linear_regression.ipynb

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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/AnsilNaseem/ICT-ML/blob/main/linear_regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qKI5tJecpI2L"
      },
      "source": [
        "# import pandas\n",
        "import pandas as pd\n",
        "import numpy as np"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I0un-EXRrrPG",
        "outputId": "f05a2fee-bf83-4142-9bfb-ea51db2d3a8e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 128
        }
      },
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        "from google.colab import files\n",
        "files.upload()"
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      "execution_count": 2,
      "outputs": [
        {
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              "//\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",
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        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving Advertising.csv to Advertising.csv\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
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            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "byx3jU7npI2Q",
        "outputId": "76f30f02-26af-46d2-c4eb-1fff84f858e6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        }
      },
      "source": [
        "# read CSV file from the 'data' subdirectory using a relative path\n",
        "data = pd.read_csv('Advertising.csv', index_col=0)\n",
        "\n",
        "# display the first 5 rows\n",
        "data.head(10)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       TV  Radio  Newspaper  Sales\n",
              "1   230.1   37.8       69.2   22.1\n",
              "2    44.5   39.3       45.1   10.4\n",
              "3    17.2   45.9       69.3    9.3\n",
              "4   151.5   41.3       58.5   18.5\n",
              "5   180.8   10.8       58.4   12.9\n",
              "6     8.7   48.9       75.0    7.2\n",
              "7    57.5   32.8       23.5   11.8\n",
              "8   120.2   19.6       11.6   13.2\n",
              "9     8.6    2.1        1.0    4.8\n",
              "10  199.8    2.6       21.2   10.6"
            ],
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>TV</th>\n",
              "      <th>Radio</th>\n",
              "      <th>Newspaper</th>\n",
              "      <th>Sales</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>230.1</td>\n",
              "      <td>37.8</td>\n",
              "      <td>69.2</td>\n",
              "      <td>22.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>44.5</td>\n",
              "      <td>39.3</td>\n",
              "      <td>45.1</td>\n",
              "      <td>10.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>17.2</td>\n",
              "      <td>45.9</td>\n",
              "      <td>69.3</td>\n",
              "      <td>9.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>151.5</td>\n",
              "      <td>41.3</td>\n",
              "      <td>58.5</td>\n",
              "      <td>18.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>180.8</td>\n",
              "      <td>10.8</td>\n",
              "      <td>58.4</td>\n",
              "      <td>12.9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>8.7</td>\n",
              "      <td>48.9</td>\n",
              "      <td>75.0</td>\n",
              "      <td>7.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>57.5</td>\n",
              "      <td>32.8</td>\n",
              "      <td>23.5</td>\n",
              "      <td>11.8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>120.2</td>\n",
              "      <td>19.6</td>\n",
              "      <td>11.6</td>\n",
              "      <td>13.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>8.6</td>\n",
              "      <td>2.1</td>\n",
              "      <td>1.0</td>\n",
              "      <td>4.8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>199.8</td>\n",
              "      <td>2.6</td>\n",
              "      <td>21.2</td>\n",
              "      <td>10.6</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
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              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-b7b4a66a-5419-4ec5-ad9f-e5213152c4fd');\n",
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              "          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",
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              "\n",
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              "    </g>\n",
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              "  </button>\n",
              "\n",
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              "      --bg-color: #E8F0FE;\n",
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              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
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              "\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",
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              "  .colab-df-quickchart-complete:disabled,\n",
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              "    background-color: var(--disabled-bg-color);\n",
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              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
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              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
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              "      border-color: transparent;\n",
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              "      border-top-color: var(--fill-color);\n",
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              "    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",
