DSO_579_HW_2.ipynb

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      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "import matplotlib.pyplot as plt\n",
        "import statsmodels.api as sm\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.model_selection import train_test_split\n",
        "from statsmodels.stats.outliers_influence import variance_inflation_factor"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#web scraping from basketball-reference.com\n",
        "url = \"https://www.basketball-reference.com/leagues/NBA_2020.html\"\n",
        "#read the html content, generate df\n",
        "dflist = pd.read_html(url) #reading in the html content\n",
        "table = dflist[10] #extract the desired table\n",
        "advancedf = pd.DataFrame(table) #get it to be a df"
      ],
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        "id": "hPC7V86zeEmC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
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      "source": [
        "from google.colab import files\n",
        "z = files.upload()"
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              "      Upload widget is only available when the cell has been executed in the\n",
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              "      <script>// Copyright 2017 Google LLC\n",
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              "// you may not use this file except in compliance with the License.\n",
              "// You may obtain a copy of the License at\n",
              "//\n",
              "//      http://www.apache.org/licenses/LICENSE-2.0\n",
              "//\n",
              "// Unless required by applicable law or agreed to in writing, software\n",
              "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
              "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
              "// See the License for the specific language governing permissions and\n",
              "// limitations under the License.\n",
              "\n",
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            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving DSO 579 HW 2 data.csv to DSO 579 HW 2 data.csv\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df = pd.read_csv('DSO 579 HW 2 data.csv')"
      ],
      "metadata": {
        "id": "C5ZIjvVSdxD-"
      },
      "execution_count": null,
      "outputs": []
    },
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      "source": [
        "df.head()"
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      "outputs": [
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              "   Rk                   Team   Age   W   L  PW  PL    MOV   SOS   SRS  ...  \\\n",
              "0   1       Milwaukee Bucks*  29.2  56  17  57  16  10.08 -0.67  9.41  ...   \n",
              "1   2        Boston Celtics*  25.3  48  24  50  22   6.31 -0.47  5.83  ...   \n",
              "2   3  Los Angeles Clippers*  27.4  49  23  50  22   6.44  0.21  6.66  ...   \n",
              "3   4       Toronto Raptors*  26.6  53  19  50  22   6.24 -0.26  5.97  ...   \n",
              "4   5    Los Angeles Lakers*  29.5  52  19  48  23   5.79  0.49  6.28  ...   \n",
              "\n",
              "   ORB%  FT/FGA  eFG%.1  TOV%.1  DRB%  FT/FGA.1             Arena  Attend.  \\\n",
              "0  20.7   0.201   0.489    12.0  81.6     0.178      Fiserv Forum  549,036   \n",
              "1  23.9   0.207   0.509    13.5  77.4     0.215         TD Garden  610,864   \n",
              "2  23.5   0.233   0.506    12.2  77.6     0.206    STAPLES Center  610,176   \n",
              "3  21.3   0.210   0.502    14.6  76.7     0.202  Scotiabank Arena  633,456   \n",
              "4  24.5   0.201   0.515    14.1  78.8     0.205    STAPLES Center  588,907   \n",
              "\n",
              "   Attend./G   Year  \n",
              "0     17,711  19-20  \n",
              "1     19,090  19-20  \n",
              "2     19,068  19-20  \n",
              "3     19,796  19-20  \n",
              "4     18,997  19-20  \n",
              "\n",
              "[5 rows x 29 columns]"
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              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Rk</th>\n",
              "      <th>Team</th>\n",
              "      <th>Age</th>\n",
              "      <th>W</th>\n",
              "      <th>L</th>\n",
              "      <th>PW</th>\n",
              "      <th>PL</th>\n",
              "      <th>MOV</th>\n",
              "      <th>SOS</th>\n",
              "      <th>SRS</th>\n",
              "      <th>...</th>\n",
              "      <th>ORB%</th>\n",
              "      <th>FT/FGA</th>\n",
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              "      <th>TOV%.1</th>\n",
              "      <th>DRB%</th>\n",
              "      <th>FT/FGA.1</th>\n",
              "      <th>Arena</th>\n",
              "      <th>Attend.</th>\n",
              "      <th>Attend./G</th>\n",
              "      <th>Year</th>\n",
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              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>Milwaukee Bucks*</td>\n",
              "      <td>29.2</td>\n",
              "      <td>56</td>\n",
              "      <td>17</td>\n",
              "      <td>57</td>\n",
              "      <td>16</td>\n",
              "      <td>10.08</td>\n",
              "      <td>-0.67</td>\n",
              "      <td>9.41</td>\n",
              "      <td>...</td>\n",
              "      <td>20.7</td>\n",
              "      <td>0.201</td>\n",
