regresi_linear.ipynb

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        "## **Tugas Besar Analisa Data**\n",
        "Kelas DS-45-01\n",
        "\n",
        "---\n",
        "**Nama Kelompok**\n",
        "\n",
        "\n",
        "1.   Akmal Muzakki Bakir (1305210087)\n",
        "2.   Namira Salsabilla (1305210091)\n",
        "3.   Haura Adzkia Delfina (1305213006)\n",
        "\n",
        "\n",
        "---\n",
        "**Rincian Tugas**\n",
        "1. Pelajari data yang diberikan, kemudian buatlah model regresi linier dengan metode Regresi Bertahap. Variabel dependen (Y) adalah GDP, sedangkan variabel independennya  adalah: Export (X1), Import (X2), Industrial production growth rate (X3), Investment (X4), Unemployment rate  (X5).\n",
        "2.\tLakukan analisis terhadap model regresi yang diperoleh.\n",
        "3.\tTugas dikerjakan menggunakan Python (Colab), tidak boleh menggunakan library regresi linier bertahap. Kerjakan secara bertahap Langkah-langkah pada metode regresi linier bertahap.\n",
        "\n"
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      "source": [
        "# Data Preparation"
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      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "import scipy.stats as stats"
      ]
    },
    {
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      "source": [
        "Data Description\n",
        "\n",
        "---\n",
        "Data factbook merupakan data dengan atribut-atribut yang memuat informasi mengenai 149 negara yang berada pada berbagai benua. Pada penugasan Analisa Data ini, kami akan menggunakan beberapa atribut yang akan dijadikan variabel dependen dan independen. Atribut tersebut antara lain:\n",
        "\n",
        "\n",
        "*   Variabel independen(Y)\n",
        "1. GDP: Total nilai produksi barang dan jasa yang dihasilkan dalam batas wilayah suatu negara dalam satu tahun. Dinyatakan dalam dolar AS.\n",
        "*   Variabel dependen(X)\n",
        "1.  Export (X1): Nilai total barang dan jasa yang diekspor suatu negara dalam dolar AS.\n",
        "2. Import (X2): Nilai total barang dan jasa yang diimpor suatu negara dalam dolar AS.\n",
        "3. Industrial production growth rate (X3): Tingkat pertumbuhan produksi industri suatu negara dalam satu tahun. Dinyatakan dalam persen.\n",
        "4. Investment (X4): Total nilai investasi suatu negara dalam dolar AS.\n",
        "5. Unemployment rate (X5): Persentase angka pengangguran dalam populasi angkatan kerja suatu negara.\n",
        "\n",
        "\n",
        "\n",
        "\n"
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              "   Unnamed: 0       Country      Area  Birth rate  Current account balance  \\\n",
              "0           0         Japan    377835        9.47             170200000000   \n",
              "1           1       Germany    357021        8.33              73590000000   \n",
              "2           2  Saudi Arabia   1960582       29.56              51500000000   \n",
              "3           3        Russia  17075200        9.80              46040000000   \n",
              "4           4   Switzerland      4129        9.77              40950000000   \n",
              "\n",
              "   Death rate  Electricity consumption  Electricity production       Exports  \\\n",
              "0        8.95             971000000000           1044000000000  538800000000   \n",
              "1       10.55             519500000000            560000000000  893300000000   \n",
              "2        2.62             128500000000            138200000000  113000000000   \n",
              "3       14.52             894300000000            915000000000  162500000000   \n",
              "4        8.48              54530000000             63470000000  130700000000   \n",
              "\n",
              "             GDP  ...  Life expectancy at birth  Military expenditures  \\\n",
              "0  3745000000000  ...                     81.15                    1.0   \n",
              "1  2362000000000  ...                     78.65                    1.5   \n",
              "2   310200000000  ...                     75.46                   10.0   \n",
              "3  1408000000000  ...                     67.10                    0.0   \n",
              "4   251900000000  ...                     80.39                    1.0   \n",
              "\n",
              "   Natural gas consumption  Oil consumption  Population  Public debt  \\\n",
              "0             804200000000         52900000  1274172440        164.3   \n",
              "1             995500000000         28910000   824313900         65.8   \n",
              "2             564000000000         15500000   264175990         75.0   \n",
              "3            4058000000000         23100000  1434203090         28.2   \n",
              "4              30930000000             2904    74893700         57.2   \n",
              "\n",
              "   Railways  Reserves of foreign exchange & gold  Total fertility rate  \\\n",
              "0     23705                        6646000000000                  1.39   \n",
              "1     46039                         968400000000                  1.39   \n",
              "2      1392                         236200000000                  4.05   \n",
              "3     87157                        1245000000000                  1.27   \n",
              "4      4533                         695800000000                  1.42   \n",
              "\n",
              "   Unemployment rate  \n",
              "0                4.7  \n",
              "1               10.6  \n",
              "2               25.0  \n",
              "3                8.3  \n",
              "4                3.4  \n",
              "\n",
              "[5 rows x 30 columns]"
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              "      <th>3</th>\n",
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      ],
      "source": [
        "# Membaca data Factbook\n",
        "df = pd.read_csv('factbook_transform.csv')\n",
        "df.head()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Pengambilan Atribut\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "Melakukan pengambilan data atribut yang diperlukan sebagai variabel dependen dan independen untuk di lakukan pemodelan regresi linear dengan metode regresi bertahap."
      ],
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              "             GDP       Exports       Imports  \\\n",
              "0  3745000000000  538800000000  401800000000   \n",
              "1  2362000000000  893300000000  716700000000   \n",
              "2   310200000000  113000000000   36210000000   \n",
              "3  1408000000000  162500000000   92910000000   \n",
              "4   251900000000  130700000000  121100000000   \n",
              "\n",
              "   Industrial production growth rate  Investment  Unemployment rate  \n",
              "0                                6.6        24.0                4.7  \n",
              "1                                2.2        17.6               10.6  \n",
              "2                                2.8        17.2               25.0  \n",
              "3                                6.4        19.1                8.3  \n",
              "4                                4.7        20.4                3.4  "
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              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-706cd664-c712-4572-8c08-61892ccde58f')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
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              "      </button>\n",
              "      \n",
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              "\n",
              "    .colab-df-convert {\n",
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              "\n",
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              "      background-color: #434B5C;\n",
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              "\n",
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              "          const element = document.querySelector('#df-706cd664-c712-4572-8c08-61892ccde58f');\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",
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              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 91
        }
      ],
      "source": [
        "# Mengambil data GDP, Export, Import, Industrial production growth rate, Investment, dan Unemployment rate\n",
        "df = df[['GDP', 'Exports', 'Imports', 'Industrial production growth rate', 'Investment', 'Unemployment rate']]\n",
        "df.head()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Pengecekan missing value\n",
        "\n",
        "---\n",
        "mengecek missing value pada tiap atribut agar data siap untuk dilakukan pemodelan. didapatkan hasil bahwa tidak ada missing value pada setiap atribut. Sehingga tidak diperlukan penanganan missing value."