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              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
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              "\n",
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              "    async function quickchart(key) {\n",
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              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
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              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
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              "    (() => {\n",
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              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "data",
              "summary": "{\n  \"name\": \"data\",\n  \"rows\": 200,\n  \"fields\": [\n    {\n      \"column\": \"TV\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 85.85423631490808,\n        \"min\": 0.7,\n        \"max\": 296.4,\n        \"num_unique_values\": 190,\n        \"samples\": [\n          287.6,\n          286.0,\n          78.2\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Radio\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 14.846809176168724,\n        \"min\": 0.0,\n        \"max\": 49.6,\n        \"num_unique_values\": 167,\n        \"samples\": [\n          8.2,\n          36.9,\n          44.5\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Newspaper\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 21.778620838522826,\n        \"min\": 0.3,\n        \"max\": 114.0,\n        \"num_unique_values\": 172,\n        \"samples\": [\n          22.3,\n          5.7,\n          17.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Sales\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 5.217456565710478,\n        \"min\": 1.6,\n        \"max\": 27.0,\n        \"num_unique_values\": 121,\n        \"samples\": [\n          11.4,\n          21.2,\n          12.9\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "dfgit = pd.read_csv(\"https://raw.githubusercontent.com/navan0/tot/master/Advertising.csv\" , index_col=0)\n",
        "dfgit.head(10)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        },
        "id": "ACvuWmElgeN4",
        "outputId": "34db170c-6473-4907-90c4-b82cfee56137"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       TV  Radio  Newspaper  Sales\n",
              "1   230.1   37.8       69.2   22.1\n",
              "2    44.5   39.3       45.1   10.4\n",
              "3    17.2   45.9       69.3    9.3\n",
              "4   151.5   41.3       58.5   18.5\n",
              "5   180.8   10.8       58.4   12.9\n",
              "6     8.7   48.9       75.0    7.2\n",
              "7    57.5   32.8       23.5   11.8\n",
              "8   120.2   19.6       11.6   13.2\n",
              "9     8.6    2.1        1.0    4.8\n",
              "10  199.8    2.6       21.2   10.6"
            ],
            "text/html": [
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              "      <th></th>\n",
              "      <th>TV</th>\n",
              "      <th>Radio</th>\n",
              "      <th>Newspaper</th>\n",
              "      <th>Sales</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
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              "      <th>1</th>\n",
              "      <td>230.1</td>\n",
              "      <td>37.8</td>\n",
              "      <td>69.2</td>\n",
              "      <td>22.1</td>\n",
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              "    <tr>\n",
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              "      <td>11.8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>120.2</td>\n",
              "      <td>19.6</td>\n",
              "      <td>11.6</td>\n",
              "      <td>13.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>8.6</td>\n",
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              "      fill: #D2E3FC;\n",
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              "\n",
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              "      background-color: #434B5C;\n",
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              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-99deafc2-ef2f-4431-af49-b7a57e48c37f');\n",
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              "                                                    [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",
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              "<div id=\"df-cc5ece49-b872-484c-9ed2-dc5c04dd9128\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-cc5ece49-b872-484c-9ed2-dc5c04dd9128')\"\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",
              "    }\n",
              "    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-cc5ece49-b872-484c-9ed2-dc5c04dd9128 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "dfgit",
              "summary": "{\n  \"name\": \"dfgit\",\n  \"rows\": 200,\n  \"fields\": [\n    {\n      \"column\": \"TV\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 85.85423631490808,\n        \"min\": 0.7,\n        \"max\": 296.4,\n        \"num_unique_values\": 190,\n        \"samples\": [\n          287.6,\n          286.0,\n          78.2\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Radio\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 14.846809176168724,\n        \"min\": 0.0,\n        \"max\": 49.6,\n        \"num_unique_values\": 167,\n        \"samples\": [\n          8.2,\n          36.9,\n          44.5\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Newspaper\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 21.778620838522826,\n        \"min\": 0.3,\n        \"max\": 114.0,\n        \"num_unique_values\": 172,\n        \"samples\": [\n          22.3,\n          5.7,\n          17.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Sales\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 5.217456565710478,\n        \"min\": 1.6,\n        \"max\": 27.0,\n        \"num_unique_values\": 121,\n        \"samples\": [\n          11.4,\n          21.2,\n          12.9\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G4YSsk38pI2W"
