Exploratory_Time_Series_Analysis.ipynb

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  "metadata": {
    "colab": {
      "name": "Exploratory Time Series Analysis.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyMT+7bdPbPkymrSb/oTbMjm"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
    }
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5zN7L2hlTijS"
      },
      "source": [
        "# Exploratory Time Series Analysis\n",
        "\n",
        "We have a time series dataset of the distance flown by all UK airlines between 1963-1970 in miles. We use this data to perform some basic Exploratory Time Series Analysis in Python.\n",
        "\n",
        "Attempts have been made to add comments and explain steps wherever possible. \n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6HLtvNZjwoNw",
        "outputId": "4bf6ee4e-42b8-46dc-a47e-af476b18d4e1"
      },
      "source": [
        "import pandas            as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import statsmodels.api   as sm\n",
        "import seaborn           as sns\n",
        "import numpy             as np\n",
        "import numpy.linalg      as la\n",
        "\n",
        "from datetime                    import datetime"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "resources": {
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              "data": 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              "ok": true,
              "headers": [
                [
                  "content-type",
                  "application/javascript"
                ]
              ],
              "status": 200,
              "status_text": ""
            }
          },
          "base_uri": "https://localhost:8080/",
          "height": 72
        },
        "id": "wYnpH0Ijyg7S",
        "outputId": "9a52e29d-5c70-4f35-92af-b7adf76740b6"
      },
      "source": [
        "from google.colab import files\n",
        "import io\n",
        "uploaded = files.upload()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-837d437c-987a-42da-94d7-a6621a63d71d\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-837d437c-987a-42da-94d7-a6621a63d71d\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script src=\"/nbextensions/google.colab/files.js\"></script> "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving airline.dta to airline.dta\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gqae3mRoyF4e"
      },
      "source": [
        "#Setting visualisation preferences for Seaborn\n",
        "\n",
        "sns.set_style('darkgrid')\n",
        "pd.plotting.register_matplotlib_converters()\n",
        "sns.mpl.rc('figure',figsize=(16, 6))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "W-W6eReoyITg"
      },
      "source": [
        "#Reading the data and setting it as the dataframe\n",
        "\n",
        "df = pd.read_stata(\"airline.dta\")\n",
        "\n",
        "df['year'] = df['year'].astype(int)\n",
        "df['month'] = df['month'].astype(int)\n",
        "\n",
        "df['year'] = df['year'].astype(str)\n",
        "df['month'] = df['month'].astype(str)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fYBx1W77ythd",
        "outputId": "41da61af-d972-4dcd-dc44-4ae858f18f1b"
      },
      "source": [
        "#Finding the fundamental attributes of the dataset\n",
        "\n",
        "df['miles'].describe()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "count       96.000000\n",
              "mean     10385.739258\n",
              "std       2202.500488\n",
              "min       6178.000000\n",
              "25%       8600.250000\n",
              "50%      10401.000000\n",
              "75%      11768.000000\n",
              "max      16234.000000\n",
              "Name: miles, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 421
        },
        "id": "VPRxv7nQyvRY",
        "outputId": "e16b9214-a79b-4496-e02c-ce66ada3b5d4"
      },
      "source": [
        "df.head(12)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>year</th>\n",
              "      <th>month</th>\n",
              "      <th>miles</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1963</td>\n",
              "      <td>1</td>\n",
              "      <td>6827.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1963</td>\n",
              "      <td>2</td>\n",
              "      <td>6178.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1963</td>\n",
              "      <td>3</td>\n",
              "      <td>7084.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1963</td>\n",
              "      <td>4</td>\n",
              "      <td>8162.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1963</td>\n",
              "      <td>5</td>\n",
              "      <td>8462.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>1963</td>\n",
              "      <td>6</td>\n",
              "      <td>9644.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>1963</td>\n",
              "      <td>7</td>\n",
              "      <td>10466.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>1963</td>\n",
              "      <td>8</td>\n",
              "      <td>10748.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>1963</td>\n",
