Geoscience_ML_notebook_3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bivariate pay-production prediction interval\n",
    "\n",
    "\n",
    "Matteo Niccoli, MyCarta - Calgary, Alberta, Canada\n",
    "\n",
    "mycarta.wordpress.com\n",
    "\n",
    "matteo@mycarta.ca"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### This notebook is intended to show how to use the Prediction Interval of a regression to discuss economic risk."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's first define the Prediction Interval:\n",
    "\n",
    "we look at any specific value of x, say x0, and at that x0 we find an interval around the predicted value of y, y0 such that there is a 95% probability that the value of a new point, for example the next well to be drilled, is within this interval (prediction of a future value).\n",
    "\n",
    "I have found very useful to go through the examples AND the explanation of the difference between Confidence Interval and Prediction Interval, in both [Brown's Prediction Interval for Responses to a Particular x](https://brownmath.com/stat/infregr.htm#IndivResp) and in [this great answer on Cross Validated](https://stats.stackexchange.com/a/271232/54871)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data we will use comes from the paper [Many correlation coefficients, null hypotheses, and high value](http://csegrecorder.com/features/view/value-of-integrated-geophysics-201312) (Lee Hunt, CSEG Recorder, December 2013).\n",
    "\n",
    "\n",
    "The target variable to be predicted is oil production (measured in tens of barrels of oil per day) from a marine barrier sand. The independent variable is gross pay in meters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we import the Python libraries we will need, and the data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv('Table2_Hunt_2013_edit.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We quickly dispaly some statistics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Gross pay</th>\n",
       "      <th>Phi-h</th>\n",
       "      <th>Position</th>\n",
       "      <th>Pressure</th>\n",
       "      <th>Random 1</th>\n",
       "      <th>Random 2</th>\n",
       "      <th>Gross pay transform</th>\n",
       "      <th>Production</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>21.000000</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>21.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>9.823810</td>\n",
       "      <td>68.880952</td>\n",
       "      <td>1.885714</td>\n",
       "      <td>15.285714</td>\n",
       "      <td>10.190476</td>\n",
       "      <td>292.714286</td>\n",
       "      <td>16.579524</td>\n",
       "      <td>33.428571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>5.948521</td>\n",
       "      <td>45.167894</td>\n",
       "      <td>0.708721</td>\n",
       "      <td>2.759400</td>\n",
       "      <td>6.439092</td>\n",
       "      <td>59.429069</td>\n",
       "      <td>6.543793</td>\n",
       "      <td>15.141909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.100000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>210.000000</td>\n",
       "      <td>3.540000</td>\n",
       "      <td>7.710000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>4.900000</td>\n",
       "      <td>24.600000</td>\n",
       "      <td>1.100000</td>\n",
       "      <td>14.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>245.000000</td>\n",
       "      <td>11.520000</td>\n",
       "      <td>22.670000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>10.000000</td>\n",
       "      <td>72.900000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>273.000000</td>\n",
       "      <td>16.900000</td>\n",
       "      <td>36.420000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>15.100000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>2.200000</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>340.000000</td>\n",
       "      <td>21.970000</td>\n",
       "      <td>44.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>19.100000</td>\n",
       "      <td>160.000000</td>\n",
       "      <td>2.900000</td>\n",
       "      <td>20.000000</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>395.000000</td>\n",
       "      <td>29.250000</td>\n",
       "      <td>59.200000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Gross pay       Phi-h   Position   Pressure   Random 1    Random 2  \\\n",