      },
      "source": [
        "Primary object types:\n",
        "\n",
        "- **DataFrame:** rows and columns (like a spreadsheet)\n",
        "- **Series:** a single column"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n2Hkp3U7pI2Y",
        "outputId": "55258990-d7aa-449b-ef7b-cd0a56d87d10",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        }
      },
      "source": [
        "# display the last 5 rows\n",
        "data.tail()"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "        TV  Radio  Newspaper  Sales\n",
              "196   38.2    3.7       13.8    7.6\n",
              "197   94.2    4.9        8.1    9.7\n",
              "198  177.0    9.3        6.4   12.8\n",
              "199  283.6   42.0       66.2   25.5\n",
              "200  232.1    8.6        8.7   13.4"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-c062d8e1-9a2b-47a1-9977-b84d5a29a9c5\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>TV</th>\n",
              "      <th>Radio</th>\n",
              "      <th>Newspaper</th>\n",
              "      <th>Sales</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>196</th>\n",
              "      <td>38.2</td>\n",
              "      <td>3.7</td>\n",
              "      <td>13.8</td>\n",
              "      <td>7.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>197</th>\n",
              "      <td>94.2</td>\n",
              "      <td>4.9</td>\n",
              "      <td>8.1</td>\n",
              "      <td>9.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>198</th>\n",
              "      <td>177.0</td>\n",
              "      <td>9.3</td>\n",
              "      <td>6.4</td>\n",
              "      <td>12.8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>199</th>\n",
              "      <td>283.6</td>\n",
              "      <td>42.0</td>\n",
              "      <td>66.2</td>\n",
              "      <td>25.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>200</th>\n",
              "      <td>232.1</td>\n",
              "      <td>8.6</td>\n",
              "      <td>8.7</td>\n",
              "      <td>13.4</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-c062d8e1-9a2b-47a1-9977-b84d5a29a9c5')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\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",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\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-c062d8e1-9a2b-47a1-9977-b84d5a29a9c5 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-c062d8e1-9a2b-47a1-9977-b84d5a29a9c5');\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",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-c467e93e-23fd-4890-8d7f-8deb0057a52d\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-c467e93e-23fd-4890-8d7f-8deb0057a52d')\"\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",
              "    }\n",
              "    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-c467e93e-23fd-4890-8d7f-8deb0057a52d button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "summary": "{\n  \"name\": \"data\",\n  \"rows\": 5,\n  \"fields\": [\n    {\n      \"column\": \"TV\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 99.75375682148518,\n        \"min\": 38.2,\n        \"max\": 283.6,\n        \"num_unique_values\": 5,\n        \"samples\": [\n          94.2,\n          232.1,\n          177.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Radio\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 15.997656078313472,\n        \"min\": 3.7,\n        \"max\": 42.0,\n        \"num_unique_values\": 5,\n        \"samples\": [\n          4.9,\n          8.6,\n          9.3\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Newspaper\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 25.61782582499928,\n        \"min\": 6.4,\n        \"max\": 66.2,\n        \"num_unique_values\": 5,\n        \"samples\": [\n          8.1,\n          8.7,\n          6.4\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Sales\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 6.951618516575834,\n        \"min\": 7.6,\n        \"max\": 25.5,\n        \"num_unique_values\": 5,\n        \"samples\": [\n          9.7,\n          13.4,\n          12.8\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1iKeROtqpI2d",
        "outputId": "f719cbf1-b392-4166-8fed-24055dabf1cb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# check the shape of the DataFrame (rows, columns)\n",
        "data.shape"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(200, 4)"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-CUyzQGWpI2i"
      },
      "source": [
        "What are the features?\n",
        "- **TV:** advertising dollars spent on TV for a single product in a given market (in thousands of dollars)\n",
        "- **Radio:** advertising dollars spent on Radio\n",
        "- **Newspaper:** advertising dollars spent on Newspaper\n",
        "\n",
        "What is the response?\n",
        "- **Sales:** sales of a single product in a given market (in thousands of items)\n",
        "\n",
        "What else do we know?\n",
        "- Because the response variable is continuous, this is a **regression** problem.\n",
        "- There are 200 **observations** (represented by the rows), and each observation is a single market."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gCuelhk1pI2k"
      },
      "source": [
        "## Visualizing data\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3fkNfhLBpI2m"
      },
      "source": [
        "# conventional way to import seaborn\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# allow plots to appear within the notebook\n",