              "      <td>9</td>\n",
              "      <td>9963.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>1963</td>\n",
              "      <td>10</td>\n",
              "      <td>8194.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>1963</td>\n",
              "      <td>11</td>\n",
              "      <td>6848.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>1963</td>\n",
              "      <td>12</td>\n",
              "      <td>7027.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    year month    miles\n",
              "0   1963     1   6827.0\n",
              "1   1963     2   6178.0\n",
              "2   1963     3   7084.0\n",
              "3   1963     4   8162.0\n",
              "4   1963     5   8462.0\n",
              "5   1963     6   9644.0\n",
              "6   1963     7  10466.0\n",
              "7   1963     8  10748.0\n",
              "8   1963     9   9963.0\n",
              "9   1963    10   8194.0\n",
              "10  1963    11   6848.0\n",
              "11  1963    12   7027.0"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 421
        },
        "id": "XRRs25knyz0k",
        "outputId": "2b54fee7-f86d-4dd9-beab-6876ddce1985"
      },
      "source": [
        "df['dat'] = df['year'] + '-' + df['month']\n",
        "df.head(12)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>year</th>\n",
              "      <th>month</th>\n",
              "      <th>miles</th>\n",
              "      <th>dat</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1963</td>\n",
              "      <td>1</td>\n",
              "      <td>6827.0</td>\n",
              "      <td>1963-1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1963</td>\n",
              "      <td>2</td>\n",
              "      <td>6178.0</td>\n",
              "      <td>1963-2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1963</td>\n",
              "      <td>3</td>\n",
              "      <td>7084.0</td>\n",
              "      <td>1963-3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1963</td>\n",
              "      <td>4</td>\n",
              "      <td>8162.0</td>\n",
              "      <td>1963-4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1963</td>\n",
              "      <td>5</td>\n",
              "      <td>8462.0</td>\n",
              "      <td>1963-5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>1963</td>\n",
              "      <td>6</td>\n",
              "      <td>9644.0</td>\n",
              "      <td>1963-6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>1963</td>\n",
              "      <td>7</td>\n",
              "      <td>10466.0</td>\n",
              "      <td>1963-7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>1963</td>\n",
              "      <td>8</td>\n",
              "      <td>10748.0</td>\n",
              "      <td>1963-8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>1963</td>\n",
              "      <td>9</td>\n",
              "      <td>9963.0</td>\n",
              "      <td>1963-9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>1963</td>\n",
              "      <td>10</td>\n",
              "      <td>8194.0</td>\n",
              "      <td>1963-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>1963</td>\n",
              "      <td>11</td>\n",
              "      <td>6848.0</td>\n",
              "      <td>1963-11</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>1963</td>\n",
              "      <td>12</td>\n",
              "      <td>7027.0</td>\n",
              "      <td>1963-12</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    year month    miles      dat\n",
              "0   1963     1   6827.0   1963-1\n",
              "1   1963     2   6178.0   1963-2\n",
              "2   1963     3   7084.0   1963-3\n",
              "3   1963     4   8162.0   1963-4\n",
              "4   1963     5   8462.0   1963-5\n",
              "5   1963     6   9644.0   1963-6\n",
              "6   1963     7  10466.0   1963-7\n",
              "7   1963     8  10748.0   1963-8\n",
              "8   1963     9   9963.0   1963-9\n",
              "9   1963    10   8194.0  1963-10\n",
              "10  1963    11   6848.0  1963-11\n",
              "11  1963    12   7027.0  1963-12"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "erpnxHJNYaA2"
      },
      "source": [
        "**Here we create a preliminary plot of the data with matplotlib. Here we visually notice a trend and a seasonality.** \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "OpTMY2jmzNDX",
        "outputId": "67485eca-c8b7-4799-fa57-fc33e305afbb"
      },
      "source": [
        "df['miles'].plot()\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "L1Kl50-0zPaJ"
      },
      "source": [
        "df1 = df[df['year']<='1966']"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "id": "moyKq0yzzVI3",
        "outputId": "57d7a3af-bc82-433c-937b-1ecc2a84c65f"
      },
      "source": [
        "df1.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "  <thead>\n",
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              "      <th></th>\n",
              "      <th>year</th>\n",
