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   "source": [
    "# Linear and Polynomial Regression with the taxis dataset"
   ]
  },
  {
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   "source": [
    "import pandas as pd\n",
    "import altair as alt\n",
    "alt.data_transformers.enable('default', max_rows=10000)\n",
    "import seaborn as sns"
   ]
  },
  {
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   "outputs": [],
   "source": [
    "df = sns.load_dataset(\"taxis\").dropna()"
   ]
  },
  {
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   "source": [
    "## Linear regression\n",
    "\n",
    "* Fit a linear regression model to the data from the taxis dataset, using multiple input variables (also called features, also called predictors), and with \"total\" as the output variable (the target)."
   ]
  },
  {
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    {
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       "      <th></th>\n",
       "      <th>pickup</th>\n",
       "      <th>dropoff</th>\n",
       "      <th>passengers</th>\n",
       "      <th>distance</th>\n",
       "      <th>fare</th>\n",
       "      <th>tip</th>\n",
       "      <th>tolls</th>\n",
       "      <th>total</th>\n",
       "      <th>color</th>\n",
       "      <th>payment</th>\n",
       "      <th>pickup_zone</th>\n",
       "      <th>dropoff_zone</th>\n",
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       "      <th>0</th>\n",
       "      <td>2019-03-23 20:21:09</td>\n",
       "      <td>2019-03-23 20:27:24</td>\n",
       "      <td>1</td>\n",
       "      <td>1.60</td>\n",
       "      <td>7.0</td>\n",
       "      <td>2.15</td>\n",
       "      <td>0.0</td>\n",
       "      <td>12.95</td>\n",
       "      <td>yellow</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Lenox Hill West</td>\n",
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       "      <td>Manhattan</td>\n",
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       "      <th>1</th>\n",
       "      <td>2019-03-04 16:11:55</td>\n",
       "      <td>2019-03-04 16:19:00</td>\n",
       "      <td>1</td>\n",
       "      <td>0.79</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>9.30</td>\n",
       "      <td>yellow</td>\n",
       "      <td>cash</td>\n",
       "      <td>Upper West Side South</td>\n",
       "      <td>Upper West Side South</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2019-03-27 17:53:01</td>\n",
       "      <td>2019-03-27 18:00:25</td>\n",
       "      <td>1</td>\n",
       "      <td>1.37</td>\n",
       "      <td>7.5</td>\n",
       "      <td>2.36</td>\n",
       "      <td>0.0</td>\n",
       "      <td>14.16</td>\n",
       "      <td>yellow</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Alphabet City</td>\n",
       "      <td>West Village</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2019-03-10 01:23:59</td>\n",
       "      <td>2019-03-10 01:49:51</td>\n",
       "      <td>1</td>\n",
       "      <td>7.70</td>\n",
       "      <td>27.0</td>\n",
       "      <td>6.15</td>\n",
       "      <td>0.0</td>\n",
       "      <td>36.95</td>\n",
       "      <td>yellow</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Hudson Sq</td>\n",
       "      <td>Yorkville West</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2019-03-30 13:27:42</td>\n",
       "      <td>2019-03-30 13:37:14</td>\n",
       "      <td>3</td>\n",
       "      <td>2.16</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>13.40</td>\n",
       "      <td>yellow</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Midtown East</td>\n",
       "      <td>Yorkville West</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
       "    </tr>\n",
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       "                pickup              dropoff  passengers  distance  fare   tip  \\\n",
       "0  2019-03-23 20:21:09  2019-03-23 20:27:24           1      1.60   7.0  2.15   \n",
       "1  2019-03-04 16:11:55  2019-03-04 16:19:00           1      0.79   5.0  0.00   \n",
       "2  2019-03-27 17:53:01  2019-03-27 18:00:25           1      1.37   7.5  2.36   \n",
       "3  2019-03-10 01:23:59  2019-03-10 01:49:51           1      7.70  27.0  6.15   \n",
       "4  2019-03-30 13:27:42  2019-03-30 13:37:14           3      2.16   9.0  1.10   \n",
       "\n",
       "   tolls  total   color      payment            pickup_zone  \\\n",
       "0    0.0  12.95  yellow  credit card        Lenox Hill West   \n",
       "1    0.0   9.30  yellow         cash  Upper West Side South   \n",
       "2    0.0  14.16  yellow  credit card          Alphabet City   \n",
       "3    0.0  36.95  yellow  credit card              Hudson Sq   \n",
       "4    0.0  13.40  yellow  credit card           Midtown East   \n",
       "\n",
       "            dropoff_zone pickup_borough dropoff_borough  \n",
       "0    UN/Turtle Bay South      Manhattan       Manhattan  \n",
       "1  Upper West Side South      Manhattan       Manhattan  \n",
       "2           West Village      Manhattan       Manhattan  \n",
       "3         Yorkville West      Manhattan       Manhattan  \n",
       "4         Yorkville West      Manhattan       Manhattan  "
      ]
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   "source": [
    "df.head()"
   ]
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   "source": [
    "What are the rows with the biggest values in the \"tolls\" column?"
   ]
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    {
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       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5364</th>\n",
       "      <td>2019-03-17 16:59:17</td>\n",
       "      <td>2019-03-17 18:04:08</td>\n",
       "      <td>2</td>\n",
       "      <td>36.70</td>\n",
       "      <td>150.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>24.02</td>\n",
       "      <td>174.82</td>\n",
       "      <td>yellow</td>\n",
       "      <td>cash</td>\n",
       "      <td>JFK Airport</td>\n",
       "      <td>JFK Airport</td>\n",
       "      <td>Queens</td>\n",
       "      <td>Queens</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2122</th>\n",
       "      <td>2019-03-08 00:40:32</td>\n",
       "      <td>2019-03-08 01:11:53</td>\n",
       "      <td>1</td>\n",
       "      <td>15.51</td>\n",
       "      <td>44.00</td>\n",
       "      <td>16.27</td>\n",
       "      <td>17.28</td>\n",
       "      <td>81.35</td>\n",
       "      <td>yellow</td>\n",
       "      <td>credit card</td>\n",
       "      <td>TriBeCa/Civic Center</td>\n",
       "      <td>West Brighton</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Staten Island</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3640</th>\n",
       "      <td>2019-03-22 07:54:09</td>\n",
       "      <td>2019-03-22 09:05:13</td>\n",
       "      <td>1</td>\n",
       "      <td>16.42</td>\n",
       "      <td>52.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>12.50</td>\n",
       "      <td>67.80</td>\n",
       "      <td>yellow</td>\n",
       "      <td>cash</td>\n",
       "      <td>JFK Airport</td>\n",
       "      <td>Murray Hill</td>\n",
       "      <td>Queens</td>\n",
       "      <td>Manhattan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5911</th>\n",
       "      <td>2019-03-09 12:27:51</td>\n",
       "      <td>2019-03-09 13:11:18</td>\n",
       "      <td>1</td>\n",
       "      <td>11.40</td>\n",
       "      <td>39.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>11.52</td>\n",
       "      <td>51.32</td>\n",
       "      <td>green</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Windsor Terrace</td>\n",
       "      <td>Clinton East</td>\n",
       "      <td>Brooklyn</td>\n",
       "      <td>Manhattan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5728</th>\n",
       "      <td>2019-03-01 17:07:09</td>\n",
       "      <td>2019-03-01 18:05:41</td>\n",
       "      <td>1</td>\n",
       "      <td>21.27</td>\n",
       "      <td>65.59</td>\n",
       "      <td>0.00</td>\n",
       "      <td>11.52</td>\n",
       "      <td>77.61</td>\n",
       "      <td>green</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Cambria Heights</td>\n",
       "      <td>Morningside Heights</td>\n",
       "      <td>Queens</td>\n",
       "      <td>Manhattan</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",
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       "    <tr>\n",
       "      <th>2203</th>\n",
       "      <td>2019-03-03 00:24:50</td>\n",
       "      <td>2019-03-03 00:56:17</td>\n",
       "      <td>1</td>\n",
       "      <td>4.72</td>\n",
       "      <td>22.00</td>\n",
       "      <td>5.16</td>\n",
       "      <td>0.00</td>\n",
       "      <td>30.96</td>\n",
       "      <td>yellow</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Meatpacking/West Village West</td>\n",
       "      <td>Williamsburg (South Side)</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Brooklyn</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2202</th>\n",
       "      <td>2019-03-14 22:32:33</td>\n",
       "      <td>2019-03-14 22:49:39</td>\n",
       "      <td>1</td>\n",
       "      <td>2.90</td>\n",
       "      <td>13.00</td>\n",
       "      <td>3.36</td>\n",
       "      <td>0.00</td>\n",
       "      <td>20.16</td>\n",
       "      <td>yellow</td>\n",
       "      <td>credit card</td>\n",
       "      <td>East Chelsea</td>\n",
       "      <td>East Village</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2201</th>\n",
       "      <td>2019-03-18 21:16:42</td>\n",
       "      <td>2019-03-18 21:27:49</td>\n",
       "      <td>1</td>\n",
       "      <td>3.00</td>\n",
       "      <td>11.50</td>\n",
       "      <td>3.06</td>\n",
       "      <td>0.00</td>\n",
       "      <td>18.36</td>\n",
       "      <td>yellow</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Clinton East</td>\n",
       "      <td>Upper East Side North</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2200</th>\n",
       "      <td>2019-03-03 07:21:40</td>\n",
       "      <td>2019-03-03 07:39:12</td>\n",
       "      <td>1</td>\n",
       "      <td>7.20</td>\n",
       "      <td>22.00</td>\n",
       "      <td>7.55</td>\n",
       "      <td>0.00</td>\n",
       "      <td>32.85</td>\n",
       "      <td>yellow</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Midtown Center</td>\n",
       "      <td>World Trade Center</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6432</th>\n",
       "      <td>2019-03-13 19:31:22</td>\n",
       "      <td>2019-03-13 19:48:02</td>\n",
       "      <td>1</td>\n",
       "      <td>3.85</td>\n",
       "      <td>15.00</td>\n",
       "      <td>3.36</td>\n",
       "      <td>0.00</td>\n",
       "      <td>20.16</td>\n",
       "      <td>green</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Boerum Hill</td>\n",
       "      <td>Windsor Terrace</td>\n",
       "      <td>Brooklyn</td>\n",
       "      <td>Brooklyn</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>6341 rows × 14 columns</p>\n",
       "</div>"
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       "                   pickup              dropoff  passengers  distance    fare  \\\n",