        "%matplotlib inline"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "outputId": "913314a5-d8cc-477b-b9fb-8e554caf3743",
        "id": "w1vXhqHdxx6y",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "data.plot(kind='scatter',x='Newspaper',y='Sales',color='red')\n",
        "data.plot(kind='scatter',x='Radio',y='Sales',color='blue')\n",
        "data.plot(kind='scatter',x='TV',y='Sales',color='green')"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: xlabel='TV', ylabel='Sales'>"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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Nw49x+DzyMSLZFwDCVm3SbZjcBmPd3cVf56OP3P29OCW/2jD8GKfPIx9jpl8DAKrT3Cydf37hi6tXvQtxS341ffgxbp9HLla/BoCIyxxymD69ulW3E4lk4b1ij5vQS+HHMIuJw4+2fB6VsGL1awAwTWbRM9sLoOWr+LtvnzR+fPbzyuldMD35tdolJ4op1eMVBtM/jyCQIwMAyp9nkMnGnIN8Qw5tbcnAJZGorHfB9OTXYsMsbnqcbGP65xEEemQAQPkvgJlsyzkotfyCVFnvgslrN3m15IRNTP48gkIgAyD2Cl0AM9l2MfRzyMHU5Ne4DrOY+nkEhaElALFX6gKYqdz1l8Li55CDqbV34jrMYurnERQCGQCxV+oCmMmWi2EQ9U9Mq73j1Xu2tbCcaZ9HUBhaAhB7hfIMMtmYcxDHIYdq3rOfM57gH+rIAICSF6vcMv+Zqp21FOZdfhyHHCp5zxMmVFdjB95ye/0mkAGADJkXQKn6AKDc8vG2DmvYLsqF5Wzl9vpNjgwAZMjNM6j24uW2rknc18sJm5sZTwQyZiJHBgB8Uk5dk7ivlxO2uM54igICGQDwidu6JnEs5GYaCsvZi0AGAEqodM0lt3f5cSrkZvL6VdXO8jL5vUUZgQwAFFDtdFy3d/lxGNawYWpzqrBcIiEtWJD876JFpXOUbHhvUUYgAwAFeJG34uYuPw7DGjblAJW7yrVN7y2KmH4NAHl4PR23VF2TfHVsojJrKcpTm6P83sLG9GsAqILX03FLlY+P8no5UZ7aHOX3ZgsCGQAVi3LxtrDyVqK4Xk6Uc4Ci/N5sQY4MgLLFIbkxDnkrQYnyvozye7MFgQyAssUluTGOiy76Jcr7MsrvzQYk+wJIczNUFHRyownDV1HMWwlLlPdllN9bGEj2BeBaOev8BJXcaNLaQ27yVkwIuMJSznuPYg5QSpTfm8kYWgJQ1lBRUMmNtgxfxSFfqJA4v3eYg0AGiLly1/kJIrnRprWHbAm4/BCX987SA2YjkAFirpJ1fvxMbkwkpEcfLb9NYbAp4MrkxYXZ1vdeDnqc7EAgA8RcJUNFla5JU0zmRWPGjOLPrasz4w7ZtsUevbww2/beKxGXHifbEcgAMVfNUFG5a9IUk++ikau2Vho4MNkuE+6QbSuG5uWF2bb3Xq449DhFBYEMgNDrYBS6aOQaMEDasSN7W5h3yGEVQ6tkaMjrC3PUC8HFoccpKghkAPgyVFSOUheNmTOTF9utW827Qw4yCKxmaMiPC3PYAbCfot7jFCXUkQGQFlYdjFIXjcmTS19ow1qcL8jFHosNDS1aVPzf+nFhjvJCl6kep6VLs4PnurpksBaV9xmF+kf0yADwldthkJNPLj5MYfodspf5QvlUOzTk51CQ3+89LFHucYrSjCwCGQC+cHOizHzO6tU9L9KZF42o52SU4sXQUJQvzH4Ie8jVT1GakcVaSwB8MWFC4W751DBIvufU1kqf+1yylkxucLJ9e/JEa8KyBUHzco2rKA4Fwb2g10urFGstAQhNahgkV+YwiOPkf053d7J3Jp8o52SU4mXOBmsCxVtQ66UFhaElAJ5zc6KsZqgkqjkZpTA0BC+Ynm9WLnpkAHjOzYmy1KC2bSfTIMS5RwreidqMLHpkAHjOTWJu3JN3qxHXHil4J0q9ewQyQJlYCdcdNyfKKJ1MAZtEaUYWs5YAl7ZtS05ZjOOMmWq4GQZhqARhiEIxuChze/0mkAFccjOdGID5uCmxg9vrN0NLgAtBr4Rr2vCVae2B3cL+PkWpGBwIZABXgloJ17Sy4aa1B3Yz4fsU9E0J/EcgA7jgRd0FN3ehpt0pmtYe2M2E71NQNyUIDoEM4DO3d6Gm3Sma1h7YzZTvU9SKwYFABnClmrs4t3ehpt0plmrPnDkEM3DPlO839Yuih0AGcKHSu7hy7kJNu1Ms1Z4ZM6KTMxN28mkcmPT9pn5RtBDIAC5UehdXzl1oob+RMn16sAFDqfak2JwzY0LyaVyY1BMSpWJwIJABXKvkLq7cu9B8fyMljIChWHtSbM6ZMSH5NE5M6wlhqYdooCAeUKZyq9CWW0gvkUj2EBSSSAR/4n3qqeRdczELFiQvCrYwcT/HRdwqOVNBuDKBFsTbv3+/2tvbtZ3+WMRAuXdx5d6FepEU6XXOR26OTz62zfYwJfnUdH7kD8WlJ4Shy2BUFMhcf/31uv/++yUlg5jx48fr5JNPVlNTk5599lkv2wdYr9zx+GqSIv06cZZq0xln2HdRMin51ERchKvH0GUwKgpknnjiCY0aNUqS9OSTT2rDhg3605/+pBtuuEH//M//7GkDgahwexdaTVKkXyfOVJtq85wxBg6U5s2r7vXDYFLyqYm4CFfHlLo5cVBRIPPBBx+osbFRkrRgwQJ9+ctf1ogRI3T11Vfr9ddfd/06zz33nC688EINGTJENTU1+t3vfpf1+FVXXaWampqsnwkTJlTSZERQlKfMVpIU6feJc84c6dxzs7eNG5d8XVtnewSRfGrj95SLcPUYugxOr0r+0aBBg/TGG29o8ODBWrRoke655x5J0t/+9jfVlZqrmWH37t0aNWqUrr76al188cV5nzNhwgQ9+OCD6d/r6+sraTIiJA4r16aGo8pJimxrK/74unXV9TJU0qZMJiY8VvueirH5e+rmImzKZ2gqhi6DU1Eg87WvfU1f+cpXNHjwYNXU1Kjl41ualStX6rjjjnP9Oueff77OLzHNob6+Pt37g/jKvAhOn164yzvfLCATub2oNzeXvmDku2Dm49WJ002bMtlwQS/3PblRbGjG9O8pF+HqpYYuC81YJBD0TkVDS7fddpvuu+8+TZkyRX/4wx/SvSR1dXW6+eabPW3gs88+qyOPPFIjR47Uddddp61btxZ9fldXlzo7O7N+YK98CYc2d3n7kUCZ74KZKeycjzjmWtg+NEP+kDdMq5sTWU6VPvzww2pfwnEcx5HkzJ07N2vbnDlznHnz5jmvvfaaM3fuXOfTn/60M3r0aOejjz4q+DozZsxwJPX46ejo8KSdCFZrq+PU1TmO5O5nwYKwW1xcvvdTV5fcXsratcn3l0hkbyu1T1pbHWfbNv/eU6k2F2tb5nuJkgUL7P6eOk7yO9Paas53yWaJRM9jNwrynZO81NHR4er6XVEg89FHHzk/+MEPnCFDhjh1dXXO+vXrHcdxnO9973vOfffdV8lL5g1kcq1fv96R5CxdurTgc/bs2eN0dHSkfzZt2kQgYyk3F2mbLoyVXtS3bi18QSl1wbz33mDfY65qL+h+nyj9EqUALqoX4Tjw6/gpdk7ykttApqKhpX/5l3/RQw89pDvuuEO9e/dObz/hhBN03333VddFVMQxxxyjww8/XOuKpHvX19erX79+WT+wU6mEw0w2dHlXOouh2NBMqVyG8ePdt8+NcmfgVJprYXsNkygNzcSleF2U+H38GDdcXEmUdOyxx6Z7Rfr06ZPukXnzzTed/v37V/KSrnpkNm3a5NTU1Djz5s1z/bpuIzqYp5weGRu6vCu5S3fzb6oZrnKrmjuwStoXxHvyG0MzCIufx0+QvY2+9si88847Gp7nVqq7u1v79u1z/Tq7du1Se3u72tvbJUkbNmxQe3u7Nm7cqF27dummm27SihUr9Oc//1lPP/20Jk6cqOHDh6u11KIviIRSd7W2rVxbyV26m16cIBIKq7kDK7d9tifKprDCMsLg9/FjYn2cigKZ448/Xs8//3yP7U888YROOukk16/zyiuv6KSTTkr/mxtvvFEnnXSSbr31VtXV1em1117TRRddpBEjRuiaa67RKaecoueff55aMjFS7CJoY5d3uRd1N0MzjuNN2wqp9sRY7gXdxBNlNWz8nsJefh8/Jk7Nr6iOzK233qorr7xS77zzjrq7u/Xb3/5Wa9eu1cMPP6z58+e7fp2zzjpLTpGz8OJShTEQeX4WLAtDue/HTS2K1OrambysV+JVcTS3tVpMPFGWYmKxP8ST38ePkfVxKh27eu6555yWlhbniCOOcA455BDnC1/4grN48eJKX8435MjAdsVyLYIYrw5jBo4tOTJBzd4AyuH38RNU/pfb63eN4/jdMR2uzs5ONTQ0qKOjgxlMCI0Xd+z5enEWLkzOSihkwYLksEa1Ur0++e7A/KhSu317skfJ5GrAUvD7BXAjqOPH755yt9dvAhnAR36X508kklMsiz3uxQkmrMDC5CHFSvY9Q1AIksnHjxtur9+uc2QGDBigmpoaV8/dtm2b25cFIs3v9XaCGq8OK1fJjzWQvFJO7pAN600hekw+frzkOpD56U9/6mMzgOhJzfbJlTnbx4uTzJw5PXtL/FrPJS4nRjfKSaq0eQFJwHSuA5krr7zSz3YAkePVbJ9SojazyxZue8OCCmiBuKqojkymPXv2sNo0kEfQ04ipVxI8N3WBolYXBzBNRXVkdu/ere9+97t6/PHHtXXr1h6P78+tnAXEkJH1FuApN71hNtbFQfBIBK9cRT0y3/nOd7Rs2TLdc889qq+v13333aeZM2dqyJAhevjhh71uI2CtIJYPQPiK9YZFaQFJeM/2BVJNUNH066OOOkoPP/ywzjrrLPXr10+rV6/W8OHD9Z//+Z+aM2eOFixY4EdbK8L0a5iA/JV4s6UuDoJHLaLCPJ9+nWnbtm065phjJEn9+vVLT7ceN26crrvuukpeEhGW22UaxS7UUu+J2T7xRkI28iER3BsVDS0dc8wx2rBhgyTpuOOO0+OPPy5JevLJJ9W/f3/PGge75esyPfzwaHWh0i2MckQ9ITuRSFabtmWF8rCRCO6NigKZr33ta/qf//kfSdLNN9+s2bNn6+CDD9YNN9ygm266ydMGwnyFTl75amfk5oanamnYqlh9EFPlfl5cfFAtAvrKkAjuDU+WKPjLX/6iVatWafjw4TrxxBO9aJdnyJHxT7FqpX/9a/Hy7bm8KqUfpKCWB/BKvs9r4MDs4JK8DVSCPI/Kse8Kc3v9LqtH5sUXX9T8+fOztqWSfq+99lr9/Oc/V1dXV2UthnWK9UaU6jLNZWMXqm3dwnHoIUPwUnkeuVU3MvM8UBgzG6tXViDzgx/8QH/84x/Tv7/++uu65ppr1NLSoltuuUVPPvmkZs2a5XkjYZ5SJ6/cqaal2NiFalO3cKHPKxcXH5TLtoDeNKlE8EQiuVp9IpH8nV5R98oKZNrb23XOOeekf3/00Uc1ZswY3Xvvvbrhhht01113pRN/EW2lTl779+evnZHLi1oaYeV4mFwfJHefxKGHLBN5P8GxKaA3WdQTwf1UViCzfft2DRo0KP17W1ubzj///PTvo0eP1qZNm7xrHYzl5uSVr8s0VzVdqCYkGJrWLVxonxx+eHmvY+vFx4TvRNyYHNAjHsoKZAYNGpSedr13716tXr1ap59+evrxnTt36qCDDvK2hShLUHeibk5eqS7TceOk2pxvWm1tcntmF2q5bTdhxpBp3cKF9sn3vx9cD1mYTPhOxJFpAT1ixinDtdde64wdO9Z57rnnnBtvvNEZOHCg09XVlX7817/+tXPqqaeW85K+6+jocCQ5HR0dYTelYmvXOs6CBY6TSBR+ztatjtPa6jjSgZ/WVsfZts2/dm3bVvpvrl2b/XjuTyJRWdvdvG7clNonL7/ccz8PHBjsd8ZPfCfCl0iUPlcBbrm9fpdV2feHP/yhLr74Yo0fP159+vTRr371K/Xu3Tv9+AMPPKDzzjvP41ArvopNb8694y92J+rXFD431UrdJAJOn1687fmq5rp5XVt7FSpVap/89a/5P6+oVJvlOxGMYlWsqWCNMFRUR6ajo0N9+vRRXU4/9bZt29SnT5+s4CZsNteRcVtfwOR6JqXatnhxMjgrZNw4afnyA7+7rVNjWg2XIJj8PQhC3N+/38q5sQK84EsdmZSGhoYeQYwkHXbYYUYFMTYrpzZDudMfg5zRUSqXptR04BdeyP491VNDgmFPcd8ncX//fqs2/4iZZPBLRYEM/FdOcOJ2+mNYMzqKJQKWant3d/bvmYGcCQmGpp2cTdgnYYr7+/dLNUXvmEkGv3myRIHJbB1aKreb3M0wVNilsAvlYuRrV21tzyAm04IFyZoLxV7XT6Z3s0cl76VScX//Xlu4MBmEFJJ5POYK+7wDe7m9fhPIGKycE8Dbb0unnZZdcn7gQOnll6Vhw8zOH9i+Pdk9nRkU5ObG5Ao734GTM+Kk0vOHyecdmM/XHBkEo5xu8m98Q9qxI3vbjh3Sddcl/7/UUFVbW6WtrF6+WizPP29uvgNryyBuKs0/YvkCBIFAxmBui625ubCWykX5+tfDH7fOLdFtar4DJ2fEUSXHI8sXIAhl1ZFBOPLVZsis5eDmwnr++ck7p8zhm1x+150pl5s6NWHg5BwfxWqmxE0lx2OqJ6fQMGzc9ym8QSBjmXxJpuPGFf83qQvrD39YPJDJ7MEx6QRDkS0EzfRk7jCVezzOmdMzB86EnlVEB0NLlrnsMmnJkuxtL76YTOwtNX79wQfu/gZDI8WV6gGbM8ffPBnTpnxHEWs2ece09cgQPQQyBil1gXrppeRdTb7aKlu3Sp//fPb23LueUkMiKQyNFFdqP86Y4U+tDOpx+CP3uItaMrcpgW9uDhzgFQIZA7i9QKVmIBVyyy0H7noWL5a++c3sXphCMw9Syp0RVOgEacqJ0y+l9mOK13fw9BJ4q9Bx195e/N/Z0mNJ4IvY8H35ypDZsPp1a6vj1NVlr9RbV5fcnlJqZV+3K0nnW7G63JWPC/2N9euDX4E7LMX2ox+rLrOys/cKHXfjxkVjX7s5rwAmc3v9piBeyNwWjCpVWbNvX6mz032httTMg169pI8+Km9WRqG/0b9/snZNob8dxRkgqaUSZswo/JxiVU/dqqayKnoqddydcUZynS9bCx5SiA6ZbD33UhDPEqUSR199NfnfUnkZO3dKTz3lfmw/NV597rnljVsXyx/YurXw3z7jjGh1caeGzyTp//7f4s/1IueIKd/eKnXcTZtmZg0jt6h1BCk+w4sEMiErdYG6++7kf0eMKH6HJUkrVhR/3IuTV6kTZCGFVrG2Tb4Tw//7f9LZZ/tbhZiVnb1V6rg76SS7Z9oQ+EKKT14dgUzIRowoXgdm+fLkekkTJkhr1xZ/rdNPL/54ED0DhRRbxdomhU4MkjR+fPb2/fulffu8u/sxtdKxjdwGhrbOtCHwRdRm3xVDIGOA6dOLP37ttT1rx+QaN0467zz/T17FTpD5atnUlviG2dTFXezEsGxZMmjJfb9tbd7d/QRdjyM1fPbUU9GchRb1wDDq7w/FxWp4MZDU4xDZMGvJzYykUj+PPZZ8rXyzaVIzh9audZwFC6qfdVHob7z9ds/tUZkB4jjJfVfp52PT+8w3Ky3Ks9ASCW+OC1NF/f0hvyjMdGTW0sdMn7WUUmgm0KhR0urVpf997iyEzPVQBg70p9x6oTVXcre7nUllulIzQYqxaVZRvs8rxcbPDYgr28+9rq/fgYRVIbKhR8ZxCvdyvPRS8ajaTV2IsOtJFOslsk3Ua4+47R205f0AcWb7uZcemY/Z0iOTkq+Xo9gdcqmeFbf1JLyqM1DsdUxbxboS27f3XAAv9RlMnmz33Y9Uul5Nik09TEDc2XrudXv9JpCxQL6L58knS7/8pXTqqcX/bakL02OPSQ88UP2wU9xWC853YigW5FSzD4IsZuV2+IyCarCVrcXh4ohA5mNRCGRSKomqS12Yxo1Lrp5dbS+C7WOxXvLq7ies4JAcGZis0kDEzfFEkGMWcmQ+ZkuOjJ/8zuuIQna8icLKbfJiPS7Aa6XWkSul2PFU7WvDH26v39SRiYFC9SRK1a9xW2fAj3oFUV9Bu5Qwi1nl1qt56ik7q9siWqqpUlvqeJo0KR4VcKOqV9gNQH5ednGmLky5Qx6JRPF/57YSsJfl0PN1/7rNByrGti5jN8Gh3++judmOfYXoSwUiuTID+2Lf1VLH0/PPV/7aCB89Mobxc5Gv3HLrXpUx97Icer67rtWrpdGjK9sPpi+aVqjnibVygAOq7fWtdGkVN6+N8BHIGOb//J+edx6LFye3+8GrMuZevE6h7t+UJUvK7+o1ddG0UgEWa+UAB1Qb2Bc7noqtdefmtWGAgHJ2QmNTsm+YSbOLFzvOzJmO89RT1b1ONeXQ3S4BEIUkZDeJvLYXswK85OaYKbYMS7HjKeyiocjP7fWbHJmQpXI36uqk+fOLP7etzfs7ca+n+FaTV+G2+9dtfogJeSb5uB3vL5TbBMRRquhk5rGT6vV1cx4rdjwVe22Yj0AmJPkOvDAUG3oJulZIqvu3UA2TlDCSkL1UboBF0i1QPBBJ1T7KVOg8lu944qbBbhTEC0jurJliRceKvYaXB5fb5QuClK86bkpUCvWZuN+jrNSMNdtmtCEbx1N0ub1+k+zrs3xJnWecUTypNVdNjXT22d4fjH7Uf6lW6s7o5ZeT064zhZWE7DUSeYNRKqHa9BltcMfE8xiCFWog89xzz+nCCy/UkCFDVFNTo9/97ndZjzuOo1tvvVWDBw/WIYccopaWFr1lWYW0fEM3L7xQ3mucd570xBPetSnF1KEXKVkzZtWqA0XZKi3GllvczZSibiYGWFFTasaaqTPaUB6Tz2MIRqiBzO7duzVq1CjNnj077+N33HGH7rrrLv3iF7/QypUr9YlPfEKtra3as2dPwC2tTKHpxN3d7v79vff6e+G1oWcgt/ZNPm6qALt5nSCZGmBFRalKrk89FV7lZHjLhvMYfBbEFCo3JDlz585N/97d3e00NjY6d955Z3rbjh07nPr6emfOnDmuXzfM6delphPX1ubfHuS0P5un+LI+CgopdezNnFn88QULwn4HKIfN5zEUZv1aSxs2bNDmzZvVktH/3tDQoDFjxujFF18s+O+6urrU2dmZ9ROWUl2en/98/u1BDjHY3DPA0AAKKXXsnX568ccZjrCLzecxVM/Y6debN2+WJA0aNChr+6BBg9KP5TNr1izNnDnT17a5VWg6ceasmdR0v169pI8+8nfmRLHZGV5N8Q1qBkg5a69ktslxeraPWSvRU+rYO++84o/zPbATpQriydhAplK33HKLbrzxxvTvnZ2dampqCq09+QotjRol/ehHyf8P4sDzuuhdWH8jk5uZCgMHFq/Vc/bZyf8uW3Zgm59tRrDyHXuf//yB3k6KoAHRYOzQUmNjoyRpy5YtWdu3bNmSfiyf+vp69evXL+snTKkuz5deko4/PrmtmkUQKxHEEEzQwzxuZirka1OmZ57JDmIkhqZs4SbBe8AA6ZFHstfSef755Oe7fTvDEVHh5ruAaDM2kBk2bJgaGxv19NNPp7d1dnZq5cqVGjt2bIgtK9+2bckZM2+8kb29kkUQy1Vq9oYXB38QfyNXqZkKjlO6Vk++UpDMWjFbubVfLrtMyk2pyw1WTZvRBneoA4SUUAOZXbt2qb29Xe3t7ZKSCb7t7e3auHGjampqdP311+tHP/qRfv/73+v111/XFVdcoSFDhmjSpElhNtuVzLuEiROlrVt7Pqe72/+LZhDFosIqSFWsFkupNpVCES0zldPzF0aAjeCQ7I+UUHNkXnnlFX3xi19M/57Kbbnyyiv10EMP6Tvf+Y52796tKVOmaMeOHRo3bpwWLVqkgw8+OKwml1TJGkp+Ll4YRLEor/5GuUm3xdZHcbsAZSHMWjFPOQnekrmLhqJ65X4XooqJCh8LaDp4aIKuI5NvOfhSP/mWnPe7TV7Xqqnmb/hVD6bUZ1FTE24NH5SnVG2Y3Nova9eGe9xF2dq1yf0d1j4s97sQNXGpoWV9HRkbFerKLmbcOP8j6SDK4VfzN/zqIs7Xpkxf/OKBmUspzFoxV7k9f1R89Z4peSlxX5aAYbVsrH7toYULkwe3WwMHJrtAg5olEcQS9eX+jSBWrs1sk9SzfUHsF3ij3NXM862mzhT7ypm0mrxJbQlSnFb7dnv9JpDxUKkvWKYzzpDmzeNkWir4W7AgOaMEkCoPTAhWq2faBTSuQWqczplur9+RK4gXplLVRO++m5Nprrh3EaM8xRK8i6Hia/VMS56u9LtgO86ZPdEj47G43iVUI65dxIBNTOuRibO4nDPdXr9J9q1QoWqSVAstXxDJyECceVH9luRpc3DOzEaPTJny1YkZN06aPl066SR7D2YT6hHErYsY8JvXa6DR41wdr8+zUT9nkuz7Ma8DmXxdeplsO6jznehIRAaiwa8hiKhfQL0W9KK6UUEg8zEvAxk3s5JsG6csFJgFPTUcgLfIaTFHXHJavEaOjA/crN9j0zouxQr4bd0qXXRR8G0CvBTnlZHDWgMN2Vjzy38EMmUoZ/0eG04SpU50y5fbf5DF+UIWZ6ZUoA0T03TNQEDpPwKZMhTK2s/HhpOEm8DM1oOMC1m8UcKdWUamIKD0H4FMmUqt32PTSWLEiOSMq2JsPci4kMUXXfkHME03fASU/iOQKVNmnZjHHusZCNh2kvj975OJvblqa+09yLiQxRtd+QdQ18oMBJT+YomCCqVKnn/lK9VPRQyzhsuAAcn2X3RRMicm5dxz7T3ITCuljmDRld8TSzSEK67LKQSFQMYDlZ4kTKktMGCA9Pzz0TnIuJDFW6k1z2z+bkedCYU5/URA6Q+GlkJkWh5Hc3Ny1VTbDzTGpEFXvl1Izkc1KIgXEopV+YtS6pCi08sYdRSMQz5ur98MLYWEPA5/MSYNia58G6SS83NlJufzGaIYApmQkMcRDC5kgNm4qUO1yJEJCXkcAMBNHapHIBMiLxISKcEPr/GdQpC4qUO1CGRCVE2xKrL84TW+UwgLs8xQDWYtWYosf3iN7xTCRnI+Mrm9fhPIWIip2/Aa3ykApnF7/WZoKWBe5B+wlgy8xncKQSIPC14ikAmIl/kHZPn3xImxOnynEATysOxl8jmWQCYgXi5HQJb/AZwYvcF3CkEwbVkWlGbDOZZAJgCpypWZSZRSduXKcpHln8SJ0TuUA4Cf/DgPwn82nGOp7BsAPypXUoKf0uZeq+Y7ZcpK7jAXFXztY8s5lh6ZAPiZfxCVFasrQYKqPyr5Ttlw14ZwkYdlH1vOsQQyASiUfyBJAwdKhx8efJuigBOjGRgygBvkYdnHlnMsgUxA5syR+vfvuX37du5aK1XJiZEcDu/ZcteG8JHbZxdbgk8CmYD89a/S1q09t3d3c9daDbcnRhsy721ly10bwlfNsiwIhw3BJ8m+ASHRzR9uE1SL5XCEWX4/kUh+N2xO1k7dtRVa3sDW9wX/NDd7872IwvFjOhsmlrBEQUAoAR