tonicanada/statistics_causality_fixed_effects.ipynb

## statistics_causality_fixed_effects.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Causality // Fixed effects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Basado en curso: \n",
    "https://www.youtube.com/watch?v=eBij0BFc-RM&list=PLcTBLulJV_AKmUTH-nUsxxFyRQoWnUzxU&index=1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Fixed effects` is a particular way of controlling, when you control for individual."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = []\n",
    "seed = 42\n",
    "individuals = 4\n",
    "mean = 0\n",
    "std = 1\n",
    "for i in range(individuals*2):\n",
    "    np.random.seed(seed)\n",
    "    s.append(np.random.normal(mean,1,100))\n",
    "    seed += 1\n",
    "    mean += 0.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ind_0_x</th>\n",
       "      <th>ind_0_y</th>\n",
       "      <th>ind_1_x</th>\n",
       "      <th>ind_1_y</th>\n",
       "      <th>ind_2_x</th>\n",
       "      <th>ind_2_y</th>\n",
       "      <th>ind_3_x</th>\n",
       "      <th>ind_3_y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.496714</td>\n",
       "      <td>0.557400</td>\n",
       "      <td>-0.150615</td>\n",
       "      <td>0.926375</td>\n",
       "      <td>1.784876</td>\n",
       "      <td>0.651991</td>\n",
       "      <td>0.806369</td>\n",
       "      <td>1.056841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.138264</td>\n",
       "      <td>-0.608481</td>\n",
       "      <td>1.916357</td>\n",
       "      <td>1.160322</td>\n",
       "      <td>2.431196</td>\n",
       "      <td>2.805906</td>\n",
       "      <td>0.736599</td>\n",
       "      <td>1.279144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.647689</td>\n",
       "      <td>-0.078503</td>\n",
       "      <td>1.846140</td>\n",
       "      <td>0.504854</td>\n",
       "      <td>2.021900</td>\n",
       "      <td>2.424208</td>\n",
       "      <td>1.161924</td>\n",
       "      <td>2.765146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.523030</td>\n",
       "      <td>-0.234916</td>\n",
       "      <td>-1.004916</td>\n",
       "      <td>0.695699</td>\n",
       "      <td>0.400772</td>\n",
       "      <td>2.140412</td>\n",
       "      <td>2.861589</td>\n",
       "      <td>3.922627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.234153</td>\n",
       "      <td>1.158073</td>\n",
       "      <td>-0.868144</td>\n",
       "      <td>-0.371633</td>\n",
       "      <td>1.612053</td>\n",
       "      <td>0.445263</td>\n",
       "      <td>1.642596</td>\n",
       "      <td>0.658417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>-1.463515</td>\n",
       "      <td>0.077564</td>\n",
       "      <td>0.881184</td>\n",
       "      <td>-0.130188</td>\n",
       "      <td>0.581684</td>\n",
       "      <td>-0.638071</td>\n",
       "      <td>2.258804</td>\n",
       "      <td>3.439436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>0.296120</td>\n",
       "      <td>0.396932</td>\n",
       "      <td>1.198646</td>\n",
       "      <td>1.485846</td>\n",
       "      <td>0.894685</td>\n",
       "      <td>2.487993</td>\n",
       "      <td>0.767387</td>\n",
       "      <td>2.542107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>0.261055</td>\n",
       "      <td>0.111616</td>\n",
       "      <td>1.627174</td>\n",
       "      <td>1.271830</td>\n",
       "      <td>1.526829</td>\n",
       "      <td>2.320487</td>\n",
       "      <td>-0.064482</td>\n",
       "      <td>2.560592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>0.005113</td>\n",
       "      <td>1.891602</td>\n",
       "      <td>0.606942</td>\n",
       "      <td>-1.507145</td>\n",
       "      <td>1.381195</td>\n",
       "      <td>2.081124</td>\n",
       "      <td>1.542698</td>\n",
       "      <td>1.169963</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>-0.234587</td>\n",
       "      <td>0.885811</td>\n",
       "      <td>-1.153310</td>\n",
       "      <td>1.863983</td>\n",
       "      <td>0.244390</td>\n",
       "      <td>3.277451</td>\n",
       "      <td>2.392591</td>\n",
       "      <td>2.431214</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     ind_0_x   ind_0_y   ind_1_x   ind_1_y   ind_2_x   ind_2_y   ind_3_x  \\\n",
       "0   0.496714  0.557400 -0.150615  0.926375  1.784876  0.651991  0.806369   \n",
       "1  -0.138264 -0.608481  1.916357  1.160322  2.431196  2.805906  0.736599   \n",
       "2   0.647689 -0.078503  1.846140  0.504854  2.021900  2.424208  1.161924   \n",
       "3   1.523030 -0.234916 -1.004916  0.695699  0.400772  2.140412  2.861589   \n",
       "4  -0.234153  1.158073 -0.868144 -0.371633  1.612053  0.445263  1.642596   \n",
       "..       ...       ...       ...       ...       ...       ...       ...   \n",
       "95 -1.463515  0.077564  0.881184 -0.130188  0.581684 -0.638071  2.258804   \n",
       "96  0.296120  0.396932  1.198646  1.485846  0.894685  2.487993  0.767387   \n",
       "97  0.261055  0.111616  1.627174  1.271830  1.526829  2.320487 -0.064482   \n",
       "98  0.005113  1.891602  0.606942 -1.507145  1.381195  2.081124  1.542698   \n",
       "99 -0.234587  0.885811 -1.153310  1.863983  0.244390  3.277451  2.392591   \n",
       "\n",
       "     ind_3_y  \n",
       "0   1.056841  \n",
       "1   1.279144  \n",
       "2   2.765146  \n",
       "3   3.922627  \n",
       "4   0.658417  \n",
       "..       ...  \n",
       "95  3.439436  \n",
       "96  2.542107  \n",
       "97  2.560592  \n",
       "98  1.169963  \n",
       "99  2.431214  \n",
       "\n",
       "[100 rows x 8 columns]"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for idx, i in enumerate(range(individuals*2)[::2]):\n",
    "    df[f'ind_{idx}_x'] = s[i]\n",
    "    df[f'ind_{idx}_y'] = s[i+1]\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "colors = ['aqua', 'orange', 'green', 'red']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "\n",
    "for ind in range(individuals):\n",
    "    ax.plot(df[f'ind_{ind}_x'], df[f'ind_{ind}_y'], marker='o', linestyle='', label=ind, color=colors[ind], alpha=0.5)\n",
    "ax.legend(title=\"Individual\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now we are going to control for variable `hired`\n",
    "# This will mess up our analysis because `hired` is a collider variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: [-0.10384651739409387, 0.3645826294798152],\n",
       " 1: [0.5102936712481219, 0.7608204610271829],\n",
       " 2: [1.133218009931516, 1.4941988319207165],\n",
       " 3: [1.8041529709583104, 2.172862087250989]}"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we're going to find:\n",
    "# X_exp = Part of X explained by W\n",
    "# Y_exp = Part of Y explained by W\n",
    "\n",
    "means = {}\n",
    "\n",
    "for ind in range(individuals):\n",
    "    means[ind] = [df[f'ind_{ind}_x'].mean(), df[f'ind_{ind}_y'].mean()]\n",
    "\n",
    "means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "for ind in range(individuals):\n",
    "    ax.plot(df[f'ind_{ind}_x'], df[f'ind_{ind}_y'], marker='o', linestyle='', label=ind, color=colors[ind], alpha=0.5)\n",
    "for mean in means:\n",
    "    ax.axvline(x=means[mean][0], color=colors[mean])\n",
    "    ax.axhline(y=means[mean][1], color=colors[mean])\n",
    "ax.legend(title=\"Individual\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now we are going to close the back door for W computing the residuals\n",
    "df['ind_0_x_res'] = df['ind_0_x']\n",
    "df['ind_0_y_res'] = df['ind_0_y']\n",
    "for idx, i in enumerate(range(individuals*2)[2::2]):\n",
    "    df[f'ind_{idx+1}_x_res'] = df[f'ind_{idx+1}_x'] - (means[idx+1][0]-means[0][0])\n",
    "    df[f'ind_{idx+1}_y_res'] = df[f'ind_{idx+1}_y'] -(means[idx+1][1]-means[0][1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ind_0_x</th>\n",
       "      <th>ind_0_y</th>\n",
       "      <th>ind_1_x</th>\n",
       "      <th>ind_1_y</th>\n",
       "      <th>ind_2_x</th>\n",
       "      <th>ind_2_y</th>\n",
       "      <th>ind_3_x</th>\n",