      ],
      "metadata": {
        "id": "ipzl09niuOej"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.776613Z",
          "start_time": "2023-06-04T13:48:28.086673400Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "e9DH_gowlJif",
        "outputId": "170789d9-c146-490f-e395-ce1c098c4b35"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "GDP                                  0\n",
              "Exports                              0\n",
              "Imports                              0\n",
              "Industrial production growth rate    0\n",
              "Investment                           0\n",
              "Unemployment rate                    0\n",
              "dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 92
        }
      ],
      "source": [
        "df.isnull().sum()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Penamaan Atribut\n",
        "\n",
        "---\n",
        "Atribut yang diperlukan untuk regresi bertahap telah diambil, selanjutnya untuk memudahkan pengolahan data, kami melakukan pengubahan nama atribut sesuai dengan variabel yang telah ditentukan agar memperjelas makna dari masing-masing atribut.\n"
      ],
      "metadata": {
        "id": "i17qvqYBvTQB"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.776613Z",
          "start_time": "2023-06-04T13:48:28.112813700Z"
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        "colab": {
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        },
        "id": "hen5v9gwlJif",
        "outputId": "3066cbc8-51b0-4bd4-8e03-e5db7ce1fa22"
      },
      "outputs": [
        {
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              "                  Y            X1             X2   X3    X4    X5\n",
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              "..              ...           ...            ...  ...   ...   ...\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",
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              "  "
            ]
          },
          "metadata": {},
          "execution_count": 93
        }
      ],
      "source": [
        "# rename kolom\n",
        "df = df.rename(columns={'GDP': 'Y', 'Exports': 'X1', 'Imports': 'X2', 'Industrial production growth rate': 'X3', 'Investment' : 'X4', 'Unemployment rate': 'X5'})\n",
        "df"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Normalisasi\n",
        "\n",
        "---\n",
        "dilakukan normalisasi atau penskalaan data dengan rentang 0-100. Pada regresi bertahap, proses ini sangat penting untuk memastikan bahwa setiap variabel memiliki skala yang serupa dan tidak mendominasi sehingga mengabaikan pengaruh dari variabel lainnya. Dengan normalisasi, kita dapat melakukan perbandingan dan evaluasi dari setiap variabel\n"
      ],
      "metadata": {
        "id": "mtWgu3xX0DNi"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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          "height": 423
        },
        "id": "ybW8ICHglJig",
        "outputId": "6cc763d8-db43-4919-ffb0-37057dbdf689"
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              "              Y          X1          X2         X3         X4         X5\n",
              "0     31.871100   60.315386   27.220201  38.095238  36.866359   6.714286\n",
              "1     20.100672  100.000000   48.555482  26.455026  27.035330  15.142857\n",
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              "      <td>2.638227</td>\n",
              "      <td>12.649071</td>\n",
              "      <td>2.450542</td>\n",
              "      <td>28.042328</td>\n",
              "      <td>26.420891</td>\n",
              "      <td>35.714286</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>11.981376</td>\n",
              "      <td>18.190364</td>\n",
              "      <td>6.292112</td>\n",
              "      <td>37.566138</td>\n",
              "      <td>29.339478</td>\n",
              "      <td>11.857143</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2.142048</td>\n",
              "      <td>14.630503</td>\n",
              "      <td>8.202057</td>\n",
              "      <td>33.068783</td>\n",
              "      <td>31.336406</td>\n",
              "      <td>4.857143</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>144</th>\n",
              "      <td>13.692045</td>\n",
              "      <td>37.657654</td>\n",
              "      <td>22.308140</td>\n",
              "      <td>22.486772</td>\n",
              "      <td>29.646697</td>\n",
              "      <td>12.285714</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>145</th>\n",
              "      <td>7.977898</td>\n",
              "      <td>19.309817</td>\n",
              "      <td>15.038290</td>\n",
              "      <td>28.571429</td>\n",
              "      <td>39.016897</td>\n",
              "      <td>14.857143</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>146</th>\n",
              "      <td>15.164412</td>\n",
              "      <td>38.866663</td>\n",
              "      <td>29.767697</td>\n",
              "      <td>23.015873</td>\n",
              "      <td>24.884793</td>\n",
              "      <td>6.857143</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>147</th>\n",
              "      <td>5.204231</td>\n",
              "      <td>9.726178</td>\n",
              "      <td>6.643748</td>\n",
              "      <td>25.661376</td>\n",
              "      <td>38.863287</td>\n",
              "      <td>7.285714</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>148</th>\n",
              "      <td>100.000000</td>\n",
              "      <td>88.995776</td>\n",
              "      <td>100.000000</td>\n",
              "      <td>32.275132</td>\n",
              "      <td>24.116743</td>\n",
              "      <td>7.857143</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>149 rows × 6 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-46a5a9a6-7e58-4f45-af9d-375575474a7b')\"\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 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\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",
              "    [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-46a5a9a6-7e58-4f45-af9d-375575474a7b 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-46a5a9a6-7e58-4f45-af9d-375575474a7b');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 94
        }
      ],
      "source": [
        "# MinMax Scaller dengan rentang 0-100\n",
        "def scaler(x):\n",
        "    return (x - x.min()) / (x.max() - x.min()) * 100\n",
        "\n",
        "for column in df.columns:\n",
        "    df[column] = scaler(df[column])\n",
        "\n",
        "df"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": false,
        "id": "SzHMTAP6lJig"
      },
      "source": [
        "# Model Regressi Linear\n",
        "model ini merupakan salah satu metode yang digunakan untuk memodelkan hubungan linear antara variabel dependen dan independen.\n",
        ">\n",
        "Model regresi linear dapat dinyatakan dengan persamaan matematis berikut:\n",
        ">\n",
        "Y = β0 + β1X1 + β2X2 + ... + βn*Xn + ε\n",
        "\n",
        "Dalam persamaan tersebut:\n",
        "\n",
        "* Y merupakan variabel dependen yang ingin diprediksi.\n",
        "*β0 merupakan konstanta atau intercept yang merupakan titik temu garis regresi dengan sumbu Y ketika semua variabel independen bernilai nol.\n",
        "* β1, β2, ..., βn merupakan koefisien regresi yang menggambarkan seberapa besar perubahan dalam variabel dependen terkait dengan perubahan dalam variabel independen.\n",
        "* X1, X2, ..., Xn merupakan variabel independen.\n",
        "* ε merupakan error atau gangguan yang mengindikasikan ketidaktepatan dalam memprediksi variabel dependen dengan menggunakan variabel independen."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": false,
        "id": "4pErq60dlJih"
      },
      "source": [
        "## Membuat persamaan normal berdasarkan perhitungan nilai zigma\n",
        "melakukan perhitungan zigma pada atribut yang dibutuhkan untuk mendapatkan persamaan"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Menghitung Zigma Tiap Atribut\n",
        "\n",
        "---\n",
        "Akan dilakukan perhitungan nilai zigma dari masing-masing atribut yang ada, yaitu x1, x2, x3, x4, x5, dan Y\n"
      ],
      "metadata": {
        "id": "teR_tZcQUqMo"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.809246300Z",
          "start_time": "2023-06-04T13:48:28.205407400Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zpc4rylFlJih",
        "outputId": "cb77ee1f-c303-4185-b50f-87a4c1f89a00"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'X1': 977.1731266763111,\n",
              " 'X2': 589.8722593242766,\n",
              " 'X3': 5288.888888888889,\n",
              " 'X4': 4810.4454685099845,\n",
              " 'X5': 2625.2857142857147,\n",
              " 'Y': 469.99296838257305}"
            ]
          },
          "metadata": {},
          "execution_count": 95
        }
      ],
      "source": [
        "# Hitung zigma setiap kolom\n",
        "column_names = ['X1', 'X2', 'X3', 'X4', 'X5','Y']\n",
        "zigma_values = {}\n",
        "\n",
        "for column in column_names:\n",
        "    zigma_values[column] = df[column].sum()\n",
        "\n",
        "zigma_values"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Menghitung Zigma Kuadrat Tiap Kolom\n",
        "\n",
        "---\n",
        "Nilai dari masing-masing kolom akan dikuadratkan lalu dilakukan penjumlahan. Sehingga akan menghasilkan zigma dari tiap nilai yang dikuadratkan.\n"
      ],
      "metadata": {
        "id": "bK1s-D_BU7_G"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.812738300Z",
          "start_time": "2023-06-04T13:48:28.236916700Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CMhXDdHdlJii",
        "outputId": "53742deb-db00-4daf-acdc-914aefcbbaba"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'X1': 39821.64173271906,\n",
              " 'X2': 19380.026915542134,\n",
              " 'X3': 219407.21144424853,\n",
              " 'X4': 182949.7806753642,\n",
              " 'X5': 96242.30612244898,\n",
              " 'Y': 17606.97504266749}"
            ]
          },
          "metadata": {},
          "execution_count": 96
        }
      ],
      "source": [
        "# Hitung zigma kuadrat setiap kolom\n",
        "column_names = ['X1', 'X2', 'X3', 'X4', 'X5','Y']\n",
        "zigma_squared_values = {}\n",
        "\n",
        "for column in column_names:\n",
        "    zigma_squared_values[column] = (df[column] ** 2).sum()\n",
        "\n",