       "count  21.000000   21.000000  21.000000  21.000000  21.000000   21.000000   \n",
       "mean    9.823810   68.880952   1.885714  15.285714  10.190476  292.714286   \n",
       "std     5.948521   45.167894   0.708721   2.759400   6.439092   59.429069   \n",
       "min     0.100000    0.500000   1.000000  10.000000   1.000000  210.000000   \n",
       "25%     4.900000   24.600000   1.100000  14.000000   6.000000  245.000000   \n",
       "50%    10.000000   72.900000   2.000000  16.000000  10.000000  273.000000   \n",
       "75%    15.100000  100.000000   2.200000  17.000000  13.000000  340.000000   \n",
       "max    19.100000  160.000000   2.900000  20.000000  21.000000  395.000000   \n",
       "\n",
       "       Gross pay transform  Production  \n",
       "count            21.000000   21.000000  \n",
       "mean             16.579524   33.428571  \n",
       "std               6.543793   15.141909  \n",
       "min               3.540000    7.710000  \n",
       "25%              11.520000   22.670000  \n",
       "50%              16.900000   36.420000  \n",
       "75%              21.970000   44.200000  \n",
       "max              29.250000   59.200000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And since we are only interested in Production and Gross Pay (the highest predictor, as shown in <a href=\"https://github.com/mycarta/predict/blob/master/Geoscience_ML_notebook_2.ipynb\"> this notebook</a>), we drop the other variables. We also change the index for the wells so as to be one-based (default indexing for Pandas is zero-based)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Gross pay</th>\n",
       "      <th>Production</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.1</td>\n",
       "      <td>15.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>21.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.9</td>\n",
       "      <td>22.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.1</td>\n",
       "      <td>15.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4.1</td>\n",
       "      <td>7.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4.9</td>\n",
       "      <td>22.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.9</td>\n",
       "      <td>18.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>7.0</td>\n",
       "      <td>24.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>8.1</td>\n",
       "      <td>24.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>8.9</td>\n",
       "      <td>25.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>10.0</td>\n",
       "      <td>36.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>11.1</td>\n",
       "      <td>36.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>11.9</td>\n",
       "      <td>39.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>13.0</td>\n",
       "      <td>51.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>14.1</td>\n",
       "      <td>48.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>15.1</td>\n",
       "      <td>51.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>15.9</td>\n",
       "      <td>59.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>16.0</td>\n",
       "      <td>58.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>17.1</td>\n",
       "      <td>41.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>18.0</td>\n",
       "      <td>44.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>19.1</td>\n",
       "      <td>37.51</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Gross pay  Production\n",
       "1         0.1       15.10\n",
       "2         1.0       21.30\n",
       "3         1.9       22.75\n",
       "4         3.1       15.72\n",
       "5         4.1        7.71\n",
       "6         4.9       22.67\n",
       "7         5.9       18.11\n",
       "8         7.0       24.30\n",
       "9         8.1       24.04\n",
       "10        8.9       25.11\n",
       "11       10.0       36.80\n",
       "12       11.1       36.42\n",
       "13       11.9       39.59\n",
       "14       13.0       51.60\n",
       "15       14.1       48.05\n",
       "16       15.1       51.72\n",
       "17       15.9       59.20\n",
       "18       16.0       58.30\n",
       "19       17.1       41.80\n",
       "20       18.0       44.20\n",
