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raov5/What caused the Challenger disaster?.ipynb

Created October 27, 2017 01:42
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The motivation for this notebook is to examine the reasons behind the explosion of the USA Space Shuttle Challenger on 28 January, 1986. Let's dive in!
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What caused the Challenger disaster?.ipynb
{
"cells": [
{
"cell_type": "markdown",
"source": "# What caused the Challenger disaster?",
"metadata": {
"collapsed": true
}
},
{
"cell_type": "markdown",
"source": "Analysis by Venky Rao [email protected]",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "## Background",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "Space shuttle Challenger was the second orbiter (after Columbia) of the U.S. space agency, NASA's space shuttle program. The Space Shuttle orbiter was the reusable spaceplane component of the Space Shuttle program. Operated by NASA, this vehicle could carry astronauts and payloads into low Earth orbit, perform in-space operations, then re-enter the atmosphere and land as a glider, returning its crew and any on-board payload to the Earth. Challenger launched and landed nine times before exploding and breaking apart 73 seconds into its tenth mission, on January 28, 1986, resulting in the death of all seven crew members, including a civilian school teacher. (Source: Wikipedia)\n\nAn investigation ensued into the reliability of the shuttle's propulsion system. The explosion was eventually traced to the failure of one of the three field joints on one of the two solid booster rockets. Each of these six field joints includes two O-rings, designated as primary and secondary, which fail when phenomena called erosion and blowby both occur. To better understand the relationship between failure and physical conditions experieced (temperature and pressure), a dataset was collected by David Draper of UCLA.\n\nThis dataset contains 23 observations, one for each space shuttle flight carried out before the Challenger was launched on its ultimate journey. It contains the following attributes:\n1. Number of O-rings at risk on a given flight \n2. Number experiencing thermal distress \n3. Launch temperature (degrees F) \n4. Leak-check pressure (psi) \n5. Temporal order of flight\n\nThe coolest temperature at launch among all 23 flights before the Challenger's last flight was 53 \u00b0F. Forecasts for January 28, 1986 predicted an unusually cold morning, with temperatures close to \u22121 \u00b0C (30 \u00b0F), the minimum temperature permitted for launch. The Shuttle was never certified to operate in temperatures that low. The O-rings, as well as many other critical components, had no test data to support any expectation of a successful launch in such conditions. Despite several objections from the engineering teams, NASA went ahead with the launch. The spacecraft disintegrated over the Atlantic Ocean, off the coast of Cape Canaveral, Florida, at 11:39 EST, a mere 73 seconds into its flight. (Source: Wikipedia)\n\nDisintegration of the vehicle began after an O-ring seal in its right Solid Rocket Booster (SRB) failed at liftoff. Its failure caused a breach in the SRB joint it sealed, allowing pressurized burning gas from within the solid rocket motor to reach the outside and impinge upon the adjacent SRB aft field joint attachment hardware and external fuel tank. This led to the separation of the right-hand SRB's aft field joint attachment and the structural failure of the external tank. Consequently, aerodynamic forces broke up the orbiter. (Source: Wikipedia)",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "## Focus of my analysis",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "My analysis focuses on understanding the relationship between the response variable (number of O-rings experiencing thermal distress) and the two predictor variables (1. launch temperature; and 2. leak-check pressure). I will begin my analysis by examining these three numerical variables independently. Then I will try to understand the relationship between the response variable and each of the predictor variables using covariance and correlation analysis. Next, based on the results of the correlation analysis, I will fit a linear regression model between the response variable and the predictor variable with which it shares a greater correlation. Finally, I will create a prediction equation to predict the number of O-rings experiencing distress based on the predictor variable with which it shares a greater correlation. My analysis will also include relevant charts / graphs.",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "## Dataset",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "I downloaded the dataset from the following url: https://archive.ics.uci.edu/ml/datasets/Challenger+USA+Space+Shuttle+O-Ring\n\nI then stored the dataset (file = \"orings.csv\") into an object store on IBM's Bluemix platform-as-a-service (https://www.ibm.com/cloud-computing/bluemix/). I then accessed this data from the object store and imported into an R Jupyter notebook that I created using IBM's Data Science Experience (https://datascience.ibm.com/). I stored the data into an R data frame called \"orings\".\n\nThe cells below shows the process of importing the data into my R Jupyter notebook. Most of the content in this cell is hidden since it includes my credentials to access my object storage.",
"metadata": {}
},
{
"cell_type": "code",
"source": "# The code was removed by DSX for sharing.",
"metadata": {},
"execution_count": 1,
"outputs": [
{
"output_type": "stream",
"text": "Loading required package: httr\nLoading required package: RCurl\nLoading required package: bitops\n\nAttaching package: \u2018RCurl\u2019\n\nThe following object is masked from \u2018package:SparkR\u2019:\n\n base64\n\n",
"name": "stderr"
}
]
},
{
"cell_type": "markdown",
"source": "The cell below prints the dataset in its entirety as well printing its structure:",
"metadata": {}
},
{
"cell_type": "code",
"source": "orings #prints the entire dataset\nstr(orings) #prints the structure of the dataset",
"metadata": {},