        "zigma_squared_values"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Menghitung Zigma Kolom Dikali Kolom\n",
        "\n",
        "---\n",
        "dilakukan perkalian dari nilai satu kolom ke kolom lain lalu hasil akhirnya merupakan zigma dari operasi tersebut.\n"
      ],
      "metadata": {
        "id": "kly2bKoOV316"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.814243500Z",
          "start_time": "2023-06-04T13:48:28.262888800Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LHeHlIhnlJii",
        "outputId": "32ba90f7-8707-42b7-b3b4-eacda5379894"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'X1_X2': 25953.00146464189,\n",
              " 'X1_X3': 34018.94994302863,\n",
              " 'X1_X4': 32660.556559644567,\n",
              " 'X1_X5': 11164.042171655316,\n",
              " 'X2_X3': 20336.387156278495,\n",
              " 'X2_X4': 19373.28609246052,\n",
              " 'X2_X5': 6506.713204286646,\n",
              " 'X3_X4': 176539.3493120068,\n",
              " 'X3_X5': 94359.41043083901,\n",
              " 'X4_X5': 84354.35593592277}"
            ]
          },
          "metadata": {},
          "execution_count": 97
        }
      ],
      "source": [
        "# Hitung zigma setiap kolom dikali kolom lain\n",
        "column_names = ['X1', 'X2', 'X3', 'X4', 'X5']\n",
        "zigma_multiply_values = {}\n",
        "\n",
        "for i in range(len(column_names)):\n",
        "    for j in range(i+1, len(column_names)):\n",
        "        column_1 = column_names[i]\n",
        "        column_2 = column_names[j]\n",
        "        zigma_multiply_values[column_1 + '_' + column_2] = (df[column_1] * df[column_2]).sum()\n",
        "\n",
        "zigma_multiply_values"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Menghitung Zigma Kolom Dikali Y\n",
        "\n",
        "---\n",
        "Kali ini operasi perkalian dilakukan antara nilai dari masing masing atribut independen yang dikalikan dengan atribut dependen. Hasil akhir berupa zigma dari operasi tersebut.\n"
      ],
      "metadata": {
        "id": "7I1CpasYbM_4"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.841051600Z",
          "start_time": "2023-06-04T13:48:28.284308300Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "auuuSFFMlJij",
        "outputId": "00b958c3-4491-4bd9-cf4b-99dae02e41a5"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'X1_Y': 21068.877649082177,\n",
              " 'X2_Y': 16666.246787662265,\n",
              " 'X3_Y': 18069.522323494268,\n",
              " 'X4_Y': 16591.85263095826,\n",
              " 'X5_Y': 5625.304345360601}"
            ]
          },
          "metadata": {},
          "execution_count": 98
        }
      ],
      "source": [
        "# Hitung zigma setiap kolom dikali Y\n",
        "column_names = ['X1', 'X2', 'X3', 'X4', 'X5']\n",
        "zigma_multiply_y_values = {}\n",
        "\n",
        "for column in column_names:\n",
        "    zigma_multiply_y_values[column + '_Y'] = (df[column] * df['Y']).sum()\n",
        "\n",
        "zigma_multiply_y_values"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Menentukan Persamaan\n",
        "\n",
        "---\n",
        "Pertama-tama pada matriks A akan dilakukan perhitungan persamaan yaitu:\n",
        ">\n",
        "Y = β0 + β1X1 + β2X2 + ... + βn*Xn + ε\n",
        ">\n",
        "setelah itu, hasil yang didapatkan akan disimpan pada Vektor B. Selanjutnya akan dilakukan penyelesaian sistem persamaan linear yang hasil akhirnya adalah nilai-nilai koefisien(b0,b1,b2,b3,b4 dan b5) dalam model regresi linear berganda.\n"
      ],
      "metadata": {
        "id": "sRYMqeIgbq8i"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.842049100Z",
          "start_time": "2023-06-04T13:48:28.331790Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 237
        },
        "id": "cA2-9HA9lJij",
        "outputId": "2b008e3d-d44a-4fad-83c1-4758b7c6cef8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    Koefisien\n",
              "b0  -3.174322\n",
              "b1  -0.253982\n",
              "b2   1.200869\n",
              "b3   0.054361\n",
              "b4   0.035958\n",
              "b5   0.008498"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-3179cb3d-956f-4b13-b028-b76ee80268c9\">\n",
              "    <div 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>Koefisien</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>b0</th>\n",
              "      <td>-3.174322</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>b1</th>\n",
              "      <td>-0.253982</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>b2</th>\n",
              "      <td>1.200869</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>b3</th>\n",
              "      <td>0.054361</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>b4</th>\n",
              "      <td>0.035958</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>b5</th>\n",
              "      <td>0.008498</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-3179cb3d-956f-4b13-b028-b76ee80268c9')\"\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 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\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",
              "    [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-3179cb3d-956f-4b13-b028-b76ee80268c9 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-3179cb3d-956f-4b13-b028-b76ee80268c9');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 99
        }
      ],
      "source": [
        "# Matriks Persamaan Normal\n",
        "A = np.array([[len(df), zigma_values['X1'], zigma_values['X2'], zigma_values['X3'], zigma_values['X4'], zigma_values['X5']],\n",
        "              [zigma_values['X1'], zigma_squared_values['X1'], zigma_multiply_values['X1_X2'], zigma_multiply_values['X1_X3'], zigma_multiply_values['X1_X4'], zigma_multiply_values['X1_X5']],\n",
        "              [zigma_values['X2'], zigma_multiply_values['X1_X2'], zigma_squared_values['X2'], zigma_multiply_values['X2_X3'], zigma_multiply_values['X2_X4'], zigma_multiply_values['X2_X5']],\n",
        "              [zigma_values['X3'], zigma_multiply_values['X1_X3'], zigma_multiply_values['X2_X3'], zigma_squared_values['X3'], zigma_multiply_values['X3_X4'], zigma_multiply_values['X3_X5']],\n",
        "              [zigma_values['X4'], zigma_multiply_values['X1_X4'], zigma_multiply_values['X2_X4'], zigma_multiply_values['X3_X4'], zigma_squared_values['X4'], zigma_multiply_values['X4_X5']],\n",
        "              [zigma_values['X5'], zigma_multiply_values['X1_X5'], zigma_multiply_values['X2_X5'], zigma_multiply_values['X3_X5'], zigma_multiply_values['X4_X5'], zigma_squared_values['X5']]])\n",
        "# Vektor hasil\n",
        "B = np.array([zigma_values['Y'], zigma_multiply_y_values['X1_Y'], zigma_multiply_y_values['X2_Y'], zigma_multiply_y_values['X3_Y'], zigma_multiply_y_values['X4_Y'], zigma_multiply_y_values['X5_Y']])\n",
        "\n",
        "# Menyelesaikan sistem persamaan linear\n",
        "x = np.linalg.solve(A, B)\n",
        "\n",
        "# Membuat dataframe baru dengan nilai koefisien\n",
        "df_coef = pd.DataFrame(x, index=['b0', 'b1', 'b2', 'b3', 'b4', 'b5'], columns=['Koefisien'])\n",
        "df_coef"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Output diatas adalah terdiri dari intercept (b0) dan koefisien (b1, b2, b3, b4, b5)"
      ],
      "metadata": {
        "id": "aDTdNeLkqm1o"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Membuat persamaan normal menggunakan matriks"
      ],
      "metadata": {
        "collapsed": false,
        "id": "A4xYtS-AlJik"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Persamaan regresi linear berganda dalam notasi matriks\n",
        "\n",
        "---\n",
        "secara keseluruhan, notasi matriks dalm regresi linear berganda memberikan keuntungan, antara lain:\n",
        "* keuntungan dalam representasi\n",
        "* kemudahan komputasi\n",
        "\n",
        "Dalam notasi matriks, model regresi linear berganda dapat dituliskan menjadi:\n",
        ">\n",
        "Y = Xβ + ε\n",
        "\n",
        "Dalam persamaan tersebut:\n",
        "\n",
        "* Y adalah vektor kolom dengan ukuran n x 1, yang merupakan variabel dependen yang ingin diprediksi.\n",
        "* X adalah matriks desain dengan ukuran n x (p+1), di mana n adalah jumlah observasi dan p adalah jumlah variabel independen. Kolom pertama matriks X biasanya diisi dengan nilai konstan 1 untuk mengakomodasi intercept dalam model.\n",
        "* β adalah vektor kolom dengan ukuran (p+1) x 1, yang merupakan vektor koefisien regresi yang menghubungkan variabel independen dengan variabel dependen.\n",
        "* ε adalah vektor kolom dengan ukuran n x 1, yang merupakan vektor error."
      ],
      "metadata": {
        "id": "TAeslUyFBl3w"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [],
      "source": [
        "# Membuat matriks Y\n",
        "Y = np.array(df['Y'])\n",
        "# Membuat matriks X\n",
        "X = np.array([[1, df['X1'][i], df['X2'][i], df['X3'][i], df['X4'][i], df['X5'][i]] for i in range(len(df))])"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.842049100Z",
          "start_time": "2023-06-04T13:48:28.375668700Z"
        },
        "id": "Rb0vg7vTlJik"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Menghitung Nilai g\n",
        "\n",
        "---\n",
        "Matriks g yang dihasilkan akan berisi nilai-nilai yang menyatakan sumbu gradien dari persamaan regresi linear berganda. Masing-masing nilai menyatakan kontribusi terhadap perubahan nilai variabel dependen untuk seriap unit perubahan dalam variabel independen yang sesuai.\n"
      ],
      "metadata": {
        "id": "TdMpaCcTEwds"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([  469.99296838, 21068.87764908, 16666.24678766, 18069.52232349,\n",
              "       16591.85263096,  5625.30434536])"
            ]
          },
          "metadata": {},
          "execution_count": 101
        }
      ],
      "source": [
        "# Menghitung nilai g\n",
        "g = X.T.dot(Y)\n",
        "g"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.854204300Z",
          "start_time": "2023-06-04T13:48:28.443340Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3jDBQTJelJil",
        "outputId": "843384fe-7e88-43d3-9453-b64a52f87148"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Menghitung Nilai β\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "Jika matriks X^T^X mempunyai invers, maka nilai β dapat ditulis menjadi:\n",
        ">\n",
        "β = (X^T X)^-1^ X^T Y\n",
        "\n",
        "Dengan menggunakan solusi ini, kita dapat memperkirakan vektor koefisien regresi β yang memberikan hubungan linier terbaik antara variabel independen dan variabel dependen dalam model regresi linear berganda."