       "21       19.1       37.51"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = data.drop(['Phi-h','Position','Pressure','Random 1','Random 2','Gross pay transform'], axis=1)\n",
    "indexed_data = data.set_index([np.arange(1,22,1)])\n",
    "display(indexed_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use Statsmodels' <a href=\"http://statsmodels.sourceforge.net/devel/examples/notebooks/generated/ols.html\"> Ordinary Least Square</a> to perform the regression and also to calculate the Prediction Interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "sort_data = indexed_data.sort_values(by='Gross pay', ascending=True)\n",
    "\n",
    "X = sort_data.loc[:,'Gross pay']\n",
    "X = sm.add_constant(X, prepend=False) # add intercept\n",
    "y = sort_data.loc[:,'Production']\n",
    "\n",
    "model = sm.OLS(y, X)\n",
    "results = model.fit()\n",
    "predicted = results.predict()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you do not want to see a summary of the statistics, comment out the code in the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             Production   R-squared:                       0.721\n",
      "Model:                            OLS   Adj. R-squared:                  0.707\n",
      "Method:                 Least Squares   F-statistic:                     49.15\n",
      "Date:                Sun, 13 Nov 2016   Prob (F-statistic):           1.12e-06\n",
      "Time:                        22:22:40   Log-Likelihood:                -72.940\n",
      "No. Observations:                  21   AIC:                             149.9\n",
      "Df Residuals:                      19   BIC:                             152.0\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "Gross pay      2.1617      0.308      7.011      0.000         1.516     2.807\n",
      "const         12.1920      3.518      3.465      0.003         4.828    19.556\n",
      "==============================================================================\n",
      "Omnibus:                        0.572   Durbin-Watson:                   0.905\n",
      "Prob(Omnibus):                  0.751   Jarque-Bera (JB):                0.638\n",
      "Skew:                          -0.187   Prob(JB):                        0.727\n",
      "Kurtosis:                       2.232   Cond. No.                         22.6\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we predict the lower and upper boundaries of the prediction interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.sandbox.regression.predstd import wls_prediction_std\n",
    "pred_std, iv_l, iv_u = wls_prediction_std(results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can display the regression with the data and the prediction interval in a single plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YHNu2kjv5Apr/biKujQWEDjuc4umzwFf3RmtvUv5MmIiIiIgdml3wR7wffoDl91N+zQ1U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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117176dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 10))\n",
    "ax = plt.subplot(111)\n",
    "ax.plot(range(21), y, 'o', label = \"True: 21 wells\")\n",
    "ax.plot(range(21), predicted, '-', lw=2, label = \"Predicted OLS\")\n",
    "ax.plot(range(21), iv_l, 'r--', lw=2)\n",
    "ax.plot(range(21), iv_u, 'r--', lw=2)\n",
    "ax.legend(loc='best');\n",
    "ax.get_xaxis().set_minor_locator(mpl.ticker.AutoMinorLocator())\n",
    "ax.get_yaxis().set_minor_locator(mpl.ticker.AutoMinorLocator())\n",
    "ax.grid(b=True, which='major', color='w', linewidth=1.0)\n",
    "ax.grid(b=True, which='minor', color='w', linewidth=0.5)\n",
    "\n",
    "# P.arrow( x, y, dx, dy, **kwargs )\n",
    "ax.arrow(0,20,3.1,0,fc='g',ec='g',head_width=1, head_length=.3)\n",
    "ax.arrow(3.5,20,0,-18.7,fc='g',ec='g',head_width=.3, head_length=1)\n",
    "ax.arrow(0,20,11.6,0,fc='m',ec='m',head_width=1, head_length=.3)\n",
    "ax.arrow(12,20,0,-18.7,fc='m',ec='m',head_width=.3, head_length=1)\n",
    "plt.xticks(list(plt.xticks()[0]) + [3.5, 12])\n",
    "ax.set_xlabel('Gross Pay')\n",
    "ax.set_ylabel('Production')\n",
    "ax.set_ylim([0, 80])\n",