       "5364  2019-03-17 16:59:17  2019-03-17 18:04:08           2     36.70  150.00   \n",
       "2122  2019-03-08 00:40:32  2019-03-08 01:11:53           1     15.51   44.00   \n",
       "3640  2019-03-22 07:54:09  2019-03-22 09:05:13           1     16.42   52.00   \n",
       "5911  2019-03-09 12:27:51  2019-03-09 13:11:18           1     11.40   39.00   \n",
       "5728  2019-03-01 17:07:09  2019-03-01 18:05:41           1     21.27   65.59   \n",
       "...                   ...                  ...         ...       ...     ...   \n",
       "2203  2019-03-03 00:24:50  2019-03-03 00:56:17           1      4.72   22.00   \n",
       "2202  2019-03-14 22:32:33  2019-03-14 22:49:39           1      2.90   13.00   \n",
       "2201  2019-03-18 21:16:42  2019-03-18 21:27:49           1      3.00   11.50   \n",
       "2200  2019-03-03 07:21:40  2019-03-03 07:39:12           1      7.20   22.00   \n",
       "6432  2019-03-13 19:31:22  2019-03-13 19:48:02           1      3.85   15.00   \n",
       "\n",
       "        tip  tolls   total   color      payment  \\\n",
       "5364   0.00  24.02  174.82  yellow         cash   \n",
       "2122  16.27  17.28   81.35  yellow  credit card   \n",
       "3640   0.00  12.50   67.80  yellow         cash   \n",
       "5911   0.00  11.52   51.32   green  credit card   \n",
       "5728   0.00  11.52   77.61   green  credit card   \n",
       "...     ...    ...     ...     ...          ...   \n",
       "2203   5.16   0.00   30.96  yellow  credit card   \n",
       "2202   3.36   0.00   20.16  yellow  credit card   \n",
       "2201   3.06   0.00   18.36  yellow  credit card   \n",
       "2200   7.55   0.00   32.85  yellow  credit card   \n",
       "6432   3.36   0.00   20.16   green  credit card   \n",
       "\n",
       "                        pickup_zone               dropoff_zone pickup_borough  \\\n",
       "5364                    JFK Airport                JFK Airport         Queens   \n",
       "2122           TriBeCa/Civic Center              West Brighton      Manhattan   \n",
       "3640                    JFK Airport                Murray Hill         Queens   \n",
       "5911                Windsor Terrace               Clinton East       Brooklyn   \n",
       "5728                Cambria Heights        Morningside Heights         Queens   \n",
       "...                             ...                        ...            ...   \n",
       "2203  Meatpacking/West Village West  Williamsburg (South Side)      Manhattan   \n",
       "2202                   East Chelsea               East Village      Manhattan   \n",
       "2201                   Clinton East      Upper East Side North      Manhattan   \n",
       "2200                 Midtown Center         World Trade Center      Manhattan   \n",
       "6432                    Boerum Hill            Windsor Terrace       Brooklyn   \n",
       "\n",
       "     dropoff_borough  \n",
       "5364          Queens  \n",
       "2122   Staten Island  \n",
       "3640       Manhattan  \n",
       "5911       Manhattan  \n",
       "5728       Manhattan  \n",
       "...              ...  \n",
       "2203        Brooklyn  \n",
       "2202       Manhattan  \n",
       "2201       Manhattan  \n",
       "2200       Manhattan  \n",
       "6432        Brooklyn  \n",
       "\n",
       "[6341 rows x 14 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.sort_values(\"tolls\", ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try to use the following columns as the inputs for our linear regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "cell_id": "5d200510d6cd473993055fac958d6d84",
    "deepnote_cell_height": 81,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 0,
    "execution_start": 1651867531843,
    "source_hash": "4f299aee",
    "tags": []
   },
   "outputs": [],
   "source": [
    "cols = [\"distance\", \"tip\", \"tolls\", \"pickup_borough\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "cell_id": "6036759038e14127a3afc5ec29642a02",
    "deepnote_cell_height": 81,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_start": 1651867578382,
    "source_hash": "9527aab5",
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "cell_id": "dd4831013cb34e028b80b06e30264260",
    "deepnote_cell_height": 81,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 2,
    "execution_start": 1651867602454,
    "source_hash": "cd72858e",
    "tags": []
   },
   "outputs": [],
   "source": [
    "reg = LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This doesn't work, because the values in the \"pickup_borough\" column are strings, not numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "cell_id": "ae2578df1ea04c38965807b8338abbde",
    "deepnote_cell_height": 144.1875,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 645,
    "execution_start": 1651867712330,
    "source_hash": "623c24f0",
    "tags": [
     "output_scroll"
    ]
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "could not convert string to float: 'Manhattan'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/8j/gshrlmtn7dg4qtztj4d4t_w40000gn/T/ipykernel_15733/3118760667.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mreg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdf\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcols\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mdf\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"total\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/miniconda3/envs/math10s22/lib/python3.7/site-packages/sklearn/linear_model/_base.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, X, y, sample_weight)\u001b[0m\n\u001b[1;32m    661\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    662\u001b[0m         X, y = self._validate_data(\n\u001b[0;32m--> 663\u001b[0;31m             \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maccept_sparse\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0maccept_sparse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_numeric\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmulti_output\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    664\u001b[0m         )\n\u001b[1;32m    665\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/math10s22/lib/python3.7/site-packages/sklearn/base.py\u001b[0m in \u001b[0;36m_validate_data\u001b[0;34m(self, X, y, reset, validate_separately, **check_params)\u001b[0m\n\u001b[1;32m    579\u001b[0m                 \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcheck_array\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mcheck_y_params\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    580\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 581\u001b[0;31m                 \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcheck_X_y\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mcheck_params\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    582\u001b[0m             \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    583\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/math10s22/lib/python3.7/site-packages/sklearn/utils/validation.py\u001b[0m in \u001b[0;36mcheck_X_y\u001b[0;34m(X, y, accept_sparse, accept_large_sparse, dtype, order, copy, force_all_finite, ensure_2d, allow_nd, multi_output, ensure_min_samples, ensure_min_features, y_numeric, estimator)\u001b[0m\n\u001b[1;32m    974\u001b[0m         \u001b[0mensure_min_samples\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mensure_min_samples\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    975\u001b[0m         \u001b[0mensure_min_features\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mensure_min_features\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 976\u001b[0;31m         \u001b[0mestimator\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mestimator\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    977\u001b[0m     )\n\u001b[1;32m    978\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/math10s22/lib/python3.7/site-packages/sklearn/utils/validation.py\u001b[0m in \u001b[0;36mcheck_array\u001b[0;34m(array, accept_sparse, accept_large_sparse, dtype, order, copy, force_all_finite, ensure_2d, allow_nd, ensure_min_samples, ensure_min_features, estimator)\u001b[0m\n\u001b[1;32m    744\u001b[0m                     \u001b[0marray\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0marray\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcasting\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"unsafe\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    745\u001b[0m                 \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 746\u001b[0;31m                     \u001b[0marray\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    747\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mComplexWarning\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mcomplex_warning\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    748\u001b[0m                 raise ValueError(\n",
      "\u001b[0;32m~/miniconda3/envs/math10s22/lib/python3.7/site-packages/pandas/core/generic.py\u001b[0m in \u001b[0;36m__array__\u001b[0;34m(self, dtype)\u001b[0m\n\u001b[1;32m   1991\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1992\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__array__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mNpDtype\u001b[0m \u001b[0;34m|\u001b[0m \u001b[0;32mNone\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndarray\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1993\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_values\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1994\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1995\u001b[0m     def __array_wrap__(\n",
      "\u001b[0;31mValueError\u001b[0m: could not convert string to float: 'Manhattan'"
     ]
    }
   ],
   "source": [
    "reg.fit(df[cols],df[\"total\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make a new column called \"Manhattan\".  This will contain `1` for the \"Manhattan\" pickup borough rows, and contain `0` for all the other rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "cell_id": "4f3fe280d62344b1aace68032c9bfaba",
    "deepnote_cell_height": 81,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 4,
    "execution_start": 1651867826643,
    "source_hash": "abd1c605",
    "tags": []
   },
   "outputs": [],
   "source": [
    "df[\"Manhattan\"] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "cell_id": "4f8410183e764b71ac30ecd43bce7cd7",
    "deepnote_cell_height": 329.328125,
    "deepnote_cell_type": "code",
    "deepnote_output_heights": [
     232.34375
    ],
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 4,
    "execution_start": 1651867882020,
    "source_hash": "716201ae",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0        True\n",
       "1        True\n",
       "2        True\n",
       "3        True\n",
       "4        True\n",
       "        ...  \n",
       "6428     True\n",
       "6429    False\n",
       "6430    False\n",
       "6431    False\n",
       "6432    False\n",