       "      <th>ind_3_y</th>\n",
       "      <th>ind_1_x_res</th>\n",
       "      <th>ind_2_x_res</th>\n",
       "      <th>ind_3_x_res</th>\n",
       "      <th>ind_1_yres</th>\n",
       "      <th>ind_2_yres</th>\n",
       "      <th>ind_3_yres</th>\n",
       "      <th>ind_0_x_res</th>\n",
       "      <th>ind_0_y_res</th>\n",
       "      <th>ind_1_y_res</th>\n",
       "      <th>ind_2_y_res</th>\n",
       "      <th>ind_3_y_res</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.496714</td>\n",
       "      <td>0.557400</td>\n",
       "      <td>-0.150615</td>\n",
       "      <td>0.926375</td>\n",
       "      <td>1.784876</td>\n",
       "      <td>0.651991</td>\n",
       "      <td>0.806369</td>\n",
       "      <td>1.056841</td>\n",
       "      <td>-0.764755</td>\n",
       "      <td>0.547811</td>\n",
       "      <td>-1.101631</td>\n",
       "      <td>0.530137</td>\n",
       "      <td>-0.477626</td>\n",
       "      <td>-0.751439</td>\n",
       "      <td>0.496714</td>\n",
       "      <td>0.557400</td>\n",
       "      <td>0.530137</td>\n",
       "      <td>-0.477626</td>\n",
       "      <td>-0.751439</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.138264</td>\n",
       "      <td>-0.608481</td>\n",
       "      <td>1.916357</td>\n",
       "      <td>1.160322</td>\n",
       "      <td>2.431196</td>\n",
       "      <td>2.805906</td>\n",
       "      <td>0.736599</td>\n",
       "      <td>1.279144</td>\n",
       "      <td>1.302217</td>\n",
       "      <td>1.194131</td>\n",
       "      <td>-1.171400</td>\n",
       "      <td>0.764084</td>\n",
       "      <td>1.676290</td>\n",
       "      <td>-0.529135</td>\n",
       "      <td>-0.138264</td>\n",
       "      <td>-0.608481</td>\n",
       "      <td>0.764084</td>\n",
       "      <td>1.676290</td>\n",
       "      <td>-0.529135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.647689</td>\n",
       "      <td>-0.078503</td>\n",
       "      <td>1.846140</td>\n",
       "      <td>0.504854</td>\n",
       "      <td>2.021900</td>\n",
       "      <td>2.424208</td>\n",
       "      <td>1.161924</td>\n",
       "      <td>2.765146</td>\n",
       "      <td>1.232000</td>\n",
       "      <td>0.784836</td>\n",
       "      <td>-0.746075</td>\n",
       "      <td>0.108617</td>\n",
       "      <td>1.294592</td>\n",
       "      <td>0.956866</td>\n",
       "      <td>0.647689</td>\n",
       "      <td>-0.078503</td>\n",
       "      <td>0.108617</td>\n",
       "      <td>1.294592</td>\n",
       "      <td>0.956866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.523030</td>\n",
       "      <td>-0.234916</td>\n",
       "      <td>-1.004916</td>\n",
       "      <td>0.695699</td>\n",
       "      <td>0.400772</td>\n",
       "      <td>2.140412</td>\n",
       "      <td>2.861589</td>\n",
       "      <td>3.922627</td>\n",
       "      <td>-1.619056</td>\n",
       "      <td>-0.836293</td>\n",
       "      <td>0.953589</td>\n",
       "      <td>0.299461</td>\n",
       "      <td>1.010796</td>\n",
       "      <td>2.114347</td>\n",
       "      <td>1.523030</td>\n",
       "      <td>-0.234916</td>\n",
       "      <td>0.299461</td>\n",
       "      <td>1.010796</td>\n",
       "      <td>2.114347</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.234153</td>\n",
       "      <td>1.158073</td>\n",
       "      <td>-0.868144</td>\n",
       "      <td>-0.371633</td>\n",
       "      <td>1.612053</td>\n",
       "      <td>0.445263</td>\n",
       "      <td>1.642596</td>\n",
       "      <td>0.658417</td>\n",
       "      <td>-1.482284</td>\n",
       "      <td>0.374989</td>\n",
       "      <td>-0.265404</td>\n",
       "      <td>-0.767870</td>\n",
       "      <td>-0.684353</td>\n",
       "      <td>-1.149863</td>\n",
       "      <td>-0.234153</td>\n",
       "      <td>1.158073</td>\n",
       "      <td>-0.767870</td>\n",
       "      <td>-0.684353</td>\n",
       "      <td>-1.149863</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>-1.463515</td>\n",