"execution_count": 2,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/html": "<table>\n<thead><tr><th scope=col>OringsAtRisk</th><th scope=col>OringsThermalDistress</th><th scope=col>LaunchTempDegF</th><th scope=col>LeakCheckPressurePsi</th><th scope=col>TemporalOrderOfFlight</th></tr></thead>\n<tbody>\n\t<tr><td>6 </td><td>0 </td><td>66 </td><td> 50</td><td> 1 </td></tr>\n\t<tr><td>6 </td><td>1 </td><td>70 </td><td> 50</td><td> 2 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>69 </td><td> 50</td><td> 3 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>68 </td><td> 50</td><td> 4 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>67 </td><td> 50</td><td> 5 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>72 </td><td> 50</td><td> 6 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>73 </td><td>100</td><td> 7 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>70 </td><td>100</td><td> 8 </td></tr>\n\t<tr><td>6 </td><td>1 </td><td>57 </td><td>200</td><td> 9 </td></tr>\n\t<tr><td>6 </td><td>1 </td><td>63 </td><td>200</td><td>10 </td></tr>\n\t<tr><td>6 </td><td>1 </td><td>70 </td><td>200</td><td>11 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>78 </td><td>200</td><td>12 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>67 </td><td>200</td><td>13 </td></tr>\n\t<tr><td>6 </td><td>2 </td><td>53 </td><td>200</td><td>14 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>67 </td><td>200</td><td>15 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>75 </td><td>200</td><td>16 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>70 </td><td>200</td><td>17 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>81 </td><td>200</td><td>18 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>76 </td><td>200</td><td>19 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>79 </td><td>200</td><td>20 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>75 </td><td>200</td><td>21 </td></tr>\n\t<tr><td>6 </td><td>0 </td><td>76 </td><td>200</td><td>22 </td></tr>\n\t<tr><td>6 </td><td>1 </td><td>58 </td><td>200</td><td>23 </td></tr>\n</tbody>\n</table>\n",
"text/latex": "\\begin{tabular}{r|lllll}\n OringsAtRisk & OringsThermalDistress & LaunchTempDegF & LeakCheckPressurePsi & TemporalOrderOfFlight\\\\\n\\hline\n\t 6 & 0 & 66 & 50 & 1 \\\\\n\t 6 & 1 & 70 & 50 & 2 \\\\\n\t 6 & 0 & 69 & 50 & 3 \\\\\n\t 6 & 0 & 68 & 50 & 4 \\\\\n\t 6 & 0 & 67 & 50 & 5 \\\\\n\t 6 & 0 & 72 & 50 & 6 \\\\\n\t 6 & 0 & 73 & 100 & 7 \\\\\n\t 6 & 0 & 70 & 100 & 8 \\\\\n\t 6 & 1 & 57 & 200 & 9 \\\\\n\t 6 & 1 & 63 & 200 & 10 \\\\\n\t 6 & 1 & 70 & 200 & 11 \\\\\n\t 6 & 0 & 78 & 200 & 12 \\\\\n\t 6 & 0 & 67 & 200 & 13 \\\\\n\t 6 & 2 & 53 & 200 & 14 \\\\\n\t 6 & 0 & 67 & 200 & 15 \\\\\n\t 6 & 0 & 75 & 200 & 16 \\\\\n\t 6 & 0 & 70 & 200 & 17 \\\\\n\t 6 & 0 & 81 & 200 & 18 \\\\\n\t 6 & 0 & 76 & 200 & 19 \\\\\n\t 6 & 0 & 79 & 200 & 20 \\\\\n\t 6 & 0 & 75 & 200 & 21 \\\\\n\t 6 & 0 & 76 & 200 & 22 \\\\\n\t 6 & 1 & 58 & 200 & 23 \\\\\n\\end{tabular}\n",
"text/plain": " OringsAtRisk OringsThermalDistress LaunchTempDegF LeakCheckPressurePsi\n1 6 0 66 50 \n2 6 1 70 50 \n3 6 0 69 50 \n4 6 0 68 50 \n5 6 0 67 50 \n6 6 0 72 50 \n7 6 0 73 100 \n8 6 0 70 100 \n9 6 1 57 200 \n10 6 1 63 200 \n11 6 1 70 200 \n12 6 0 78 200 \n13 6 0 67 200 \n14 6 2 53 200 \n15 6 0 67 200 \n16 6 0 75 200 \n17 6 0 70 200 \n18 6 0 81 200 \n19 6 0 76 200 \n20 6 0 79 200 \n21 6 0 75 200 \n22 6 0 76 200 \n23 6 1 58 200 \n TemporalOrderOfFlight\n1 1 \n2 2 \n3 3 \n4 4 \n5 5 \n6 6 \n7 7 \n8 8 \n9 9 \n10 10 \n11 11 \n12 12 \n13 13 \n14 14 \n15 15 \n16 16 \n17 17 \n18 18 \n19 19 \n20 20 \n21 21 \n22 22 \n23 23 "
}
},
{
"output_type": "stream",
"text": "'data.frame':\t23 obs. of 5 variables:\n $ OringsAtRisk : num 6 6 6 6 6 6 6 6 6 6 ...\n $ OringsThermalDistress: num 0 1 0 0 0 0 0 0 1 1 ...\n $ LaunchTempDegF : num 66 70 69 68 67 72 73 70 57 63 ...\n $ LeakCheckPressurePsi : num 50 50 50 50 50 50 100 100 200 200 ...\n $ TemporalOrderOfFlight: num 1 2 3 4 5 6 7 8 9 10 ...\n",
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"source": "As can be seen from the output, the \"orings\" dataset has 23 observations and 5 variables. All 5 variables are numeric. For additional information on the variables in the dataset, see here: https://archive.ics.uci.edu/ml/machine-learning-databases/space-shuttle/o-ring-erosion.names.",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "## Exploring the variables in the dataset",
"metadata": {
"collapsed": true
}
},
{
"cell_type": "markdown",
"source": "### O-rings at risk",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "Each solid booster rocket has three field joints that each have 2 O-rings. Therefore, the total number of O-rings at risk in any space shuttle flight is 3 X 2 = 6 O-rings. You can see that, by definition (and indeed by design), every observation in the dataset has 6 O-rings at risk. Therefore, this variable does not have any bearing on the Challenger disaster and can be ignored in the remainder of our analysis.",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "### O-rings experiencing thermal distress",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "This variable is our response variable, that is, this is the variable we are trying to predict. The Challenger space shuttle disaster occurred as a result of an O-ring failure, a leading indicator of which is an O-ring experiencing thermal distress. Our analysis of this variable is provided below:",
"metadata": {}
},
{
"cell_type": "code",
"source": "summary(orings$OringsThermalDistress) #summary \"OringsThermalDistress\"\ntable(orings$OringsThermalDistress)",
"metadata": {},
"execution_count": 3,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": " Min. 1st Qu. Median Mean 3rd Qu. Max. \n 0.0000 0.0000 0.0000 0.3043 0.5000 2.0000 "
}
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "\n 0 1 2 \n17 5 1 "
}
}
]
},
{
"cell_type": "markdown",
"source": "From the above result, we can see that O-rings experiencing thermal distress is a discrete numerical variable. Of the 23 observations, in 17 cases, none of the O-rings experienced thermal distress, in 5 cases, 1 O-ring experienced thermal distress and in 1 case, 2 O-rings experienced thermal distress. A dotchart of this variable is provided below:",
"metadata": {}
},
{
"cell_type": "code",
"source": "dotchart(orings$OringsThermalDistress, main = \"O-rings Experiencing Thermal Distress\", col = \"red\", pch = 19, xlab = \"Number of O-rings\")",
"metadata": {},
"execution_count": 4,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