              "      <th>month</th>\n",
              "      <th>miles</th>\n",
              "      <th>dat</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1963</td>\n",
              "      <td>1</td>\n",
              "      <td>6827.0</td>\n",
              "      <td>1963-1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1963</td>\n",
              "      <td>2</td>\n",
              "      <td>6178.0</td>\n",
              "      <td>1963-2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1963</td>\n",
              "      <td>3</td>\n",
              "      <td>7084.0</td>\n",
              "      <td>1963-3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1963</td>\n",
              "      <td>4</td>\n",
              "      <td>8162.0</td>\n",
              "      <td>1963-4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1963</td>\n",
              "      <td>5</td>\n",
              "      <td>8462.0</td>\n",
              "      <td>1963-5</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   year month   miles     dat\n",
              "0  1963     1  6827.0  1963-1\n",
              "1  1963     2  6178.0  1963-2\n",
              "2  1963     3  7084.0  1963-3\n",
              "3  1963     4  8162.0  1963-4\n",
              "4  1963     5  8462.0  1963-5"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
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        "id": "p_gw1a1szk0F",
        "outputId": "cd23b1c9-5eba-4fc3-8b64-df313c98e542"
      },
      "source": [
        "df1.tail()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>year</th>\n",
              "      <th>month</th>\n",
              "      <th>miles</th>\n",
              "      <th>dat</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>43</th>\n",
              "      <td>1966</td>\n",
              "      <td>8</td>\n",
              "      <td>11577.0</td>\n",
              "      <td>1966-8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>44</th>\n",
              "      <td>1966</td>\n",
              "      <td>9</td>\n",
              "      <td>12417.0</td>\n",
              "      <td>1966-9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>45</th>\n",
              "      <td>1966</td>\n",
              "      <td>10</td>\n",
              "      <td>9637.0</td>\n",
              "      <td>1966-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>46</th>\n",
              "      <td>1966</td>\n",
              "      <td>11</td>\n",
              "      <td>8094.0</td>\n",
              "      <td>1966-11</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>47</th>\n",
              "      <td>1966</td>\n",
              "      <td>12</td>\n",
              "      <td>9280.0</td>\n",
              "      <td>1966-12</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    year month    miles      dat\n",
              "43  1966     8  11577.0   1966-8\n",
              "44  1966     9  12417.0   1966-9\n",
              "45  1966    10   9637.0  1966-10\n",
              "46  1966    11   8094.0  1966-11\n",
              "47  1966    12   9280.0  1966-12"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XwT4kPD1znM0",
        "outputId": "cd94a4c8-fcea-43ce-e116-4f73ccb02d4c"
      },
      "source": [
        "df1['miles'].describe()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "count       48.000000\n",
              "mean      9174.583008\n",
              "std       1641.827515\n",
              "min       6178.000000\n",
              "25%       7826.500000\n",
              "50%       9089.000000\n",
              "75%      10509.000000\n",
              "max      12417.000000\n",
              "Name: miles, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tQQzKQo4Xg3g"
      },
      "source": [
        "**Creating a trend variable and then regressing 'miles' variable on it in the next step.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "id": "n9mGYsP5z9Vb",
        "outputId": "22485ae3-85a2-4bb5-d0d7-e4235eb7a2c4"
      },
      "source": [
        "df['trend']= range(1,len(df['miles'])+1)\n",
        "df.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "      <th></th>\n",
              "      <th>year</th>\n",
              "      <th>month</th>\n",
              "      <th>miles</th>\n",
              "      <th>dat</th>\n",
              "      <th>trend</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1963</td>\n",
              "      <td>1</td>\n",
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              "      <td>1963-1</td>\n",
              "      <td>1</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1963</td>\n",
              "      <td>2</td>\n",
              "      <td>6178.0</td>\n",
              "      <td>1963-2</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1963</td>\n",
              "      <td>3</td>\n",
              "      <td>7084.0</td>\n",
              "      <td>1963-3</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1963</td>\n",
              "      <td>4</td>\n",
              "      <td>8162.0</td>\n",
              "      <td>1963-4</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1963</td>\n",