       "Name: pickup_borough, Length: 6341, dtype: bool"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"pickup_borough\"] == \"Manhattan\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(I think we could also store Boolean values directly in this new \"Manhattan\" column, but I think it's less confusing to have `0` and `1`.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "cell_id": "4d049b7bea014e5aa1d3f39e922cd447",
    "deepnote_cell_height": 99,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 4,
    "execution_start": 1651867950135,
    "source_hash": "8abe422d",
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Put a 1 (for True) where the value is Manhattan\n",
    "df.loc[df[\"pickup_borough\"] == \"Manhattan\", \"Manhattan\"] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "cell_id": "40e9bffea7c1449a97e3b221edd3583c",
    "deepnote_cell_height": 600,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 173,
    "execution_start": 1651867954447,
    "source_hash": "f804c160",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pickup</th>\n",
       "      <th>dropoff</th>\n",
       "      <th>passengers</th>\n",
       "      <th>distance</th>\n",
       "      <th>fare</th>\n",
       "      <th>tip</th>\n",
       "      <th>tolls</th>\n",
       "      <th>total</th>\n",
       "      <th>color</th>\n",
       "      <th>payment</th>\n",
       "      <th>pickup_zone</th>\n",
       "      <th>dropoff_zone</th>\n",
       "      <th>pickup_borough</th>\n",
       "      <th>dropoff_borough</th>\n",
       "      <th>Manhattan</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2019-03-23 20:21:09</td>\n",
       "      <td>2019-03-23 20:27:24</td>\n",
       "      <td>1</td>\n",
       "      <td>1.60</td>\n",
       "      <td>7.0</td>\n",
       "      <td>2.15</td>\n",
       "      <td>0.0</td>\n",
       "      <td>12.95</td>\n",
       "      <td>yellow</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Lenox Hill West</td>\n",
       "      <td>UN/Turtle Bay South</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2019-03-04 16:11:55</td>\n",
       "      <td>2019-03-04 16:19:00</td>\n",
       "      <td>1</td>\n",
       "      <td>0.79</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>9.30</td>\n",
       "      <td>yellow</td>\n",
       "      <td>cash</td>\n",
       "      <td>Upper West Side South</td>\n",
       "      <td>Upper West Side South</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2019-03-27 17:53:01</td>\n",
       "      <td>2019-03-27 18:00:25</td>\n",
       "      <td>1</td>\n",
       "      <td>1.37</td>\n",
       "      <td>7.5</td>\n",
       "      <td>2.36</td>\n",
       "      <td>0.0</td>\n",
       "      <td>14.16</td>\n",
       "      <td>yellow</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Alphabet City</td>\n",
       "      <td>West Village</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2019-03-10 01:23:59</td>\n",
       "      <td>2019-03-10 01:49:51</td>\n",
       "      <td>1</td>\n",
       "      <td>7.70</td>\n",
       "      <td>27.0</td>\n",
       "      <td>6.15</td>\n",
       "      <td>0.0</td>\n",
       "      <td>36.95</td>\n",
       "      <td>yellow</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Hudson Sq</td>\n",
       "      <td>Yorkville West</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2019-03-30 13:27:42</td>\n",
       "      <td>2019-03-30 13:37:14</td>\n",
       "      <td>3</td>\n",
       "      <td>2.16</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>13.40</td>\n",
       "      <td>yellow</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Midtown East</td>\n",
       "      <td>Yorkville West</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>1</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6428</th>\n",
       "      <td>2019-03-31 09:51:53</td>\n",
       "      <td>2019-03-31 09:55:27</td>\n",
       "      <td>1</td>\n",
       "      <td>0.75</td>\n",
       "      <td>4.5</td>\n",
       "      <td>1.06</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.36</td>\n",
       "      <td>green</td>\n",
       "      <td>credit card</td>\n",
       "      <td>East Harlem North</td>\n",
       "      <td>Central Harlem North</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6429</th>\n",
       "      <td>2019-03-31 17:38:00</td>\n",
       "      <td>2019-03-31 18:34:23</td>\n",
       "      <td>1</td>\n",
       "      <td>18.74</td>\n",
       "      <td>58.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>58.80</td>\n",
       "      <td>green</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Jamaica</td>\n",
       "      <td>East Concourse/Concourse Village</td>\n",
       "      <td>Queens</td>\n",
       "      <td>Bronx</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6430</th>\n",
       "      <td>2019-03-23 22:55:18</td>\n",
       "      <td>2019-03-23 23:14:25</td>\n",
       "      <td>1</td>\n",
       "      <td>4.14</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>17.30</td>\n",
       "      <td>green</td>\n",
       "      <td>cash</td>\n",
       "      <td>Crown Heights North</td>\n",
       "      <td>Bushwick North</td>\n",
       "      <td>Brooklyn</td>\n",
       "      <td>Brooklyn</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6431</th>\n",
       "      <td>2019-03-04 10:09:25</td>\n",
       "      <td>2019-03-04 10:14:29</td>\n",
       "      <td>1</td>\n",
       "      <td>1.12</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.80</td>\n",
       "      <td>green</td>\n",
       "      <td>credit card</td>\n",
       "      <td>East New York</td>\n",
       "      <td>East Flatbush/Remsen Village</td>\n",
       "      <td>Brooklyn</td>\n",
       "      <td>Brooklyn</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6432</th>\n",
       "      <td>2019-03-13 19:31:22</td>\n",
       "      <td>2019-03-13 19:48:02</td>\n",
       "      <td>1</td>\n",
       "      <td>3.85</td>\n",
       "      <td>15.0</td>\n",
       "      <td>3.36</td>\n",
       "      <td>0.0</td>\n",
       "      <td>20.16</td>\n",
       "      <td>green</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Boerum Hill</td>\n",
       "      <td>Windsor Terrace</td>\n",
       "      <td>Brooklyn</td>\n",
       "      <td>Brooklyn</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>6341 rows × 15 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   pickup              dropoff  passengers  distance  fare  \\\n",
       "0     2019-03-23 20:21:09  2019-03-23 20:27:24           1      1.60   7.0   \n",
       "1     2019-03-04 16:11:55  2019-03-04 16:19:00           1      0.79   5.0   \n",
       "2     2019-03-27 17:53:01  2019-03-27 18:00:25           1      1.37   7.5   \n",
       "3     2019-03-10 01:23:59  2019-03-10 01:49:51           1      7.70  27.0   \n",
       "4     2019-03-30 13:27:42  2019-03-30 13:37:14           3      2.16   9.0   \n",
       "...                   ...                  ...         ...       ...   ...   \n",
       "6428  2019-03-31 09:51:53  2019-03-31 09:55:27           1      0.75   4.5   \n",
       "6429  2019-03-31 17:38:00  2019-03-31 18:34:23           1     18.74  58.0   \n",
       "6430  2019-03-23 22:55:18  2019-03-23 23:14:25           1      4.14  16.0   \n",
       "6431  2019-03-04 10:09:25  2019-03-04 10:14:29           1      1.12   6.0   \n",
       "6432  2019-03-13 19:31:22  2019-03-13 19:48:02           1      3.85  15.0   \n",
       "\n",
       "       tip  tolls  total   color      payment            pickup_zone  \\\n",
       "0     2.15    0.0  12.95  yellow  credit card        Lenox Hill West   \n",
       "1     0.00    0.0   9.30  yellow         cash  Upper West Side South   \n",
       "2     2.36    0.0  14.16  yellow  credit card          Alphabet City   \n",
       "3     6.15    0.0  36.95  yellow  credit card              Hudson Sq   \n",
       "4     1.10    0.0  13.40  yellow  credit card           Midtown East   \n",
       "...    ...    ...    ...     ...          ...                    ...   \n",
       "6428  1.06    0.0   6.36   green  credit card      East Harlem North   \n",
       "6429  0.00    0.0  58.80   green  credit card                Jamaica   \n",
       "6430  0.00    0.0  17.30   green         cash    Crown Heights North   \n",
       "6431  0.00    0.0   6.80   green  credit card          East New York   \n",
       "6432  3.36    0.0  20.16   green  credit card            Boerum Hill   \n",
       "\n",
       "                          dropoff_zone pickup_borough dropoff_borough  \\\n",
       "0                  UN/Turtle Bay South      Manhattan       Manhattan   \n",
       "1                Upper West Side South      Manhattan       Manhattan   \n",
       "2                         West Village      Manhattan       Manhattan   \n",
       "3                       Yorkville West      Manhattan       Manhattan   \n",
       "4                       Yorkville West      Manhattan       Manhattan   \n",
       "...                                ...            ...             ...   \n",
       "6428              Central Harlem North      Manhattan       Manhattan   \n",
       "6429  East Concourse/Concourse Village         Queens           Bronx   \n",
       "6430                    Bushwick North       Brooklyn        Brooklyn   \n",
       "6431      East Flatbush/Remsen Village       Brooklyn        Brooklyn   \n",
       "6432                   Windsor Terrace       Brooklyn        Brooklyn   \n",
       "\n",
       "      Manhattan  \n",
       "0             1  \n",
       "1             1  \n",
       "2             1  \n",
       "3             1  \n",
       "4             1  \n",
       "...         ...  \n",
       "6428          1  \n",
       "6429          0  \n",
       "6430          0  \n",
       "6431          0  \n",
       "6432          0  \n",
       "\n",
       "[6341 rows x 15 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now replace the old \"pickup_borough\" column with the newly created \"Manhattan\" column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "cell_id": "a49045990af24d4c81824ab7ddc663c7",
    "deepnote_cell_height": 81,
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    "execution_millis": 0,
    "execution_start": 1651868159514,
    "source_hash": "eb320fc1",
    "tags": []
   },
   "outputs": [],
   "source": [
    "cols = ['distance', 'tip', 'tolls', 'Manhattan']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "cell_id": "b457cc6309874598b39086ba14bf2265",
    "deepnote_cell_height": 118.1875,
    "deepnote_cell_type": "code",
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     21.1875
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    "execution_millis": 17,
    "execution_start": 1651868183429,
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.fit(df[cols],df[\"total\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The goal of the `fit` method is to find the following coefficients, as well as the intercept."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "cell_id": "84d9871e471e464abd94766d4a1ce6fe",
    "deepnote_cell_height": 118.1875,
    "deepnote_cell_type": "code",
    "deepnote_output_heights": [
     21.1875
    ],
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 9,
    "execution_start": 1651868204225,