    "ax.set_xlim([-0.2, 20.2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How do we use this figure then? Let's say we drilled the 21 wells; we're obviously in an appraisal stage. Our minimum economic production cutoff is 20 (bbl/d x10). With 21 wells the regression would suggest a minimum gross pay of 3.5 m to be above the cutoff value. But how likely is that? If we used the prediction interval, we could constrain the probability, but we'd have to pick a minimum gross pay of 12 m for the next well, which is equivalent to saying that there's a 95 % probability the production will be between 20 (our cutoff) and 56 (bbl/d x10)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But, what would happen if we had less wells? Let's say we are in earlier stages of the appraisal process. \n",
    "To simulate that, we randomly select only 7 of the 21 wells and repeat the exercise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  1  4  6  9 18 19]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(37)\n",
    "rfew = np.sort(np.random.choice(range(21), 7, replace=False))\n",
    "print rfew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "sort_data_few = sort_data.iloc[rfew]\n",
    "Xfew = sort_data_few.loc[:,'Gross pay']\n",
    "Xfew = sm.add_constant(Xfew, prepend=False) # add intercept:\n",
    "                        \n",
    "yfew = sort_data_few.loc[:,'Production']\n",
    "\n",
    "modelfew = sm.OLS(yfew, Xfew)\n",
    "resultsfew = modelfew.fit()\n",
    "\n",
    "predictedf = resultsfew.predict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pred_stdf, iv_lf, iv_uf = wls_prediction_std(resultsfew)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AEtM0p6UzBxEREZFslNYrYaZpPmGa5gmmaZ4ILABuBn4I3G6a5nGA2zCMc9OZg4iIiEg2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\nREREbKAiTERERMQGKsJEREREbPD/AFMjsbHRSXBQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11718c3d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 10))\n",
    "ax = plt.subplot(111)\n",
    "ax.plot(rfew, yfew, 'o', label = \"True, 7 wells\")\n",
    "ax.plot(rfew, predictedf, '-', lw=2, label = \"Predicted OLS\")\n",
    "ax.plot(rfew, iv_lf, 'r--', lw=2)\n",
    "ax.plot(rfew, iv_uf, 'r--', lw=2)\n",
    "ax.legend(loc='best');\n",
    "ax.get_xaxis().set_minor_locator(mpl.ticker.AutoMinorLocator())\n",
    "ax.get_yaxis().set_minor_locator(mpl.ticker.AutoMinorLocator())\n",
    "ax.grid(b=True, which='major', color='w', linewidth=1.0)\n",
    "ax.grid(b=True, which='minor', color='w', linewidth=0.5)\n",
    "\n",
    "# P.arrow( x, y, dx, dy, **kwargs )\n",
    "ax.arrow(0,20,4.6,0,fc='g',ec='g',head_width=1, head_length=.3)\n",
    "ax.arrow(5,20,0,-18.7,fc='g',ec='g',head_width=.3, head_length=1)\n",
    "ax.arrow(0,20,17.3,0,fc='m',ec='m',head_width=1, head_length=.3)\n",
    "ax.arrow(17.5,20,0,-18.7,fc='m',ec='m',head_width=.3, head_length=1)\n",
    "plt.xticks(list(plt.xticks()[0]) + [17.5])\n",
    "ax.set_xlabel('Gross Pay')\n",
    "ax.set_ylabel('Production')\n",
    "ax.set_ylim([0, 80])\n",
    "ax.set_xlim([-0.2, 20.2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With 7 wells the minimum gross pay suggested by the regression is not a lot higher: 5 m instead of 3.5. However, using the wider prediction interval, now the minimum gross pay has gone up from 12 m to 17.5 m.\n",
    "\n",
    "This is in part due to a wider prediction interval, in part to the fact that the regression is more flat (smaller angle from x axis).\n",
    "\n",
    "Perhaps we can live with this result. As Hunt suggests in the paper, what is important is that we should understand the statistics, and either choose to accept the statistical nature of the outcomes we endure, improve the conditions of our investigative techniques (or drill more wells), or if we are not comfortable move on to something else.\n",
    "\n",
    "Going back to the 21 well example, we can make conclusions via inductive confirmation:\n",
    "IF production is higher than 20 (bbl/d x10), then the gross pay will likely be greater than 12.5 m. Next well drilled has gross pay greater than 9.5 m: there is a 95% probability that the production will be higher than the minimum economic of 20 (bbl/d x10)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that in some cases, fewer wells may result in better production estimates (a narrower prediction intervals and or a steeper regression fit - larger angle to x axis). What you get depends just on the lack of the draw (the random choice of 7 wells)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "py36",
   "language": "python",
   "name": "conda-env-py36-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}