              "      <td>5</td>\n",
              "      <td>8462.0</td>\n",
              "      <td>1963-5</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   year month   miles     dat  trend\n",
              "0  1963     1  6827.0  1963-1      1\n",
              "1  1963     2  6178.0  1963-2      2\n",
              "2  1963     3  7084.0  1963-3      3\n",
              "3  1963     4  8162.0  1963-4      4\n",
              "4  1963     5  8462.0  1963-5      5"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
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          "height": 204
        },
        "id": "XMLYBUc80KWV",
        "outputId": "004f7c62-64b2-4f4d-c666-57e917878347"
      },
      "source": [
        "df.tail()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "      <th></th>\n",
              "      <th>year</th>\n",
              "      <th>month</th>\n",
              "      <th>miles</th>\n",
              "      <th>dat</th>\n",
              "      <th>trend</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>187</th>\n",
              "      <td>1978</td>\n",
              "      <td>8</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1978-8</td>\n",
              "      <td>188</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>188</th>\n",
              "      <td>1978</td>\n",
              "      <td>9</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1978-9</td>\n",
              "      <td>189</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>189</th>\n",
              "      <td>1978</td>\n",
              "      <td>10</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1978-10</td>\n",
              "      <td>190</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>190</th>\n",
              "      <td>1978</td>\n",
              "      <td>11</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1978-11</td>\n",
              "      <td>191</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>191</th>\n",
              "      <td>1978</td>\n",
              "      <td>12</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1978-12</td>\n",
              "      <td>192</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "     year month  miles      dat  trend\n",
              "187  1978     8    NaN   1978-8    188\n",
              "188  1978     9    NaN   1978-9    189\n",
              "189  1978    10    NaN  1978-10    190\n",
              "190  1978    11    NaN  1978-11    191\n",
              "191  1978    12    NaN  1978-12    192"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JgUMpzi3XsVE"
      },
      "source": [
        "**Regressing the trend variable on the miles variable.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VNCnZEnQ0MeJ",
        "outputId": "1dfd4081-bbb2-4ad0-dd9c-1b065e27e0aa"
      },
      "source": [
        "X = df[['trend']]\n",
        "X = sm.add_constant(X)\n",
        "Y = df[['miles']]\n",
        "\n",
        "reg = sm.OLS(Y, X, missing='drop')\n",
        "\n",
        "result = reg.fit()\n",
        "print(result.summary())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                  miles   R-squared:                       0.473\n",
            "Model:                            OLS   Adj. R-squared:                  0.468\n",
            "Method:                 Least Squares   F-statistic:                     84.52\n",
            "Date:                Mon, 27 Sep 2021   Prob (F-statistic):           9.53e-15\n",
            "Time:                        10:33:19   Log-Likelihood:                -843.87\n",
            "No. Observations:                  96   AIC:                             1692.\n",
            "Df Residuals:                      94   BIC:                             1697.\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const       7747.1741    330.542     23.438      0.000    7090.876    8403.473\n",
            "trend         54.4034      5.917      9.194      0.000      42.654      66.153\n",
            "==============================================================================\n",
            "Omnibus:                       16.733   Durbin-Watson:                   0.768\n",
            "Prob(Omnibus):                  0.000   Jarque-Bera (JB):                4.674\n",
            "Skew:                           0.125   Prob(JB):                       0.0966\n",
            "Kurtosis:                       1.948   Cond. No.                         113.\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 421
        },
        "id": "IXma6iIS0SHb",
        "outputId": "7134c760-8b60-4f1e-8f8f-6792ee9da0ff"
      },
      "source": [
        "#PCarrying out the regression\n",
        "\n",
        "df['yhat'] = result.predict(X)\n",
        "df.head(12)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "      <th></th>\n",
              "      <th>year</th>\n",
              "      <th>month</th>\n",
              "      <th>miles</th>\n",
              "      <th>dat</th>\n",
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              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1963</td>\n",
              "      <td>1</td>\n",
              "      <td>6827.0</td>\n",