    "source_hash": "c0bd65f9",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.6294669 , 1.3306588 , 1.11487961, 1.55477579])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should interpret the following as saying that the total cost of the taxi ride will be modeled by a formula involving 2.63 times the distance traveled.  This can be interpreted as $2.63 per mile."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "cell_id": "0c6bbb2f0f84437786d04013365833c6",
    "deepnote_cell_height": 194.953125,
    "deepnote_cell_type": "code",
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     97.96875
    ],
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 11,
    "execution_start": 1651868224851,
    "source_hash": "77d2cb3a",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "distance     2.629467\n",
       "tip          1.330659\n",
       "tolls        1.114880\n",
       "Manhattan    1.554776\n",
       "dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(reg.coef_, index=cols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "cell_id": "3638c804896b4ed28087b03c47ca16b6",
    "deepnote_cell_height": 118.1875,
    "deepnote_cell_type": "code",
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     21.1875
    ],
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 9,
    "execution_start": 1651868437350,
    "source_hash": "1661cbe7",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.170557177757704"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "cell_id": "bf636924d7214855bbd7ab4eecb6bcbd",
    "deepnote_cell_height": 272,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 102,
    "execution_start": 1651868520714,
    "source_hash": "610ca1b2",
    "tags": []
   },
   "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>pickup</th>\n",
       "      <th>dropoff</th>\n",
       "      <th>passengers</th>\n",
       "      <th>distance</th>\n",
       "      <th>fare</th>\n",
       "      <th>tip</th>\n",
       "      <th>tolls</th>\n",
       "      <th>total</th>\n",
       "      <th>color</th>\n",
       "      <th>payment</th>\n",
       "      <th>pickup_zone</th>\n",
       "      <th>dropoff_zone</th>\n",
       "      <th>pickup_borough</th>\n",
       "      <th>dropoff_borough</th>\n",
       "      <th>Manhattan</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2019-03-23 20:21:09</td>\n",
       "      <td>2019-03-23 20:27:24</td>\n",
       "      <td>1</td>\n",
       "      <td>1.60</td>\n",
       "      <td>7.0</td>\n",
       "      <td>2.15</td>\n",
       "      <td>0.0</td>\n",
       "      <td>12.95</td>\n",
       "      <td>yellow</td>\n",
       "      <td>credit card</td>\n",
       "      <td>Lenox Hill West</td>\n",
       "      <td>UN/Turtle Bay South</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2019-03-04 16:11:55</td>\n",
       "      <td>2019-03-04 16:19:00</td>\n",
       "      <td>1</td>\n",
       "      <td>0.79</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>9.30</td>\n",
       "      <td>yellow</td>\n",
       "      <td>cash</td>\n",
       "      <td>Upper West Side South</td>\n",
       "      <td>Upper West Side South</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>Manhattan</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                pickup              dropoff  passengers  distance  fare   tip  \\\n",
       "0  2019-03-23 20:21:09  2019-03-23 20:27:24           1      1.60   7.0  2.15   \n",
       "1  2019-03-04 16:11:55  2019-03-04 16:19:00           1      0.79   5.0  0.00   \n",
       "\n",
       "   tolls  total   color      payment            pickup_zone  \\\n",
       "0    0.0  12.95  yellow  credit card        Lenox Hill West   \n",
       "1    0.0   9.30  yellow         cash  Upper West Side South   \n",
       "\n",
       "            dropoff_zone pickup_borough dropoff_borough  Manhattan  \n",
       "0    UN/Turtle Bay South      Manhattan       Manhattan          1  \n",
       "1  Upper West Side South      Manhattan       Manhattan          1  "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "cell_id": "7b17c01060a14ecab3ce50f8caf56c3a",
    "deepnote_cell_height": 118.1875,
    "deepnote_cell_type": "code",
    "deepnote_output_heights": [
     21.1875
    ],
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 7,
    "execution_start": 1651868561204,
    "source_hash": "dea74e1c",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([14.79339642,  9.80261182])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.predict(df[:2][cols])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, we can view `14.8` as the predicted output for the 0th row.  The `predict` method isn't doing anything mysterious.  It's just evaluating this linear function on the given inputs.  Here is the by-hand computation for the 0th row."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.787500000000001"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2.63*1.6+1.33*2.15+1.11*0+1.55*1+6.17"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "e6a10e193f07477694fbe10b4c9276e5",
    "deepnote_cell_height": 189.5625,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "## Polynomial regression\n",
    "\n",
    "Last time, we fit a degree 9 polynomial model to this data, using \"distance\" as the (only) input variable and using \"total\" as the output variable.  The code from last time is below.\n",
    "\n",
    "Using 100 training points, adapt the code from last time to fit models of different degrees, for each degree from 1 to 25.  Plot the resulting polynomials for $0 \\leq x \\leq M$, where $M$ is the maximum \"distance\" value within the training data.\n",
    "\n",
    "A lot of this code was copied from last time, and then adjusted to the current goals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "cell_id": "2235c85242b94664b25889188080e731",
    "deepnote_cell_height": 81,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 0,
    "execution_start": 1651868813242,
    "source_hash": "746a4dbc",
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're using 100 data points, instead of 40 from last time, so we should expect that there will be slightly less overfitting this time, since we are using more data points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "cell_id": "302431b4d1b9448e9756128e893b371c",
    "deepnote_cell_height": 81,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 10,
    "execution_start": 1651868851207,
    "source_hash": "e5cb177c",
    "tags": []
   },
   "outputs": [],
   "source": [
    "df_train, df_test = train_test_split(df, train_size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "cell_id": "f2b50781bde34eb8835d5af09977b66f",
    "deepnote_cell_height": 118.1875,
    "deepnote_cell_type": "code",
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     21.1875
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    "deepnote_to_be_reexecuted": false,
    "execution_millis": 10,
    "execution_start": 1651868856995,
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    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 15)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "cell_id": "5a8731f236144a1788b72601b501d36f",
    "deepnote_cell_height": 135,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 0,
    "execution_start": 1651868879671,
    "source_hash": "1fb53adb",
    "tags": []
   },
   "outputs": [],
   "source": [
    "c = alt.Chart(df_train).mark_circle().encode(\n",
    "    x=\"distance\",\n",
    "    y=\"total\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "cell_id": "6dfedd23462546f09646ff7c68163dbc",
    "deepnote_cell_height": 458,
    "deepnote_cell_type": "code",
    "deepnote_output_heights": [
     361
    ],
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 722,
    "execution_start": 1651868881576,
    "source_hash": "957caa7e",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<div id=\"altair-viz-cca2da8fefce4c07a38fb4ce80b9c958\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-cca2da8fefce4c07a38fb4ce80b9c958\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-cca2da8fefce4c07a38fb4ce80b9c958\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm//vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm//vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm//vega-lite@4.17.0?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm//vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"4.17.0\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 400, \"continuousHeight\": 300}}, \"data\": {\"name\": \"data-fe3f211559be63cf247c22c97a18653f\"}, \"mark\": \"circle\", \"encoding\": {\"x\": {\"field\": \"distance\", \"type\": \"quantitative\"}, \"y\": {\"field\": \"total\", \"type\": \"quantitative\"}}, \"$schema\": \"https://vega.github.io/schema/vega-lite/v4.17.0.json\", \"datasets\": {\"data-fe3f211559be63cf247c22c97a18653f\": [{\"pickup\": \"2019-03-16 09:12:31\", \"dropoff\": \"2019-03-16 09:31:50\", \"passengers\": 1, \"distance\": 8.83, \"fare\": 26.5, \"tip\": 7.11, \"tolls\": 5.76, \"total\": 42.67, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"LaGuardia Airport\", \"dropoff_zone\": \"Midtown South\", \"pickup_borough\": \"Queens\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-14 16:48:56\", \"dropoff\": \"2019-03-14 16:53:23\", \"passengers\": 1, \"distance\": 0.66, \"fare\": 5.0, \"tip\": 1.0, \"tolls\": 0.0, \"total\": 10.3, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Lincoln Square West\", \"dropoff_zone\": \"Lincoln Square West\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-16 18:29:51\", \"dropoff\": \"2019-03-16 18:34:16\", \"passengers\": 1, \"distance\": 0.64, \"fare\": 5.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 5.8, \"color\": \"green\", \"payment\": \"cash\", \"pickup_zone\": \"Central Harlem North\", \"dropoff_zone\": \"Hamilton Heights\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-12 05:36:56\", \"dropoff\": \"2019-03-12 05:42:01\", \"passengers\": 3, \"distance\": 1.21, \"fare\": 6.5, \"tip\": 2.06, \"tolls\": 0.0, \"total\": 12.36, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Penn Station/Madison Sq West\", \"dropoff_zone\": \"Times Sq/Theatre District\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-23 21:54:35\", \"dropoff\": \"2019-03-23 22:05:40\", \"passengers\": 1, \"distance\": 1.9, \"fare\": 9.0, \"tip\": 1.28, \"tolls\": 0.0, \"total\": 14.08, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Lenox Hill West\", \"dropoff_zone\": \"Murray Hill\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-31 02:46:01\", \"dropoff\": \"2019-03-31 03:03:41\", \"passengers\": 4, \"distance\": 4.48, \"fare\": 16.0, \"tip\": 3.96, \"tolls\": 0.0, \"total\": 23.76, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"West Village\", \"dropoff_zone\": \"Yorkville West\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-19 19:19:53\", \"dropoff\": \"2019-03-19 19:25:14\", \"passengers\": 2, \"distance\": 1.82, \"fare\": 7.0, \"tip\": 2.26, \"tolls\": 0.0, \"total\": 13.56, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Sutton Place/Turtle Bay North\", \"dropoff_zone\": \"Upper East Side North\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-09 21:41:33\", \"dropoff\": \"2019-03-09 21:46:23\", \"passengers\": 1, \"distance\": 0.77, \"fare\": 5.