              "      <td>0.489</td>\n",
              "      <td>12.0</td>\n",
              "      <td>81.6</td>\n",
              "      <td>0.178</td>\n",
              "      <td>Fiserv Forum</td>\n",
              "      <td>549,036</td>\n",
              "      <td>17,711</td>\n",
              "      <td>19-20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>Boston Celtics*</td>\n",
              "      <td>25.3</td>\n",
              "      <td>48</td>\n",
              "      <td>24</td>\n",
              "      <td>50</td>\n",
              "      <td>22</td>\n",
              "      <td>6.31</td>\n",
              "      <td>-0.47</td>\n",
              "      <td>5.83</td>\n",
              "      <td>...</td>\n",
              "      <td>23.9</td>\n",
              "      <td>0.207</td>\n",
              "      <td>0.509</td>\n",
              "      <td>13.5</td>\n",
              "      <td>77.4</td>\n",
              "      <td>0.215</td>\n",
              "      <td>TD Garden</td>\n",
              "      <td>610,864</td>\n",
              "      <td>19,090</td>\n",
              "      <td>19-20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>Los Angeles Clippers*</td>\n",
              "      <td>27.4</td>\n",
              "      <td>49</td>\n",
              "      <td>23</td>\n",
              "      <td>50</td>\n",
              "      <td>22</td>\n",
              "      <td>6.44</td>\n",
              "      <td>0.21</td>\n",
              "      <td>6.66</td>\n",
              "      <td>...</td>\n",
              "      <td>23.5</td>\n",
              "      <td>0.233</td>\n",
              "      <td>0.506</td>\n",
              "      <td>12.2</td>\n",
              "      <td>77.6</td>\n",
              "      <td>0.206</td>\n",
              "      <td>STAPLES Center</td>\n",
              "      <td>610,176</td>\n",
              "      <td>19,068</td>\n",
              "      <td>19-20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>Toronto Raptors*</td>\n",
              "      <td>26.6</td>\n",
              "      <td>53</td>\n",
              "      <td>19</td>\n",
              "      <td>50</td>\n",
              "      <td>22</td>\n",
              "      <td>6.24</td>\n",
              "      <td>-0.26</td>\n",
              "      <td>5.97</td>\n",
              "      <td>...</td>\n",
              "      <td>21.3</td>\n",
              "      <td>0.210</td>\n",
              "      <td>0.502</td>\n",
              "      <td>14.6</td>\n",
              "      <td>76.7</td>\n",
              "      <td>0.202</td>\n",
              "      <td>Scotiabank Arena</td>\n",
              "      <td>633,456</td>\n",
              "      <td>19,796</td>\n",
              "      <td>19-20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>Los Angeles Lakers*</td>\n",
              "      <td>29.5</td>\n",
              "      <td>52</td>\n",
              "      <td>19</td>\n",
              "      <td>48</td>\n",
              "      <td>23</td>\n",
              "      <td>5.79</td>\n",
              "      <td>0.49</td>\n",
              "      <td>6.28</td>\n",
              "      <td>...</td>\n",
              "      <td>24.5</td>\n",
              "      <td>0.201</td>\n",
              "      <td>0.515</td>\n",
              "      <td>14.1</td>\n",
              "      <td>78.8</td>\n",
              "      <td>0.205</td>\n",
              "      <td>STAPLES Center</td>\n",
              "      <td>588,907</td>\n",
              "      <td>18,997</td>\n",
              "      <td>19-20</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
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              "<div id=\"df-98906c12-352a-4263-a017-03d3e3f932e9\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-98906c12-352a-4263-a017-03d3e3f932e9')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
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              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-98906c12-352a-4263-a017-03d3e3f932e9 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Jbk7xHdXiwSp",
        "outputId": "464921ce-d137-4af2-b4f3-f080caa53d94"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(240, 29)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df['Team'] = df['Team'].astype(str)\n",
        "playoff = []\n",
        "for i in df['Team']:\n",
        "  if '*' in i:\n",
        "    playoff.append(True)\n",
        "  else:\n",
        "    playoff.append(False)"
      ],
      "metadata": {
        "id": "_0rvWO8Giutd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "## data processing\n",
        "## win_rate columns\n",
        "## add columns that we think it relevant\n",
        "df['Game_played'] = list(df['W']+df['L'])\n",
        "df['Win_rate'] = list(round(df['W']/(df['W'] + df['L']), 3))\n",
        "df['Playoff'] = playoff"
      ],
      "metadata": {
        "id": "MxH64xnJd9Tr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "## find highly correlated variables\n",
        "df.corr()['Win_rate']"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pP07CJPx8Bez",
        "outputId": "7549085e-d406-4729-bfb2-546920c1b6f5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-19-52843d459a16>:2: FutureWarning: The default value of numeric_only in DataFrame.corr is deprecated. In a future version, it will default to False. Select only valid columns or specify the value of numeric_only to silence this warning.\n",
            "  df.corr()['Win_rate']\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Rk            -0.941872\n",