              "      <td>1963-1</td>\n",
              "      <td>1</td>\n",
              "      <td>7801.577534</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1963</td>\n",
              "      <td>2</td>\n",
              "      <td>6178.0</td>\n",
              "      <td>1963-2</td>\n",
              "      <td>2</td>\n",
              "      <td>7855.980946</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1963</td>\n",
              "      <td>3</td>\n",
              "      <td>7084.0</td>\n",
              "      <td>1963-3</td>\n",
              "      <td>3</td>\n",
              "      <td>7910.384357</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1963</td>\n",
              "      <td>4</td>\n",
              "      <td>8162.0</td>\n",
              "      <td>1963-4</td>\n",
              "      <td>4</td>\n",
              "      <td>7964.787769</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1963</td>\n",
              "      <td>5</td>\n",
              "      <td>8462.0</td>\n",
              "      <td>1963-5</td>\n",
              "      <td>5</td>\n",
              "      <td>8019.191181</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>1963</td>\n",
              "      <td>6</td>\n",
              "      <td>9644.0</td>\n",
              "      <td>1963-6</td>\n",
              "      <td>6</td>\n",
              "      <td>8073.594592</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>1963</td>\n",
              "      <td>7</td>\n",
              "      <td>10466.0</td>\n",
              "      <td>1963-7</td>\n",
              "      <td>7</td>\n",
              "      <td>8127.998004</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>1963</td>\n",
              "      <td>8</td>\n",
              "      <td>10748.0</td>\n",
              "      <td>1963-8</td>\n",
              "      <td>8</td>\n",
              "      <td>8182.401415</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>1963</td>\n",
              "      <td>9</td>\n",
              "      <td>9963.0</td>\n",
              "      <td>1963-9</td>\n",
              "      <td>9</td>\n",
              "      <td>8236.804827</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>1963</td>\n",
              "      <td>10</td>\n",
              "      <td>8194.0</td>\n",
              "      <td>1963-10</td>\n",
              "      <td>10</td>\n",
              "      <td>8291.208238</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>1963</td>\n",
              "      <td>11</td>\n",
              "      <td>6848.0</td>\n",
              "      <td>1963-11</td>\n",
              "      <td>11</td>\n",
              "      <td>8345.611650</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>1963</td>\n",
              "      <td>12</td>\n",
              "      <td>7027.0</td>\n",
              "      <td>1963-12</td>\n",
              "      <td>12</td>\n",
              "      <td>8400.015061</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    year month    miles      dat  trend         yhat\n",
              "0   1963     1   6827.0   1963-1      1  7801.577534\n",
              "1   1963     2   6178.0   1963-2      2  7855.980946\n",
              "2   1963     3   7084.0   1963-3      3  7910.384357\n",
              "3   1963     4   8162.0   1963-4      4  7964.787769\n",
              "4   1963     5   8462.0   1963-5      5  8019.191181\n",
              "5   1963     6   9644.0   1963-6      6  8073.594592\n",
              "6   1963     7  10466.0   1963-7      7  8127.998004\n",
              "7   1963     8  10748.0   1963-8      8  8182.401415\n",
              "8   1963     9   9963.0   1963-9      9  8236.804827\n",
              "9   1963    10   8194.0  1963-10     10  8291.208238\n",
              "10  1963    11   6848.0  1963-11     11  8345.611650\n",
              "11  1963    12   7027.0  1963-12     12  8400.015061"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 421
        },
        "id": "Uw02huUB0W13",
        "outputId": "ac314afe-f61e-4442-a40a-a6d68aae96e8"
      },
      "source": [
        "#Here we generate a trend variable and regress 'miles' on it\n",
        "\n",
        "df['ehat'] = df['miles'] - result.predict(X)\n",
        "df.head(12)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>year</th>\n",
              "      <th>month</th>\n",
              "      <th>miles</th>\n",
              "      <th>dat</th>\n",
              "      <th>trend</th>\n",
              "      <th>yhat</th>\n",
              "      <th>ehat</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1963</td>\n",
              "      <td>1</td>\n",
              "      <td>6827.0</td>\n",
              "      <td>1963-1</td>\n",
              "      <td>1</td>\n",
              "      <td>7801.577534</td>\n",
              "      <td>-974.577534</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1963</td>\n",
              "      <td>2</td>\n",
              "      <td>6178.0</td>\n",
              "      <td>1963-2</td>\n",
              "      <td>2</td>\n",
              "      <td>7855.980946</td>\n",
              "      <td>-1677.980946</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1963</td>\n",
