better linear regression model

module3/exo3/exercice.ipynb

@@ -597,6 +597,222 @@
     "Ce modèle n'est pas particulièrement adapté, il sous-estime très nettement la quantité de $CO_2$."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Utlisation des lags comme attributs du modèle. \n",
+    "\n",
+    "On complexifie légèrement le modèle afin d'utiliser des attributs correspondants aux \"lags\" des valeurs de $CO2$ dans celui-ci."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 76,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "data['ppm_lag1'] = data['ppm'].shift(1)\n",
+    "data['ppm_lag2'] = data['ppm'].shift(2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 81,
+   "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>ppm</th>\n",
+       "      <th>year</th>\n",
+       "      <th>ppm_lag1</th>\n",
+       "      <th>ppm_lag2</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>index</th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>1958-04-12</th>\n",
+       "      <td>317.69</td>\n",
+       "      <td>1958</td>\n",
+       "      <td>317.31</td>\n",
+       "      <td>316.19</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1958-04-19</th>\n",
+       "      <td>317.58</td>\n",
+       "      <td>1958</td>\n",
+       "      <td>317.69</td>\n",
+       "      <td>317.31</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1958-04-26</th>\n",
+       "      <td>316.48</td>\n",
+       "      <td>1958</td>\n",
+       "      <td>317.58</td>\n",
+       "      <td>317.69</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1958-05-03</th>\n",
+       "      <td>316.95</td>\n",
+       "      <td>1958</td>\n",
+       "      <td>316.48</td>\n",
+       "      <td>317.58</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1958-05-17</th>\n",
+       "      <td>317.56</td>\n",
+       "      <td>1958</td>\n",
+       "      <td>316.95</td>\n",
+       "      <td>316.48</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "               ppm  year  ppm_lag1  ppm_lag2\n",
+       "index                                       \n",
+       "1958-04-12  317.69  1958    317.31    316.19\n",
+       "1958-04-19  317.58  1958    317.69    317.31\n",
+       "1958-04-26  316.48  1958    317.58    317.69\n",
+       "1958-05-03  316.95  1958    316.48    317.58\n",
+       "1958-05-17  317.56  1958    316.95    316.48"
+      ]
+     },
+     "execution_count": 81,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "data.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 77,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Suppression des lignes contenant des NaN dues au décalage\n",
+    "data = data.dropna()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 90,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "X = data[['ppm_lag1', 'ppm_lag2']]\n",
+    "y = data['ppm']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 91,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
+      ]
+     },
+     "execution_count": 91,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "model = LinearRegression()\n",
+    "model.fit(X, y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "On utilise les 2 dernières semaines disponibles dans les données pour prédire la semaine à venir, et ainsi de suite (en utilisation les prédictions au fur et à mesure) jusqu'à 2025."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 95,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ppm = list(data['ppm'].values)\n",
+    "ppm_preds = []\n",
+    "\n",
+    "for i in range(weeks_until_target_year):\n",
+    "    new_data = {\n",
+    "        'ppm_lag1': [ppm[-1]],\n",
+    "        'ppm_lag2': [ppm[-2]]\n",
+    "    }\n",
+    "    pred = model.predict(pd.DataFrame(new_data))\n",
+    "    ppm.append(pred)\n",
+    "    ppm_preds.append(float(pred))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 97,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(1, 1)\n",
+    "ax.plot(res.trend, label='Tendance')\n",
+    "ax.plot(weeks_untils_2025, ppm_preds, color='r', label='prédictions')\n",
+    "plt.legend();"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Ce modèle semble plus cohérent que le précédent."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,