       "      <td>0.077564</td>\n",
       "      <td>0.881184</td>\n",
       "      <td>-0.130188</td>\n",
       "      <td>0.581684</td>\n",
       "      <td>-0.638071</td>\n",
       "      <td>2.258804</td>\n",
       "      <td>3.439436</td>\n",
       "      <td>0.267044</td>\n",
       "      <td>-0.655380</td>\n",
       "      <td>0.350805</td>\n",
       "      <td>-0.526426</td>\n",
       "      <td>-1.767688</td>\n",
       "      <td>1.631156</td>\n",
       "      <td>-1.463515</td>\n",
       "      <td>0.077564</td>\n",
       "      <td>-0.526426</td>\n",
       "      <td>-1.767688</td>\n",
       "      <td>1.631156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>0.296120</td>\n",
       "      <td>0.396932</td>\n",
       "      <td>1.198646</td>\n",
       "      <td>1.485846</td>\n",
       "      <td>0.894685</td>\n",
       "      <td>2.487993</td>\n",
       "      <td>0.767387</td>\n",
       "      <td>2.542107</td>\n",
       "      <td>0.584505</td>\n",
       "      <td>-0.342380</td>\n",
       "      <td>-1.140612</td>\n",
       "      <td>1.089608</td>\n",
       "      <td>1.358377</td>\n",
       "      <td>0.733828</td>\n",
       "      <td>0.296120</td>\n",
       "      <td>0.396932</td>\n",
       "      <td>1.089608</td>\n",
       "      <td>1.358377</td>\n",
       "      <td>0.733828</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>0.261055</td>\n",
       "      <td>0.111616</td>\n",
       "      <td>1.627174</td>\n",
       "      <td>1.271830</td>\n",
       "      <td>1.526829</td>\n",
       "      <td>2.320487</td>\n",
       "      <td>-0.064482</td>\n",
       "      <td>2.560592</td>\n",
       "      <td>1.013034</td>\n",
       "      <td>0.289764</td>\n",
       "      <td>-1.972482</td>\n",
       "      <td>0.875592</td>\n",
       "      <td>1.190870</td>\n",
       "      <td>0.752312</td>\n",
       "      <td>0.261055</td>\n",
       "      <td>0.111616</td>\n",
       "      <td>0.875592</td>\n",
       "      <td>1.190870</td>\n",
       "      <td>0.752312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>0.005113</td>\n",
       "      <td>1.891602</td>\n",
       "      <td>0.606942</td>\n",
       "      <td>-1.507145</td>\n",
       "      <td>1.381195</td>\n",
       "      <td>2.081124</td>\n",
       "      <td>1.542698</td>\n",
       "      <td>1.169963</td>\n",
       "      <td>-0.007198</td>\n",
       "      <td>0.144131</td>\n",
       "      <td>-0.365301</td>\n",
       "      <td>-1.903383</td>\n",
       "      <td>0.951508</td>\n",
       "      <td>-0.638316</td>\n",
       "      <td>0.005113</td>\n",
       "      <td>1.891602</td>\n",
       "      <td>-1.903383</td>\n",
       "      <td>0.951508</td>\n",
       "      <td>-0.638316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>-0.234587</td>\n",
       "      <td>0.885811</td>\n",
       "      <td>-1.153310</td>\n",
       "      <td>1.863983</td>\n",
       "      <td>0.244390</td>\n",
       "      <td>3.277451</td>\n",
       "      <td>2.392591</td>\n",
       "      <td>2.431214</td>\n",
       "      <td>-1.767450</td>\n",
       "      <td>-0.992674</td>\n",
       "      <td>0.484591</td>\n",
       "      <td>1.467745</td>\n",
       "      <td>2.147835</td>\n",
       "      <td>0.622935</td>\n",
       "      <td>-0.234587</td>\n",
       "      <td>0.885811</td>\n",
       "      <td>1.467745</td>\n",
       "      <td>2.147835</td>\n",
       "      <td>0.622935</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 19 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     ind_0_x   ind_0_y   ind_1_x   ind_1_y   ind_2_x   ind_2_y   ind_3_x  \\\n",
       "0   0.496714  0.557400 -0.150615  0.926375  1.784876  0.651991  0.806369   \n",
       "1  -0.138264 -0.608481  1.916357  1.160322  2.431196  2.805906  0.736599   \n",
       "2   0.647689 -0.078503  1.846140  0.504854  2.021900  2.424208  1.161924   \n",
       "3   1.523030 -0.234916 -1.004916  0.695699  0.400772  2.140412  2.861589   \n",