      ],
      "metadata": {
        "collapsed": false,
        "id": "Qo5KR1WzlJik"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    Koefisien\n",
              "b0  -3.174322\n",
              "b1  -0.253982\n",
              "b2   1.200869\n",
              "b3   0.054361\n",
              "b4   0.035958\n",
              "b5   0.008498"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-bdc0e037-c43e-48f0-be52-f240fd39b671\">\n",
              "    <div 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>Koefisien</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>b0</th>\n",
              "      <td>-3.174322</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>b1</th>\n",
              "      <td>-0.253982</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>b2</th>\n",
              "      <td>1.200869</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>b3</th>\n",
              "      <td>0.054361</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>b4</th>\n",
              "      <td>0.035958</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>b5</th>\n",
              "      <td>0.008498</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-bdc0e037-c43e-48f0-be52-f240fd39b671')\"\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 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\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",
              "    [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-bdc0e037-c43e-48f0-be52-f240fd39b671 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-bdc0e037-c43e-48f0-be52-f240fd39b671');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 102
        }
      ],
      "source": [
        "# Menghitung nilai b\n",
        "b = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Y)\n",
        "df_coef = pd.DataFrame(b, index=['b0', 'b1', 'b2', 'b3', 'b4', 'b5'], columns=['Koefisien'])\n",
        "df_coef"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.852693200Z",
          "start_time": "2023-06-04T13:48:28.413173900Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 237
        },
        "id": "EIBGraGGlJik",
        "outputId": "0a263343-b741-48d5-d7d5-d43f3d96d942"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Output diatas adalah terdiri dari intercept (b0) dan koefisien (b1, b2, b3, b4, b5), jika di amati lagi, output yang dihasilkan sama jika menggunakan persamaan normal berdasarkan perhitungan nilai zigma"
      ],
      "metadata": {
        "id": "4B5AczCurE1e"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Pemilihan model"
      ],
      "metadata": {
        "collapsed": false,
        "id": "luP7EABVlJil"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Ukuran yang dapat menjadi patokan bahwa model regresi yang dibangun sudah baik adalah:**\n",
        "1. Koefisien Determinasi (R^2^): R^2^ menggambarkan proporsi variasi dalam variabel dependen yang dapat dijelaskan oleh variabel independen dalam model regresi. Semakin tinggi nilai R^2^, semakin baik model regresi dalam menjelaskan variasi dalam data. Nilai R^2^ berkisar antara 0 hingga 1, di mana nilai 1 menunjukkan model yang sempurna cocok dengan data.\n",
        "\n",
        "2. Uji Signifikansi Model: Uji signifikansi model (misalnya, uji F) digunakan untuk menguji apakah model regresi secara keseluruhan memiliki pengaruh yang signifikan terhadap variabel dependen. Jika nilai p-value dari uji tersebut cukup rendah (biasanya kurang dari 0,05), maka kita dapat menyimpulkan bahwa model secara signifikan mempengaruhi variabel dependen.\n",
        "\n",
        "3. Evaluasi Residual: Melihat residual (galat) dari model juga penting. Residual adalah selisih antara nilai yang diamati dan nilai yang diprediksi oleh model. Dalam model yang baik, residual seharusnya tersebar secara acak dan tidak memiliki pola tertentu. Jika ada pola yang tersisa dalam residual, itu bisa menunjukkan adanya struktur yang tidak tercakup oleh model."
      ],
      "metadata": {
        "collapsed": false,
        "id": "3PpbAL_TlJil"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Menghitung Jumlah Kuadrat Total (JKT)\n",
        "\n",
        "---\n",
        "JKT merupakan jumlah kuadrat dari selisih antara nilai variabel dependen yang diamati (Y) dengan nilai rata-rata dari variabel dependen yang diamati (Ȳ).\n",
        "\n",
        "JKT = ∑ (y[i]^2) - (∑ (y[i]))^2"
      ],
      "metadata": {
        "collapsed": false,
        "id": "d5jBGcy5lJil"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "16124.469067304657"
            ]
          },
          "metadata": {},
          "execution_count": 103
        }
      ],
      "source": [
        "# Menghitung JKT\n",
        "JKT = 0\n",
        "for i in range(len(Y)):\n",
        "    JKT += Y[i]**2\n",
        "JKT = JKT - (zigma_values['Y'])**2 / len(Y)\n",
        "JKT"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.854204300Z",
          "start_time": "2023-06-04T13:48:28.455239700Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dsmH5OzplJil",
        "outputId": "ce2b477b-2601-407d-821c-cfaf5132966a"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Menghitung Jumlah Kuadrat Regresi (JKR)\n",
        "\n",
        "---\n",
        "JKR merupakan jumlah kuadrat dari selisih antara nilai variabel dependen yang diprediksi oleh model regresi linear berganda (Y_prediksi) dengan nilai rata-rata dari variabel dependen yang diamati (Ȳ).\n",
        "\n",
        "JKR = ∑ (b[j] * g[j]) - (∑ (y[i]))^2"
      ],
      "metadata": {
        "id": "-NfFof1LKTdl"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "13315.129376087632"
            ]
          },
          "metadata": {},
          "execution_count": 104
        }
      ],
      "source": [
        "# Menghitung JKR\n",
        "JKR = 0\n",
        "for i in range(len(b)):\n",
        "    JKR += b[i] * g[i]\n",
        "JKR = JKR - (zigma_values['Y'])**2 / len(Y)\n",
        "JKR"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.854204300Z",
          "start_time": "2023-06-04T13:48:28.471068400Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "T8SOo7PPlJil",
        "outputId": "74c71248-71e3-402e-e037-1776728a0683"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Menghitung Koefisien Determinasi Darab(R^2)\n",
        "\n",
        "---\n",
        "R^2 menunjukkan proporsi variasai total dalam y yang diterangkan oleh model.\n",
        "\n",
        "\n",
        "**Koefisien determinasi darab**\n",
        ">\n",
        "R^2 = JKR / JKT"
      ],
      "metadata": {
        "collapsed": false,
        "id": "az9jlPnPlJil"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8257716468374465"
            ]
          },
          "metadata": {},
          "execution_count": 105
        }
      ],
      "source": [
        "# Menghitung koefisien determinasi darab (R^2)\n",
        "R2 = JKR / JKT\n",
        "R2"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.880994500Z",
          "start_time": "2023-06-04T13:48:28.486901400Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OkQnQNHXlJil",
        "outputId": "87e769b9-c651-4b46-9009-5952a4f7f4a8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Artinya 82,58% variasi dari variabel dependen (Y) dapat dijelaskan oleh variabel independen (X1, X2, X3, X4, X5) dalam model regresi linear berganda, nilai ini di peroleh ketika semua koefisien dalam model dimasukkan, maka dari itu, kita perlu mengevaluasi lebih lanjut mengenai koefisien yang paling berpengaruh terhadap model dengan menggunakan Stepwise regression"
      ],
      "metadata": {
        "collapsed": false,
        "id": "vGicpv4QlJim"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Pemilihan peubah bebas yang masuk ke dalam model dapat dilakukan melalui beberapa pendekatan:**\n",
        "\n",
        "1. Pendekatan Pemilihan Maju (Forward Selection): Dimulai dengan model yang hanya termasuk satu peubah bebas, dan secara bertahap menambahkan peubah bebas yang memiliki pengaruh yang signifikan berdasarkan uji statistik. Proses ini berlanjut dengan menambahkan peubah satu per satu hingga tidak ada peubah bebas lain yang signifikan yang dapat ditambahkan.\n",
        "\n",
        "2. Pendekatan Penyisihan Mundur (Backward Elimination): Dimulai dengan model yang termasuk semua peubah bebas yang relevan, kemudian secara bertahap menghapus peubah yang memiliki pengaruh yang tidak signifikan berdasarkan uji statistik (misalnya, uji t). Peubah yang memiliki kontribusi yang paling rendah atau tidak signifikan secara statistik dapat dihapus dari model satu per satu hingga hanya tersisa peubah yang signifikan.\n",
        "\n",
        "3. Pendekatan Regresi Bertahap (Stepwise Regression): Menggabungkan pendekatan penyisihan mundur dan pemilihan maju, di mana peubah bebas ditambahkan atau dihapus berdasarkan kriteria statistik seperti nilai p-value atau peningkatan R^2^. Pendekatan ini memungkinkan penambahan dan penghapusan peubah bebas secara iteratif untuk mencapai model yang lebih baik."