8eE/d91Gb5pIZIo/J+YLaoHT/IjyUKDGPLWGMUmZjDEbVZPgwZIEhRO35QHQKZANkw1hhFpuVwRHmWT5zLASAYUT5+UBkCmQBx1xoO03rDTOwhAmzB8YNcBDIh4K41eCb1hpnWQwTYhOMHuQhkEAsm9YaZ1kME2ITjB7kIZBArpvSGmdRDBNiG4weZmH4NhMjk2gyA6Th+os3t9ZuCeBFDgSi7eFUYDIgjjh9IDC1FBiX4AQBxRCATERSIAgDEEYFMBFAgCvAWq6QD9iCQiQAKRNmJi6V5GKIF7EMgEwEUiLILF0tzuR2iJQgFzEEgEwEUiLIL+UxmcjNESxAKmIdAJiIoEGUH8pnM5WaIliAUMA91ZDwSdv2WVAl+CkSZzc3Fks8tHKWGaOvqksFmrswg1O1nF/b5AogSemSqZFpXsykl+JEf+UzmKjVEm9uLlstNUr1p5wsgCghkqkRXM8pBPpPZig3RehGEcr4AvMdaS1VIJJJ3VsUe58KEXNu3Jy9cmcMUra3Ji2UYq3Gjp0JDtBMmJAOPzN6ZurpksLNoUfHX5HwBlMft9dvoHpnbbrtNNTU1WT/HHXdc2M1Ko34LKpHKZ0okpAULkv9dtIggxiSFhmirSarnfAH4w/hk38985jNamtEX26uXOU0m3wHVYME7+1STVM/5AvCHOVFBAb169VJjY2PYzcgrle9QqKuZixQQTZUEoZwvAH8YPbQkSW+99ZaGDBmiY445Rpdffrk2btxY9PldXV3q7OzM+vGTV/VbqBQKRB/1ngDvGZ3su3DhQu3atUsjR47Ue++9p5kzZ+qdd97RmjVr1Ldv37z/5rbbbtPMmTN7bPcj2TdTpfVbtm1LzmQg8ROID+o9AaW5TfY1OpDJtWPHDh199NH68Y9/rGuuuSbvc7q6utTV1ZX+vbOzU01NTb4HMpWqZhYEAABR5TaQMT5HJlP//v01YsQIrSuS3l9fX6/6+voAW1W5VLn6XJVUCgUAII6Mz5HJtGvXLq1fv16DBw8OuymeYDomAADVMTqQ+fa3v622tjb9+c9/1gsvvKAvfelLqqur0+SIlMFkOiYAANUxemjpf//3fzV58mRt3bpVRxxxhMaNG6cVK1boiCOOCLtpnmA6JgAA1bEq2bcSfi5R4AXK1QMA0FMkk32jqJpKoQAAxB2BjCEoVw8AQPmMTvYFAAAohkAGAABYi0AGAABYi0AGAABYi0AGAABYi0AGAABYi0AGAABYi0AGAABYi0AGAABYi0AGAABYi0AGAABYi7WWEGmJhLR+PYtxAkBU0SODSNq2TZowQRo5UrrgAmnEiOTv27eH3TIAgJcIZBBJl10mLV2avW3pUmny5HDaAwDwB4EMIieRkBYvlvbvz96+f39y+1tvhdMuAID3CGQQOevXF3983bpg2gEA8B+BDCLn2GOLPz58eDDtAAD4j0AGkTNihNTaKtXVZW+vq0tuZ/YSAEQHgQwiac4cqaUle1tLS3I7ACA6qCODSBowQFq0KJnYu24ddWQAIKoIZBBpzc0EMAAQZQwtAQAAaxHIAAAAaxHIAAAAaxHIAAAAaxHIAAAAaxHIAAAAaxHIAAAAaxHIAAAAaxHIAAAAaxHIAAAAaxHIAAAAa7HWEgAgUhIJaf16FouNC3pkAACRsG2bNGGCNHKkdMEF0ogRyd+3bw+7ZfATgQwAIBIuu0xaujR729Kl0uTJ4bQHwSCQAQBYL5GQFi+W9u/P3r5/f3L7W2+F0y74j0AGAGC99euLP75uXTDtQPAIZAAA1jv22OKPDx8eTDsQPAIZAID1RoyQWlulurrs7XV1ye3MXoouAhkAQCTMmSO1tGRva2lJbkd0UUcGABAJAwZIixYlE3vXraOOTFwQyAAAIqW5mQAmThhaAgAA1iKQAQAA1iKQAQAA1iKQAQAA1iKQAQAA1iKQAQAA1iKQAQAA1iKQAQAA1iKQAQAA1iKQAQAA1or8EgWO40iSOjs7Q24JAABwK3XdTl3HC4l8ILNz505JUlNTU8gtAQAA5dq5c6caGhoKPl7jlAp1LNfd3a13331Xffv2VU1NjWev29nZqaamJm3atEn9+vXz7HXRE/s6OOzr4LCvg8O+Do6X+9pxHO3cuVNDhgxRbW3hTJjI98jU1tZq6NChvr1+v379ODACwr4ODvs6OOzr4LCvg+PVvi7WE5NCsi8AALAWgQwAALAWgUyF6uvrNWPGDNXX14fdlMhjXweHfR0c9nVw2NfBCWNfRz7ZFwAARBc9MgAAwFoEMgAAwFoEMgAAwFoEMgAAwFoEMhWaPXu2PvWpT+nggw/WmDFj9NJLL4XdJOs999xzuvDCCzVkyBDV1NTod7/7XdbjjuPo1ltv1eDBg3XIIYeopaVFb731VjiNtdysWbM0evRo9e3bV0ceeaQmTZqktWvXZj1nz549mjp1qgYOHKg+ffrokksu0ZYtW0JqsZ3uuecenXjiieniYGPHjtXChQvTj7OP/XP77berpqZG119/fXob+9sbt912m2pqarJ+jjvuuPTjQe9nApkKPPbYY7rxxhs1Y8YMrV69WqNGjVJra6vef//9sJtmtd27d2vUqFGaPXt23sfvuOMO3XXXXfrFL36hlStX6hOf+IRaW1u1Z8+egFtqv7a2Nk2dOlUrVqzQkiVLtG/fPp133nnavXt3+jk33HCDnnzySf3mN79RW1ub3n33XV188cUhtto+Q4cO1e23365Vq1bplVde0dlnn62JEyfqj3/8oyT2sV9efvll/fKXv9SJJ56YtZ397Z3PfOYzeu+999I/y5cvTz8W+H52ULbTTjvNmTp1avr3/fv3O0OGDHFmzZoVYquiRZIzd+7c9O/d3d1OY2Ojc+edd6a37dixw6mvr3fmzJkTQguj5f3333ckOW1tbY7jJPftQQcd5PzmN79JP+fNN990JDkvvvhiWM2MhAEDBjj33Xcf+9gnO3fudJqbm50lS5Y448ePd775zW86jsN32kszZsxwRo0alfexMPYzPTJl2rt3r1atWqWWlpb0ttraWrW0tOjFF18MsWXRtmHDBm3evDlrvzc0NGjMmDHsdw90dHRIkg477DBJ0qpVq7Rv376s/X3cccfpqKOOYn9XaP/+/Xr00Ue1e/dujR07ln3sk6lTp+rv/u7vsvarxHfaa2+99ZaGDBmiY445Rpdffrk2btwoKZz9HPlFI732wQcfaP/+/Ro0aFDW9kGDBulPf/pTSK2Kvs2bN0tS3v2eegyV6e7u1vXXX68vfOELOuGEEyQl93fv3r3Vv3//rOeyv8v3+uuva+zYsdqzZ4/69OmjuXPn6vjjj1d7ezv72GOPPvqoVq9erZdffrnHY3ynvTNmzBg99NBDGjlypN577z3NnDlTZ5xxhtasWRPKfiaQAWJu6tSpWrNmTdYYN7wzcuRItbe3q6OjQ0888YSuvPJKtbW1hd2syNm0aZO++c1vasmSJTr44IPDbk6knX/++en/P/HEEzVmzBgdffTRevzxx3XIIYcE3h6Glsp0+OGHq66urkcG9pYtW9TY2BhSq6IvtW/Z796aNm2a5s+fr2eeeUZDhw5Nb29sbNTevXu1Y8eOrOezv8vXu3dvDR8+XKeccopmzZqlUaNG6Wc/+xn72GOrVq3S+++/r5NPPlm9evVSr1691NbWprvuuku9evXSoEGD2N8+6d+/v0aMGKF169aF8r0mkClT7969dcopp+jpp59Ob+vu7tbTTz+tsWPHhtiyaBs2bJgaGxuz9ntnZ6dWrlzJfq+A4ziaNm2a5s6dq2XLlmnYsGFZj59yyik66KCDsvb32rVrtXHjRvZ3lbq7u9XV1cU+9tg555yj119/Xe3t7emfU089VZdffnn6/9nf/ti1a5fWr1+vwYMHh/O99iWFOOIeffRRp76+3nnooYecN954w5kyZYrTv39/Z/PmzWE3zWo7d+50Xn31VefVV191JDk//vGPnVdffdX5y1/+4jiO49x+++1O//79nXnz5jmvvfaaM3HiRGfYsGHOhx9+GHLL7XPdddc5DQ0NzrPPPuu899576Z+//e1v6edce+21zlFHHeUsW7bMeeWVV5yxY8c6Y8eODbHV9rn55pudtrY2Z8OGDc5rr73m3HzzzU5NTY3z1FNPOY7DPvZb5qwlx2F/e+Vb3/qW8+yzzzobNmxw/vCHPzgtLS3O4Ycf7rz//vuO4wS/nwlkKnT33Xc7Rx11lNO7d2/ntNNOc1asWBF2k6z3zDPPOJJ6/Fx55ZWO4ySnYH//+993Bg0a5NTX1zvnnHOOs3bt2nAbbal8+1mS8+CDD6af8+GHHzrf+MY3nAEDBjiHHnqo86Uvfcl57733wmu0ha6++mrn6KOPdnr37u0cccQRzjnnnJMOYhyHfey33ECG/e2NSy+91Bk8eLDTu3dv55Of/KRz6aWXOuvWrUs/HvR+rnEcx/GnrwcAAMBf5MgAAABrEcgAAABrEcgAAABrEcgAAABrEcgAAABrEcgAAABrEcgAAABrEcgAAABrEcgAiJSzzjpL119/ffr3T33qU/rpT38aWnsA+ItABkAorrrqKtXU1KimpkYHHXSQhg0bpu985zvas2ePp3/n5Zdf1pQpUzx9TQDm6BV2AwDE14QJE/Tggw9q3759WrVqla688krV1NTo3/7t3zz7G0cccYRnrwXAPPTIAAhNfX29Ghsb1dTUpEmTJqmlpUVLliyRJG3dulWTJ0/WJz/5SR166KH67Gc/qzlz5mT9+927d+uKK65Qnz59NHjwYP37v/97j7+RO7S0ceNGTZw4UX369FG/fv30la98RVu2bPH1fQLwD4EMACOsWbNGL7zwgnr37i1J2rNnj0455RT993//t9asWaMpU6boH/7hH/TSSy+l/81NN92ktrY2zZs3T0899ZSeffZZrV69uuDf6O7u1sSJE7Vt2za1tbVpyZIlevvtt3XppZf6/v4A+IOhJQChmT9/vvr06aOPPvpIXV1dqq2t1c9//nNJ0ic/+Ul9+9vfTj93+vTpWrx4sR5//HGddtpp2rVrl+6//379+te/1jnnnCNJ+tWvfqWhQ4cW/HtPP/20Xn/9dW3YsEFNTU2SpIcfflif+cxn9PLLL2v06NE+vlsAfiCQARCaL37xi7rnnnu0e/du/eQnP1GvXr10ySWXSJL279+vf/3Xf9Xjjz+ud955R3v37lVXV5cOPfRQSdL69eu1d+9ejRkzJv16hx12mEaOHFnw77355ptqampKBzGSdPzxx6t///568803CWQACzG0BCA0n/jEJzR8+HCNGjVKDzzwgFauXKn7779fknTnnXfqZz/7mb773e/qmWeeUXt7u1pbW7V3796QWw3AJAQyAIxQW1urf/qnf9L3vvc9ffjhh/rDH/6giRMn6qtf/apGjRqlY445RolEIv38Y489VgcddJBWrlyZ3rZ9+/as5+T69Kc/rU2bNmnTpk3pbW+88YZ27Nih448/3p83BsBXBDIAjPHlL39ZdXV1mj17tpqbm7VkyRK98MILevPNN/WP//iPWbOL+vTpo2uuuUY33XSTli1bpjVr1uiqq65SbW3h01pLS4s++9nP6vLLL9fq1av10ksv6YorrtD48eN16qmnBvEWAXiMHBkAxujVq5emTZumO+64Q6+++qrefvtttba26tBDD9WUKVM0adIkdXR0pJ9/5513ateuXbrwwgvVt29ffetb38p6PFdNTY3mzZun6dOn68wzz1Rtba0mTJigu+++O4i3B8AHNY7jOGE3AgAAoBIMLQEAAGsRyAAAAGsRyAAAAGsRyAAAAGsRyAAAAGsRyAAAAGsRyAAAAGsRyAAAAGsRyAAAAGsRyAAAAGsRyAAAAGv9fymVe7VzjwEVAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qfbyxHpYpI2w"
      },
      "source": [