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 6.3, \"color\": \"green\", \"payment\": \"cash\", \"pickup_zone\": \"Jackson Heights\", \"dropoff_zone\": \"Elmhurst\", \"pickup_borough\": \"Queens\", \"dropoff_borough\": \"Queens\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-08 02:27:41\", \"dropoff\": \"2019-03-08 02:32:23\", \"passengers\": 5, \"distance\": 1.95, \"fare\": 7.0, \"tip\": 2.0, \"tolls\": 0.0, \"total\": 12.8, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Midtown East\", \"dropoff_zone\": \"Yorkville West\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-15 21:25:41\", \"dropoff\": \"2019-03-15 21:51:22\", \"passengers\": 2, \"distance\": 3.67, \"fare\": 18.0, \"tip\": 4.41, \"tolls\": 0.0, \"total\": 26.46, \"color\": \"green\", \"payment\": \"credit card\", \"pickup_zone\": \"DUMBO/Vinegar Hill\", \"dropoff_zone\": \"West Village\", \"pickup_borough\": \"Brooklyn\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-15 22:59:38\", \"dropoff\": \"2019-03-15 23:04:56\", \"passengers\": 6, \"distance\": 1.16, \"fare\": 6.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 9.8, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"Upper West Side South\", \"dropoff_zone\": \"Upper West Side North\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-19 07:23:39\", \"dropoff\": \"2019-03-19 07:32:59\", \"passengers\": 1, \"distance\": 1.3, \"fare\": 8.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 11.3, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"Midtown East\", \"dropoff_zone\": \"East Chelsea\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-27 16:55:01\", \"dropoff\": \"2019-03-27 17:13:12\", \"passengers\": 2, \"distance\": 2.77, \"fare\": 13.0, \"tip\": 4.33, \"tolls\": 0.0, \"total\": 21.63, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Lenox Hill West\", \"dropoff_zone\": \"Stuy Town/Peter Cooper Village\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-15 17:33:10\", \"dropoff\": \"2019-03-15 17:48:38\", \"passengers\": 1, \"distance\": 1.66, \"fare\": 11.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 15.3, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"Lincoln Square East\", \"dropoff_zone\": \"Midtown East\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-02 18:23:13\", \"dropoff\": \"2019-03-02 18:33:08\", \"passengers\": 1, \"distance\": 1.65, \"fare\": 8.5, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 9.3, \"color\": \"green\", \"payment\": \"cash\", \"pickup_zone\": \"DUMBO/Vinegar Hill\", \"dropoff_zone\": \"Boerum Hill\", \"pickup_borough\": \"Brooklyn\", \"dropoff_borough\": \"Brooklyn\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-23 20:50:49\", \"dropoff\": \"2019-03-23 21:02:07\", \"passengers\": 1, \"distance\": 2.6, \"fare\": 10.5, \"tip\": 2.0, \"tolls\": 0.0, \"total\": 16.3, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Midtown Center\", \"dropoff_zone\": \"East Harlem South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-22 08:18:14\", \"dropoff\": \"2019-03-22 08:35:44\", \"passengers\": 5, \"distance\": 1.41, \"fare\": 11.5, \"tip\": 2.96, \"tolls\": 0.0, \"total\": 17.76, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Midtown South\", \"dropoff_zone\": \"East Chelsea\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-27 15:40:59\", \"dropoff\": \"2019-03-27 15:48:37\", \"passengers\": 5, \"distance\": 0.73, \"fare\": 6.5, \"tip\": 2.94, \"tolls\": 0.0, \"total\": 12.74, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Midtown South\", \"dropoff_zone\": \"Gramercy\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-15 19:49:49\", \"dropoff\": \"2019-03-15 19:51:18\", \"passengers\": 1, \"distance\": 0.15, \"fare\": 3.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 4.8, \"color\": \"green\", \"payment\": \"cash\", \"pickup_zone\": \"Hamilton Heights\", \"dropoff_zone\": \"Central Harlem North\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-04 12:30:56\", \"dropoff\": \"2019-03-04 12:41:37\", \"passengers\": 1, \"distance\": 1.3, \"fare\": 8.0, \"tip\": 2.25, \"tolls\": 0.0, \"total\": 13.55, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Murray Hill\", \"dropoff_zone\": \"Upper East Side South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-06 12:35:27\", \"dropoff\": \"2019-03-06 12:41:58\", \"passengers\": 1, \"distance\": 0.84, \"fare\": 6.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 6.8, \"color\": \"green\", \"payment\": \"cash\", \"pickup_zone\": \"Astoria\", \"dropoff_zone\": \"Woodside\", \"pickup_borough\": \"Queens\", \"dropoff_borough\": \"Queens\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-09 22:07:31\", \"dropoff\": \"2019-03-09 22:23:10\", \"passengers\": 1, \"distance\": 1.7, \"fare\": 11.0, \"tip\": 2.95, \"tolls\": 0.0, \"total\": 17.75, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Gramercy\", \"dropoff_zone\": \"Meatpacking/West Village West\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-29 00:34:04\", \"dropoff\": \"2019-03-29 00:50:16\", \"passengers\": 2, \"distance\": 3.3, \"fare\": 13.0, \"tip\": 1.5, \"tolls\": 0.0, \"total\": 18.3, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"East Chelsea\", \"dropoff_zone\": \"World Trade Center\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-01 11:39:14\", \"dropoff\": \"2019-03-01 11:51:17\", \"passengers\": 1, \"distance\": 1.0, \"fare\": 8.5, \"tip\": 1.0, \"tolls\": 0.0, \"total\": 12.8, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Times Sq/Theatre District\", \"dropoff_zone\": \"UN/Turtle Bay South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-19 19:22:56\", \"dropoff\": \"2019-03-19 19:45:28\", \"passengers\": 1, \"distance\": 8.7, \"fare\": 27.0, \"tip\": 7.41, \"tolls\": 5.76, \"total\": 44.47, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"LaGuardia Airport\", \"dropoff_zone\": \"Garment District\", \"pickup_borough\": \"Queens\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-16 18:58:47\", \"dropoff\": \"2019-03-16 19:12:47\", \"passengers\": 1, \"distance\": 1.1, \"fare\": 9.5, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 12.8, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"Midtown North\", \"dropoff_zone\": \"Garment District\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-16 13:19:56\", \"dropoff\": \"2019-03-16 13:39:32\", \"passengers\": 1, \"distance\": 2.97, \"fare\": 14.0, \"tip\": 2.96, \"tolls\": 0.0, \"total\": 17.76, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"East Flatbush/Remsen Village\", \"dropoff_zone\": \"Stuyvesant Heights\", \"pickup_borough\": \"Brooklyn\", \"dropoff_borough\": \"Brooklyn\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-02 01:26:11\", \"dropoff\": \"2019-03-02 02:01:00\", \"passengers\": 1, \"distance\": 8.7, \"fare\": 30.5, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 34.3, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"Union Sq\", \"dropoff_zone\": \"Washington Heights South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-19 06:28:02\", \"dropoff\": \"2019-03-19 06:29:04\", \"passengers\": 1, \"distance\": 0.17, \"fare\": 3.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 7.3, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"Lincoln Square West\", \"dropoff_zone\": \"Lincoln Square West\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-18 20:04:16\", \"dropoff\": \"2019-03-18 20:19:16\", \"passengers\": 1, \"distance\": 1.9, \"fare\": 11.0, \"tip\": 3.7, \"tolls\": 0.0, \"total\": 18.5, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Kips Bay\", \"dropoff_zone\": \"East Chelsea\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-10 14:02:13\", \"dropoff\": \"2019-03-10 14:15:11\", \"passengers\": 4, \"distance\": 1.94, \"fare\": 10.0, \"tip\": 2.66, \"tolls\": 0.0, \"total\": 15.96, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Gramercy\", \"dropoff_zone\": \"TriBeCa/Civic Center\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-12 17:41:35\", \"dropoff\": \"2019-03-12 17:46:28\", \"passengers\": 1, \"distance\": 0.9, \"fare\": 5.5, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 7.3, \"color\": \"green\", \"payment\": \"cash\", \"pickup_zone\": \"Sheepshead Bay\", \"dropoff_zone\": \"Sheepshead Bay\", \"pickup_borough\": \"Brooklyn\", \"dropoff_borough\": \"Brooklyn\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-29 17:55:03\", \"dropoff\": \"2019-03-29 17:59:32\", \"passengers\": 1, \"distance\": 0.3, \"fare\": 5.0, \"tip\": 1.85, \"tolls\": 0.0, \"total\": 11.15, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"West Chelsea/Hudson Yards\", \"dropoff_zone\": \"Clinton West\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-12 08:34:26\", \"dropoff\": \"2019-03-12 09:32:22\", \"passengers\": 1, \"distance\": 7.09, \"fare\": 36.5, \"tip\": 0.0, \"tolls\": 5.76, \"total\": 43.06, \"color\": \"green\", \"payment\": \"credit card\", \"pickup_zone\": \"Middle Village\", \"dropoff_zone\": \"Times Sq/Theatre District\", \"pickup_borough\": \"Queens\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-12 13:01:22\", \"dropoff\": \"2019-03-12 13:04:25\", \"passengers\": 1, \"distance\": 0.6, \"fare\": 4.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 7.3, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"Kips Bay\", \"dropoff_zone\": \"Murray Hill\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-21 20:50:17\", \"dropoff\": \"2019-03-21 20:51:55\", \"passengers\": 6, \"distance\": 0.48, \"fare\": 3.5, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 7.3, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"Upper East Side North\", \"dropoff_zone\": \"Upper East Side North\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-05 18:09:27\", \"dropoff\": \"2019-03-05 18:21:07\", \"passengers\": 1, \"distance\": 1.12, \"fare\": 8.5, \"tip\": 2.56, \"tolls\": 0.0, \"total\": 15.36, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Gramercy\", \"dropoff_zone\": \"Murray Hill\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-04 15:12:05\", \"dropoff\": \"2019-03-04 15:38:33\", \"passengers\": 2, \"distance\": 4.9, \"fare\": 21.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 21.8, \"color\": \"green\", \"payment\": \"cash\", \"pickup_zone\": \"Norwood\", \"dropoff_zone\": \"West Concourse\", \"pickup_borough\": \"Bronx\", \"dropoff_borough\": \"Bronx\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-14 13:27:37\", \"dropoff\": \"2019-03-14 13:32:26\", \"passengers\": 1, \"distance\": 0.74, \"fare\": 5.5, \"tip\": 1.76, \"tolls\": 0.0, \"total\": 10.56, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Upper East Side South\", \"dropoff_zone\": \"Upper East Side North\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-15 17:07:20\", \"dropoff\": \"2019-03-15 17:11:24\", \"passengers\": 1, \"distance\": 0.49, \"fare\": 4.5, \"tip\": 1.32, \"tolls\": 0.0, \"total\": 10.12, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Upper West Side South\", \"dropoff_zone\": \"Upper West Side South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-11 10:48:05\", \"dropoff\": \"2019-03-11 11:20:00\", \"passengers\": 1, \"distance\": 2.2, \"fare\": 19.