      ],
      "metadata": {
        "collapsed": false,
        "id": "tJLQprDglJim"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Metode Regresi Bertahap\n",
        "Dalam melakukan metode regresi bertahap, melibatkan dua langkah utama yaitu Forward Selection dan Backward Elimination. Regresi bertahap merupakan penyempurnaan dari seleksi maju. Dimana peubah yang telah masuk ke model akan diuji lagi apakah tetap berada pada model setelah peubah baru dimasukkan.\n",
        ">\n",
        "Regresi bertahap diperlukan guna memilih dan membangun model regresi yang sederhana dan efisien, hal tersebut dilakukan dengan mengeliminasi variabel yang tidak signifikan. Metode ini membantu dalam menghindari overfitting dan meningkatkan interpretasi model regresi. Kami mengasumsikan menggunakan taraf signifikansi 5% untuk keperluan analisis nilai F"
      ],
      "metadata": {
        "collapsed": false,
        "id": "oaoTh_KXlJim"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Langkah 1\n",
        "\n",
        "---\n",
        "Pada langkah ini akan dibuat persamaan regresi sederhana GDP terhadap 5 perubah bebas. Setelah itu akan didapatkan Jumlah kuadrat regresi dari masing-masing model.\n"
      ],
      "metadata": {
        "id": "wLUIihL4PO5B"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "               R\n",
              "X1   9682.315933\n",
              "X2  12860.575826\n",
              "X3     60.711477\n",
              "X4     72.752881\n",
              "X5    141.090408"
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              "      <th>X1</th>\n",
              "      <td>9682.315933</td>\n",
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              "      <td>12860.575826</td>\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",
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              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 106
        }
      ],
      "source": [
        "# Langkah 1: Pilih peubah yang memberikan R terbesar\n",
        "R = []\n",
        "\n",
        "for var in ['X1', 'X2', 'X3', 'X4', 'X5']:\n",
        "    X = np.array([[1, df[var][i]] for i in range(len(df))]) # Y = B0 + BiXi\n",
        "    b = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Y)\n",
        "    g = X.T.dot(Y)\n",
        "\n",
        "    JKR = 0\n",
        "    for i in range(len(b)):\n",
        "        JKR += b[i] * g[i]\n",
        "    JKR = JKR - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "    R.append(JKR)\n",
        "\n",
        "# Konversikan ke dataframe\n",
        "df_R = pd.DataFrame(R, index=['X1', 'X2', 'X3', 'X4', 'X5'], columns=['R'])\n",
        "df_R"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.914604400Z",
          "start_time": "2023-06-04T13:48:28.512507800Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "0k-7b-mqlJim",
        "outputId": "b799f65d-9464-4fee-a4c9-c414d362faaf"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Memilih Peubah dengan Nilai R Terbesar\n",
        "\n",
        "---\n",
        "Setelah mendapatkan nilai R dari masing-masing peubah, langkah selanjutnya adalah untuk memilih peubah dengan nilai R terbesar untuk diperiksa dengan nilai F Tabel.\n"
      ],
      "metadata": {
        "id": "s8b5O_spQVNg"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "               R\n",
              "X2  12860.575826"
            ],
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>R</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>X2</th>\n",
              "      <td>12860.575826</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-c492c7b9-1521-422b-be9e-25b934b817d1')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
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              "\n",
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              "    }\n",
              "\n",
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              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
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              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-c492c7b9-1521-422b-be9e-25b934b817d1 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-c492c7b9-1521-422b-be9e-25b934b817d1');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 107
        }
      ],
      "source": [
        "# Mengambil nilai R terbesar\n",
        "df_R[df_R['R'] == df_R['R'].max()]"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.968043700Z",
          "start_time": "2023-06-04T13:48:28.561940100Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 81
        },
        "id": "rpj9JnCvlJim",
        "outputId": "36e5df23-5202-4302-c97b-a712198f1241"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Kita mendapatkan bahwa peubah bebas yang memiliki R terbesar adalah X2."
      ],
      "metadata": {
        "collapsed": false,
        "id": "NkV1iQUJlJim"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Mencari nilai s^2 (rataan kuadrat galat untuk model yang memuat X2)\n",
        "X = np.array([[1, df['X2'][i]] for i in range(len(df))]) # Y = B0 + B2X2\n",
        "b = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Y)\n",
        "g = X.T.dot(Y)\n",
        "\n",
        "JKT = 0\n",
        "for i in range(len(Y)):\n",
        "    JKT += Y[i]**2\n",
        "JKT = JKT - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "JKR = 0\n",
        "for i in range(len(b)):\n",
        "    JKR += b[i] * g[i]\n",
        "JKR = JKR - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "JKG = JKT - JKR\n",
        "s2 = JKG / (len(Y) - 2)\n",
        "s2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MbvtzE_6Q-hZ",
        "outputId": "034db0d0-9bfd-4099-8535-4b01047342ca"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "22.20335538570003"
            ]
          },
          "metadata": {},
          "execution_count": 108
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Nilai F Hitung\n",
        "\n",
        "---\n",
        "Setelah didapatkan s^2 maka akan dilakukan perhitungan nilai f hitung. Apabila nilai F hitung telah diketahui maka akan dibandingkan dengan nilai F tabel. Apabila F hitung < F tabel maka peubah tidak masuk ke model."
      ],
      "metadata": {
        "id": "SHYrbUyAi0Aa"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Membandingan dengan nilai f tabel\n",
        "f_hitung = JKR / s2 # R(B2) / s^2\n",
        "f_tabel = stats.f.isf(0.05, 1, len(Y) - 2)\n",
        "\n",
        "if f_hitung > f_tabel:\n",
        "    print('f_hitung =', f_hitung, '>', 'f_tabel =', f_tabel)\n",
        "    print('Maka, X2 masuk ke dalam model')\n",
        "else:\n",
        "    print('f_hitung =', f_hitung, '<', 'f_tabel =', f_tabel)\n",
        "    print('Maka, X2 tidak masuk ke dalam model')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5SXq3HeWRWAt",
        "outputId": "48c4eac3-0c44-41dd-b383-18347a9dec38"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "f_hitung = 579.2176723834069 > f_tabel = 3.905498091187382\n",
            "Maka, X2 masuk ke dalam model\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###Langkah 2\n",
        "\n",
        "---\n",
        "Setelah peubah x2 masuk ke dalam model, maka empat persamaan regresi yang mengandung peubah x2, yaitu (x2,x1), (x2,x3), (x2,x4) dan (x2,x5)akan dicocokan pada langkah ini. Pada langkah ini akan diketahui Jumlah kuadrat regresi untuk keempat persamaan regresi tersebut.\n"
      ],
      "metadata": {
        "id": "JWiJCTaifzLF"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "               R\n",
              "X1_2  298.408107\n",
              "X3_2  115.173818\n",
              "X4_2   46.372963\n",
              "X5_2   10.564431"
            ],
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              "\n",
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              "<style scoped>\n",
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              "\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>R</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>X1_2</th>\n",
              "      <td>298.408107</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X3_2</th>\n",
              "      <td>115.173818</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X4_2</th>\n",
              "      <td>46.372963</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X5_2</th>\n",
              "      <td>10.564431</td>\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",
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              "        }\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 110
        }
      ],
      "source": [
        "# Langkah 2: Pilih peubah yang memberikan peningkatan R terbesar bersama dengan peubah yang telah dipilih sebelumnya\n",
        "Ri_2 = []\n",
        "\n",
        "for var in ['X1', 'X3', 'X4', 'X5']:\n",
        "    X = np.array([[1, df['X2'][i], df[var][i]] for i in range(len(df))]) # Y = B0 + B2X2 + BiXi\n",
        "    b = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Y)\n",
        "    g = X.T.dot(Y)\n",
        "\n",
        "    JKR = 0\n",
        "    for i in range(len(b)):\n",
        "        JKR += b[i] * g[i]\n",
        "    JKR = JKR - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "    Ri_2.append(JKR - R[1]) # R(B2, Bi) - R(B2)\n",
        "\n",
        "# Konversikan ke dataframe\n",
        "df_R2 = pd.DataFrame(Ri_2, index=['X1_2', 'X3_2', 'X4_2', 'X5_2'], columns=['R'])\n",
        "df_R2"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:29.990133100Z",
          "start_time": "2023-06-04T13:48:28.605878700Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 175
        },
        "id": "CfpgaMoSlJim",
        "outputId": "65c7d50f-224b-42f5-de75-b3d860c53c2c"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Memilih Peubah dengan Nilai R Terbesar\n",
        "\n",
        "---\n",
        "Setelah mendapatkan nilai R dari masing-masing peubah, langkah selanjutnya adalah untuk memilih peubah dengan nilai R terbesar untuk diperiksa dengan nilai F Tabel.\n"
      ],
      "metadata": {
        "id": "Cv4VukoEg0s7"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "               R\n",
              "X1_2  298.408107"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-39bf9a85-d4d6-48f3-82ab-2ede3678bad4\">\n",
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              "\n",
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              "        vertical-align: top;\n",
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              "\n",
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              "        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>R</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>X1_2</th>\n",
              "      <td>298.408107</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-39bf9a85-d4d6-48f3-82ab-2ede3678bad4')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
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              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
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              "      gap: 12px;\n",
              "    }\n",
              "\n",
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              "      width: 32px;\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
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              "      fill: #174EA6;\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-39bf9a85-d4d6-48f3-82ab-2ede3678bad4 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-39bf9a85-d4d6-48f3-82ab-2ede3678bad4');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 111
        }
      ],
      "source": [
        "# Mengambil nilai R terbesar\n",
        "df_R2[df_R2['R'] == df_R2['R'].max()]"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.022362300Z",
          "start_time": "2023-06-04T13:48:28.638755200Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 81
        },
        "id": "kwr4ayj0lJin",
        "outputId": "9aa88d26-94d3-42cd-ac3f-c533ed225987"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Kita mendapatkan bahwa peubah bebas yang memiliki peningkatan R terbesar adalah X1.Regresi antara X2 dan X1 menghasilkan s^2 yang baru, yaitu\n",
        ">\n",
        "s^2 = 20.311"
      ],
      "metadata": {
        "collapsed": false,
        "id": "N44SDSYYlJin"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "20.311542017341832"
            ]
          },
          "metadata": {},
          "execution_count": 112
        }
      ],
      "source": [
        "# Mencari nilai s^2 (rataan kuadrat galat untuk model yang memuat X1_2)\n",
        "X = np.array([[1, df['X2'][i], df['X1'][i]] for i in range(len(df))]) # Y = B0 + B2X2 + B1X1\n",
        "b = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Y)\n",
        "g = X.T.dot(Y)\n",
        "\n",
        "JKT = 0\n",
        "for i in range(len(Y)):\n",
        "    JKT += Y[i]**2\n",
        "JKT = JKT - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "JKR = 0\n",
        "for i in range(len(b)):\n",
        "    JKR += b[i] * g[i]\n",
        "JKR = JKR - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "JKG = JKT - JKR\n",
        "s2 = JKG / (len(Y) - 3)\n",
        "s2"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.023361500Z",
          "start_time": "2023-06-04T13:48:28.682792200Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WucmSx79lJin",
        "outputId": "3ba076a8-3ba3-47c4-9dcf-990ce036fe1b"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Perbandingan Nilai F\n",
        "\n",
        "---\n",
        "Setelah didapatkan s^2 maka akan dilakukan perhitungan nilai f hitung. Apabila nilai F hitung telah diketahui maka akan dibandingkan dengan nilai F tabel. Apabila F hitung < F tabel maka peubah tidak masuk ke model."