              "Age            0.536154\n",
              "W              0.980449\n",
              "L             -0.971986\n",
              "PW             0.943153\n",
              "PL            -0.932858\n",
              "MOV            0.960321\n",
              "SOS           -0.524384\n",
              "SRS            0.958927\n",
              "ORtg           0.636280\n",
              "DRtg          -0.545061\n",
              "NRtg           0.960231\n",
              "Pace          -0.078589\n",
              "FTr            0.055628\n",
              "3PAr           0.160678\n",
              "TS%            0.604416\n",
              "eFG%           0.587243\n",
              "TOV%          -0.270476\n",
              "ORB%           0.090181\n",
              "FT/FGA         0.143835\n",
              "eFG%.1        -0.527903\n",
              "TOV%.1         0.028209\n",
              "DRB%           0.307260\n",
              "FT/FGA.1      -0.219626\n",
              "Game_played    0.073381\n",
              "Win_rate       1.000000\n",
              "Playoff        0.801891\n",
              "Name: Win_rate, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df[['Win_rate']].describe()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "id": "p9u6gyYQo0_Y",
        "outputId": "0566c27b-6ea9-4802-e1b3-4bb4956d15aa"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "         Win_rate\n",
              "count  240.000000\n",
              "mean     0.499337\n",
              "std      0.143236\n",
              "min      0.122000\n",
              "25%      0.402000\n",
              "50%      0.512000\n",
              "75%      0.599250\n",
              "max      0.890000"
            ],
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              "\n",
              "  <div id=\"df-02aebce5-289a-48e4-9784-ad40106124e4\" class=\"colab-df-container\">\n",
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              "    .dataframe tbody tr th:only-of-type {\n",
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              "      <th>Win_rate</th>\n",
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              "      <th>count</th>\n",
              "      <td>240.000000</td>\n",
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              "      <th>mean</th>\n",
              "      <td>0.499337</td>\n",
              "    </tr>\n",
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              "      <th>std</th>\n",
              "      <td>0.143236</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>0.122000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>0.402000</td>\n",
              "    </tr>\n",
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              "      <th>50%</th>\n",
              "      <td>0.512000</td>\n",
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              "      <td>0.890000</td>\n",
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              "\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
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              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-02aebce5-289a-48e4-9784-ad40106124e4 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-02aebce5-289a-48e4-9784-ad40106124e4');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
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              "\n",
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              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
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              "      --hover-bg-color: #E2EBFA;\n",
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              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
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              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
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              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
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              "\n",
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              "    border: 2px solid var(--fill-color);\n",
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              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
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              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
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              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
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              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-18b03948-dd07-43ab-a8e8-536ae1e66fc3 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "sns.histplot(data = df, x = 'Win_rate')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 467
        },
        "id": "2uTyYNZ-ompY",
        "outputId": "c3ad4817-f2f3-4185-d2fc-12bdcb049283"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: xlabel='Win_rate', ylabel='Count'>"
            ]
          },
          "metadata": {},
          "execution_count": 21
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## create a regression with all the numerical variables\n",
        "X = sm.add_constant(df[['Age', 'W', 'L', 'PW', 'PL', 'MOV', 'SOS',\n",
        "                        'SRS', 'ORtg', 'DRtg', 'NRtg', 'Pace', 'FTr',\n",
        "                        '3PAr', 'TS%', 'eFG%', 'TOV%', 'ORB%', 'FT/FGA',\n",
        "                        'eFG%', 'TOV%', 'DRB%', 'FT/FGA','Game_played'\n",
        "                        ]])\n",
        "y = df[['Win_rate']]\n",
