"source": [
"pip install statsmodels"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimization terminated successfully.\n",
" Current function value: 0.666457\n",
" Iterations 6\n"
]
},
{
"data": {
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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import pandas as pd\n",
"import numpy as np\n",
"import statsmodels.api as sm\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"\n",
"# Read data from CSV file into a Pandas DataFrame\n",
"df = pd.read_csv(\"shuttle.csv\")\n",
"\n",
"# Extracting data for plotting\n",
"x = df['Temperature']\n",
"y = df['Pressure']\n",
"z = df['Malfunction']\n",
"\n",
"# Poisson regression model\n",
"# Add constant term for the intercept\n",
"X = sm.add_constant(df[['Temperature', 'Pressure']])\n",
"\n",
"# Fit Poisson regression model\n",
"model = sm.Poisson(z, X)\n",
"results = model.fit()\n",
"\n",
"# Generate predictions from the model\n",
"predictions = results.predict(X)\n",
"\n",
"# Create a figure and a 3D Axes\n",
"fig = plt.figure(figsize=(10, 8))\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"\n",
"# Scatter plot of actual data\n",
"sc = ax.scatter(x, y, z, c=z, cmap='viridis', s=100, alpha=0.7, label='Actual Malfunction')\n",
"\n",
"# Plot the prediction line\n",
"ax.plot_trisurf(x, y, predictions, color='b', alpha=0.3, label='Prediction Line')\n",
"\n",
"# Labeling axes\n",
"ax.set_xlabel('Temperature')\n",
"ax.set_ylabel('Pressure')\n",
"ax.set_zlabel('Malfunction')\n",
"\n",
"# Adding color bar which maps malfunction values to colors\n",
"cbar = fig.colorbar(sc, orientation='vertical')\n",
"cbar.set_label('Malfunction')\n",
"\n",
"# Annotation for the scatter plot\n",
"ax.text2D(0.05, 0.95, \"Actual Malfunction\", transform=ax.transAxes, fontsize=12, color='blue')\n",
"ax.text2D(0.05, 0.90, \"Prediction Line\", transform=ax.transAxes, fontsize=12, color='black')\n",
"\n",
"# Title\n",
"plt.title('3D Scatter Plot of Temperature, Pressure, and Malfunction with Poisson Regression')\n",
"\n",
"# Show plot\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The data set shows us the date of each test, the number of O-rings (there are 6 on the main launcher), the temperature (in Fahrenheit) and pressure (in psi), and finally the number of identified malfunctions."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0 1 2]\n"
]
}
],
"source": [
"# Check the unique values in the 'Malfunction' column\n",
"print(data['Malfunction'].unique())"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Predict the number of malfunctions for a range of temperatures\n",
"#temperatures = np.linspace(data['Temperature'].min(), data['Temperature'].max(), 100)\n",
"temperatures = np.linspace(30, 90, 121)\n",
"X_new = sm.add_constant(pd.DataFrame({'Temperature': temperatures}))\n",
"predictions = model.predict(X_new)\n",
"\n",
"# Plot the predicted number of malfunctions\n",
"plt.figure(figsize=(10, 6))\n",
"plt.plot(temperatures, predictions, label='Predicted Number of Malfunctions')\n",
"plt.scatter(data['Temperature'], data['Malfunction'], color='red', label='Actual Data') #real data\n",
"plt.xlabel('Temperature')\n",
"plt.ylabel('Number of Malfunctions')\n",
"plt.title('Predicted Number of O-ring Malfunctions vs Temperature')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Generalized Linear Model Regression Results \n",
"==============================================================================\n",
"Dep. Variable: Malfunction No. Observations: 23\n",
"Model: GLM Df Residuals: 21\n",
"Model Family: Poisson Df Model: 1\n",
"Link Function: log Scale: 1.0000\n",
"Method: IRLS Log-Likelihood: -16.031\n",
"Date: Thu, 27 Jun 2024 Deviance: 16.834\n",
"Time: 08:22:11 Pearson chi2: 28.2\n",
"No. Iterations: 5 Covariance Type: nonrobust\n",
"===============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"-------------------------------------------------------------------------------\n",
"const 5.9691 2.763 2.161 0.031 0.554 11.384\n",
"Temperature -0.1034 0.043 -2.405 0.016 -0.188 -0.019\n",
"===============================================================================\n"
]
}
],
"source": [
"# Prepare the data for Poisson regression\n",
"X = data[['Temperature']]\n",
"X = sm.add_constant(X) # Adds a constant term to the predictor\n",