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27W9/uzLDhg0brrzyyssvv/zyyy9/8skn+22126KTMm0f++WCCy7ovNSyo6Pjc5/7XOfgsGHDjv1AaDWb+gQfANXo91ZV9naKNmwf48cOVs5TP/roo50j+/btmzdv3rFrVr+tjl2zVCpt2bLl3//7f195hF9xxRVdz5Aee5Pqn4mV23Y779ljw9Vv8yobOMFXDE4rgh2D2tGjR/s9x7pgwYJuF3T3oY+3jSrfonobb21tPffccyvjdXV1nV9j1lVl5cp3Upx99tnvfve73/e+982cObPycbnOH7is5q/oQ+Wzmfv376+8x1x11VVdY80ZZ5xx7PGqTmPHju36PXZz5szpupE7f8mtU0NDw4033njNNdd0/kBnRPzRH/1R5d20tw3Y46ITn/bY8ddee63yKZxisfiOd7yj6/fYffazn+17X1d/R8f1AKhGv7eqvrdTsWH7GD92sOtXuF144YXveMc7Kv9h6NTW1lblX33svfSmpqbmV7/6Vd+NVf9MHD16dOfgNddc8zd/8zf9bpkqt3mVDZzgKwanFcGOwe7QoUOVU67H+vM///Pj+tb1Pt42elzU2/o9jq9bt67y6l/R47ddvPzyy13jRVeXXHLJq6++WuVf0YdKsKu8JUTEz3/+8857r/wSw8yZMw8fPtx1zltvvbXbVBdeeOEzzzzTtYH29vZjf4mh07ve9a6up8WP/dv7WHTi0/Y4/rOf/azHi/OuvfbaSp7o7bbHdUfVPwCq0e+tqu/tFG3Y3saPHex6zLhToVBYtmxZJZo89thjVf7Vx95Lj84888z//t//e7/dVv9MfN/73ldZ1OMvT3S7ryq3eZUNnOArBqcVwY43h8cee+zjH//41KlThw0bNmzYsKlTp3784x+vvBlUr7dX4d4W9bZ+b+O7du362Mc+NmPGjLe85S3z5s3rPH3Z48qtra3f/va3582bV19fXywWJ0yYcNVVV91zzz2vvfZa9X9FHzqD3dq1aysjixYtqszw1a9+tTK+bNmyrnO2t7ffc88906dPHzp06OWXX/6Zz3zmlVde6bGNf/iHf1i8ePGMGTOGDh06ZcqU66+//ic/+Um3K4qOd4Of4LS9jT/33HOf/vSn3/nOd44aNercc8/9F//iX/zd3/1dNXOeugdAv/q91fH2dio2bPUbbePGje95z3vGjRs3adKkD3zgA53f4nb55ZfX1tbW1tb+6Z/+aZV/9bH30tXZZ5996aWX/uVf/mXlG476bazKZ+ILL7zw/ve/f8yYMWeffXblOx37bbiabV5lAyfyisFppVCu7k0CGJh9+/Z1nqEbNmxYj5/tHSQqn+nzmnByvVkeAEAafN0JnBwLFiy44oorrrjiiq9//etdx3/0ox91/uPtb397Hn2REQ8AYDAY0v8qQBVGjBjxs5/9LCK2bds2bty497///YcOHfrRj370hS98oXOF97///bk2yKnlAQAMBk7Fwsnx4osvzp07d/fu3T0uff/73//www9XvltrEHIq9gS92R8AQBq8ysDJUVdX98wzz6xYsWLKlCmVn04aMWJEY2Pjj3/8Y2/qyfMAAAYDR+zg5Dt69OjevXtHjBgxevTok/7bZQx+HgBAXgQ7AIBEODUAAJAIwQ4AIBGCHQBAIgQ7AIBECHYAAIkQ7AAAEiHYAQAkQrADAEiEYAcAkAjBDgAgEYIdAEAiBDsAgEQIdgAAiRDsAAASIdgBACRCsAMASIRgBwCQCMEOACARgh0AQCIEOwCARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHAJAIwQ4AIBGCHQBAIgQ7AIBECHYAAIkQ7AAAEiHYAQAkQrADAEjEkLwbeHPYsmXL0aNH8+4CABgUhgwZMmfOnLy76IFg179f/epXV155Zd5dAACDyOOPP37FFVfk3UV3gl3/SqVSRLS1tRWLxbx7AQByViqVamtrO+PBYOMaOwCARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHAJAIwQ4AIBGCHQBAIgQ7AIBECHYAAIkQ7AAAEiHYAQAkQrADAEiEYAcAkAjBDgAgEYIdAEAiBDsAgEQIdgAAiRDsAAASIdgBVGHNmli8OGbMiBkzYvHiWLMm74YAejAk7wYABrdyOW66KVaufH3k2WfjoYdi6dK4//4oFPLrDKA7R+wA+nTffW9IdRUrV8b992feDUBfBDuAPn3jGwNZBJAHp2Kr1dLSMmnSpJqamo6Ojpdeeikixo8fr1Qq0y737dw5YceOXl8Xtm9v2b593IUXDqqelUrlqS5bWloioqOjo9cXh/wIdtXau3fvuHHjhg0bduTIkb1790bEqFGjlEpl2uW+3bsn9PnKsG/37rPPP39Q9axUKrMp29vb+3x5yEehXC7n3cNg19zc3NjY2NbWViwW8+4FyFZ7e4weHQcO9Lx05MjYvz9qarLtCchZqVSqra1tampqaGjIu5fuXGMH0Luamrjhhl6XfvCDUh0wqAh2AH1asSLOO6+H8cmTY8WKzLsB6ItgB9Cnurpobo7rr3/9K+sKhbj++mhqirq6XDsD6M6HJwD6M3lyrFkTr7wS27ZFRMycGWPG5N0TQA8EO4DqjB4d8+bl3QRAX5yKBQBIhGAHAJAIwQ4AIBGCHQBAIgQ7AIBECHYAAIkQ7AAAEiHYAQAkQrADAEiEYAcAkAjBDgAgEYIdAEAiBDsAgEQIdplrbY3W1rybAAASJNhl5fDhWL48pk2LkSNj5MiYNi2WL4/Dh/NuCwBIx5C8Gzg9HDwYCxZEc/PrI7t2xZ13xrp1sW5dDB+eX2cAQDocscvE3Xe/IdVVNDfH3Xdn3g0AkCbB7tQrl+PBB3td+uCDUS5n2A0AkCynYqu1c+fO6dOnF4vFo0eP7tq1KyIuuOCCasrdTzwxraWl13lbWn69efPkyy4bwMxKpVKpVCqzL3fu3BkR7e3tMfg4YgcAkIhC2XnA/jQ3Nzc2Nra1tRWLxYHcvlyOiROjt4N2dXXxwgtRKJxIhwBAZkqlUm1tbVNTU0NDQ969dOeI3alXKMSNN/a69BOfkOoAgJNCsMvEbbdFj6G+oSFuuy3zbgCANAl2mRg+PNavjzvuiKlTo1CIQiGmTo077oj1632JHQBwsvhUbFaGDo3ly2P58j/8ntiIEXk3BACkRrDLnEgHAJwaTsUCACRCsAMASIRgBwCQCMEOACARgh0AQCIEOwCARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHAJAIwQ4AIBGCHQBAIobk3cBpZv/+eOaZiIiZM2PMmLy7AQCS4ohdVvbsiUWLYuzYmD8/5s+PsWNj0aLYsyfvtgCAdDhil4kXX4yGhnj++ddHyuV45JHYsiU2bYq6uvw6AwDS4YhdJpYte0Oqq9izJ5Yty7wbACBNgt2p194eDz3U69KHH4729gy7AQCS5VRstZ588sk5c+YMGzasra1t27ZtEXHJJZdUU27/+c9nHzjQ67yvvvr0+vXT580bwMxKpVKpVCqzL5966qmIOHLkSAw+gl21Jk6cWCwWI+LMM8+cOHFiRFRZjq+v73vm8fX1A5tZqVQqlUplXmVNTU0MPoVyuZx3D4Ndc3NzY2NjW1tb5x4diIsuih07el307LMD7g0AyFipVKqtrW1qampoaMi7l+5cY5eJW28dyCIAgOMh2GXi5ptj6dIexpcujZtuyrwbACBNrrHLRKEQDzwQixbFqlWxdWtExKxZ8ZGPxKJFeXcGAKRDsMvQokWSHABw6jgVCwCQCMEOACARgh0AQCIEOwCARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHAJAIwQ4AIBGCHQBAIgQ7AIBECHYAAIkQ7AAAEjEk7wZOJ6VSbNgQ27ZFRFx6acyfH8Vi3j0BAOkQ7LKyYUN89KOxe/frI/X18f3vx/z5+fUEACTFqdhMPP10LFz4hlQXEbt3x8KF8fTTOfUEAKRGsMvEbbfFwYM9jB88GF/6UubdAABpEuxOvVIp1q3rdemjj0aplGE3AECyXGNXrQ0bNsydO/ess846dOjQpk2bIuLKK6+spvzHn/50bh/RrVTauGbN7Pe8ZwAzK5VKpVKpzL5samqKiLa2thh8CuVyOe8eBrvm5ubGxsaXX355zJgxnSOtra0RMWLEiKrKfftGTJgQvW3nQqG1pWXE+PEDmVmpVCqVSmXm5f79+88555ympqaGhoYYZAS7/nUGu7a2tuKAv51k7tz45S97XnT11bFx44B7AwAyViqVamtrB2ewc41dJm6/fSCLAACOh2CXiYUL4957u38dcbEY994bCxfm1BMAkBofnsjKzTfHu98dq1fH1q0REbNmxeLFMWVK3m0BAOkQ7DI0ZUp88Yt5NwEAJMupWACARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHAJAIwQ4AIBGCHQBAIgQ7AIBECHYAAIkQ7AAAEiHYAQAkQrADAEiEYAcAkIgheTdwOnnuuVi9OrZujYiYNSsWL44pU/LuCQBIh2CXlfvui09/Okql10duvz2++c24+eb8egIAkuJUbCbWro1bbnlDqouIUiluuSXWrs2pJwAgNYJdJu68s9dFX/5yhn0AACkT7KrV2tra9d/HUe7bF5s39zrvpk2t+/YNcGalUqlUKpV5lDFY1SxfvjzvHga7PXv2fPe7312wYMG5555bLBYPHTr0+OOP7927d9y4cdWUT69fP3n16j7mf+Lqq8fU1w9gZqVSqVQqldmXmzdvXrVq1ZIlS6YMvg9BFsrlct49DHbNzc2NjY1tbW3FYnEgty+V4i1v6X6BXUWxGAcOxMBmBgAyVyqVamtrm5qaGhoa8u6lO6diT71iMa67rtel110n1QEAJ4Vgl4m77orhw3sYHz487ror824AgDQJdpmYPTvWro36+jcM1tfH2rUxe3ZOPQEAqfEFxVmZPz927IjHHvvDL09cemnMn+8kLABwEgl2GSoW49pr49pr8+4DAEiTU7EAAIkQ7AAAEiHYAQAkQrADAEiEYAcAkAjBDgAgEYIdAEAiBDsAgEQIdgAAiRDsAAASIdgBACRCsAMASIRgBwCQCMEOACARgl2G1qyJxYtjxoyYMSMWL441a/JuCABIypC8Gzg9lMtx002xcuXrI88+Gw89FEuXxv33R6GQX2cAQDocscvEffe9IdVVrFwZ99+feTcAQJoEu0x84xsDWQQAcDyciq1WS0vLpEmTampqOjo6XnrppYgYP358NeW+nTsn7NjR67zbt7ds3z7uwgsHMLNSqVQqlcrsy5aWlojo6OiIwUewq9bevXvHjRs3bNiwI0eO7N27NyJGjRpVTblv9+4Jfc68b/fus88/fwAzK5VKpVKpzKtsb2+PwadQLpfz7mGwa25ubmxsbGtrKxaLA7l9e3uMHh0HDvS8dOTI2L8/ampOpEMAIDOlUqm2trapqamhoSHvXrpzjd2pV1MTN9zQ69IPflCqAwBOCsEuEytWxHnn9TA+eXKsWJF5NwBAmgS7TNTVRXNzXH/9619ZVyjE9ddHU1PU1eXaGQCQDh+eyMrkybFmTbzySmzbFhExc2aMGZN3TwBAUgS7bI0eHfPm5d0EAJAmp2IBABIh2AEAJEKwAwBIhGAHAJAIwQ4AIBGCHQBAIgQ7AIBECHYAAIkQ7AAAEiHYAQAkQrADAEiEYAcAkAjBDgAgEYJd5lpbo7U17yYAgAQJdlk5fDiWL49p02LkyBg5MqZNi+XL4/DhvNsCANIxJO8GTg8HD8aCBdHc/PrIrl1x552xbl2sWxfDh+fXGQCQDkfsMnH33W9IdRXNzXH33Zl3AwCkSbA79crlePDBXpc++GCUyxl2AwAky6nYau3cuXP69OnFYvHo0aO7du2KiAsuuKCacvcTT0xrael13paWX2/ePPmyywYws1KpVCqVyuzLnTt3RkR7e3sMPo7YAQAkolB2HrA/zc3NjY2NbW1txWJxILcvl2PixOjtoF1dXbzwQhQKJ9IhAJCZUqlUW1vb1MMfvD8AACAASURBVNTU0NCQdy/dOWJ36hUKceONvS79xCekOgDgpBDsMnHbbdFjqG9oiNtuy7wbACBNgl0mhg+P9evjjjti6tQoFKJQiKlT4447Yv16X2IHAJwsPhWblaFDY/nyWL78D78nNmJE3g0BAKkR7DIn0gEAp4ZTsQAAiRDsAAASIdgBACRCsAMASIRgBwCQCMEOACARgh0AQCIEOwCARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHAJCIIXk3cJrZvz+eeSYiYubMGDMm724AgKQ4YpeVPXti0aIYOzbmz4/582Ps2Fi0KPbsybstACAdjthl4sUXo6Ehnn/+9ZFyOR55JLZsiU2boq4uv84AgHQ4YpeJZcvekOoq9uyJZcsy7wYASJNgd+q1t8dDD/W69OGHo709w24AgGQ5FVutJ598cs6cOcOGDWtra9u2bVtEXHLJJdWU23/+89kHDvQ676uvPr1+/fR58wYws1KpVCqVyuzLp556KiKOHDkSg49gV62JEycWi8WIOPPMMydOnBgRVZbj6+v7nnl8ff3AZlYqlUqlUplXWVNTE4NPoVwu593DYNfc3NzY2NjW1ta5Rwfiootix45eFz377IB7AwAyViqVamtrm5qaGhoa8u6lO9fYZeLWWweyCADgeAh2mbj55li6tIfxpUvjppsy7wYASJNr7DJRKMQDD8SiRbFqVWzdGhExa1Z85COxaFHenQEA6RDsMrRokSQHAJw6TsUCACRCsAMASIRgBwCQCMEOACARgh0AQCIEOwCARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHAJAIwQ4AIBGCHQBAIgQ7AIBEDMm7gdNJqRQbNsS2bRERl14a8+dHsZh3TwBAOgS7rGzYEB/9aOze/fpIfX18//sxf35+PQEASXEqNhNPPx0LF74h1UXE7t2xcGE8/XROPQEAqRHsMnHbbXHwYA/jBw/Gl76UeTcAQJoEu1OvVIp163pd+uijUSpl2A0AkCzX2FVrw4YNc+fOPeussw4dOrRp06aIuPLKK6sp//GnP53bR3QrlTauWTP7Pe8ZwMxKpVKpVCqzL5uamiKira0tBp9CuVzOu4fBrrm5ubGx8eWXXx4zZkznSGtra0SMGDGiqnLfvhETJkRv27lQaG1pGTF+/EBmViqVSqVSmXm5f//+c845p6mpqaGhIQYZwa5/ncGura2tOOBvJ5k7N375y54XXX11bNw44N4AgIyVSqXa2trBGexcY5eJ228fyCIAgOMh2GVi4cK4997uX0dcLMa998bChTn1BACkxocnsnLzzfHud8fq1bF1a0TErFmxeHFMmZJ3WwBAOgS7DE2ZEl/8Yt5NAADJcioWACARgh0AQCIEOwCARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHAJAIwQ4AIBGCHQBAIgQ7AIBECHYAAIkQ7AAAEiHYAQAkYkjeDQAAnErPPRerV8fWrRERs2bF4sUxZUrePZ0qgh0AkK777otPfzpKpddHbr89vvnNuPnm/Ho6hZyKBQAStXZt3HLLG1JdRJRKccstsXZtTj2dWoIdAJCoO+/sddGXv5xhH9kR7KrV2tra9d9KpVKpVCoHdblvX2zeHL3ZtKl1374B31Gv0+atZvny5Xn3MNjt2bPnu9/97oIFC84999xisXjo0KHHH398796948aNUyqVSqVSOTjLp9evn7x6dR/v709cffWY+voBzLx58+ZVq1YtWbJkyuD7EEahXC7n3cNg19zc3NjY2NbWViwW8+4FAKhOqRRveUv3C+wqisU4cCAG9M5eKpVqa2ubmpoaGhpOqMNTwKlYACBFxWJcd12vS6+7bmCpbpAT7ACARN11Vwwf3sP48OFx112Zd5MFwQ4ASNTs2bF2bdTXv2Gwvj7Wro3Zs3Pq6dTyBcUAQLrmz48dO+Kxx/7wyxOXXhrz5yd5EraTYAcAJK1YjGuvjWuvzbuPLDgVCwCQCMEOACARgh0AQCIEOwCARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHAJAIwQ4AIBGCHQBAIgQ7AIBECHYAAIkQ7AAAEiHYZWjNmli8OGbMiBkzYvHiWLMm74YAgKQMybuB00O5HDfdFCtXvj7y7LPx0EOxdGncf38UCvl1BgCkwxG7TNx33xtSXcXKlXH//Zl3AwCkSbDLxDe+MZBFAADHw6nYarW0tEyaNKmmpqajo+Oll16KiPHjx1dT7tu5c8KOHb3Ou317y/bt4y68cAAzK5VKpVKpzL5saWmJiI6Ojhh8BLtq7d27d9y4ccOGDTty5MjevXsjYtSoUdWU+3bvntDnzPt27z77/PMHMLNSqVQqlcq8yvb29hh8CuVyOe8eBrvm5ubGxsa2trZisTiQ27e3x+jRceBAz0tHjoz9+6Om5kQ6BAAyUyqVamtrm5qaGhoa8u6lO9fYnXo1NXHDDb0u/eAHpToA4KQQ7DKxYkWcd14P45Mnx4oVmXcDAKRJsMtEXV00N8f117/+lXWFQlx/fTQ1RV1drp0BAOnw4YmsTJ4ca9bEK6/Etm0RETNnxpgxefcEACRFsMvW6NExb17eTQAAaXIqFgAgEYIdAEAiBDsAgEQIdgAAiRDsAAASIdgBACRCsAMASIRgBwCQCMEOACARgh0AQCIEOwCARAh2AACJEOwAABIh2GWutTVaW/NuAgBIkGCXlcOHY/nymDYtRo6MkSNj2rRYvjwOH867LQAgHUPybuD0cPBgLFgQzc2vj+zaFXfeGevWxbp1MXx4fp0BAOlwxC4Td9/9hlRX0dwcd9+deTcAQJoEu1OvXI4HH+x16YMPRrmcYTcAQLKciq3Wzp07p0+fXiwWjx49umvXroi44IILqil3P/HEtJaWXudtafn15s2TL7tsADMrlUqlUqnMvty5c2dEtLe3x+DjiB0AQCIKZecB+9Pc3NzY2NjW1lYsFgdy+3I5Jk6M3g7a1dXFCy9EoXAiHQIAmSmVSrW1tU1NTQ0NDXn30p0jdqdeoRA33tjr0k98QqoDAE4KwS4Tt90WPYb6hoa47bbMuwEA0iTYZWL48Fi/Pu64I6ZOjUIhCoWYOjXuuCPWr/cldgDAyeJTsVkZOjSWL4/ly//we2IjRuTdEACQGsEucyIdAHBqOBULAJAIwQ4AIBGCHQBAIgQ7AIBECHYAAIkQ7AAAEiHYAQAkQrADAEiEYAcAkAjBDgAgEYIdAEAiBDsAgEQIdgAAiRiSdwMAbxL798czz0REzJwZY8bk3Q1ADxyxA+jPnj2xaFGMHRvz58f8+TF2bCxaFHv25N0WQHeO2AH06cUXo6Ehnn/+9ZFyOR55JLZsiU2boq4uv84AunPEDqBPy5a9IdVV7NkTy5Zl3g1AXwQ7gN61t8dDD/W69OGHo709w24A+uFUbLWefPLJOXPmDBs2rK2tbdu2bRFxySWXKJXKtMvtP//57AMHen1dePXVp9evnz5v3qDqWalUnuryqaeeiogjR470+uKQH8GuWhMnTiwWixFx5plnTpw4MSKUSmXy5fj6+ujT+Pr63JtUKpW5lDU1NTH4FMrlct49DHbNzc2NjY1tbW2dexQ4vVx0UezY0euiZ5/Nthsgf6VSqba2tqmpqaGhIe9eunONHUCfbr11IIsA8iDYAfTp5ptj6dIexpcujZtuyrwbgL64xg6gT4VCPPBALFoUq1bF1q0REbNmxUc+EosW5d0ZQHeCHUAVFi2S5IDBz6lYAIBECHYAAIkQ7AAAEiHYAQAkQrADAEiEYAcAkAjBDgAgEYIdAEAiBDsAgEQIdgAAiRDsAAASIdgBACRCsAMASIRgBwCQiCF5NwDwZlAqxYYNsW1bRMSll8b8+VEs5t0TQHeCHUB/NmyIj340du9+faS+Pr7//Zg/P7+eAHrgVCxAn55+OhYufEOqi4jdu2Phwnj66Zx6AuiZYAfQp9tui4MHexg/eDC+9KXMuwHoi2AH0LtSKdat63Xpo49GqZRhNwD9cI1dtTZs2DB37tyzzjrr0KFDmzZtiogrr7xSqVSmXf7jT386t4/oViptXLNm9nveM6h6ViqVp7psamqKiLa2tl5fHPJTKJfLefcw2DU3Nzc2Nr788stjxozpHGltbY2IESNGKJXKxMt9+0ZMmBC9vU4WCq0tLSPGjx9cPSuVylNc7t+//5xzzmlqampoaIhBRrDrX2ewa2trK/p2AzgNzZ0bv/xlz4uuvjo2bsy2GyB/pVKptrZ2cAY719gB9On22weyCCAPgh1AnxYujHvv7f51xMVi3HtvLFyYU08APfPhCYD+3HxzvPvdsXp1bN0aETFrVixeHFOm5N0WQHeCHUAVpkyJL34x7yYA+uFULABAIgQ7AIBECHYAAIkQ7AAAEiHYAQAkQrADAEiEYAcAkAjBDgAgEYIdAEAiBDsAgEQIdgAAiRDsAAASIdgBACRCsAMASMSQvBsAeDN47rlYvTq2bo2ImDUrFi+OKVPy7gmgO8EOoD/33Ref/nSUSq+P3H57fPObcfPN+fUE0AOnYgH6tHZt3HLLG1JdRJRKccstsXZtTj0B9EywA+jTnXf2uujLX86wD4D+CXbVam1t7fpvpVJ5WpT79sXmzdGbTZta9+3Lv0mlUpl5GYNVzfLly/PuYbDbs2fPd7/73QULFpx77rnFYvHQoUOPP/743r17x40bp1Qq0y6fXr9+8urVfbw+PHH11WPq6wdVz0ql8lSXmzdvXrVq1ZIlS6YMvg9RFcrlct49DHbNzc2NjY1tbW3FYjHvXoBslUrxlrd0v8CuoliMAwfCKwOcZkqlUm1tbVNTU0NDQ969dOdULEDvisW47rpel153nVQHDCqCHUCf7rorhg/vYXz48Ljrrsy7AeiLYAfQp9mzY+3aqK9/w2B9faxdG7Nn59QTQM98QTFAf+bPjx074rHH/vDLE5deGvPnOwkLDEKCHUAVisW49tq49tq8+wDoi1OxAACJEOwAABIh2AEAJEKwAwBIhGAHAJAIwQ4AIBGCHQBAIgQ7AIBECHYAAIkQ7AAAEiHYAQAkQrADAEiEYAcAkAjBDgAgEYJdhtasicWLY8aMmDEjFi+ONWvybggASMqQvBs4PZTLcdNNsXLl6yPPPhsPPRRLl8b990ehkF9nAEA6HLHLxH33vSHVVaxcGfffn3k3AECaBLtMfOMbA1kEAHA8nIqtVktLy6RJk2pqajo6Ol566aWIGD9+fDXlvp07J+zY0eu827e3bN8+7sILBzCzUqlUKpXK7MuWlpaI6OjoiMFHsKvW3r17x40bN2zYsCNHjuzduzciRo0aVU25b/fuCX3OvG/37rPPP38AMyuVSqVSqcyrbG9vj8GnUC6X8+5hsGtubm5sbGxraysWiwO5fXt7jB4dBw70vHTkyNi/P2pqTqRDACAzpVKptra2qampoaEh7166c43dqVdTEzfc0OvSD35QqgMATgrBLhMrVsR55/UwPnlyrFiReTcAQJoEu0zU1UVzc1x//etfWVcoxPXXR1NT1NXl2hkAkA4fnsjK5MmxZk288kps2xYRMXNmjBmTd08AQFIEu2yNHh3z5uXdBACQJqdiAQASIdgBACRCsAMASIRgBwCQCMEOACARgh0AQCIEOwCARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHAJAIwQ4AIBGCXeZaW6O1Ne8mAIAECXZZOXw4li+PadNi5MgYOTKmTYvly+Pw4bzbAgDSMSTvBk4PBw/GggXR3Pz6yK5dceedsW5drFsXw4fn1xkAkA5H7DJx991vSHUVzc1x992ZdwMApEmwO/XK5XjwwV6XPvhglMsZdgMAJMup2Grt3Llz+vTpxWLx6NGju3btiogLLrigmnL3E09Ma2npdd6Wll9v3jz5sssGMLNSqVQqlcrsy507d0ZEe3t7DD6O2AEAJKJQdh6wP83NzY2NjW1tbcVicSC3L5dj4sTo7aBdXV288EIUCifSIQCQmVKpVFtb29TU1NDQkHcv3Tlid+oVCnHjjb0u/cQnpDoA4KQQ7DJx223RY6hvaIjbbsu8GwAgTYJdJoYPj/Xr4447YurUKBSiUIipU+OOO2L9el9iBwCcLD4Vm5WhQ2P58li+/A+/JzZiRN4NAQCpEewyJ9IBAKeGU7EAAIkQ7AAAEiHYAQAkQrADAEiEYAcAkAjBDgAgEYIdAEAiBDsAgEQIdgAAiRDsAAASIdgBACRCsAMASIRgBwCQiCF5N3Ca2b8/nnkmImLmzBgzJu9uAICkOGKXlT17YtGiGDs25s+P+fNj7NhYtCj27Mm7LQAgHY7YZeLFF6OhIZ5//vWRcjkeeSS2bIlNm6KuLr/OAIB0OGKXiWXL3pDqKvbsiWXLMu8GAEiTYHfqtbfHQw/1uvThh6O9PcNuAIBkORVbrSeffHLOnDnDhg1ra2vbtm1bRFxyySXVlNt//vPZBw70Ou+rrz69fv30efMGMLNSqVQqlcrsy6eeeioijhw5EoOPYFetiRMnFovFiDjzzDMnTpwYEVWW4+vr+555fH39wGZWKpVKpVKZV1lTUxODT6FcLufdw2DX3Nzc2NjY1tbWuUcH4qKLYseOXhc9++yAewMAMlYqlWpra5uamhoaGvLupTvX2GXi1lsHsggA4HgIdpm4+eZYurSH8aVL46abMu8GAEiTa+wyUSjEAw/EokWxalVs3RoRMWtWfOQjsWhR3p0BAOkQ7DK0aJEkBwCcOk7FAgAkQrADAEiEYAcAkAjBDgAgEYIdAEAiBDsAgEQIdgAAiRDsAAASIdgBACRCsAMASIRgBwCQCMEOACARgh0AQCIEOwCARAzJu4HTSakUGzbEtm0REZdeGvPnR7GYd08AQDoEu6xs2BAf/Wjs3v36SH19fP/7MX9+fj0BAElxKjYTTz8dCxe+IdVFxO7dsXBhPP10Tj0BAKkR7DJx221x8GAP4wcPxpe+lHk3AECaBLtTr1SKdet6Xfroo1EqZdgNAJAs19hVa8OGDXPnzj3rrLMOHTq0adOmiLjyyiurKf/xpz+d20d0K5U2rlkz+z3vGcDMSqVSqVQqsy+bmpoioq2tLQafQrlczruHwa65ubmxsfHll18eM2ZM50hra2tEjBgxoqpy374REyZEb9u5UGhtaRkxfvxAZlYqlUqlUpl5uX///nPOOaepqamhoSEGGcGuf53Brq2trTjgbyeZOzd++cueF119dWzcOODeAICMlUql2trawRnsXGOXidtvH8giAIDjIdhlYuHCuPfe7l9HXCzGvffGwoU59QQApMaHJ7Jy883x7nfH6tWxdWtExKxZsXhxTJmSd1sAQDoEuwxNmRJf/GLeTQAAyXIqFgAgEYIdAEAiBDsAgEQIdgAAiRDsAAASIdgBACRCsAMASIRgBwCQCMEOACARgh0AQCIEOwCARAh2AACJEOwAABIh2AEAJGJI3g2cTp57Llavjq1bIyJmzYrFi2PKlLx7AgDSIdhl5b774tOfjlLp9ZHbb49vfjNuvjm/ngCApDgVm4m1a+OWW96Q6iKiVIpbbom1a3PqCQBIjWCXiTvv7HXRl7+cYR8AQMoEu2q1trZ2/fdxlPv2xebNvc67aVPrvn0DnFmpVCqVSmUeZQxWNcuXL8+7h8Fuz5493/3udxcsWHDuuecWi8VDhw49/vjje/fuHTduXDXl0+vXT169uo/5n7j66jH19QOYWalUKpVKZfbl5s2bV61atWTJkimD70OQhXK5nHcPg11zc3NjY2NbW1uxWBzI7UuleMtbul9gV1EsxoEDMbCZAYDMlUql2trapqamhoaGvHvpzqnYU69YjOuu63XpdddJdQDASSHYZeKuu2L48B7Ghw+Pu+7KvBsAIE2CXSZmz461a6O+/g2D9fWxdm3Mnp1TTwBAanxBcVbmz48dO+Kxx/7wyxOXXhrz5zsJCwCcRIJdhorFuPbauPbavPsAANLkVCwAQCIEOwCARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHAJAIwQ4AIBGCHQBAIgQ7AIBECHYAAIkQ7AAAEiHYAQAkQrADAEiEYJehNWti8eKYMSNmzIjFi2PNmrwbAgCSMiTvBk4P5XLcdFOsXPn6yLPPxkMPxdKlcf/9USjk1xkAkA5H7DJx331vSHUVK1fG/fdn3g0AkCbBLhPf+MZAFgEAHA+nYqvV0tIyadKkmpqajo6Ol156KSLGjx9fTblv584JO3b0Ou/27S3bt4+78MIBzKxUKpVKpTL7sqWlJSI6Ojpi8BHsqrV3795x48YNGzbsyJEje/fujYhRo0ZVU+7bvXtCnzPv27377PPPH8DMSqVSqVQq8yrb29tj8CmUy+W8exjsmpubGxsb29raisXiQG7f3h6jR8eBAz0vHTky9u+PmpoT6RAAyEypVKqtrW1qampoaMi7l+5cY3fq1dTEDTf0uvSDH5TqAICTQrDLxIoVcd55PYxPnhwrVmTeDQCQJsEuE3V10dwc11//+lfWFQpx/fXR1BR1dbl2BgCkw4cnsjJ5cqxZE6+8Etu2RUTMnBljxuTdEwCQFMEuW6NHx7x5eTcBAKTJqVgAgEQIdgAAiRDsAAASIdgBACRCsAMASIRgBwCQCMEOACARgh0AQCIEOwCARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHULXW1mhtzbsJgF4JdgD9OXw4li+PadNi5MgYOTKmTYvly+Pw4bzbAuhuSN4NAAxuBw/GggXR3Pz6yK5dceedsW5drFsXw4fn1xlAd47YAfTp7rvfkOoqmpvj7rsz7wagL4IdQO/K5XjwwV6XPvhglMsZdgPQD6diq7Vz587p06cXi8WjR4/u2rUrIi644AKlUpl2ufuJJ6a1tPT6utDS8uvNmydfdtmg6lmpVJ7qcufOnRHR3t7e64tDfhyxAwBIRKHsPEJ/mpubGxsb29raisVi3r0A2SqXY+LE6O2gXV1dvPBCFArZ9gTkrFQq1dbWNjU1NTQ05N1Ld47YAfSuUIgbb+x16Sc+IdUBg4pgB9Cn226LHv9T3tAQt92WeTcAfRHsAPo0fHisXx933BFTp0ahEIVCTJ0ad9wR69f7EjtgsPGpWID+DB0ay5fH8uV/+D2xESPybgigZ4IdQNVEOmBwcyoWACARgh0AQCIEOwCARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHAJAIwQ4AIBGCHQBAIgQ7AIBECHYAAIkQ7AAAEjEk7wZOM/v3xzPPRETMnBljxuTdDQCQFEfssrJnTyxaFGPHxvz5MX9+jB0bixbFnj15twUApMMRu0y8+GI0NMTzz78+Ui7HI4/Eli2xaVPU1eXXGQCQDkfsMrFs2RtSXcWePbFsWebdAABpEuxOvfb2eOihXpc+/HC0t2fYDQCQLKdiq/Xkk0/OmTNn2LBhbW1t27Zti4hLLrmkmnL7z38++8CBXud99dWn16+fPm/eAGZWKpVKpVKZffnUU09FxJEjR2LwEeyqNXHixGKxGBFnnnnmxIkTI6LKcnx9fd8zj6+vH9jMSqVSqVQq8yprampi8CmUy+W8exjsmpubGxsb29raOvfoQFx0UezY0euiZ58dcG8AQMZKpVJtbW1TU1NDQ0PevXTnGrtM3HrrQBYBABwPwS4TN98cS5f2ML50adx0U+bdAABpco1dJgqFeOCBWLQoVq2KrVsjImbNio98JBYtyrszACAdgl2GFi2S5ACAU8epWACARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHAJAIwQ4AIBGCHQBAIgQ7AIBECHYAAIkQ7AAAEiHYAQAkQrADAEiEYAcAkAjBDgAgEYIdAEAiBDsAgEQIdgAAiRDsAAASMSTvBt4EisViRNTW1ubdCAAwWHTGg8GmUC6X8+7hTWDLli1Hjx49KVMtW7bs4MGDS5cuPSmzMdisXLkyIuzfVNm/abN/07Zy5crhw4evWLHipMw2ZMiQOXPmnJSpTi5H7KpyEnfehAkTImLJkiUna0IGlfXr14f9my77N232b9o69+/ll1+edyOnlmvsAAASIdgBACRCsAMASIRgBwCQCMEOACARgh0AQCIEOwCARAh2AACJEOwAABLhlyeyNjh/Wo6Txf5Nm/2bNvs3bafJ/vVbsVl75ZVXImL06NF5N8IpYf+mzf5Nm/2bttNk/wp2AACJcI0dAEAiBDsAgEQIdgAAiRDsAAASIdgBACRCsAMASIRgBwCQCMEOACARgh0AQCIEOwCARAh2AACJEOwAABIh2AEAJEKwAwBIhGAHAJAIwe4kK5fL3/72t6+++uqRI0deddVV3/rWt8rl8km/CXk53p31z//8z4We/OIXv8isZwbgr/7qry6++OJq1vT8fTOqcv96/r65/OY3v/nYxz42adKkoUOHXnTRRZ/85Cf/6Z/+qe+bpPn8LXNSfepTn4qIKVOmLFmy5IILLoiIT33qUyf9JuTleHfWr371q4i4+OKLr32jp59+OrOeOV579+4dO3bsRRddVM3Knr9vOtXvX8/fN5EdO3aMHj06Iq666qqlS5e+/e1vj4i6urp9+/b1caskn7+C3cn03HPPnXHGGXPmzHnttdfK5XJra+vb3va2M84447nnnjuJNyEvA9hZP/jBDyLipz/9aXZdMlClUul//I//8Td/8zeTJk2KiGre+D1/30QGsH89f99EPvzhD0dE5yG3crnc0dHx13/91xHx8Y9/vLebpPr8FexOps997nMR8cMf/rAy8sMf/jAiPve5z53Em5CXAeysr3zlKxHxZn+ZOE10O2tTzRu/5++byAD27//X3r3HRHEtcBw/wCq4gCiL8hDfiyAoPrDqpoKpqEWrFQttVeqK9QFtoVVqfWuCVihJU41GQ6pYBTWmqcbGFrWtTappNa3KH5X4gPgq8hARqyCwsDv3j8ndu5fHCri8xu/nw0PM5gAADxlJREFUr52z58yc4XiWn2d2BuZvV2EymZydnX18fCwLa2pqnJycBg4c2FQrpc5fvmNnS/K6/fTp080l06ZNE0JcvnzZhk3QUVoxWPn5+T169Lh37150dPS4ceNiYmLkD5F26C1aSqPRVP1XM5swf7uQVowv87erePr0qYeHR0REhGWhnZ2do6Pj48ePm2ql1Pmr6ugOKEphYaGLi0uvXr3MJb1793ZxcSkqKrJhE3SUVgxWXl6ewWCYPHmyvHn58uUjR44cP3786NGjdnZ2bd5jtISdnZ2Tk1OLmjB/u5BWjC/zt6vo2bPnnTt36hWePn3633//nTlzZlOtlDp/WbGzpcLCQnd393qF7u7uhYWFNmyCjtKKwcrPzzcajZs3b75161ZpaemhQ4c8PDy+/fbbAwcOtG1f0S6Yv8rG/O26srOz58+f7+TktGXLlqbqKHX+smJnS5IkNfxvnCRJtbW1NmyCjtLSwZIk6fDhwxqNZsyYMXJJTEyMq6vrnDlzvvnmm8WLF7dtd9H2mL8KxvztogoKCtavX5+VlaXRaA4fPhwSEtJUTaXOX4KdLXl5eTV8ak55ebmPj48Nm6CjtHSw7Ozspk6dWq9w1qxZTk5OV69ebZMuon0xfxWM+dvlSJK0b9++pKSkZ8+eLV68ODU11dPT00p9pc5fLsXakpeX15MnT54+fWouefr0aUVFhfVg19Im6Cg2GSx7e3t3d/cePXq0QQfR3pi/Lxvmb6dlMpliY2OXL18eGBj4999/79+/33qqE8qdvwQ7W5o0aZIQ4uzZs+YS+bVOp7NhE3SUlg7Wjz/+qNVqMzIyLAsfPnxYWFgYFBTUlj1FO2H+Khjzt2tJTU3NzMxMSEg4f/58YGBgc5oodv52wCNWlOvmzZtCiNDQUIPBIEmSwWAICwsTQuTl5ZnrlJaWPnr0qEVN0Em0dHxLSkocHR19fX3v378vl1RXV8tP0Tx+/Hj79x/NJ5p4zhnzVxmaM77M3y6kqqpKo9EMHTq0rq7OSrWXZP4S7GwsNjZWCDFx4sS1a9eOHz9eCLF06VLLCg0/UJ7bBJ1HS8d3165dQoiePXvOmzdPr9cPGTJECKHX600mU7v3HS3Q1C9+5q8yNHN8mb9dxe+//y6E6NevX3hjzNVekvlLsLMxg8GQkpKi0+lcXV11Ol1aWlptba1lhYb/sJ7bBJ1HK8b3zJkz0dHRgwcPdnNzCwsLO3DgAL8VOr/mBzvmb1fU/PFl/nYJWVlZzbky+ZLMXzuJh2gDAAAoAjdPAAAAKATBDgAAQCEIdgAAAApBsAMAAFAIgh0AAIBCEOwAAAAUgmAHAACgEAQ7AAAAhSDYAQAAKATBDgAAQCEIdgAAAApBsAMAAFAIgh0AAIBCEOwAAAAUgmAHAACgEAQ7AAAAhSDYAQAAKATBDgAAQCEIdgAAAApBsAMAAFAIgh0AAIBCEOwAAAAUgmAHAACgEAQ7AAAAhSDYAQAAKATBDgAAQCEIdgAAAApBsAMAAFAIgh0AAIBCEOwAAAAUgmAHAACgEAQ7AAAAhSDYAWilgIAAOzu7hISERt+1s7MLCAhou6O39f6br7y8fP78+b1793Z1dX1u5Zs3byYkJAQEBKjVajc3t1GjRq1bt66oqKjVR5dHodXNASgMwQ7AC9mzZ8/Fixc7uhcdacOGDUePHvXz81u/fr2VapIkbd++PSgoaPfu3Q8ePJg0aVJwcHB+fv4XX3zh5+d37NixduswAAVTdXQHAHRtkiQtW7bsypUr3bp16+i+dIw//vhDCPHdd98NGDDASrX09PSkpCQ3N7d9+/ZFRUXJy2xGo3HXrl2rV69+++23f/rpp6lTp7b06Hq9/sGDB63uPACFYcUOwAuJj4+/evXql19+2dEd6TDV1dVCCOuprri4OCkpqXv37hcuXIiOjjZfPHVwcFixYsWJEyckSVqyZEltbW1Lj75+/fodO3a0rucAlIdgB+CFpKamenl5bdmyJT8/v6P70nmlp6dXV1cnJiYOHz684bszZ86MiIi4d+/e999/3/59A6AkBDsAL6RXr147d+6srq6Oj4+XJKnROo1+wd/y7ge5Qk1Nzccff6zVar28vBYuXFhZWXn37t25c+d6e3trNJq5c+cWFBTU20lBQUFUVFTfvn0HDx68ePHihw8fWr5bW1v7+eefv/LKK2q1un///suXL7937169XplMpoSEBLVa/cMPPzR1jpWVlatWrQoODnZ2dh41atSqVasqKyvNZ3Hjxg35hZWbGM6cOSOEWLZsWVMVli9fLoT4+eefm6rQVIctf7bya6PRmJKSMmTIECcnp6FDhyYnJ9fV1ckVJEnKzMwMCwtzc3MbPXr0pk2bjEaj5UCYTKavv/564sSJGo3GxcVl5MiRaWlprVhHBNBhJABoFX9/f/kzxGQyzZo1SwiRmZlpflcI4e/vX6+mpYYVIiIiIiMjN23aNGLECCHE5MmTPT095ZLAwEC5gmVzLy8vrVY7atSo2NhYeQ/9+/d//PixXKG2tjY0NNTR0fHNN9/86KOPoqKinJ2dNRrNrVu3LA+6detWlUoVFBR0/vz5Rk+zqqoqKChICDF69OilS5eOHTtWCBEYGFhVVSVJUlZWlpeXlxAiKysrKyurqZ+Vu7u7SqUyGAxNVcjNzRVChIWFNVWhqQ5b/mzl10uXLh05cuSaNWsSExN79uwphNi8ebNcITExUQjh4eExb968mJgYT0/PqKgoy4FYvXq1EEKj0URGRs6fP9/Hx0cIkZSUZKVXADoVgh2AVrKMFHfv3nV2dvbw8CgtLZVLWhHszPmjtLS0e/fuliUlJSXdunVTq9WWzYUQ7733Xl1dnSRJBoNBzigbN26UK+zZs8fBwSE3N9fc5P79+15eXgsWLLA8qFar/eeff6ycZmpqqhAiNjbWaDRKkmQ0Gt9//30hRFpampWzq8fBwaF///5WKlRUVAghRowYYaVOox1uGOwiIiJqamrkkl9//VUIERISIknShQsXhBDBwcElJSXyu2VlZSEhIZYDodFoXF1dHz16JG8+efLEw8Nj0KBB1s8OQOdBsAPQSvUCzVdffSWEWLRokbzZimBnDhySJGm12kZLLJsLIQoKCswlt2/fFkKMHTtW3pw0aZJKpfL/f2q12tvb2/Kg2dnZ1k9z/PjxQoiioiJzSWFhoRBCp9NZObt6nrtiJ1/PNa/Y1eu2lQ43DHZ//vmn+V35Kqq8h7i4uIbNT506ZTkQQ4YMsbe3P3v2rMlksn5GADonHncCwDYSExMPHTp08OBBvV4/ZcqUVuyhb9++5tcODg6NltSr369fP/PmoEGDNBpNXl6evHn9+vW6ujo5MFkyf+FMJi9ZWZGXl+fp6Slfb5V5e3v36dPHfKDmGDZs2MWLF2/fvj1s2LBGK1y7dk0IIYdXIUTDbje/w/KFY5lK9b8PefkQEyZMsKw8btw4y80DBw7o9frw8HB/f//XXntt8uTJM2bMcHNzs35EAJ0HN08AsA2VSrV37157e/u4uLiqqirrlZ9boTka3qxgb2/v6Ogov66rq/P19W3439mamhrLJpbZsUUHatEtBa+//roQYu/evU1VyMjIEEK88cYb8ma9Preow2q1utFyg8HQsNDe/v9+C4SGhubl5Z07d+7dd9+9efPmggULBg4cePLkSetHBNB5EOwA2MzYsWNXrFiRn5+/bdu2hu8ajUbza/legRdUUlIiXxWV3b17t7S0dOjQofLmsGHDioqKSkpKzBUkSdqwYYOVdNUorVZbXFxsuR95U77u2UxxcXGOjo47d+6Ul83qyc7OPnnypFarle9BaSPySt5ff/1lWXj58mXLzTNnzuTm5oaGhiYnJ589ezY3N7eysrKpvxoHoBMi2AGwpeTk5AEDBqSlpVkWymtI8pf3hRC1tbXJyck2OdzatWvlvGgwGD799FMhRHR0tPzWW2+9ZTQa4+PjzStV+/fvT0lJaeliYWRkpBBiw4YNJpNJCGEymdatWyeEmDNnTvN34u3tvX37doPBoNPpjh07Zl6EMxqNO3bsiIyMVKlU6enp8i0jbeSdd94RQqxbt66srEwuKS8vr/dn0OLi4mbPnm3+iXl4eDg6Oja61Aegc+I7dgBsycXFZc+ePfVWniIiInJycmbPnr1o0SK1Wp2dnW3+MtkLKi4uDgkJGTNmzIULF27cuOHn5/fBBx/Ib61YseLIkSMnTpwICgoKCwsrKio6derUuHHjrDxMrlErV648fPhwRkZGTk5OSEjIpUuXcnJygoKCkpKSWrSf+Pj4qqqq1atXR0dHu7u7h4SEVFdXX7lypbKysk+fPunp6eHh4S3aYUtNnz592bJle/fuDQwMDA8PV6lUv/zyS3h4+KVLl8yBMiYmJiUlJSAgYMqUKWVlZb/99pv8DL827RgAW2qHGzQAKJKVu0HlxSHzvZY1NTUbN24cPHiwWq2eMGHC1q1b5S+6Wblt9rkl8idYRUXFkiVLfH19fX19Fy1aVFZWZtnk2bNna9asCQ4O7tGjh1ar/eyzz8rLy5vT/3oqKiqSkpJGjBihVqtHjhy5atWqioqKVuxHkqRr1659+OGHfn5+Tk5Offv2DQsL27hxo/nZe9Y1eqCGd8XWq2D5czaZTJmZmTqdztXVdcyYMdu2bSsuLhZCTJs2Ta5gMBjS0tKGDx+uVqt79+49YcKEjIwM7pAFuhA7qYknxQMAlOT69euXLl3S6XTmryEKIU6fPj1jxgy9Xn/w4MEO7BsAW+E7dgDwUnjw4MHChQv1ev2dO3eEEJIk5eTkrFy5UljcjQugq2PFDgBeCkajMTIyUv4Lsz4+Ps+ePXv8+LEQ4tVXXz137ly9554A6KIIdgDwsqiqqtq9e3dWVtatW7ecnJz8/f0jIyM/+eSTbt26dXTXANgGwQ4AAEAhWHsHAABQCIIdAACAQhDsAAAAFIJgBwAAoBAEOwAAAIUg2AEAACgEwQ4AAEAhCHYAAAAKQbADAABQCIIdAACAQhDsAAAAFIJgBwAAoBAEOwAAAIUg2AEAACgEwQ4AAEAhCHYAAAAKQbADAABQCIIdAACAQhDsAAAAFIJgBwAAoBAEOwAAAIUg2AEAACgEwQ4AAEAhCHYAAAAKQbADAABQCIIdAACAQvwHvDbIX1zvVawAAAAASUVORK5CYII="
}
}
]
},
{
"cell_type": "markdown",
"source": "Another way of visually representing this variable is through a Histogram and a Desnity curve. Here, we plot probability densities instead of the frequencies on the y-axis. From the output produced below, you can tell that chance of zero O-rings experiencing thermal distress is approximately 3 times the chance of 1 O-ring experiencing thermal distress and > 15 times the chance of 2 O-rings experiencing thermal distress.",
"metadata": {}
},
{
"cell_type": "code",
"source": "hist(orings$OringsThermalDistress, main = \"O-rings Experiencing Thermal Distress\", col = \"green\", xlab = \"Number of O-rings\", freq = F)\nlines(density(orings$OringsThermalDistress), col = \"blue\", lwd = 2) #adds a density curve",
"metadata": {},
"execution_count": 5,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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"
}
}
]
},
{
"cell_type": "markdown",
"source": "### Launch temperature in degrees Farenheight",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "This variable is one of our predictor variables. From the analysis below, we can see that in the 23 flights prior to the Challeger's final flight, the mean launch temperature was 69.57 \u00b0F with the median being 70 \u00b0F. The lowest launch temperature recorded was 53 \u00b0F which is much higher than the temperature recorded on the day of the Challenger's final launch (30 \u00b0F or below freezing).",
"metadata": {}
},
{
"cell_type": "code",
"source": "summary(orings$LaunchTempDegF)",
"metadata": {},
"execution_count": 6,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": " Min. 1st Qu. Median Mean 3rd Qu. Max. \n 53.00 67.00 70.00 69.57 75.00 81.00 "
}
}
]
},
{
"cell_type": "markdown",
"source": "A good way of visually representing this variable is by using a kernel density plot. The code below generates this plot:",
"metadata": {}
},
{
"cell_type": "code",
"source": "d <- density(orings$LaunchTempDegF) #stores the density in object d\nplot(d, main = \"Kernel Density of Launch Temperature\", xlab = \"Temperature in \u00b0F\") #creates a minimal graph with a title\npolygon(d, col = \"red\", border = \"blue\") #colors the curve blue and fills the area under the curve with red\nrug(orings$LaunchTempDegF, col = \"brown\") #adds a brown rug, i.e. creates a set of tick marks along the base of a plot",
"metadata": {},
"execution_count": 7,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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"
}
}
]
},
{
"cell_type": "markdown",
"source": "From the chart, you can tell that the distribution is bimodal and slightly skewed to the left which is why the mean (69.7 \u00b0F) is slightly below the median (70 \u00b0F). Another way of representing this data visually is by using a box plot as shown below:",
"metadata": {}
},
{
"cell_type": "code",
"source": "boxplot(orings$LaunchTempDegF, data = orings, #formula, data\n main = \"Launch Temperature\", #title\n xlab = \"Temperature in \u00b0F\") #x-axis label",
"metadata": {},
"execution_count": 8,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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"
}
}
]
},
{
"cell_type": "markdown",
"source": "From the chart above, you can tell that 53 \u00b0F is an outlier (< 1.5 times the Interquartile Range). By examining the dataset, you can also tell that this value was recorded for flight #14 and that was the only flight in our dataset where the number of O-rings experiencing thermal pressure was equal to 2. This appears to suggest that a lower launch temperature may be associated with an increase in the number of O-rings experiencing thermal pressure.",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "### Leak-check pressure per square inch",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "This variable is one of our predictor variables. Our analysis is provided below.",
"metadata": {}
},