        "model1 = sm.OLS(y, X).fit()"
      ],
      "metadata": {
        "id": "QElhnwXeWuTb"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model1.summary()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 978
        },
        "id": "QW7ufqToYRO4",
        "outputId": "256a50bf-b83f-49e9-c29b-3cc236411557"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                            OLS Regression Results                            \n",
              "==============================================================================\n",
              "Dep. Variable:               Win_rate   R-squared:                       0.998\n",
              "Model:                            OLS   Adj. R-squared:                  0.998\n",
              "Method:                 Least Squares   F-statistic:                     6773.\n",
              "Date:                Sat, 10 Feb 2024   Prob (F-statistic):          6.84e-292\n",
              "Time:                        05:44:44   Log-Likelihood:                 884.10\n",
              "No. Observations:                 240   AIC:                            -1730.\n",
              "Df Residuals:                     221   BIC:                            -1664.\n",
              "Df Model:                          18                                         \n",
              "Covariance Type:            nonrobust                                         \n",
              "===============================================================================\n",
              "                  coef    std err          t      P>|t|      [0.025      0.975]\n",
              "-------------------------------------------------------------------------------\n",
              "const           0.4900      0.094      5.218      0.000       0.305       0.675\n",
              "Age            -0.0006      0.000     -1.918      0.056      -0.001    1.71e-05\n",
              "W               0.0064   7.38e-05     86.754      0.000       0.006       0.007\n",
              "L              -0.0063   7.36e-05    -85.052      0.000      -0.006      -0.006\n",
              "PW             -0.0035      0.000    -12.725      0.000      -0.004      -0.003\n",
              "PL              0.0036      0.000     13.853      0.000       0.003       0.004\n",
              "MOV             0.0072      0.076      0.095      0.924      -0.142       0.157\n",
              "SOS             0.0034      0.076      0.044      0.965      -0.146       0.153\n",
              "SRS             0.0009      0.076      0.011      0.991      -0.149       0.151\n",
              "ORtg            0.0021      0.002      1.209      0.228      -0.001       0.006\n",
              "DRtg           -0.0032      0.002     -2.010      0.046      -0.006   -6.24e-05\n",
              "NRtg            0.0053      0.003      2.058      0.041       0.000       0.010\n",
              "Pace           -0.0002      0.000     -0.824      0.411      -0.001       0.000\n",
              "FTr             0.0656      0.219      0.299      0.765      -0.366       0.498\n",
              "3PAr            0.0128      0.014      0.934      0.351      -0.014       0.040\n",
              "TS%             0.3310      0.958      0.345      0.730      -1.557       2.219\n",
              "eFG%           -0.0550      0.435     -0.126      0.900      -0.913       0.803\n",
              "TOV%           -0.0010      0.002     -0.663      0.508      -0.004       0.002\n",
              "ORB%            0.0005      0.001      0.445      0.657      -0.002       0.003\n",
              "FT/FGA         -0.0446      0.219     -0.204      0.839      -0.475       0.386\n",
              "eFG%           -0.0550      0.435     -0.126      0.900      -0.913       0.803\n",
              "TOV%           -0.0010      0.002     -0.663      0.508      -0.004       0.002\n",
              "DRB%            0.0003      0.000      1.089      0.277      -0.000       0.001\n",
              "FT/FGA         -0.0446      0.219     -0.204      0.839      -0.475       0.386\n",
              "Game_played     0.0001   5.01e-05      2.844      0.005    4.38e-05       0.000\n",
              "==============================================================================\n",
              "Omnibus:                       18.890   Durbin-Watson:                   1.165\n",
              "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               54.680\n",
              "Skew:                          -0.219   Prob(JB):                     1.34e-12\n",
              "Kurtosis:                       5.297   Cond. No.                     1.03e+21\n",
              "==============================================================================\n",
              "\n",
              "Notes:\n",
              "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
              "[2] The smallest eigenvalue is 1.22e-35. This might indicate that there are\n",
              "strong multicollinearity problems or that the design matrix is singular.\n",
              "\"\"\""
            ],