      ],
      "metadata": {
        "id": "c9OY-vXZk2Ys"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "f_hitung = 14.691553546806942 > f_tabel = 3.9059421464318516\n",
            "Maka, X1_2 masuk ke dalam model\n"
          ]
        }
      ],
      "source": [
        "# Membandingan dengan nilai f tabel\n",
        "f_hitung = (JKR - R[1]) / s2 # R(B1|B2) / s^2\n",
        "f_tabel = stats.f.isf(0.05, 1, len(Y) - 3)\n",
        "\n",
        "if f_hitung > f_tabel:\n",
        "    print('f_hitung =', f_hitung, '>', 'f_tabel =', f_tabel)\n",
        "    print('Maka, X1_2 masuk ke dalam model')\n",
        "else:\n",
        "    print('f_hitung =', f_hitung, '<', 'f_tabel =', f_tabel)\n",
        "    print('Maka, X1_2 tidak masuk ke dalam model')"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.036862500Z",
          "start_time": "2023-06-04T13:48:28.702476Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "60FQYKxWlJir",
        "outputId": "9ff56bce-a7ce-4e6b-d180-bde1670c2904"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Pengujian Ulang\n",
        "\n",
        "-----\n",
        "\n",
        "selanjutnya, perlu diuji apalah peubah X2 masih berarti dalam model jika X1 ada di dalam model. Diperoleh jumlah kuadrat regresi R(β2|β1) = 3476.67"
      ],
      "metadata": {
        "id": "KNs6E-Dq5IEd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Peubah yang telah duluan masuk diuji lagi apakah tetap dalam model setelah dimasukannya peubah baru\n",
        "X = np.array([[1, df['X1'][i], df['X2'][i]] for i in range(len(df))]) # Y = B0 + B1X1 + B2X2\n",
        "b = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Y)\n",
        "g = X.T.dot(Y)\n",
        "\n",
        "JKR = 0\n",
        "for i in range(len(b)):\n",
        "    JKR += b[i] * g[i]\n",
        "JKR = JKR - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "print(JKR - R[0]) # R(B1, B2) - R(B1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YAIGL_lYaeKv",
        "outputId": "7003f9bf-c5f0-40b4-9b07-143566386b5f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "3476.667999386851\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Perbandingan Nilai F\n",
        "\n",
        "-----\n",
        "\n",
        "\n",
        "Setelah didapatkan hasil F hitung, maka akan dilakukan perbandingan nilai dari F hitung dan F tabel. apabila nilai F hitung lebih dari F tabel maka peubah X2 tetap dalam model bersama X1."
      ],
      "metadata": {
        "id": "86ndWAa66QpX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Melakukan perbandingan nilai F hitung dan F tabel\n",
        "f_hitung = (JKR - R[0]) / s2 # R(B2|B1) / s^2\n",
        "f_tabel = stats.f.isf(0.05, 1, len(Y) - 3)\n",
        "\n",
        "if f_hitung > f_tabel:\n",
        "    print('f_hitung =', f_hitung, '>', 'f_tabel =', f_tabel)\n",
        "    print('Maka, X2_1 masuk ke dalam model')\n",
        "else:\n",
        "    print('f_hitung =', f_hitung, '<', 'f_tabel =', f_tabel)\n",
        "    print('Maka, X2_1 tidak masuk ke dalam model')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ntf3kkWSt2Gn",
        "outputId": "2354c35d-d3c5-46aa-9c31-7f8a85db8eb0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "f_hitung = 171.16711259137784 > f_tabel = 3.9059421464318516\n",
            "Maka, X2_1 masuk ke dalam model\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###Langkah 3\n",
        "\n",
        "---\n",
        "Setelah X1 dan X2 masuk ke model, maka akan dihitung Jumlah kuadrat regresi untuk model regresi dengan memasukkan peubah X3, X4, dan X5.\n"
      ],
      "metadata": {
        "id": "6awDThbhk76P"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                R\n",
              "X3_21  118.604284\n",
              "X4_21   61.663052\n",
              "X5_21    4.451365"
            ],
            "text/html": [
              "\n",
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              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "\n",
              "    .dataframe tbody tr th {\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>R</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>X3_21</th>\n",
              "      <td>118.604284</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X4_21</th>\n",
              "      <td>61.663052</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X5_21</th>\n",
              "      <td>4.451365</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
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              "        buttonEl.style.display =\n",
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              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-80f72721-610f-4943-9999-bcefa863fa27');\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",
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              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 116
        }
      ],
      "source": [
        "# Langkah 3: Pilih peubah yang memberikan peningkatan R terbesar bersama dengan peubah yang telah dipilih sebelumnya\n",
        "Ri_21 = []\n",
        "\n",
        "for var in ['X3', 'X4', 'X5']:\n",
        "    X = np.array([[1, df['X2'][i], df['X1'][i], df[var][i]] for i in range(len(df))]) # Y = B0 + B2X2 + B1X1 + BiXi\n",
        "    b = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Y)\n",
        "    g = X.T.dot(Y)\n",
        "\n",
        "    JKR = 0\n",
        "    for i in range(len(b)):\n",
        "        JKR += b[i] * g[i]\n",
        "    JKR = JKR - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "    Ri_21.append(JKR - (R[1] + Ri_2[0])) # R(B2, B1, Bi) - (R(B2, B1) + R(B2))\n",
        "\n",
        "# Konversikan ke dataframe\n",
        "df_R = pd.DataFrame(Ri_21, index=['X3_21', 'X4_21', 'X5_21'], columns=['R'])\n",
        "df_R"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.057875900Z",
          "start_time": "2023-06-04T13:48:28.746149100Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 143
        },
        "id": "fWG_aCnRlJir",
        "outputId": "e4c2dfc1-c4e7-4211-a055-4457713292a2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Memilih Peubah dengan Nilai R Terbesar\n",
        "\n",
        "---\n",
        "Setelah mendapatkan nilai R dari masing-masing peubah, langkah selanjutnya adalah untuk memilih peubah dengan nilai R terbesar untuk diperiksa dengan nilai F Tabel.\n"
      ],
      "metadata": {
        "id": "w_ymLxkTlmnb"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                R\n",
              "X3_21  118.604284"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-b4bc05f6-231a-4303-ab85-58e747426739\">\n",
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              "      <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>R</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>X3_21</th>\n",
              "      <td>118.604284</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-b4bc05f6-231a-4303-ab85-58e747426739')\"\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 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
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              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
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              "\n",
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              "      background-color: #E2EBFA;\n",
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              "      fill: #174EA6;\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-b4bc05f6-231a-4303-ab85-58e747426739 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-b4bc05f6-231a-4303-ab85-58e747426739');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 117
        }
      ],
      "source": [
        "# Mengambil nilai R terbesar\n",
        "df_R[df_R['R'] == df_R['R'].max()]"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.057875900Z",
          "start_time": "2023-06-04T13:48:28.810398Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 81
        },
        "id": "Zn5oD71VlJis",
        "outputId": "c969eab1-4c36-49a3-9659-80e3de2f1f3a"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Kita mendapatkan bahwa peubah bebas yang memiliki peningkatan R terbesar adalah X3.Untuk model regresi dengan memasukkan perubah X3 menghasilkan s^2 yang baru, yaitu\n",
        ">\n",
        "s^2 = 19.63"
      ],
      "metadata": {
        "collapsed": false,
        "id": "NHc6YCailJis"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "19.63366103592105"
            ]
          },
          "metadata": {},
          "execution_count": 118
        }
      ],
      "source": [
        "# Mencari nilai s^2 (rataan kuadrat galat untuk model yang memuat X1_2 dan X3_3)\n",
        "X = np.array([[1, df['X2'][i], df['X1'][i], df['X3'][i]] for i in range(len(df))]) # Y = B2X2 + B1X1 + B3X3\n",
        "b = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Y)\n",
        "g = X.T.dot(Y)\n",
        "\n",
        "#perulangan untuk menghitung JKT\n",
        "JKT = 0\n",
        "for i in range(len(Y)):\n",
        "    JKT += Y[i]**2\n",
        "JKT = JKT - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "#perulangan untuk menghitung JKR\n",
        "JKR = 0\n",
        "for i in range(len(b)):\n",
        "    JKR += b[i] * g[i]\n",
        "JKR = JKR - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "# perhitungan s^2\n",
        "JKG = JKT - JKR\n",
        "s2 = JKG / (len(Y) - 4)\n",
        "s2"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.060865500Z",
          "start_time": "2023-06-04T13:48:28.842182100Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qJ7xQzuSlJis",
        "outputId": "a679fb75-024d-4420-e6b8-d1ad020c4128"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Nilai F Hitung\n",
        "\n",
        "---\n",
        "Setelah didapatkan s^2 maka akan dilakukan perhitungan nilai f hitung. Apabila nilai F hitung telah diketahui maka akan dibandingkan dengan nilai F tabel. Apabila F hitung < F tabel maka peubah tidak masuk ke model."