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 22.3, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"Midtown Center\", \"dropoff_zone\": \"West Chelsea/Hudson Yards\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-25 19:11:47\", \"dropoff\": \"2019-03-25 19:22:25\", \"passengers\": 2, \"distance\": 1.77, \"fare\": 9.0, \"tip\": 1.33, \"tolls\": 0.0, \"total\": 14.63, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Garment District\", \"dropoff_zone\": \"Sutton Place/Turtle Bay North\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-20 18:07:06\", \"dropoff\": \"2019-03-20 18:29:04\", \"passengers\": 2, \"distance\": 1.2, \"fare\": 14.0, \"tip\": 1.83, \"tolls\": 0.0, \"total\": 20.13, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Penn Station/Madison Sq West\", \"dropoff_zone\": \"Times Sq/Theatre District\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-23 07:46:13\", \"dropoff\": \"2019-03-23 07:47:34\", \"passengers\": 1, \"distance\": 0.5, \"fare\": 3.5, \"tip\": 1.25, \"tolls\": 0.0, \"total\": 5.55, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"East Harlem South\", \"dropoff_zone\": \"East Harlem South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-25 05:39:13\", \"dropoff\": \"2019-03-25 05:46:41\", \"passengers\": 1, \"distance\": 1.5, \"fare\": 7.5, \"tip\": 2.8, \"tolls\": 0.0, \"total\": 14.1, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Central Park\", \"dropoff_zone\": \"Lenox Hill East\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-10 14:45:46\", \"dropoff\": \"2019-03-10 14:56:50\", \"passengers\": 1, \"distance\": 1.1, \"fare\": 8.0, \"tip\": 1.7, \"tolls\": 0.0, \"total\": 13.0, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Lincoln Square East\", \"dropoff_zone\": \"Upper East Side South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-04 07:11:30\", \"dropoff\": \"2019-03-04 07:17:49\", \"passengers\": 1, \"distance\": 0.8, \"fare\": 6.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 9.3, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Garment District\", \"dropoff_zone\": \"Murray Hill\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-22 22:58:23\", \"dropoff\": \"2019-03-22 23:12:02\", \"passengers\": 4, \"distance\": 3.2, \"fare\": 13.0, \"tip\": 3.35, \"tolls\": 0.0, \"total\": 20.15, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Sutton Place/Turtle Bay North\", \"dropoff_zone\": \"Alphabet City\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-08 21:13:45\", \"dropoff\": \"2019-03-08 22:05:02\", \"passengers\": 2, \"distance\": 18.55, \"fare\": 52.0, \"tip\": 9.0, \"tolls\": 5.76, \"total\": 70.06, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"JFK Airport\", \"dropoff_zone\": \"Midtown North\", \"pickup_borough\": \"Queens\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-14 10:40:55\", \"dropoff\": \"2019-03-14 10:49:03\", \"passengers\": 1, \"distance\": 1.23, \"fare\": 7.5, \"tip\": 2.16, \"tolls\": 0.0, \"total\": 12.96, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Upper West Side North\", \"dropoff_zone\": \"Upper East Side North\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-04 21:12:08\", \"dropoff\": \"2019-03-04 21:23:43\", \"passengers\": 1, \"distance\": 3.11, \"fare\": 11.5, \"tip\": 3.06, \"tolls\": 0.0, \"total\": 18.36, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"SoHo\", \"dropoff_zone\": \"Clinton West\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-13 08:11:54\", \"dropoff\": \"2019-03-13 08:24:56\", \"passengers\": 1, \"distance\": 1.15, \"fare\": 9.5, \"tip\": 2.06, \"tolls\": 0.0, \"total\": 12.36, \"color\": \"green\", \"payment\": \"credit card\", \"pickup_zone\": \"East Harlem North\", \"dropoff_zone\": \"East Harlem South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-23 09:47:20\", \"dropoff\": \"2019-03-23 09:58:36\", \"passengers\": 1, \"distance\": 1.54, \"fare\": 9.0, \"tip\": 2.46, \"tolls\": 0.0, \"total\": 14.76, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"West Village\", \"dropoff_zone\": \"Little Italy/NoLiTa\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-21 18:33:30\", \"dropoff\": \"2019-03-21 18:40:05\", \"passengers\": 2, \"distance\": 1.1, \"fare\": 6.5, \"tip\": 2.15, \"tolls\": 0.0, \"total\": 12.95, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Murray Hill\", \"dropoff_zone\": \"East Village\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-07 21:55:40\", \"dropoff\": \"2019-03-07 21:59:18\", \"passengers\": 1, \"distance\": 0.6, \"fare\": 4.5, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 8.3, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"Upper East Side North\", \"dropoff_zone\": \"Yorkville West\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-07 21:31:45\", \"dropoff\": \"2019-03-07 21:48:30\", \"passengers\": 1, \"distance\": 2.86, \"fare\": 13.0, \"tip\": 3.36, \"tolls\": 0.0, \"total\": 20.16, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"SoHo\", \"dropoff_zone\": \"UN/Turtle Bay South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-12 17:14:54\", \"dropoff\": \"2019-03-12 17:23:18\", \"passengers\": 1, \"distance\": 1.49, \"fare\": 7.5, \"tip\": 2.36, \"tolls\": 0.0, \"total\": 14.16, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Union Sq\", \"dropoff_zone\": \"West Village\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-01 09:00:22\", \"dropoff\": \"2019-03-01 09:10:09\", \"passengers\": 1, \"distance\": 1.01, \"fare\": 7.5, \"tip\": 2.0, \"tolls\": 0.0, \"total\": 12.8, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Midtown Center\", \"dropoff_zone\": \"Midtown South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-01 21:16:20\", \"dropoff\": \"2019-03-01 21:24:11\", \"passengers\": 1, \"distance\": 1.2, \"fare\": 7.0, \"tip\": 2.0, \"tolls\": 0.0, \"total\": 12.8, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Union Sq\", \"dropoff_zone\": \"East Chelsea\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-10 23:57:00\", \"dropoff\": \"2019-03-11 00:22:22\", \"passengers\": 5, \"distance\": 10.72, \"fare\": 32.0, \"tip\": 0.0, \"tolls\": 5.76, \"total\": 39.06, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"LaGuardia Airport\", \"dropoff_zone\": \"Pelham Parkway\", \"pickup_borough\": \"Queens\", \"dropoff_borough\": \"Bronx\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-10 17:43:09\", \"dropoff\": \"2019-03-10 17:55:08\", \"passengers\": 1, \"distance\": 3.07, \"fare\": 12.0, \"tip\": 3.06, \"tolls\": 0.0, \"total\": 18.36, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Clinton West\", \"dropoff_zone\": \"Meatpacking/West Village West\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-14 15:11:21\", \"dropoff\": \"2019-03-14 15:21:02\", \"passengers\": 1, \"distance\": 0.85, \"fare\": 7.5, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 10.8, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"Manhattan Valley\", \"dropoff_zone\": \"Upper West Side North\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-18 12:03:51\", \"dropoff\": \"2019-03-18 12:11:34\", \"passengers\": 1, \"distance\": 1.16, \"fare\": 7.5, \"tip\": 2.16, \"tolls\": 0.0, \"total\": 12.96, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Financial District North\", \"dropoff_zone\": \"Battery Park City\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-29 22:58:39\", \"dropoff\": \"2019-03-29 23:26:09\", \"passengers\": 5, \"distance\": 11.25, \"fare\": 33.5, \"tip\": 8.61, \"tolls\": 5.76, \"total\": 51.67, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Union Sq\", \"dropoff_zone\": \"North Corona\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Queens\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-02 12:12:26\", \"dropoff\": \"2019-03-02 12:20:17\", \"passengers\": 1, \"distance\": 1.53, \"fare\": 7.5, \"tip\": 2.16, \"tolls\": 0.0, \"total\": 12.96, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Union Sq\", \"dropoff_zone\": \"Murray Hill\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-29 17:32:20\", \"dropoff\": \"2019-03-29 18:53:52\", \"passengers\": 1, \"distance\": 26.92, \"fare\": 75.5, \"tip\": 23.19, \"tolls\": 0.0, \"total\": 100.49, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"JFK Airport\", \"dropoff_zone\": \"Cobble Hill\", \"pickup_borough\": \"Queens\", \"dropoff_borough\": \"Brooklyn\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-26 08:27:37\", \"dropoff\": \"2019-03-26 08:41:46\", \"passengers\": 1, \"distance\": 2.74, \"fare\": 12.0, \"tip\": 2.5, \"tolls\": 0.0, \"total\": 17.8, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Lincoln Square East\", \"dropoff_zone\": \"East Harlem South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-31 12:41:16\", \"dropoff\": \"2019-03-31 12:48:07\", \"passengers\": 1, \"distance\": 0.8, \"fare\": 6.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 6.8, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"Hamilton Heights\", \"dropoff_zone\": \"Central Harlem North\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-06 11:21:48\", \"dropoff\": \"2019-03-06 11:28:03\", \"passengers\": 1, \"distance\": 0.55, \"fare\": 5.5, \"tip\": 1.76, \"tolls\": 0.0, \"total\": 10.56, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Yorkville West\", \"dropoff_zone\": \"Lenox Hill West\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-28 15:14:06\", \"dropoff\": \"2019-03-28 15:36:56\", \"passengers\": 2, \"distance\": 3.16, \"fare\": 15.5, \"tip\": 3.76, \"tolls\": 0.0, \"total\": 22.56, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"West Chelsea/Hudson Yards\", \"dropoff_zone\": \"Little Italy/NoLiTa\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-26 13:23:44\", \"dropoff\": \"2019-03-26 13:33:27\", \"passengers\": 1, \"distance\": 1.6, \"fare\": 8.5, \"tip\": 2.95, \"tolls\": 0.0, \"total\": 14.75, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Upper East Side South\", \"dropoff_zone\": \"Upper East Side North\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-21 04:42:25\", \"dropoff\": \"2019-03-21 05:05:57\", \"passengers\": 1, \"distance\": 8.2, \"fare\": 26.0, \"tip\": 0.0, \"tolls\": 4.75, \"total\": 34.8, \"color\": \"green\", \"payment\": \"cash\", \"pickup_zone\": \"Jackson Heights\", \"dropoff_zone\": \"West Chelsea/Hudson Yards\", \"pickup_borough\": \"Queens\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-12 04:07:08\", \"dropoff\": \"2019-03-12 04:19:08\", \"passengers\": 1, \"distance\": 3.93, \"fare\": 13.5, \"tip\": 5.26, \"tolls\": 0.0, \"total\": 22.81, \"color\": \"green\", \"payment\": \"credit card\", \"pickup_zone\": \"East Harlem South\", \"dropoff_zone\": \"Midtown Center\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-22 09:02:34\", \"dropoff\": \"2019-03-22 09:32:22\", \"passengers\": 1, \"distance\": 8.3, \"fare\": 27.0, \"tip\": 7.2, \"tolls\": 5.76, \"total\": 43.26, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"LaGuardia Airport\", \"dropoff_zone\": \"Kips Bay\", \"pickup_borough\": \"Queens\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-15 08:45:26\", \"dropoff\": \"2019-03-15 09:02:19\", \"passengers\": 4, \"distance\": 1.15, \"fare\": 11.0, \"tip\": 2.86, \"tolls\": 0.0, \"total\": 17.16, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Lenox Hill West\", \"dropoff_zone\": \"UN/Turtle Bay South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-11 00:05:38\", \"dropoff\": \"2019-03-11 00:15:33\", \"passengers\": 1, \"distance\": 2.2, \"fare\": 9.5, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 10.8, \"color\": \"green\", \"payment\": \"cash\", \"pickup_zone\": \"Williamsburg (North Side)\", \"dropoff_zone\": \"Bushwick South\", \"pickup_borough\": \"Brooklyn\", \"dropoff_borough\": \"Brooklyn\", \"Manhattan\": 0}, {\"pickup\": \"2019-03-16 19:05:05\", \"dropoff\": \"2019-03-16 19:10:23\", \"passengers\": 3, \"distance\": 0.4, \"fare\": 5.0, \"tip\": 1.65, \"tolls\": 0.0, \"total\": 9.95, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"East Village\", \"dropoff_zone\": \"East Village\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-21 12:06:09\", \"dropoff\": \"2019-03-21 12:19:26\", \"passengers\": 1, \"distance\": 0.91, \"fare\": 9.0, \"tip\": 2.46, \"tolls\": 0.0, \"total\": 14.76, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Garment District\", \"dropoff_zone\": \"West Chelsea/Hudson Yards\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-26 20:15:19\", \"dropoff\": \"2019-03-26 20:28:29\", \"passengers\": 1, \"distance\": 2.77, \"fare\": 11.