       "4  -0.234153  1.158073 -0.868144 -0.371633  1.612053  0.445263  1.642596   \n",
       "..       ...       ...       ...       ...       ...       ...       ...   \n",
       "95 -1.463515  0.077564  0.881184 -0.130188  0.581684 -0.638071  2.258804   \n",
       "96  0.296120  0.396932  1.198646  1.485846  0.894685  2.487993  0.767387   \n",
       "97  0.261055  0.111616  1.627174  1.271830  1.526829  2.320487 -0.064482   \n",
       "98  0.005113  1.891602  0.606942 -1.507145  1.381195  2.081124  1.542698   \n",
       "99 -0.234587  0.885811 -1.153310  1.863983  0.244390  3.277451  2.392591   \n",
       "\n",
       "     ind_3_y  ind_1_x_res  ind_2_x_res  ind_3_x_res  ind_1_yres  ind_2_yres  \\\n",
       "0   1.056841    -0.764755     0.547811    -1.101631    0.530137   -0.477626   \n",
       "1   1.279144     1.302217     1.194131    -1.171400    0.764084    1.676290   \n",
       "2   2.765146     1.232000     0.784836    -0.746075    0.108617    1.294592   \n",
       "3   3.922627    -1.619056    -0.836293     0.953589    0.299461    1.010796   \n",
       "4   0.658417    -1.482284     0.374989    -0.265404   -0.767870   -0.684353   \n",
       "..       ...          ...          ...          ...         ...         ...   \n",
       "95  3.439436     0.267044    -0.655380     0.350805   -0.526426   -1.767688   \n",
       "96  2.542107     0.584505    -0.342380    -1.140612    1.089608    1.358377   \n",
       "97  2.560592     1.013034     0.289764    -1.972482    0.875592    1.190870   \n",
       "98  1.169963    -0.007198     0.144131    -0.365301   -1.903383    0.951508   \n",
       "99  2.431214    -1.767450    -0.992674     0.484591    1.467745    2.147835   \n",
       "\n",
       "    ind_3_yres  ind_0_x_res  ind_0_y_res  ind_1_y_res  ind_2_y_res  \\\n",
       "0    -0.751439     0.496714     0.557400     0.530137    -0.477626   \n",
       "1    -0.529135    -0.138264    -0.608481     0.764084     1.676290   \n",
       "2     0.956866     0.647689    -0.078503     0.108617     1.294592   \n",
       "3     2.114347     1.523030    -0.234916     0.299461     1.010796   \n",
       "4    -1.149863    -0.234153     1.158073    -0.767870    -0.684353   \n",
       "..         ...          ...          ...          ...          ...   \n",
       "95    1.631156    -1.463515     0.077564    -0.526426    -1.767688   \n",
       "96    0.733828     0.296120     0.396932     1.089608     1.358377   \n",
       "97    0.752312     0.261055     0.111616     0.875592     1.190870   \n",
       "98   -0.638316     0.005113     1.891602    -1.903383     0.951508   \n",
       "99    0.622935    -0.234587     0.885811     1.467745     2.147835   \n",
       "\n",
       "    ind_3_y_res  \n",
       "0     -0.751439  \n",
       "1     -0.529135  \n",
       "2      0.956866  \n",
       "3      2.114347  \n",
       "4     -1.149863  \n",
       "..          ...  \n",
       "95     1.631156  \n",
       "96     0.733828  \n",
       "97     0.752312  \n",
       "98    -0.638316  \n",
       "99     0.622935  \n",
       "\n",
       "[100 rows x 19 columns]"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "ax.plot(df['ind_0_x_res'], df['ind_0_y_res'], marker='o', linestyle='', label=0, color=colors[0], alpha=0.5)\n",
    "for ind in range(individuals)[1:]:\n",
    "    ax.plot(df[f'ind_{ind}_x_res'], df[f'ind_{ind}_y_res'], marker='o', linestyle='', label=ind, color=colors[ind], alpha=0.5)\n",
    "ax.legend(title=\"Individual\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now we can see clearly a negative correlation, which is false"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.045295850033542764"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1. Not controlling `hired` variable\n",
    "df['programming_skill'].corr(df['social_skill'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.4984727390806141"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2. Controlling `hired` variable\n",
    "df['programming_skill_res'].corr(df['social_skill_res'])"
   ]
  }
 ],
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