        "## Linear regression\n",
        "\n",
        "**Pros:** fast, no tuning required, highly interpretable, well-understood\n",
        "\n",
        "**Cons:** unlikely to produce the best predictive accuracy (presumes a linear relationship between the features and response)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xUHmkNnEpI2y"
      },
      "source": [
        "### Form of linear regression\n",
        "\n",
        "$y = \\beta_0 + \\beta_1x_1 + \\beta_2x_2 + ... + \\beta_nx_n$\n",
        "\n",
        "- $y$ is the response\n",
        "- $\\beta_0$ is the intercept\n",
        "- $\\beta_1$ is the coefficient for $x_1$ (the first feature)\n",
        "- $\\beta_n$ is the coefficient for $x_n$ (the nth feature)\n",
        "\n",
        "In this case:\n",
        "\n",
        "$y = \\beta_0 + \\beta_1 \\times TV + \\beta_2 \\times Radio + \\beta_3 \\times Newspaper$\n",
        "\n",
        "The $\\beta$ values are called the **model coefficients**. These values are \"learned\" during the model fitting step using the \"least squares\" criterion. Then, the fitted model can be used to make predictions!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rxh70YEUpI2z"
      },
      "source": [
        "## Preparing X and y using pandas\n",
        "\n",
        "- scikit-learn expects X (feature matrix) and y (response vector) to be NumPy arrays.\n",
        "- However, pandas is built on top of NumPy.\n",
        "- Thus, X can be a pandas DataFrame and y can be a pandas Series!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UO9ImBFspI21",
        "outputId": "304b85b9-81f2-40d9-d0c1-11ca090d5ce2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        }
      },
      "source": [
        "# create a Python list of feature names\n",
        "feature_cols = ['TV', 'Radio', 'Newspaper']\n",
        "\n",
        "# use the list to select a subset of the original DataFrame\n",
        "X = data[feature_cols]\n",
        "\n",
        "# equivalent command to do this in one line\n",
        "X = data[['TV','Radio','Newspaper']]\n",
        "\n",
        "# print the first 5 rows\n",
        "X.head()\n"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      TV  Radio  Newspaper\n",
              "1  230.1   37.8       69.2\n",
              "2   44.5   39.3       45.1\n",
              "3   17.2   45.9       69.3\n",
              "4  151.5   41.3       58.5\n",
              "5  180.8   10.8       58.4"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-9444d79f-d012-4d86-bada-3cbd9ffb7d64\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>TV</th>\n",
              "      <th>Radio</th>\n",
              "      <th>Newspaper</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>230.1</td>\n",
              "      <td>37.8</td>\n",
              "      <td>69.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>44.5</td>\n",
              "      <td>39.3</td>\n",
              "      <td>45.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>17.2</td>\n",
              "      <td>45.9</td>\n",
              "      <td>69.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>151.5</td>\n",
              "      <td>41.3</td>\n",
              "      <td>58.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>180.8</td>\n",
              "      <td>10.8</td>\n",
              "      <td>58.4</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-9444d79f-d012-4d86-bada-3cbd9ffb7d64')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\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",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\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-9444d79f-d012-4d86-bada-3cbd9ffb7d64 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-9444d79f-d012-4d86-bada-3cbd9ffb7d64');\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",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-6e58b603-abf6-4982-aa85-3292f4697c2f\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-6e58b603-abf6-4982-aa85-3292f4697c2f')\"\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",
              "    }\n",
              "    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-6e58b603-abf6-4982-aa85-3292f4697c2f button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "X",
              "summary": "{\n  \"name\": \"X\",\n  \"rows\": 200,\n  \"fields\": [\n    {\n      \"column\": \"TV\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 85.85423631490808,\n        \"min\": 0.7,\n        \"max\": 296.4,\n        \"num_unique_values\": 190,\n        \"samples\": [\n          287.6,\n          286.0,\n          78.2\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Radio\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 14.846809176168724,\n        \"min\": 0.0,\n        \"max\": 49.6,\n        \"num_unique_values\": 167,\n        \"samples\": [\n          8.2,\n          36.9,\n          44.5\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Newspaper\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 21.778620838522826,\n        \"min\": 0.3,\n        \"max\": 114.0,\n        \"num_unique_values\": 172,\n        \"samples\": [\n          22.3,\n          5.7,\n          17.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DKeFX3OFpI27",
        "outputId": "cbc7d76f-1ebe-457a-b6c6-aa8886bad916",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# check the type and shape of X\n",
        "print(type(X))\n",
        "print(X.shape)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "(200, 3)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uiYKNxDbpI3C",
        "outputId": "397b760a-3384-4093-db4c-3b04b0be3c89",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# select a Series from the DataFrame\n",
        "lab = ['Sales']\n",
        "\n",
        "# equivalent command that works if there are no spaces in the column name\n",
        "y =  data['Sales']\n",
        "\n",