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>OLS Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>        <td>Win_rate</td>     <th>  R-squared:         </th> <td>   0.998</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.998</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   6773.</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>             <td>Sat, 10 Feb 2024</td> <th>  Prob (F-statistic):</th> <td>6.84e-292</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                 <td>05:44:44</td>     <th>  Log-Likelihood:    </th> <td>  884.10</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>No. Observations:</th>      <td>   240</td>      <th>  AIC:               </th> <td>  -1730.</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Residuals:</th>          <td>   221</td>      <th>  BIC:               </th> <td>  -1664.</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Model:</th>              <td>    18</td>      <th>                     </th>     <td> </td>    \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "       <td></td>          <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>       <td>    0.4900</td> <td>    0.094</td> <td>    5.218</td> <td> 0.000</td> <td>    0.305</td> <td>    0.675</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Age</th>         <td>   -0.0006</td> <td>    0.000</td> <td>   -1.918</td> <td> 0.056</td> <td>   -0.001</td> <td> 1.71e-05</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>W</th>           <td>    0.0064</td> <td> 7.38e-05</td> <td>   86.754</td> <td> 0.000</td> <td>    0.006</td> <td>    0.007</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>L</th>           <td>   -0.0063</td> <td> 7.36e-05</td> <td>  -85.052</td> <td> 0.000</td> <td>   -0.006</td> <td>   -0.006</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>PW</th>          <td>   -0.0035</td> <td>    0.000</td> <td>  -12.725</td> <td> 0.000</td> <td>   -0.004</td> <td>   -0.003</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>PL</th>          <td>    0.0036</td> <td>    0.000</td> <td>   13.853</td> <td> 0.000</td> <td>    0.003</td> <td>    0.004</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MOV</th>         <td>    0.0072</td> <td>    0.076</td> <td>    0.095</td> <td> 0.924</td> <td>   -0.142</td> <td>    0.157</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>SOS</th>         <td>    0.0034</td> <td>    0.076</td> <td>    0.044</td> <td> 0.965</td> <td>   -0.146</td> <td>    0.153</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>SRS</th>         <td>    0.0009</td> <td>    0.076</td> <td>    0.011</td> <td> 0.991</td> <td>   -0.149</td> <td>    0.151</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ORtg</th>        <td>    0.0021</td> <td>    0.002</td> <td>    1.209</td> <td> 0.228</td> <td>   -0.001</td> <td>    0.006</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>DRtg</th>        <td>   -0.0032</td> <td>    0.002</td> <td>   -2.010</td> <td> 0.046</td> <td>   -0.006</td> <td>-6.24e-05</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>NRtg</th>        <td>    0.0053</td> <td>    0.003</td> <td>    2.058</td> <td> 0.041</td> <td>    0.000</td> <td>    0.010</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Pace</th>        <td>   -0.0002</td> <td>    0.000</td> <td>   -0.824</td> <td> 0.411</td> <td>   -0.001</td> <td>    0.000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>FTr</th>         <td>    0.0656</td> <td>    0.219</td> <td>    0.299</td> <td> 0.765</td> <td>   -0.366</td> <td>    0.498</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>3PAr</th>        <td>    0.0128</td> <td>    0.014</td> <td>    0.934</td> <td> 0.351</td> <td>   -0.014</td> <td>    0.040</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>TS%</th>         <td>    0.3310</td> <td>    0.958</td> <td>    0.345</td> <td> 0.730</td> <td>   -1.557</td> <td>    2.219</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>eFG%</th>        <td>   -0.0550</td> <td>    0.435</td> <td>   -0.126</td> <td> 0.900</td> <td>   -0.913</td> <td>    0.803</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>TOV%</th>        <td>   -0.0010</td> <td>    0.002</td> <td>   -0.663</td> <td> 0.508</td> <td>   -0.004</td> <td>    0.002</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ORB%</th>        <td>    0.0005</td> <td>    0.001</td> <td>    0.445</td> <td> 0.657</td> <td>   -0.002</td> <td>    0.003</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>FT/FGA</th>      <td>   -0.0446</td> <td>    0.219</td> <td>   -0.204</td> <td> 0.839</td> <td>   -0.475</td> <td>    0.386</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>eFG%</th>        <td>   -0.0550</td> <td>    0.435</td> <td>   -0.126</td> <td> 0.900</td> <td>   -0.913</td> <td>    0.803</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>TOV%</th>        <td>   -0.0010</td> <td>    0.002</td> <td>   -0.663</td> <td> 0.508</td> <td>   -0.004</td> <td>    0.002</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>DRB%</th>        <td>    0.0003</td> <td>    0.000</td> <td>    1.089</td> <td> 0.277</td> <td>   -0.000</td> <td>    0.001</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>FT/FGA</th>      <td>   -0.0446</td> <td>    0.219</td> <td>   -0.204</td> <td> 0.839</td> <td>   -0.475</td> <td>    0.386</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Game_played</th> <td>    0.0001</td> <td> 5.01e-05</td> <td>    2.844</td> <td> 0.005</td> <td> 4.38e-05</td> <td>    0.000</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Omnibus:</th>       <td>18.890</td> <th>  Durbin-Watson:     </th> <td>   1.165</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  54.680</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Skew:</th>          <td>-0.219</td> <th>  Prob(JB):          </th> <td>1.34e-12</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Kurtosis:</th>      <td> 5.297</td> <th>  Cond. No.          </th> <td>1.03e+21</td>\n",
              "</tr>\n",
              "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The smallest eigenvalue is 1.22e-35. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular."