              "      <td>3</td>\n",
              "      <td>7084.0</td>\n",
              "      <td>1963-3</td>\n",
              "      <td>3</td>\n",
              "      <td>7910.384357</td>\n",
              "      <td>-826.384357</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1963</td>\n",
              "      <td>4</td>\n",
              "      <td>8162.0</td>\n",
              "      <td>1963-4</td>\n",
              "      <td>4</td>\n",
              "      <td>7964.787769</td>\n",
              "      <td>197.212231</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1963</td>\n",
              "      <td>5</td>\n",
              "      <td>8462.0</td>\n",
              "      <td>1963-5</td>\n",
              "      <td>5</td>\n",
              "      <td>8019.191181</td>\n",
              "      <td>442.808819</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>1963</td>\n",
              "      <td>6</td>\n",
              "      <td>9644.0</td>\n",
              "      <td>1963-6</td>\n",
              "      <td>6</td>\n",
              "      <td>8073.594592</td>\n",
              "      <td>1570.405408</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>1963</td>\n",
              "      <td>7</td>\n",
              "      <td>10466.0</td>\n",
              "      <td>1963-7</td>\n",
              "      <td>7</td>\n",
              "      <td>8127.998004</td>\n",
              "      <td>2338.001996</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>1963</td>\n",
              "      <td>8</td>\n",
              "      <td>10748.0</td>\n",
              "      <td>1963-8</td>\n",
              "      <td>8</td>\n",
              "      <td>8182.401415</td>\n",
              "      <td>2565.598585</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>1963</td>\n",
              "      <td>9</td>\n",
              "      <td>9963.0</td>\n",
              "      <td>1963-9</td>\n",
              "      <td>9</td>\n",
              "      <td>8236.804827</td>\n",
              "      <td>1726.195173</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>1963</td>\n",
              "      <td>10</td>\n",
              "      <td>8194.0</td>\n",
              "      <td>1963-10</td>\n",
              "      <td>10</td>\n",
              "      <td>8291.208238</td>\n",
              "      <td>-97.208238</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>1963</td>\n",
              "      <td>11</td>\n",
              "      <td>6848.0</td>\n",
              "      <td>1963-11</td>\n",
              "      <td>11</td>\n",
              "      <td>8345.611650</td>\n",
              "      <td>-1497.611650</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>1963</td>\n",
              "      <td>12</td>\n",
              "      <td>7027.0</td>\n",
              "      <td>1963-12</td>\n",
              "      <td>12</td>\n",
              "      <td>8400.015061</td>\n",
              "      <td>-1373.015061</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    year month    miles      dat  trend         yhat         ehat\n",
              "0   1963     1   6827.0   1963-1      1  7801.577534  -974.577534\n",
              "1   1963     2   6178.0   1963-2      2  7855.980946 -1677.980946\n",
              "2   1963     3   7084.0   1963-3      3  7910.384357  -826.384357\n",
              "3   1963     4   8162.0   1963-4      4  7964.787769   197.212231\n",
              "4   1963     5   8462.0   1963-5      5  8019.191181   442.808819\n",
              "5   1963     6   9644.0   1963-6      6  8073.594592  1570.405408\n",
              "6   1963     7  10466.0   1963-7      7  8127.998004  2338.001996\n",
              "7   1963     8  10748.0   1963-8      8  8182.401415  2565.598585\n",
              "8   1963     9   9963.0   1963-9      9  8236.804827  1726.195173\n",
              "9   1963    10   8194.0  1963-10     10  8291.208238   -97.208238\n",
              "10  1963    11   6848.0  1963-11     11  8345.611650 -1497.611650\n",
              "11  1963    12   7027.0  1963-12     12  8400.015061 -1373.015061"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "sX1QqcCo0aK_",
        "outputId": "28a9df6a-f9c2-487c-b840-7a478eeb9df8"
      },
      "source": [
        "#Plotting a time serioes graph of miles and the trend variable\n",
        "\n",
        "df['miles'].plot()\n",
        "df['yhat'].plot()\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "qHlOXYvs0dMU",
        "outputId": "ea427992-254c-4592-9760-77713e5bd340"
      },
      "source": [
        "df['miles'].plot()\n",
        "df['ehat'].plot()\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9SUgw9Xe0gqF",
        "outputId": "d78cce9a-c39c-4f64-c76e-7f6e3f74b85a"
      },
      "source": [
        "df['ehat'].describe()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "count    9.600000e+01\n",
              "mean     3.789561e-14\n",
              "std      1.598204e+03\n",
              "min     -3.029833e+03\n",
              "25%     -1.342751e+03\n",
              "50%     -1.993959e+02\n",
              "75%      1.449895e+03\n",
              "max      3.427309e+03\n",