{
"cell_type": "code",
"source": "summary(orings$LeakCheckPressurePsi)\ntable(orings$LeakCheckPressurePsi)",
"metadata": {},
"execution_count": 9,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": " Min. 1st Qu. Median Mean 3rd Qu. Max. \n 50.0 75.0 200.0 152.2 200.0 200.0 "
}
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "\n 50 100 200 \n 6 2 15 "
}
}
]
},
{
"cell_type": "markdown",
"source": "From the above result, we can see that Leak-check Pressure is a discrete numerical variable. Of the 23 observations, in 6 cases, the pressure was 50, in 2 cases the pressure was 100 and in 15 cases the pressure was 200. A dotchart of this variable is provided below:",
"metadata": {}
},
{
"cell_type": "code",
"source": "dotchart(orings$LeakCheckPressurePsi, main = \"Leak-check Pressure\", col = \"red\", pch = 19, xlab = \"Pressure psi\", ylab = \"Frequency\")",
"metadata": {},
"execution_count": 10,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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"
}
}
]
},
{
"cell_type": "markdown",
"source": "From the dataset, we can observe that with the exception of 1 case of an O-ring experiencing thermal distress at a leak-check pressure of 50 psi, all other instances of O-ring(s) experiencing thermal distress occurred when the leak-check pressure was 200 psi.",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "### Temporal order of flights",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "This variable is simply a temporal ordering of flight numbers and can therefore be ignored in the remainder of our analysis.",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "### Key learning from this section",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "The key learning from this section is that for future analysis, we should consider the relationship between the O-rings expriencing thermal pressure with the launch temperature and the leak-check pressure.",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "## Covariance and correlation analysis",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "### O-rings experiencing thermal pressure and launch temperature",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "From the code below, we can see that these two variables have a covariance of -2.86. This suggests a negative linear relationship, i.e., when temperature reduces, the number of O-rings experiencing thermal pressure appears to rise. The correlation coefficient of -0.73 confirms this negative relationship and additionally suggests that this relationship is very strong.",
"metadata": {}
},
{
"cell_type": "code",
"source": "round(stats::cov(orings$OringsThermalDistress, orings$LaunchTempDegF), 2)",
"metadata": {},
"execution_count": 11,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "[1] -2.86",
"text/html": "-2.86",
"text/markdown": "-2.86",
"text/latex": "-2.86"
}
}
]
},
{
"cell_type": "code",
"source": "round(stats::cor(orings$OringsThermalDistress, orings$LaunchTempDegF), 2)",
"metadata": {},
"execution_count": 12,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "[1] -0.73",
"text/html": "-0.73",
"text/markdown": "-0.73",
"text/latex": "-0.73"
}
}
]
},
{
"cell_type": "markdown",
"source": "We can confirm this relationship visually by creating a scatterplot as follows:",
"metadata": {}
},
{
"cell_type": "code",
"source": "plot(orings$LaunchTempDegF, orings$OringsThermalDistress, xlab = \"Launch Temperature \u00b0F\", ylab = \"O-rings Experiencing Thermal Distress\")\nabline(lm(orings$OringsThermalDistress ~ orings$LaunchTempDegF), col = \"red\") #adds a line of fit to the scatter plot",
"metadata": {},
"execution_count": 13,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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"
}
}
]
},
{
"cell_type": "markdown",
"source": "### O-rings experiencing thermal pressure and leak-check pressure",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "From the code below, we can see that these two variables have a covariance of 8.4. This suggests a positive linear relationship, i.e., when pressure reduces, the number of O-rings experiencing thermal pressure appears to reduce. The correlation coefficient of 0.22 confirms this positive relationship but suggests that this relationship is weak to moderate at best.",
"metadata": {}
},
{
"cell_type": "code",
"source": "round(stats::cov(orings$OringsThermalDistress, orings$LeakCheckPressurePsi), 2)",
"metadata": {},
"execution_count": 14,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "[1] 8.4",
"text/html": "8.4",
"text/markdown": "8.4",
"text/latex": "8.4"
}
}
]
},
{
"cell_type": "code",
"source": "round(stats::cor(orings$OringsThermalDistress, orings$LeakCheckPressurePsi), 2)",
"metadata": {},
"execution_count": 15,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "[1] 0.22",
"text/html": "0.22",
"text/markdown": "0.22",
"text/latex": "0.22"
}
}
]
},
{
"cell_type": "markdown",
"source": "We can confirm this relationship visually by creating a scatterplot as follows:",
"metadata": {}
},
{
"cell_type": "code",
"source": "plot(orings$LeakCheckPressurePsi, orings$OringsThermalDistress, xlab = \"Leak-check Pressure psi\", ylab = \"O-rings Experiencing Thermal Distress\")\nabline(lm(orings$OringsThermalDistress ~ orings$LeakCheckPressurePsi), col = \"red\") #adds a line of fit to the scatter plot",
"metadata": {},
"execution_count": 16,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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"
}
}
]
},
{
"cell_type": "markdown",
"source": "### Launch temperature and leak-check pressure",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "From the code below, we can see that these two variables have a covariance of 19.17. This suggests a positive linear relationship, i.e., when the launch temperature reduces, the pressure appears to reduce and vice versa. However, the correlation coefficient of 0.04 confirms that this relationship is almost non-existent.",
"metadata": {}
},
{
"cell_type": "code",
"source": "round(stats::cov(orings$LaunchTempDegF, orings$LeakCheckPressurePsi), 2)",
"metadata": {},
"execution_count": 17,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "[1] 19.17",
"text/html": "19.17",
"text/markdown": "19.17",
"text/latex": "19.17"
}
}
]
},
{
"cell_type": "code",
"source": "round(stats::cor(orings$LaunchTempDegF, orings$LeakCheckPressurePsi), 2)",
"metadata": {},
"execution_count": 18,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "[1] 0.04",
"text/html": "0.04",