            ],
            "text/latex": "\\begin{center}\n\\begin{tabular}{lclc}\n\\toprule\n\\textbf{Dep. Variable:}    &    Win\\_rate     & \\textbf{  R-squared:         } &     0.998   \\\\\n\\textbf{Model:}            &       OLS        & \\textbf{  Adj. R-squared:    } &     0.998   \\\\\n\\textbf{Method:}           &  Least Squares   & \\textbf{  F-statistic:       } &     6773.   \\\\\n\\textbf{Date:}             & Sat, 10 Feb 2024 & \\textbf{  Prob (F-statistic):} & 6.84e-292   \\\\\n\\textbf{Time:}             &     05:44:44     & \\textbf{  Log-Likelihood:    } &    884.10   \\\\\n\\textbf{No. Observations:} &         240      & \\textbf{  AIC:               } &    -1730.   \\\\\n\\textbf{Df Residuals:}     &         221      & \\textbf{  BIC:               } &    -1664.   \\\\\n\\textbf{Df Model:}         &          18      & \\textbf{                     } &             \\\\\n\\textbf{Covariance Type:}  &    nonrobust     & \\textbf{                     } &             \\\\\n\\bottomrule\n\\end{tabular}\n\\begin{tabular}{lcccccc}\n                      & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n\\midrule\n\\textbf{const}        &       0.4900  &        0.094     &     5.218  &         0.000        &        0.305    &        0.675     \\\\\n\\textbf{Age}          &      -0.0006  &        0.000     &    -1.918  &         0.056        &       -0.001    &     1.71e-05     \\\\\n\\textbf{W}            &       0.0064  &     7.38e-05     &    86.754  &         0.000        &        0.006    &        0.007     \\\\\n\\textbf{L}            &      -0.0063  &     7.36e-05     &   -85.052  &         0.000        &       -0.006    &       -0.006     \\\\\n\\textbf{PW}           &      -0.0035  &        0.000     &   -12.725  &         0.000        &       -0.004    &       -0.003     \\\\\n\\textbf{PL}           &       0.0036  &        0.000     &    13.853  &         0.000        &        0.003    &        0.004     \\\\\n\\textbf{MOV}          &       0.0072  &        0.076     &     0.095  &         0.924        &       -0.142    &        0.157     \\\\\n\\textbf{SOS}          &       0.0034  &        0.076     &     0.044  &         0.965        &       -0.146    &        0.153     \\\\\n\\textbf{SRS}          &       0.0009  &        0.076     &     0.011  &         0.991        &       -0.149    &        0.151     \\\\\n\\textbf{ORtg}         &       0.0021  &        0.002     &     1.209  &         0.228        &       -0.001    &        0.006     \\\\\n\\textbf{DRtg}         &      -0.0032  &        0.002     &    -2.010  &         0.046        &       -0.006    &    -6.24e-05     \\\\\n\\textbf{NRtg}         &       0.0053  &        0.003     &     2.058  &         0.041        &        0.000    &        0.010     \\\\\n\\textbf{Pace}         &      -0.0002  &        0.000     &    -0.824  &         0.411        &       -0.001    &        0.000     \\\\\n\\textbf{FTr}          &       0.0656  &        0.219     &     0.299  &         0.765        &       -0.366    &        0.498     \\\\\n\\textbf{3PAr}         &       0.0128  &        0.014     &     0.934  &         0.351        &       -0.014    &        0.040     \\\\\n\\textbf{TS\\%}         &       0.3310  &        0.958     &     0.345  &         0.730        &       -1.557    &        2.219     \\\\\n\\textbf{eFG\\%}        &      -0.0550  &        0.435     &    -0.126  &         0.900        &       -0.913    &        0.803     \\\\\n\\textbf{TOV\\%}        &      -0.0010  &        0.002     &    -0.663  &         0.508        &       -0.004    &        0.002     \\\\\n\\textbf{ORB\\%}        &       0.0005  &        0.001     &     0.445  &         0.657        &       -0.002    &        0.003     \\\\\n\\textbf{FT/FGA}       &      -0.0446  &        0.219     &    -0.204  &         0.839        &       -0.475    &        0.386     \\\\\n\\textbf{eFG\\%}        &      -0.0550  &        0.435     &    -0.126  &         0.900        &       -0.913    &        0.803     \\\\\n\\textbf{TOV\\%}        &      -0.0010  &        0.002     &    -0.663  &         0.508        &       -0.004    &        0.002     \\\\\n\\textbf{DRB\\%}        &       0.0003  &        0.000     &     1.089  &         0.277        &       -0.000    &        0.001     \\\\\n\\textbf{FT/FGA}       &      -0.0446  &        0.219     &    -0.204  &         0.839        &       -0.475    &        0.386     \\\\\n\\textbf{Game\\_played} &       0.0001  &     5.01e-05     &     2.844  &         0.005        &     4.38e-05    &        0.000     \\\\\n\\bottomrule\n\\end{tabular}\n\\begin{tabular}{lclc}\n\\textbf{Omnibus:}       & 18.890 & \\textbf{  Durbin-Watson:     } &    1.165  \\\\\n\\textbf{Prob(Omnibus):} &  0.000 & \\textbf{  Jarque-Bera (JB):  } &   54.680  \\\\\n\\textbf{Skew:}          & -0.219 & \\textbf{  Prob(JB):          } & 1.34e-12  \\\\\n\\textbf{Kurtosis:}      &  5.297 & \\textbf{  Cond. No.          } & 1.03e+21  \\\\\n\\bottomrule\n\\end{tabular}\n%\\caption{OLS Regression Results}\n\\end{center}\n\nNotes: \\newline\n [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. \\newline\n [2] The smallest eigenvalue is 1.22e-35. This might indicate that there are \\newline\n strong multicollinearity problems or that the design matrix is singular."