              "Name: ehat, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YkfkgMxX0jXy",
        "outputId": "ef03b972-ef81-401d-9bac-c139f5bd5d2d"
      },
      "source": [
        "df2 = df[(df['month'] <= '9') & (df['month'] >= '6')]\n",
        "df2['ehat'].describe()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "count      32.000000\n",
              "mean     1786.763255\n",
              "std       835.730770\n",
              "min      -749.799286\n",
              "25%      1451.454979\n",
              "50%      1799.959352\n",
              "75%      2271.160949\n",
              "max      3427.308602\n",
              "Name: ehat, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "id": "ojJ2xofN0pXm",
        "outputId": "907be4d1-bb9c-4279-ef23-6e241235c951"
      },
      "source": [
        "#Here we generate a set of month dummy variables.\n",
        "\n",
        "dummy = pd.get_dummies(df[\"month\"])\n",
        "dummy.columns = [\"m1\", \"m2\", \"m3\", \"m4\", \"m5\", \"m6\", \"m7\", \"m8\", \"m9\", \"m10\", \"m11\", \"m12\"]\n",
        "dummy.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>m1</th>\n",
              "      <th>m2</th>\n",
              "      <th>m3</th>\n",
              "      <th>m4</th>\n",
              "      <th>m5</th>\n",
              "      <th>m6</th>\n",
              "      <th>m7</th>\n",
              "      <th>m8</th>\n",
              "      <th>m9</th>\n",
              "      <th>m10</th>\n",
              "      <th>m11</th>\n",
              "      <th>m12</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   m1  m2  m3  m4  m5  m6  m7  m8  m9  m10  m11  m12\n",
              "0   1   0   0   0   0   0   0   0   0    0    0    0\n",
              "1   0   0   0   0   1   0   0   0   0    0    0    0\n",
              "2   0   0   0   0   0   1   0   0   0    0    0    0\n",
              "3   0   0   0   0   0   0   1   0   0    0    0    0\n",
              "4   0   0   0   0   0   0   0   1   0    0    0    0"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 309
        },
        "id": "ETmsGwVR1NhA",
        "outputId": "1f2a2e59-767a-49ea-c1b1-cc1b3c73d074"
      },
      "source": [
        "\n",
        "df2 =  pd.concat([df, dummy], axis=1)\n",
        "df2 =  df2.drop(columns=['m1'])\n",
        "\n",
        "df2.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "  <thead>\n",
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              "      <th></th>\n",
              "      <th>year</th>\n",
              "      <th>month</th>\n",
              "      <th>miles</th>\n",
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              "      <th>0</th>\n",
              "      <td>1963</td>\n",
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              "      <td>8162.0</td>\n",
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            "text/plain": [
              "   year month   miles     dat  trend         yhat  ...  m7  m8  m9  m10  m11  m12\n",
              "0  1963     1  6827.0  1963-1      1  7801.577534  ...   0   0   0    0    0    0\n",
              "1  1963     2  6178.0  1963-2      2  7855.980946  ...   0   0   0    0    0    0\n",
              "2  1963     3  7084.0  1963-3      3  7910.384357  ...   0   0   0    0    0    0\n",
              "3  1963     4  8162.0  1963-4      4  7964.787769  ...   1   0   0    0    0    0\n",
              "4  1963     5  8462.0  1963-5      5  8019.191181  ...   0   1   0    0    0    0\n",
              "\n",
              "[5 rows x 18 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "s0e-s5lY1QJ9",
        "outputId": "28057f2b-1266-4e20-87fe-ddd3300c0b26"
      },
      "source": [
        "XX = df2[[\"trend\", \"m2\", \"m3\", \"m4\", \"m5\", \"m6\", \"m7\", \"m8\", \"m9\", \"m10\", \"m11\", \"m12\"]]\n",
        "XX = sm.add_constant(XX)\n",
        "YY = df2[['miles']]\n",
        "\n",
        "reg1 = sm.OLS(YY, XX, missing='drop')\n",
        "\n",
        "result1 = reg1.fit()\n",
        "print(result1.summary())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                  miles   R-squared:                       0.906\n",
            "Model:                            OLS   Adj. R-squared:                  0.892\n",
            "Method:                 Least Squares   F-statistic:                     66.58\n",
            "Date:                Mon, 27 Sep 2021   Prob (F-statistic):           2.28e-37\n",
            "Time:                        10:37:49   Log-Likelihood:                -761.22\n",
            "No. Observations:                  96   AIC:                             1548.\n",
            "Df Residuals:                      83   BIC:                             1582.\n",
            "Df Model:                          12                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const       6214.6957    280.408     22.163      0.000    5656.975    6772.417\n",
            "trend         52.9606      2.683     19.738      0.000      47.624      58.297\n",
            "m2          1297.9799    362.238      3.583      0.001     577.504    2018.456\n",
            "m3          -188.8557    362.426     -0.521      0.604    -909.707     531.996\n",