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 14.8, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"Midtown Center\", \"dropoff_zone\": \"East Harlem South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-16 10:37:52\", \"dropoff\": \"2019-03-16 10:56:39\", \"passengers\": 2, \"distance\": 2.34, \"fare\": 13.5, \"tip\": 4.2, \"tolls\": 0.0, \"total\": 21.0, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"UN/Turtle Bay South\", \"dropoff_zone\": \"West Chelsea/Hudson Yards\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-21 20:07:31\", \"dropoff\": \"2019-03-21 20:13:01\", \"passengers\": 1, \"distance\": 0.8, \"fare\": 5.5, \"tip\": 2.79, \"tolls\": 0.0, \"total\": 12.09, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Central Park\", \"dropoff_zone\": \"Lincoln Square West\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-27 17:53:01\", \"dropoff\": \"2019-03-27 18:00:25\", \"passengers\": 1, \"distance\": 1.37, \"fare\": 7.5, \"tip\": 2.36, \"tolls\": 0.0, \"total\": 14.16, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Alphabet City\", \"dropoff_zone\": \"West Village\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-27 17:52:35\", \"dropoff\": \"2019-03-27 18:08:49\", \"passengers\": 1, \"distance\": 3.46, \"fare\": 14.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 18.3, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"East Chelsea\", \"dropoff_zone\": \"Upper East Side North\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-19 14:01:31\", \"dropoff\": \"2019-03-19 14:23:46\", \"passengers\": 1, \"distance\": 4.43, \"fare\": 18.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 18.8, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Midtown Center\", \"dropoff_zone\": \"Sunnyside\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Queens\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-17 16:53:41\", \"dropoff\": \"2019-03-17 16:59:46\", \"passengers\": 2, \"distance\": 0.8, \"fare\": 6.0, \"tip\": 1.0, \"tolls\": 0.0, \"total\": 10.3, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Murray Hill\", \"dropoff_zone\": \"Midtown South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-05 20:20:51\", \"dropoff\": \"2019-03-05 20:22:27\", \"passengers\": 1, \"distance\": 0.5, \"fare\": 3.5, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 7.3, \"color\": \"yellow\", \"payment\": \"cash\", \"pickup_zone\": \"Upper West Side North\", \"dropoff_zone\": \"Upper West Side North\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-17 19:24:50\", \"dropoff\": \"2019-03-17 19:29:58\", \"passengers\": 1, \"distance\": 0.62, \"fare\": 5.5, \"tip\": 1.0, \"tolls\": 0.0, \"total\": 9.8, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Midtown Center\", \"dropoff_zone\": \"Sutton Place/Turtle Bay North\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-20 13:59:49\", \"dropoff\": \"2019-03-20 14:05:57\", \"passengers\": 1, \"distance\": 0.9, \"fare\": 6.0, \"tip\": 1.85, \"tolls\": 0.0, \"total\": 11.15, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Garment District\", \"dropoff_zone\": \"West Chelsea/Hudson Yards\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-01 13:07:27\", \"dropoff\": \"2019-03-01 13:12:32\", \"passengers\": 1, \"distance\": 1.49, \"fare\": 6.5, \"tip\": 1.96, \"tolls\": 0.0, \"total\": 11.76, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Battery Park City\", \"dropoff_zone\": \"Financial District South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-02 22:01:50\", \"dropoff\": \"2019-03-02 22:09:59\", \"passengers\": 1, \"distance\": 0.82, \"fare\": 7.0, \"tip\": 2.16, \"tolls\": 0.0, \"total\": 12.96, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Greenwich Village North\", \"dropoff_zone\": \"Gramercy\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-14 19:12:12\", \"dropoff\": \"2019-03-14 19:53:18\", \"passengers\": 1, \"distance\": 8.3, \"fare\": 27.06, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 27.86, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Times Sq/Theatre District\", \"dropoff_zone\": \"East Concourse/Concourse Village\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Bronx\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-15 17:04:47\", \"dropoff\": \"2019-03-15 17:07:18\", \"passengers\": 1, \"distance\": 0.3, \"fare\": 3.5, \"tip\": 1.55, \"tolls\": 0.0, \"total\": 9.35, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"East Village\", \"dropoff_zone\": \"East Village\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-01 16:26:57\", \"dropoff\": \"2019-03-01 16:32:18\", \"passengers\": 6, \"distance\": 0.53, \"fare\": 5.5, \"tip\": 1.96, \"tolls\": 0.0, \"total\": 11.76, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"East Village\", \"dropoff_zone\": \"Little Italy/NoLiTa\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-21 22:13:37\", \"dropoff\": \"2019-03-21 22:21:27\", \"passengers\": 1, \"distance\": 1.4, \"fare\": 7.0, \"tip\": 2.15, \"tolls\": 0.0, \"total\": 12.95, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Union Sq\", \"dropoff_zone\": \"Alphabet City\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-05 12:42:33\", \"dropoff\": \"2019-03-05 12:46:02\", \"passengers\": 1, \"distance\": 0.4, \"fare\": 4.0, \"tip\": 1.83, \"tolls\": 0.0, \"total\": 9.13, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Central Park\", \"dropoff_zone\": \"Upper East Side South\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-04 07:23:37\", \"dropoff\": \"2019-03-04 07:25:58\", \"passengers\": 1, \"distance\": 0.79, \"fare\": 4.0, \"tip\": 1.0, \"tolls\": 0.0, \"total\": 8.3, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Upper East Side South\", \"dropoff_zone\": \"Lenox Hill West\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-06 20:37:37\", \"dropoff\": \"2019-03-06 20:45:26\", \"passengers\": 2, \"distance\": 1.22, \"fare\": 7.0, \"tip\": 1.0, \"tolls\": 0.0, \"total\": 11.8, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Central Park\", \"dropoff_zone\": \"Lincoln Square East\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-06 23:24:40\", \"dropoff\": \"2019-03-06 23:45:32\", \"passengers\": 1, \"distance\": 7.4, \"fare\": 23.5, \"tip\": 6.8, \"tolls\": 0.0, \"total\": 34.1, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Midtown East\", \"dropoff_zone\": \"Cobble Hill\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Brooklyn\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-14 16:49:58\", \"dropoff\": \"2019-03-14 17:07:29\", \"passengers\": 1, \"distance\": 3.6, \"fare\": 14.5, \"tip\": 1.5, \"tolls\": 0.0, \"total\": 20.3, \"color\": \"yellow\", \"payment\": \"credit card\", \"pickup_zone\": \"Penn Station/Madison Sq West\", \"dropoff_zone\": \"Upper East Side North\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}, {\"pickup\": \"2019-03-04 08:51:24\", \"dropoff\": \"2019-03-04 09:00:56\", \"passengers\": 1, \"distance\": 1.6, \"fare\": 8.0, \"tip\": 0.0, \"tolls\": 0.0, \"total\": 8.8, \"color\": \"green\", \"payment\": \"cash\", \"pickup_zone\": \"East Harlem North\", \"dropoff_zone\": \"Manhattanville\", \"pickup_borough\": \"Manhattan\", \"dropoff_borough\": \"Manhattan\", \"Manhattan\": 1}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "cell_id": "e2597158c406468b8a73184b3514f60c",
    "deepnote_cell_height": 118.1875,
    "deepnote_cell_type": "code",
    "deepnote_output_heights": [
     21.1875
    ],
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 18,
    "execution_start": 1651869010986,
    "source_hash": "2db08a7e",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26.92"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train[\"distance\"].max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "cell_id": "60475d07b67d4e8c949dec2eac9a1097",
    "deepnote_cell_height": 81,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 1,
    "execution_start": 1651869123315,
    "source_hash": "c2602aa8",
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "cell_id": "371c9e9cfae54cb0b669921e753c069f",
    "deepnote_cell_height": 81,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 13,
    "execution_start": 1651869125772,
    "source_hash": "feda1de0",
    "tags": []
   },
   "outputs": [],
   "source": [
    "df_plot = pd.DataFrame({\"distance\":np.arange(0,df_train[\"distance\"].max()+0.1,0.1)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "cell_id": "d1a4200eee8c40f6957efd54e0274819",
    "deepnote_cell_height": 395,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 1,
    "execution_start": 1651869265812,
    "source_hash": "58190bf0",
    "tags": []
   },
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>distance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "   distance\n",
       "0       0.0\n",
       "1       0.1\n",
       "2       0.2\n",
       "3       0.3\n",
       "4       0.4"
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     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
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    "df_plot.head()"
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   "cell_type": "code",
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    "deepnote_cell_type": "code",
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    "execution_start": 1651869560543,
    "source_hash": "c34b5e23",
    "tags": []
   },
   "outputs": [],
   "source": [
    "cols = []\n",
    "for deg in range(1,25):\n",
    "    col = f\"d{deg}\"\n",
    "    cols.append(col)\n",
    "    for x in [df_train, df_plot]:\n",
    "        x[col] = x[\"distance\"]**deg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "cell_id": "df16c1fb887e4412a443185b010a9a0d",
    "deepnote_cell_height": 395,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 39,
    "execution_start": 1651869335836,
    "source_hash": "58190bf0",
    "tags": []
   },
   "outputs": [
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       "      <td>0.0016</td>\n",
       "      <td>0.00032</td>\n",
       "      <td>0.000064</td>\n",
       "      <td>1.280000e-05</td>\n",
       "      <td>2.560000e-06</td>\n",
       "      <td>5.120000e-07</td>\n",
       "      <td>...</td>\n",
       "      <td>3.276800e-11</td>\n",
       "      <td>6.553600e-12</td>\n",
       "      <td>1.310720e-12</td>\n",