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Picking variables that are significant in our regression model\n",
        "## Meanwhile, we are aware of the potential problems of multicollinearity and too obvious correlationship between the Xs and Y\n",
        "## for example, number of wins (X), playoff(X) and win rate (Y)"
      ],
      "metadata": {
        "id": "wea_ogajiDpC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "## Removing high VIF variables one by one\n",
        "vif_data = pd.DataFrame()\n",
        "vif_data[\"Variable\"] = X.columns\n",
        "vif_data[\"VIF\"] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]\n",
        "\n",
        "# Print the VIF data\n",
        "print(vif_data)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Cuygc9hwK3yj",
        "outputId": "7d02017a-9437-4b14-cc67-00daad1c9d1c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "       Variable           VIF\n",
            "0         const  5.271528e+04\n",
            "1           Age  1.770634e+00\n",
            "2             W           inf\n",
            "3             L           inf\n",
            "4            PW           inf\n",
            "5            PL           inf\n",
            "6           MOV  7.355301e+05\n",
            "7           SOS  3.105499e+03\n",
            "8           SRS  6.876634e+05\n",
            "9          ORtg           inf\n",
            "10         DRtg           inf\n",
            "11         NRtg           inf\n",
            "12         Pace  1.619248e+00\n",
            "13          FTr  1.823170e+02\n",
            "14         3PAr  3.882183e+00\n",
            "15          TS%  2.211510e+03\n",
            "16         eFG%           inf\n",
            "17         TOV%           inf\n",
            "18         ORB%  4.364442e+01\n",
            "19       FT/FGA           inf\n",
            "20         eFG%           inf\n",
            "21         TOV%           inf\n",
            "22         DRB%  1.500195e+00\n",
            "23       FT/FGA           inf\n",
            "24  Game_played           inf\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/statsmodels/stats/outliers_influence.py:198: RuntimeWarning: divide by zero encountered in double_scalars\n",
            "  vif = 1. / (1. - r_squared_i)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X = sm.add_constant(df[['Age', 'SOS',\n",
        "                        'SRS', 'DRtg', 'Pace', 'FTr',\n",
        "                        '3PAr', 'TOV%', 'ORB%',\n",
        "                        'DRB%','Game_played'\n",
        "                        ]])\n",
        "y = df[['Win_rate']]\n",
        "model1 = sm.OLS(y, X).fit()"
      ],
      "metadata": {
        "id": "zbbrrLQfLtUc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "vif_data = pd.DataFrame()\n",
        "vif_data[\"Variable\"] = X.columns\n",
        "vif_data[\"VIF\"] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]\n",
        "\n",
        "# Print the VIF data\n",
        "print(vif_data)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "d9_tINpeL7Ev",
        "outputId": "d02df25f-a63d-4639-f068-baa69fc999c7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "       Variable           VIF\n",
            "0         const  10787.322746\n",
            "1           Age      1.691942\n",
            "2           SOS      1.405881\n",
            "3           SRS      3.700292\n",
            "4          DRtg      3.153578\n",
            "5          Pace      1.457489\n",
            "6           FTr      1.150343\n",
            "7          3PAr      1.923009\n",
            "8          TOV%      1.487397\n",
            "9          ORB%      1.449157\n",
            "10         DRB%      1.323869\n",
            "11  Game_played      1.261475\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## We ended up using two variables 'Age','SRS' ,'SRS'\n",
        "## With an alpha of 0.1\n",
        "final_X = sm.add_constant(df[['Age','SOS', 'SRS']])\n",
        "y = df[['Win_rate']]\n",
        "model2 = sm.OLS(y, final_X).fit()"
      ],
      "metadata": {
        "id": "sMU3r422o5SN"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(model2.summary())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mkh-PRkppNUD",
        "outputId": "ede2998e-f2ad-4f26-f7d3-e5cd13a0b2a2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:               Win_rate   R-squared:                       0.924\n",
            "Model:                            OLS   Adj. R-squared:                  0.923\n",
            "Method:                 Least Squares   F-statistic:                     955.3\n",
            "Date:                Sat, 10 Feb 2024   Prob (F-statistic):          1.16e-131\n",
            "Time:                        05:44:56   Log-Likelihood:                 435.45\n",
            "No. Observations:                 240   AIC:                            -862.9\n",
            "Df Residuals:                     236   BIC:                            -849.0\n",
            "Df Model:                           3                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const          0.3920      0.047      8.306      0.000       0.299       0.485\n",
            "Age            0.0041      0.002      2.290      0.023       0.001       0.008\n",
            "SOS           -0.0302      0.010     -3.043      0.003      -0.050      -0.011\n",
            "SRS            0.0289      0.001     37.748      0.000       0.027       0.030\n",
            "==============================================================================\n",
            "Omnibus:                        2.932   Durbin-Watson:                   1.807\n",
            "Prob(Omnibus):                  0.231   Jarque-Bera (JB):                2.583\n",
            "Skew:                          -0.201   Prob(JB):                        0.275\n",