            "m4           589.6838    362.635      1.626      0.108    -131.582    1310.950\n",
            "m5          -513.4606    361.442     -1.421      0.159   -1232.353     205.432\n",
            "m6          1189.5789    361.472      3.291      0.001     470.627    1908.531\n",
            "m7          1240.6183    361.521      3.432      0.001     521.567    1959.670\n",
            "m8          2051.2827    361.591      5.673      0.000    1332.093    2770.473\n",
            "m9          3325.3222    361.681      9.194      0.000    2605.954    4044.690\n",
            "m10         3113.6116    361.790      8.606      0.000    2394.026    3833.198\n",
            "m11         3312.5260    361.919      9.153      0.000    2592.683    4032.369\n",
            "m12         3811.1905    362.069     10.526      0.000    3091.051    4531.330\n",
            "==============================================================================\n",
            "Omnibus:                       28.235   Durbin-Watson:                   1.498\n",
            "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               64.871\n",
            "Skew:                          -1.060   Prob(JB):                     8.19e-15\n",
            "Kurtosis:                       6.424   Cond. No.                         696.\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 645
        },
        "id": "IjLrpD9O1Thl",
        "outputId": "843b4a67-43b5-4a8b-c3ef-4ee700713c68"
      },
      "source": [
        "df2['yhat'] = result1.predict(XX)\n",
        "df2.head(12)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "      <td>5</td>\n",
              "      <td>8530.78125</td>\n",
              "      <td>442.808819</td>\n",
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              "      <td>9644.0</td>\n",
              "      <td>1963-6</td>\n",
              "      <td>6</td>\n",
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              "      <td>1963</td>\n",
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              "      <td>10466.0</td>\n",
              "      <td>1963-7</td>\n",
              "      <td>7</td>\n",
              "      <td>9699.03125</td>\n",
              "      <td>2338.001996</td>\n",
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              "      <td>1963</td>\n",
              "      <td>8</td>\n",
              "      <td>10748.0</td>\n",
              "      <td>1963-8</td>\n",
              "      <td>8</td>\n",
              "      <td>9950.90625</td>\n",
              "      <td>2565.598585</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>1963</td>\n",
              "      <td>9</td>\n",
              "      <td>9963.0</td>\n",
              "      <td>1963-9</td>\n",
              "      <td>9</td>\n",
              "      <td>10502.53125</td>\n",
              "      <td>1726.195173</td>\n",
              "      <td>0</td>\n",
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              "      <td>8194.0</td>\n",
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              "      <td>10</td>\n",
              "      <td>8042.28125</td>\n",
              "      <td>-97.208238</td>\n",
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              "      <td>12</td>\n",
              "      <td>7027.0</td>\n",
              "      <td>1963-12</td>\n",
              "      <td>12</td>\n",
              "      <td>7439.90625</td>\n",
              "      <td>-1373.015061</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    year month    miles      dat  trend         yhat  ...  m7  m8  m9  m10  m11  m12\n",
              "0   1963     1   6827.0   1963-1      1   6267.65625  ...   0   0   0    0    0    0\n",
              "1   1963     2   6178.0   1963-2      2   5807.15625  ...   0   0   0    0    0    0\n",
              "2   1963     3   7084.0   1963-3      3   7563.15625  ...   0   0   0    0    0    0\n",
              "3   1963     4   8162.0   1963-4      4   7667.15625  ...   1   0   0    0    0    0\n",
              "4   1963     5   8462.0   1963-5      5   8530.78125  ...   0   1   0    0    0    0\n",
              "5   1963     6   9644.0   1963-6      6   9857.78125  ...   0   0   1    0    0    0\n",
              "6   1963     7  10466.0   1963-7      7   9699.03125  ...   0   0   0    1    0    0\n",
              "7   1963     8  10748.0   1963-8      8   9950.90625  ...   0   0   0    0    1    0\n",
              "8   1963     9   9963.0   1963-9      9  10502.53125  ...   0   0   0    0    0    1\n",
              "9   1963    10   8194.0  1963-10     10   8042.28125  ...   0   0   0    0    0    0\n",
              "10  1963    11   6848.0  1963-11     11   6608.40625  ...   0   0   0    0    0    0\n",
              "11  1963    12   7027.0  1963-12     12   7439.90625  ...   0   0   0    0    0    0\n",
              "\n",
              "[12 rows x 18 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "nxEylLVO1Wzv",
        "outputId": "43fda28e-79e9-4124-f4b5-14b3a1018966"
      },
      "source": [
        "df2['miles'].plot()\n",
        "df2['yhat'].plot()\n",
        "df['yhat'].plot()\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}