        "\n",
        "\n",
        "# print the first 5 values\n",
        "y.head()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1    22.1\n",
              "2    10.4\n",
              "3     9.3\n",
              "4    18.5\n",
              "5    12.9\n",
              "Name: Sales, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AfvkPrA6pI3H",
        "outputId": "02aa2699-1817-4b97-bf0c-767922917db2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# check the type and shape of y\n",
        "print(type(y))\n",
        "print(y.shape)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "<class 'pandas.core.series.Series'>\n",
            "(200,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S5NDF5GgpI3M"
      },
      "source": [
        "## Splitting X and y into training and testing sets"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4ttrUI0ipI3O"
      },
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LjEViy1MpI3S",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2fcb24bc-27d8-467d-c3c9-08606982fb59"
      },
      "source": [
        "# default split is 75% for training and 25% for testing\n",
        "print(X_train.shape)\n",
        "print(y_train.shape)\n",
        "print(X_test.shape)\n",
        "print(y_test.shape)\n",
        "# X_train = X_train[:150]\n",
        "\n",
        "print(X_test)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(150, 3)\n",
            "(150,)\n",
            "(50, 3)\n",
            "(50,)\n",
            "        TV  Radio  Newspaper\n",
            "59   210.8   49.6       37.7\n",
            "41   202.5   22.3       31.6\n",
            "35    95.7    1.4        7.4\n",
            "103  280.2   10.1       21.4\n",
            "185  253.8   21.3       30.0\n",
            "199  283.6   42.0       66.2\n",
            "96   163.3   31.6       52.9\n",
            "5    180.8   10.8       58.4\n",
            "30    70.6   16.0       40.8\n",
            "169  215.4   23.6       57.6\n",
            "172  164.5   20.9       47.4\n",
            "19    69.2   20.5       18.3\n",
            "12   214.7   24.0        4.0\n",
            "90   109.8   47.8       51.4\n",
            "111  225.8    8.2       56.5\n",
            "119  125.7   36.9       79.2\n",
            "160  131.7   18.4       34.6\n",
            "36   290.7    4.1        8.5\n",
            "137   25.6   39.0        9.3\n",
            "60   210.7   29.5        9.3\n",
            "52   100.4    9.6        3.6\n",
            "17    67.8   36.6      114.0\n",
            "45    25.1   25.7       43.3\n",
            "95   107.4   14.0       10.9\n",
            "32   112.9   17.4       38.6\n",
            "163  188.4   18.1       25.6\n",
            "39    43.1   26.7       35.1\n",
            "29   248.8   27.1       22.9\n",
            "194  166.8   42.0        3.6\n",
            "28   240.1   16.7       22.9\n",
            "48   239.9   41.5       18.5\n",
            "166  234.5    3.4       84.8\n",
            "195  149.7   35.6        6.0\n",
            "178  170.2    7.8       35.2\n",
            "177  248.4   30.2       20.3\n",
            "98   184.9   21.0       22.0\n",
            "175  222.4    3.4       13.1\n",
            "74   129.4    5.7       31.3\n",
            "70   216.8   43.9       27.2\n",
            "173   19.6   20.1       17.0\n",
            "109   13.1    0.4       25.6\n",
            "108   90.4    0.3       23.2\n",
            "190   18.7   12.1       23.4\n",
            "15   204.1   32.9       46.0\n",
            "57     7.3   28.1       41.4\n",
            "20   147.3   23.9       19.1\n",
            "115   78.2   46.8       34.5\n",
            "40   228.0   37.7       32.0\n",
            "186  205.0   45.1       19.6\n",
            "125  229.5   32.3       74.2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WHpXdcBZpI3Z"
      },
      "source": [
        "## Linear regression in scikit-learn"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bQdAJ_3MpI3a"
      },
      "source": [
        "# import model\n",
        "from sklearn.linear_model import LinearRegression\n",
        "\n",
        "# instantiate\n",
        "linreg = LinearRegression()\n",
        "\n",
        "# fit the model to the training data (learn the coefficients)\n",
        "model = linreg.fit(X_train, y_train)\n",
        "\n"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M-aOCgqN1XWA"
      },
      "source": [],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qrHhBZ3fpI3s"
      },
      "source": [
        "### Making predictions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z34zuNqhpI3v",
        "outputId": "36d986fd-a335-4709-dc5a-aee83050aacd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# make predictions on the testing set\n",
        "y_pred = linreg.predict(X_test)\n",
        "print(y_pred)"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[21.70910292 16.41055243  7.60955058 17.80769552 18.6146359  23.83573998\n",
            " 16.32488681 13.43225536  9.17173403 17.333853   14.44479482  9.83511973\n",
            " 17.18797614 16.73086831 15.05529391 15.61434433 12.42541574 17.17716376\n",
            " 11.08827566 18.00537501  9.28438889 12.98458458  8.79950614 10.42382499\n",
            " 11.3846456  14.98082512  9.78853268 19.39643187 18.18099936 17.12807566\n",
            " 21.54670213 14.69809481 16.24641438 12.32114579 19.92422501 15.32498602\n",
            " 13.88726522 10.03162255 20.93105915  7.44936831  3.64695761  7.22020178\n",
            "  5.9962782  18.43381853  8.39408045 14.08371047 15.02195699 20.35836418\n",
            " 20.57036347 19.60636679]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "IGnRsQvhpF13"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hTGDsYHcJBDn"
      },
      "source": [
        "We need an **evaluation metric** in order to compare our predictions with the actual values!"
      ]
    }
  ]
}