"y = data['Malfunction']\n",
"\n",
"# Fit the Poisson regression model\n",
"poisson_model = sm.GLM(y, X, family=sm.families.Poisson())\n",
"result = poisson_model.fit()\n",
"\n",
"# Print the summary of the model\n",
"print(result.summary())"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"31.0\n",
"15.846052720743854\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Predict the number of malfunctions for a range of temperatures\n",
"#temperatures = np.linspace(data['Temperature'].min(), data['Temperature'].max(), 100)\n",
"temperatures = np.linspace(30, 90, 61)\n",
"X_new = sm.add_constant(pd.DataFrame({'Temperature': temperatures}))\n",
"predictions = result.predict(X_new)\n",
"\n",
"print(temperatures[1])\n",
"print(predictions[1])\n",
"\n",
"# Plot the predicted number of malfunctions\n",
"plt.figure(figsize=(10, 6))\n",
"plt.plot(temperatures, predictions, label='Predicted Number of Malfunctions')\n",
"plt.scatter(data['Temperature'], data['Malfunction'], color='red', label='Actual Data') #real data\n",
"plt.xlabel('Temperature')\n",
"plt.ylabel('Number of Malfunctions')\n",
"plt.title('Predicted Number of O-ring Malfunctions vs Temperature')\n",
"plt.legend()\n",
"plt.show()\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Graphical inspection\n",
"Flights without incidents do not provide any information\n",
"on the influence of temperature or pressure on malfunction.\n",
"We thus focus on the experiments in which at least one O-ring\n",
"was defective."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
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Malfunction
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" \n",
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\n",
"
1
\n",
"
11/12/81
\n",
"
6
\n",
"
70
\n",
"
50
\n",
"
1
\n",
"
\n",
"
\n",
"
8
\n",
"
2/03/84
\n",
"
6
\n",
"
57
\n",
"
200
\n",
"
1
\n",
"
\n",
"
\n",
"
9
\n",
"
4/06/84
\n",
"
6
\n",
"
63
\n",
"
200
\n",
"
1
\n",
"
\n",
"
\n",
"
10
\n",
"
8/30/84
\n",
"
6
\n",
"
70
\n",
"
200
\n",
"
1
\n",
"
\n",
"
\n",
"
13
\n",
"
1/24/85
\n",
"
6
\n",
"
53
\n",
"
200
\n",
"
2
\n",
"
\n",
"
\n",
"
20
\n",
"
10/30/85
\n",
"
6
\n",
"
75
\n",
"
200
\n",
"
2
\n",
"
\n",
"
\n",
"
22
\n",
"
1/12/86
\n",
"
6
\n",
"
58
\n",
"
200
\n",
"
1
\n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" Date Count Temperature Pressure Malfunction\n",
"1 11/12/81 6 70 50 1\n",
"8 2/03/84 6 57 200 1\n",
"9 4/06/84 6 63 200 1\n",
"10 8/30/84 6 70 200 1\n",
"13 1/24/85 6 53 200 2\n",
"20 10/30/85 6 75 200 2\n",
"22 1/12/86 6 58 200 1"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data = data[data.Malfunction>0]\n",
"data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have a high temperature variability but\n",
"the pressure is almost always 200, which should\n",
"simplify the analysis.\n",
"\n",
"How does the frequency of failure vary with temperature?"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"pd.set_option('mode.chained_assignment',None) # this removes a useless warning from pandas\n",
"import matplotlib.pyplot as plt\n",
"\n",
"data[\"Frequency\"]=data.Malfunction/data.Count\n",
"data.plot(x=\"Temperature\",y=\"Frequency\",kind=\"scatter\",ylim=[0,1])\n",
"plt.grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"At first glance, the dependence does not look very important, but let's try to\n",
"estimate the impact of temperature $t$ on the probability of O-ring malfunction."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimation of the temperature influence\n",
"\n",
"Suppose that each of the six O-rings is damaged with the same\n",
"probability and independently of the others and that this probability\n",
"depends only on the temperature. If $p(t)$ is this probability, the\n",
"number $D$ of malfunctioning O-rings during a flight at\n",
"temperature $t$ follows a binomial law with parameters $n=6$ and\n",
"$p=p(t)$. To link $p(t)$ to $t$, we will therefore perform a\n",
"logistic regression."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"
Generalized Linear Model Regression Results
\n",
"
\n",
"
Dep. Variable:
Frequency
No. Observations:
7
\n",
"
\n",
"
\n",
"
Model:
GLM
Df Residuals:
5
\n",
"
\n",
"
\n",
"
Model Family:
Binomial
Df Model:
1
\n",
"
\n",
"
\n",
"
Link Function:
logit
Scale:
1.0000
\n",
"
\n",
"
\n",
"
Method:
IRLS
Log-Likelihood:
-2.5250
\n",
"
\n",
"
\n",
"
Date:
Sat, 13 Apr 2019
Deviance:
0.22231
\n",
"
\n",
"
\n",
"
Time:
19:12:05
Pearson chi2:
0.236
\n",
"
\n",
"
\n",
"
No. Iterations:
4
Covariance Type:
nonrobust
\n",
"
\n",
"
\n",
"
\n",
"
\n",
"
coef
std err
z
P>|z|
[0.025
0.975]
\n",
"
\n",
"
\n",
"
Intercept
-1.3895
7.828
-0.178
0.859
-16.732
13.953
\n",
"
\n",
"
\n",
"
Temperature
0.0014
0.122
0.012
0.991
-0.238
0.240
\n",
"
\n",
"
"
],
"text/plain": [
"\n",
"\"\"\"\n",
" Generalized Linear Model Regression Results \n",
"==============================================================================\n",
"Dep. Variable: Frequency No. Observations: 7\n",
"Model: GLM Df Residuals: 5\n",
"Model Family: Binomial Df Model: 1\n",
"Link Function: logit Scale: 1.0000\n",
"Method: IRLS Log-Likelihood: -2.5250\n",
"Date: Sat, 13 Apr 2019 Deviance: 0.22231\n",
"Time: 19:12:05 Pearson chi2: 0.236\n",
"No. Iterations: 4 Covariance Type: nonrobust\n",
"===============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"-------------------------------------------------------------------------------\n",
"Intercept -1.3895 7.828 -0.178 0.859 -16.732 13.953\n",
"Temperature 0.0014 0.122 0.012 0.991 -0.238 0.240\n",
"===============================================================================\n",
"\"\"\""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import statsmodels.api as sm\n",
"\n",
"data[\"Success\"]=data.Count-data.Malfunction\n",
"data[\"Intercept\"]=1\n",
"\n",
"logmodel=sm.GLM(data['Frequency'], data[['Intercept','Temperature']], family=sm.families.Binomial(sm.families.links.logit)).fit()\n",
"\n",
"logmodel.summary()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The most likely estimator of the temperature parameter is 0.0014\n",
"and the standard error of this estimator is 0.122, in other words we\n",
"cannot distinguish any particular impact and we must take our\n",
"estimates with caution."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimation of the probability of O-ring malfunction\n",
"\n",
"The expected temperature on the take-off day is 31°F. Let's try to\n",
"estimate the probability of O-ring malfunction at\n",
"this temperature from the model we just built:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"data_pred = pd.DataFrame({'Temperature': np.linspace(start=30, stop=90, num=121), 'Intercept': 1})\n",
"data_pred['Frequency'] = logmodel.predict(data_pred[['Intercept','Temperature']])\n",
"data_pred.plot(x=\"Temperature\",y=\"Frequency\",kind=\"line\",ylim=[0,1])\n",
"plt.scatter(x=data[\"Temperature\"],y=data[\"Frequency\"])\n",
"plt.grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {
"hideCode": false,
"hidePrompt": false,
"scrolled": true
},
"source": [
"As expected from the initial data, the\n",
"temperature has no significant impact on the probability of failure of the\n",
"O-rings. It will be about 0.2, as in the tests\n",
"where we had a failure of at least one joint. Let's get back\n",
"to the initial dataset to estimate the probability of failure:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.06521739130434782\n"
]
}
],
"source": [
"data = pd.read_csv(\"shuttle.csv\")\n",
"print(np.sum(data.Malfunction)/np.sum(data.Count))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This probability is thus about $p=0.065$. Knowing that there is\n",
"a primary and a secondary O-ring on each of the three parts of the\n",
"launcher, the probability of failure of both joints of a launcher\n",
"is $p^2 \\approx 0.00425$. The probability of failure of any one of the\n",
"launchers is $1-(1-p^2)^3 \\approx 1.2%$. That would really be\n",
"bad luck.... Everything is under control, so the takeoff can happen\n",
"tomorrow as planned.\n",
"\n",
"But the next day, the Challenger shuttle exploded and took away\n",
"with her the seven crew members. The public was shocked and in\n",
"the subsequent investigation, the reliability of the\n",
"O-rings was questioned. Beyond the internal communication problems\n",
"of NASA, which have a lot to do with this fiasco, the previous analysis\n",
"includes (at least) a small problem.... Can you find it?\n",
"You are free to modify this analysis and to look at this dataset\n",
"from all angles in order to to explain what's wrong."
]
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