       "      <td>2.621440e-13</td>\n",
       "      <td>5.242880e-14</td>\n",
       "      <td>1.048576e-14</td>\n",
       "      <td>2.097152e-15</td>\n",
       "      <td>4.194304e-16</td>\n",
       "      <td>8.388608e-17</td>\n",
       "      <td>1.677722e-17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.3</td>\n",
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       "      <td>0.0081</td>\n",
       "      <td>0.00243</td>\n",
       "      <td>0.000729</td>\n",
       "      <td>2.187000e-04</td>\n",
       "      <td>6.561000e-05</td>\n",
       "      <td>1.968300e-05</td>\n",
       "      <td>...</td>\n",
       "      <td>1.434891e-08</td>\n",
       "      <td>4.304672e-09</td>\n",
       "      <td>1.291402e-09</td>\n",
       "      <td>3.874205e-10</td>\n",
       "      <td>1.162261e-10</td>\n",
       "      <td>3.486784e-11</td>\n",
       "      <td>1.046035e-11</td>\n",
       "      <td>3.138106e-12</td>\n",
       "      <td>9.414318e-13</td>\n",
       "      <td>2.824295e-13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.4</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.064</td>\n",
       "      <td>0.0256</td>\n",
       "      <td>0.01024</td>\n",
       "      <td>0.004096</td>\n",
       "      <td>1.638400e-03</td>\n",
       "      <td>6.553600e-04</td>\n",
       "      <td>2.621440e-04</td>\n",
       "      <td>...</td>\n",
       "      <td>1.073742e-06</td>\n",
       "      <td>4.294967e-07</td>\n",
       "      <td>1.717987e-07</td>\n",
       "      <td>6.871948e-08</td>\n",
       "      <td>2.748779e-08</td>\n",
       "      <td>1.099512e-08</td>\n",
       "      <td>4.398047e-09</td>\n",
       "      <td>1.759219e-09</td>\n",
       "      <td>7.036874e-10</td>\n",
       "      <td>2.814750e-10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 25 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   distance   d1    d2     d3      d4       d5        d6            d7  \\\n",
       "0       0.0  0.0  0.00  0.000  0.0000  0.00000  0.000000  0.000000e+00   \n",
       "1       0.1  0.1  0.01  0.001  0.0001  0.00001  0.000001  1.000000e-07   \n",
       "2       0.2  0.2  0.04  0.008  0.0016  0.00032  0.000064  1.280000e-05   \n",
       "3       0.3  0.3  0.09  0.027  0.0081  0.00243  0.000729  2.187000e-04   \n",
       "4       0.4  0.4  0.16  0.064  0.0256  0.01024  0.004096  1.638400e-03   \n",
       "\n",
       "             d8            d9  ...           d15           d16           d17  \\\n",
       "0  0.000000e+00  0.000000e+00  ...  0.000000e+00  0.000000e+00  0.000000e+00   \n",
       "1  1.000000e-08  1.000000e-09  ...  1.000000e-15  1.000000e-16  1.000000e-17   \n",
       "2  2.560000e-06  5.120000e-07  ...  3.276800e-11  6.553600e-12  1.310720e-12   \n",
       "3  6.561000e-05  1.968300e-05  ...  1.434891e-08  4.304672e-09  1.291402e-09   \n",
       "4  6.553600e-04  2.621440e-04  ...  1.073742e-06  4.294967e-07  1.717987e-07   \n",
       "\n",
       "            d18           d19           d20           d21           d22  \\\n",
       "0  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00   \n",
       "1  1.000000e-18  1.000000e-19  1.000000e-20  1.000000e-21  1.000000e-22   \n",
       "2  2.621440e-13  5.242880e-14  1.048576e-14  2.097152e-15  4.194304e-16   \n",
       "3  3.874205e-10  1.162261e-10  3.486784e-11  1.046035e-11  3.138106e-12   \n",
       "4  6.871948e-08  2.748779e-08  1.099512e-08  4.398047e-09  1.759219e-09   \n",
       "\n",
       "            d23           d24  \n",
       "0  0.000000e+00  0.000000e+00  \n",
       "1  1.000000e-23  1.000000e-24  \n",
       "2  8.388608e-17  1.677722e-17  \n",
       "3  9.414318e-13  2.824295e-13  \n",
       "4  7.036874e-10  2.814750e-10  \n",
       "\n",
       "[5 rows x 25 columns]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_plot.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "cell_id": "29226b21f26a414cb83bdbfe73b31d37",
    "deepnote_cell_height": 118.1875,
    "deepnote_cell_type": "code",
    "deepnote_output_heights": [
     21.1875
    ],
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 16,
    "execution_start": 1651869388498,
    "source_hash": "cb73c151",
    "tags": [
     "output_scroll"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['d1',\n",
       " 'd2',\n",
       " 'd3',\n",
       " 'd4',\n",
       " 'd5',\n",
       " 'd6',\n",
       " 'd7',\n",
       " 'd8',\n",
       " 'd9',\n",
       " 'd10',\n",
       " 'd11',\n",
       " 'd12',\n",
       " 'd13',\n",
       " 'd14',\n",
       " 'd15',\n",
       " 'd16',\n",
       " 'd17',\n",
       " 'd18',\n",
       " 'd19',\n",
       " 'd20',\n",
       " 'd21',\n",
       " 'd22',\n",
       " 'd23',\n",
       " 'd24']"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "cell_id": "cf6545c1c24342d2b155a6da0170240e",
    "deepnote_cell_height": 118.1875,
    "deepnote_cell_type": "code",
    "deepnote_output_heights": [
     21.1875
    ],
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 4,
    "execution_start": 1651869644009,
    "source_hash": "4dd5a516",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['d1', 'd2', 'd3', 'd4']"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cols[:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "cell_id": "4e986530fdb645e0bf924b36c1d69302",
    "deepnote_cell_height": 279,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 311,
    "execution_start": 1651869933486,
    "source_hash": "6a82040",
    "tags": []
   },
   "outputs": [],
   "source": [
    "chart_list = []\n",
    "\n",
    "for deg in range(1,25):\n",
    "    subcols = cols[:deg]\n",
    "    reg = LinearRegression()\n",
    "    reg.fit(df_train[subcols],df_train[\"total\"])\n",
    "    df_plot[f\"Pred{deg}\"] = reg.predict(df_plot[subcols])\n",
    "    c_temp = alt.Chart(df_plot).mark_line(color=\"red\", clip=True).encode(\n",
    "        x=\"distance\",\n",
    "        y=alt.Y(f\"Pred{deg}\", scale=alt.Scale(domain=(0,200)))\n",
    "    )\n",
    "    chart_list.append(c_temp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
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    "execution_start": 1651870095040,
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    "tags": []
   },
   "outputs": [],
   "source": [
    "both_charts = [c+d for d in chart_list]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The input to `alt.vconcat` needs to be one or more Altair charts, not a list of Altair charts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
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     361
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    "deepnote_to_be_reexecuted": false,
    "execution_millis": 23,
    "execution_start": 1651870138821,
    "source_hash": "8ec9aa9",
    "tags": [
     "output_scroll"
    ]
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Only chart objects can be used in VConcatChart.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/8j/gshrlmtn7dg4qtztj4d4t_w40000gn/T/ipykernel_15733/187346778.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0malt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvconcat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mboth_charts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/miniconda3/envs/math10s22/lib/python3.7/site-packages/altair/vegalite/v4/api.py\u001b[0m in \u001b[0;36mvconcat\u001b[0;34m(*charts, **kwargs)\u001b[0m\n\u001b[1;32m   2330\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mvconcat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mcharts\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2331\u001b[0m     \u001b[0;34m\"\"\"Concatenate charts vertically\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2332\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mVConcatChart\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvconcat\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcharts\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2333\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2334\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/math10s22/lib/python3.7/site-packages/altair/vegalite/v4/api.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, data, vconcat, **kwargs)\u001b[0m\n\u001b[1;32m   2304\u001b[0m         \u001b[0;31m# TODO: move common data to top level?\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2305\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mspec\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mvconcat\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2306\u001b[0;31m             \u001b[0m_check_if_valid_subspec\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mspec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"VConcatChart\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2307\u001b[0m         \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mVConcatChart\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvconcat\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvconcat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2308\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvconcat\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_combine_subchart_data\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvconcat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/math10s22/lib/python3.7/site-packages/altair/vegalite/v4/api.py\u001b[0m in \u001b[0;36m_check_if_valid_subspec\u001b[0;34m(spec, classname)\u001b[0m\n\u001b[1;32m   2072\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2073\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mspec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSchemaBase\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdict\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2074\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Only chart objects can be used in {0}.\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mclassname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2075\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mattr\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mTOPLEVEL_ONLY_KEYS\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2076\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mspec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSchemaBase\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: Only chart objects can be used in VConcatChart."
     ]
    }
   ],
   "source": [
    "alt.vconcat(both_charts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we use list unpacking.  Notice how the overfitting gets more extreme as the degree of the polynomial gets higher."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "cell_id": "026a34dcad3a4a5ca0a824734b7c464e",
    "deepnote_cell_height": 66,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 5647,
    "execution_start": 1651870154472,
    "source_hash": "6ddab992",
    "tags": []
   },
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "alt.VConcatChart(...)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alt.vconcat(*both_charts)"
   ]
  }
 ],
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  "deepnote_execution_queue": [],
  "deepnote_notebook_id": "a77823bb-2b5b-436d-9a2e-689e1064d274",
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