      ],
      "metadata": {
        "id": "5ZvGY06unb-Q"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "f_hitung = 6.040864416797315 > f_tabel = 3.906392402723093\n",
            "Maka, X3_12 masuk ke dalam model\n"
          ]
        }
      ],
      "source": [
        "# Membandingkan dengan nilai f tabel\n",
        "f_hitung = (JKR - (R[1] + Ri_2[0])) / s2 # R(B3|B2, B1) / s^2\n",
        "f_tabel = stats.f.isf(0.05, 1, len(Y) - 4)\n",
        "\n",
        "if f_hitung > f_tabel:\n",
        "    print('f_hitung =', f_hitung, '>', 'f_tabel =', f_tabel)\n",
        "    print('Maka, X3_12 masuk ke dalam model')\n",
        "else:\n",
        "    print('f_hitung =', f_hitung, '<', 'f_tabel =', f_tabel)\n",
        "    print('Maka, X3_21 tidak masuk ke dalam model')\n"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.060865500Z",
          "start_time": "2023-06-04T13:48:28.896290600Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AY9ktHstlJis",
        "outputId": "718ac550-d0cf-4705-d170-434a7fa0ad37"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Selanjutnya akan diperiksa apakah X1 dan X2 tetap masuk ke model apabila X3 ada di dalam model. Diperoleh jumlah kuadrat R(β1,β2|β3) = 12860.58"
      ],
      "metadata": {
        "id": "kABUoqrL7LMe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Peubah yang telah duluan masuk diuji lagi apakah tetap dalam model setelah dimasukannya peubah baru\n",
        "X = np.array([[1, df['X3'][i], df['X2'][i], df['X1'][i]]for i in range(len(df))]) # Y = B0 + B3X3 + B2X2 + B1X1\n",
        "b = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Y)\n",
        "g = X.T.dot(Y)\n",
        "\n",
        "JKR = 0\n",
        "for i in range(len(b)):\n",
        "    JKR += b[i] * g[i]\n",
        "JKR = JKR - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "print(JKR - (Ri_21[0] + Ri_2[0])) # R(B3, B2, B1) - (R(B3, B2) + R(B3))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jzT7vBm9qgid",
        "outputId": "d7478b37-ca88-45df-e5ff-cff7ed6872d7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "12860.575825606738\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Perbandingan Nilai F\n",
        "\n",
        "-----\n",
        "\n",
        "\n",
        "Setelah didapatkan hasil F hitung, maka akan dilakukan perbandingan nilai dari F hitung dan F tabel. apabila nilai F hitung lebih dari F tabel maka peubah X3 tetap dalam model bersama X1 dan X2."
      ],
      "metadata": {
        "id": "KHtMStXFXFXJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Membandingkan dengan nilai f tabel\n",
        "f_hitung = (JKR - (Ri_21[0] + Ri_2[0])) / s2 # R(B1, B2|B3) / s^2\n",
        "f_tabel = stats.f.isf(0.05, 1, len(Y) - 4)\n",
        "\n",
        "if f_hitung > f_tabel:\n",
        "    print('f_hitung =', f_hitung, '>', 'f_tabel =', f_tabel)\n",
        "    print('Maka, X12_3 masuk ke dalam model')\n",
        "else:\n",
        "    print('f_hitung =', f_hitung, '<', 'f_tabel =', f_tabel)\n",
        "    print('Maka, X12_3 tidak masuk ke dalam model')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pWVtccMcuvkZ",
        "outputId": "7d182f12-2a8f-4915-c671-dfaa7d4d93ac"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "f_hitung = 655.0268848014379 > f_tabel = 3.906392402723093\n",
            "Maka, X12_3 masuk ke dalam model\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###Langkah 4\n",
        "\n",
        "---\n",
        "Setelah X1, X2 dan X3 masuk ke model, maka akan dihitung Jumlah kuadrat regresi untuk model regresi dengan memasukkan peubah X4, dan X5.\n",
        "\n"
      ],
      "metadata": {
        "id": "XSo8Km9qngxL"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "               R\n",
              "X4_213  34.01346\n",
              "X5_213   3.30221"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-53ac9547-b7ba-4ac5-b182-158c78d71f7a\">\n",
              "    <div 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",
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              "\n",
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              "</style>\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>R</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>X4_213</th>\n",
              "      <td>34.01346</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X5_213</th>\n",
              "      <td>3.30221</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-53ac9547-b7ba-4ac5-b182-158c78d71f7a')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
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              "      \n",
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              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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              "  </style>\n",
              "\n",
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              "          document.querySelector('#df-53ac9547-b7ba-4ac5-b182-158c78d71f7a 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-53ac9547-b7ba-4ac5-b182-158c78d71f7a');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 122
        }
      ],
      "source": [
        "# Langkah 4: Pilih peubah yang memberikan peningkatan R terbesar bersama dengan peubah yang telah dipilih sebelumnya\n",
        "Ri_213 = []\n",
        "\n",
        "for var in ['X4', 'X5']:\n",
        "    X = np.array([[1, df['X3'][i], df['X2'][i], df['X1'][i], df[var][i]] for i in range(len(df))]) # Y = B3X3 + B2X2 + B1X1 + BiXi\n",
        "    b = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Y)\n",
        "    g = X.T.dot(Y)\n",
        "\n",
        "    JKR = 0\n",
        "    for i in range(len(b)):\n",
        "        JKR += b[i] * g[i]\n",
        "    JKR = JKR - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "    Ri_213.append(JKR - (R[1] + Ri_2[0] + Ri_21[0])) # R(B3, B2, B1, Bi) - (R(B3, B2, B1) + R(B3, B2) + R(B2))\n",
        "\n",
        "# Konversikan ke dataframe\n",
        "df_R = pd.DataFrame(Ri_213, index=['X4_213', 'X5_213'], columns=['R'])\n",
        "df_R"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.060865500Z",
          "start_time": "2023-06-04T13:48:28.931328Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 112
        },
        "id": "LtSNQz5IlJis",
        "outputId": "4aa5dd6e-427e-4dc4-ffb9-b4c3d07bb80b"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Memilih Peubah dengan Nilai R Terbesar\n",
        "\n",
        "---\n",
        "Setelah mendapatkan nilai R dari masing-masing peubah, langkah selanjutnya adalah untuk memilih peubah dengan nilai R terbesar untuk diperiksa dengan nilai F Tabel.\n"
      ],
      "metadata": {
        "id": "cJD32VDhnzOG"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "               R\n",
              "X4_213  34.01346"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-0cd52f70-cfea-4540-9ad8-ce8d3590d7a3\">\n",
              "    <div 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>R</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>X4_213</th>\n",
              "      <td>34.01346</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-0cd52f70-cfea-4540-9ad8-ce8d3590d7a3')\"\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 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
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              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
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              "      border-radius: 50%;\n",
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              "      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",
              "    [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-0cd52f70-cfea-4540-9ad8-ce8d3590d7a3 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-0cd52f70-cfea-4540-9ad8-ce8d3590d7a3');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 123
        }
      ],
      "source": [
        "# Mengambil nilai R terbesar\n",
        "df_R[df_R['R'] == df_R['R'].max()]"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.061863500Z",
          "start_time": "2023-06-04T13:48:28.996727Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 81
        },
        "id": "tjlmnYQllJis",
        "outputId": "35d93a65-c556-4959-f7df-02e93758c900"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Kita mendapatkan bahwa peubah bebas yang memiliki peningkatan R terbesar adalah X4.\n",
        "Untuk model regresi dengan memasukkan perubah X4 menghasilkan s^2 yang baru, yaitu\n",
        ">\n",
        "s^2 = 19.53"
      ],
      "metadata": {
        "collapsed": false,
        "id": "HTflRO-qlJis"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "19.533801322269838"
            ]
          },
          "metadata": {},
          "execution_count": 124
        }
      ],
      "source": [
        "# Mencari nilai s^2 (rataan kuadrat galat untuk model yang memuat X1_2, X3_3, dan X4_4)\n",
        "X = np.array([[1, df['X4'][i], df['X3'][i], df['X2'][i], df['X1'][i]] for i in range(len(df))]) # Y = B0 + B4X4 + B3X3 + B2X2 + B1X1\n",
        "b = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Y)\n",
        "g = X.T.dot(Y)\n",
        "\n",
        "JKT = 0\n",
        "for i in range(len(Y)):\n",
        "    JKT += Y[i]**2\n",
        "JKT = JKT - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "JKR = 0\n",
        "for i in range(len(b)):\n",
        "    JKR += b[i] * g[i]\n",
        "JKR = JKR - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "JKG = JKT - JKR\n",
        "s2 = JKG / (len(Y) - 5)\n",
        "s2"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.061863500Z",
          "start_time": "2023-06-04T13:48:29.028788100Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uUcEV_wClJit",
        "outputId": "1652c5fc-37f5-4c2d-fd7c-c4f3f74d9c65"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Nilai F Hitung\n",
        "\n",
        "---\n",
        "Setelah didapatkan s^2 maka akan dilakukan perhitungan nilai f hitung. Apabila nilai F hitung telah diketahui maka akan dibandingkan dengan nilai F tabel. Apabila F hitung < F tabel maka peubah tidak masuk ke model."