            "Kurtosis:                       3.312   Cond. No.                         485.\n",
            "==============================================================================\n",
            "\n",
            "Notes:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## check multicollinearity with SOS and SRS\n",
        "df.corr()['SOS'].loc['SRS']"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "52XGuxtJnzPq",
        "outputId": "c45656d6-467e-4238-8970-35ded42b927e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-30-4e94e6f7b537>:2: FutureWarning: The default value of numeric_only in DataFrame.corr is deprecated. In a future version, it will default to False. Select only valid columns or specify the value of numeric_only to silence this warning.\n",
            "  df.corr()['SOS'].loc['SRS']\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-0.5000176892546473"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## once we finalized the variables, we can start working on the cv\n",
        "model = LinearRegression()\n",
        "final_x = df[['Age','SOS', 'SRS']]\n",
        "y = df['Win_rate']"
      ],
      "metadata": {
        "id": "jwl0MkPYclyC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "## validation-set approach\n",
        "x_train, x_test, y_train, y_test = train_test_split(final_x, y, test_size = 0.25, random_state = 42)\n",
        "LR_1 = model.fit(x_train,y_train)"
      ],
      "metadata": {
        "id": "rI-2maahTK3g"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred_1 = model.predict(x_test)"
      ],
      "metadata": {
        "id": "zb6npwnNTr70"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import mean_squared_error, r2_score\n",
        "mse = mean_squared_error(y_test, y_pred_1)\n",
        "r2 = r2_score(y_test, y_pred_1)\n",
        "rmse = np.sqrt(mse)"
      ],
      "metadata": {
        "id": "csos7LifUXSd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(r2, rmse)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tjs_ZUsaUdLp",
        "outputId": "5b614f4d-b6ae-4fad-d220-bf5af5945c21"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.9237438043894872 0.034789842889190785\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## K-fold cross validation (k=5)\n",
        "from sklearn.model_selection import cross_val_score\n",
        "\n",
        "cv_scores = cross_val_score(model, final_x, y, cv=5, scoring='neg_mean_squared_error')\n",
        "\n",
        "# Convert the negative MSE scores to positive values\n",
        "mse_scores = -cv_scores\n",
        "\n",
        "# Calculate the RMSE scores by taking the square root of the MSE scores\n",
        "rmse_scores = np.sqrt(mse_scores)\n",
        "\n",
        "# Print the average RMSE score\n",
        "print(f\"Average RMSE: {np.mean(rmse_scores):.5f}\")\n",
        "\n",
        "# Calculate cross-validation score for the multiple Regression regression model\n",
        "cv_scores = cross_val_score(model, final_x, y, cv=5)\n",
        "\n",
        "# Print the average cross-validation score\n",
        "print(f\"Average Cross-Validation Score: {np.mean(cv_scores):.3f}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JltCVMGJUe64",
        "outputId": "c1f7f479-9fd0-4e9a-8b56-2f420b851659"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Average RMSE: 0.03989\n",
            "Average Cross-Validation Score: 0.917\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Leave-One-Out Cross-Validation\n",
        "from sklearn.model_selection import LeaveOneOut\n",
        "\n",
        "loo = LeaveOneOut()\n",
        "scores = cross_val_score(model, final_x, y, cv=loo)"
      ],
      "metadata": {
        "id": "UiVet7Z5Xqhf"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Perform Leave-One-Out Cross-Validation\n",
        "scores = cross_val_score(model, final_x, y, cv=loo, scoring='neg_mean_squared_error')\n",
        "\n",
        "# Compute the mean squared error (MSE)\n",
        "mean_mse = -scores.mean()\n",
        "\n",
        "print(f\"Mean Squared Error (MSE) using LOOCV: {round(mean_mse,4)}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yahVKWpyYF6r",
        "outputId": "58921130-14e1-419c-9da9-ee90bfbc46de"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean Squared Error (MSE) using LOOCV: 0.0016\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "scores = cross_val_score(model, final_x, y, cv=loo)\n",
        "\n",
        "# Compute the average validation score\n",
        "average_score = scores.mean()\n",
        "\n",
        "# Print the average cross-validation score\n",
        "print(f\"Average Cross-Validation Score: {average_score:.3f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tYxj-kn_qMWp",
        "outputId": "cc39923c-2d2d-4e03-fc1b-9b79fb9cdbc5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Average Cross-Validation Score: nan\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/metrics/_regression.py:918: UndefinedMetricWarning: R^2 score is not well-defined with less than two samples.\n",
            "  warnings.warn(msg, UndefinedMetricWarning)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "final_x.isnull().sum()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BYicuEjUYKa6",
        "outputId": "bde876f1-69a7-41b2-b651-30e1652e7ad9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Age    0\n",
              "SOS    0\n",
              "SRS    0\n",
              "dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 270
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y.isnull().sum()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8gaDaPzMYq6I",
        "outputId": "27a603fb-6cd2-446a-825a-ad9771c68972"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {},
          "execution_count": 271
        }
      ]
    }
  ]
}