"text/markdown": "0.04",
"text/latex": "0.04"
}
}
]
},
{
"cell_type": "markdown",
"source": "### Key learning from this section",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "The key learning from this section is that for future analysis, we should only consider the relationship between the O-rings experiencing thermal pressure as the response variable and the launch temperature as the predictor variable.",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "## Simple Linear Regression between O-rings experiencing thermal distress and launch temperature",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "The code below fits a simple linear regression model between these two variables and displays the summary and coefficients of the model.",
"metadata": {
"collapsed": true
}
},
{
"cell_type": "code",
"source": "fit <- lm(OringsThermalDistress ~ LaunchTempDegF, data = orings)\nsummary(fit)\ncoef(fit)",
"metadata": {},
"execution_count": 19,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "\nCall:\nlm(formula = OringsThermalDistress ~ LaunchTempDegF, data = orings)\n\nResiduals:\n Min 1Q Median 3Q Max \n-0.50921 -0.30810 0.00794 0.20905 0.74381 \n\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 4.30159 0.83110 5.176 3.96e-05 ***\nLaunchTempDegF -0.05746 0.01189 -4.833 8.90e-05 ***\n---\nSignif. codes: 0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 0.3935 on 21 degrees of freedom\nMultiple R-squared: 0.5266,\tAdjusted R-squared: 0.5041 \nF-statistic: 23.36 on 1 and 21 DF, p-value: 8.895e-05\n"
}
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": " (Intercept) LaunchTempDegF \n 4.30158730 -0.05746032 ",
"text/html": "<dl class=dl-horizontal>\n\t<dt>(Intercept)</dt>\n\t\t<dd>4.3015873015873</dd>\n\t<dt>LaunchTempDegF</dt>\n\t\t<dd>-0.0574603174603175</dd>\n</dl>\n",
"text/markdown": "(Intercept)\n: 4.3015873015873LaunchTempDegF\n: -0.0574603174603175\n\n",
"text/latex": "\\begin{description*}\n\\item[(Intercept)] 4.3015873015873\n\\item[LaunchTempDegF] -0.0574603174603175\n\\end{description*}\n"
}
}
]
},
{
"cell_type": "markdown",
"source": "The results of the simple linear regression are as follows:\n1. The intercept of 4.3 suggests that 4.3 O-rings would experience thermal distress if the launch temperature were 0 \u00b0F.\n2. The slope of -0.06 confirms the negative relationship and suggests that for every 1 \u00b0F increase in launch temperature, the number of O-rings experiencing thermal distress would reduce by 0.06.\n3. The multiple R-squared (0.53) and the adjusted R-squared (0.5) suggest that approximately 50% of the variation in the number of O-rings experiencing thermal distress can be explained by the launch temperature.\n\nThis clearly shows a strong relationship between these two variables. Next, we will use this model to create a prediction of the number of O-rings likely to experience thermal distress based on the launch temperature. ",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "## Predictive model based on simple linear regression",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "The following code produces the predictive model based on the simple linear regression model created above:",
"metadata": {}
},
{
"cell_type": "code",
"source": "intercept <- fit$coefficients[1] #store the intercept in a separate object\nintercept",
"metadata": {},
"execution_count": 20,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "(Intercept) \n 4.301587 ",
"text/html": "<strong>(Intercept):</strong> 4.3015873015873",
"text/markdown": "**(Intercept):** 4.3015873015873",
"text/latex": "\\textbf{(Intercept):} 4.3015873015873"
}
}
]
},
{
"cell_type": "code",
"source": "slope <- fit$coefficients[2] #store the slope in a separate object\nslope",
"metadata": {},
"execution_count": 21,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "LaunchTempDegF \n -0.05746032 ",
"text/html": "<strong>LaunchTempDegF:</strong> -0.0574603174603175",
"text/markdown": "**LaunchTempDegF:** -0.0574603174603175",
"text/latex": "\\textbf{LaunchTempDegF:} -0.0574603174603175"
}
}
]
},
{
"cell_type": "code",
"source": "#create a prediction function\npredict <- function(tempF) {\n fitted <- round((intercept + (slope * tempF)))\n text <- \"O-rings likely experiencing thermal distress = \"\n return (paste(text, fitted))\n}",
"metadata": {
"collapsed": true
},
"execution_count": 22,
"outputs": []
},
{
"cell_type": "markdown",
"source": "We can now use our \"predict\" function to predict the number of O-rings likely to fail based on the actual launch temperature recorded during the Challenger's final flight (approximately 30 \u00b0F), as follows:",
"metadata": {}
},
{
"cell_type": "code",
"source": "predict(30)",
"metadata": {},
"execution_count": 23,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "[1] \"O-rings likely experiencing thermal distress = 3\"",
"text/html": "<span style=white-space:pre-wrap>'O-rings likely experiencing thermal distress = 3'</span>",
"text/markdown": "<span style=white-space:pre-wrap>'O-rings likely experiencing thermal distress = 3'</span>",
"text/latex": "'O-rings likely experiencing thermal distress = 3'"
}
}
]
},
{
"cell_type": "markdown",
"source": "As can be seen from our predictive model, the number of O-rings likely experiencing thermal distress is 3, which is greater than any of our observations. This level of thermal distress turned out to be catastrophic for the Challenger.",
"metadata": {
"collapsed": true
}
},
{
"cell_type": "markdown",
"source": "## Conclusion",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "While this dataset and my analysis above demonstrates a strong negative linear relationship between the number of O-rings experiencing failure and the launch temperature, we can only conclude that an association exists between these two variables but cannot state that a causal relationship exists (that is, correlation does not imply causation) since this is an observational study.\n\nHowever, my analysis confirms the reservations expressed by the engineers prior to launch and their reluctance to approve the launch without analyzing additional data. You can read more about this here: https://en.wikipedia.org/wiki/Space_Shuttle_Challenger_disaster#January_28_launch_and_failure and watch a documentary on this topic here: https://www.youtube.com/watch?v=2FehGJQlOf0.",
"metadata": {}
}
],
"nbformat": 4,
"metadata": {
"kernelspec": {
"language": "R",
"name": "r-spark21",
"display_name": "R with Spark 2.1"
},
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