      ],
      "metadata": {
        "id": "0n-8tCexoHfo"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "f_hitung = 1.7412616848374567 < f_tabel = 3.906848990862648\n",
            "Maka, X4_213 tidak masuk ke dalam model\n"
          ]
        }
      ],
      "source": [
        "# Membandingkan dengan nilai f tabel\n",
        "f_hitung = (JKR - (R[1] + Ri_2[0] + Ri_21[0])) / s2 # R(B4|B3, B2, B1) / s^2\n",
        "f_tabel = stats.f.isf(0.05, 1, len(Y) - 5)\n",
        "\n",
        "if f_hitung > f_tabel:\n",
        "    print('f_hitung =', f_hitung, '>', 'f_tabel =', f_tabel)\n",
        "    print('Maka, X4_213 masuk ke dalam model')\n",
        "else:\n",
        "    print('f_hitung =', f_hitung, '<', 'f_tabel =', f_tabel)\n",
        "    print('Maka, X4_213 tidak masuk ke dalam model')"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.061863500Z",
          "start_time": "2023-06-04T13:48:29.078339800Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4Qa8mPpTlJit",
        "outputId": "fddbcb3f-77ac-42d3-afc5-5ca1f839d7a7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Memasukkan peubah X5\n",
        "\n",
        "----\n",
        "Setelah memasukkan peubah X5 ke dalam model, akan dilakukan pemeriksaan nilai s^2 yang baru untuk dilakukan perhitungan nilai F. Untuk peubah X5 didapatkan nilai s^2 = 19.747"
      ],
      "metadata": {
        "id": "OaW1uhUin-kA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Mencari nilai s^2 (rataan kuadrat galat untuk model yang memuat X1, X2, X3, dan X5)\n",
        "X = np.array([[1, df['X5'][i], df['X3'][i], df['X2'][i], df['X1'][i]] for i in range(len(df))]) # Y = B0 + B5X5 + B3X3 + B2X2 + B1X1\n",
        "b = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Y)\n",
        "g = X.T.dot(Y)\n",
        "\n",
        "JKT = 0\n",
        "for i in range(len(Y)):\n",
        "    JKT += Y[i]**2\n",
        "JKT = JKT - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "JKR = 0\n",
        "for i in range(len(b)):\n",
        "    JKR += b[i] * g[i]\n",
        "JKR = JKR - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "JKG = JKT - JKR\n",
        "s2 = JKG / (len(Y) - 5)\n",
        "s2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mDBWU-IAoYs7",
        "outputId": "72f8a6f4-2dc0-4e02-af41-3ec8879ff5e3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "19.74707389336764"
            ]
          },
          "metadata": {},
          "execution_count": 126
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Nilai F Hitung\n",
        "\n",
        "---\n",
        "Setelah didapatkan s^2 maka akan dilakukan perhitungan nilai f hitung. Apabila nilai F hitung telah diketahui maka akan dibandingkan dengan nilai F tabel. Apabila F hitung < F tabel maka peubah tidak masuk ke model."
      ],
      "metadata": {
        "id": "kC6AzWAirlXB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Membandingkan dengan nilai f tabel\n",
        "f_hitung = (JKR - (R[1] + Ri_2[0] + Ri_21[0])) / s2 # R(B5|B3, B2, B1) / s^2\n",
        "f_tabel = stats.f.isf(0.05, 1, len(Y) - 5)\n",
        "\n",
        "if f_hitung > f_tabel:\n",
        "    print('f_hitung =', f_hitung, '>', 'f_tabel =', f_tabel)\n",
        "    print('Maka, X5_213 masuk ke dalam model')\n",
        "else:\n",
        "    print('f_hitung =', f_hitung, '<', 'f_tabel =', f_tabel)\n",
        "    print('Maka, X5_213 tidak masuk ke dalam model')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-Wmh-C0Mpa_v",
        "outputId": "3a04f35c-c321-448c-bf63-994ea113556f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "f_hitung = 0.16722525987612974 < f_tabel = 3.906848990862648\n",
            "Maka, X5_213 tidak masuk ke dalam model\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Persamaan regresi"
      ],
      "metadata": {
        "collapsed": false,
        "id": "O9K3dd5dlJit"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Model persamaan regresi akhirnya hanya mengandung X1, X2 dan X3 karena nilai f hitung ketika x4 dimasukkan ke dalam model adalah lebih kecil dari f tabel, maka kita akan menggunakan model regresi yang memuat X2, X1_2, dan X3_12 (X2, X1, X3)\n",
        ">\n",
        "Selanjutnya akan ditentukan persamaan taksiran dari model tersebut."
      ],
      "metadata": {
        "collapsed": false,
        "id": "Dzug-HnxlJit"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    Koefisien\n",
              "b0  -2.107608\n",
              "b1   1.195752\n",
              "b2  -0.250806\n",
              "b3   0.061216"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-01c6fe4a-a5d2-4b8d-8328-7aef8e45c312\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Koefisien</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>b0</th>\n",
              "      <td>-2.107608</td>\n",
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              "    <tr>\n",
              "      <th>b1</th>\n",
              "      <td>1.195752</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>b2</th>\n",
              "      <td>-0.250806</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>b3</th>\n",
              "      <td>0.061216</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
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              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
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              "\n",
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              "\n",
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              "\n",
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              "          document.querySelector('#df-01c6fe4a-a5d2-4b8d-8328-7aef8e45c312 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-01c6fe4a-a5d2-4b8d-8328-7aef8e45c312');\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",
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              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 128
        }
      ],
      "source": [
        "# Mencari nilai b\n",
        "X = np.array([[1, df['X2'][i], df['X1'][i], df['X3'][i]] for i in range(len(df))])\n",
        "b = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Y)\n",
        "\n",
        "# Konversikan ke dataframe\n",
        "df_b = pd.DataFrame(b, index=['b0', 'b1', 'b2', 'b3'], columns=['Koefisien'])\n",
        "df_b"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.066480500Z",
          "start_time": "2023-06-04T13:48:29.113508700Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 175
        },
        "id": "Uvw1xz4klJit",
        "outputId": "154552ea-6e0e-4fe1-b166-461ad06fc49e"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Model persamaa regresi akhirnya mengandung peubah X1, X2 dan X3. Persamaan taksiran model tersebut adalah:\n",
        ">\n",
        " ̂y = -2.107608 + 1.195752x1 + -0.250806x2 + 0.061216x3"
      ],
      "metadata": {
        "id": "4UUtYhBzr7Fc"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Koefisien Determinasi\n",
        "\n",
        "----\n",
        "untuk model ini, koefisien determinasi nya adalah: R^2 = 0.8234"
      ],
      "metadata": {
        "id": "X5fsaaXVo7Od"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.823443436287702"
            ]
          },
          "metadata": {},
          "execution_count": 129
        }
      ],
      "source": [
        "# Menghitung R2\n",
        "g = X.T.dot(Y)\n",
        "\n",
        "JKT = 0\n",
        "for i in range(len(Y)):\n",
        "    JKT += Y[i]**2\n",
        "JKT = JKT - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "JKR = 0\n",
        "for i in range(len(b)):\n",
        "    JKR += b[i] * g[i]\n",
        "JKR = JKR - (np.sum(Y)**2) / len(Y)\n",
        "\n",
        "R2 = JKR / JKT\n",
        "R2"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.066480500Z",
          "start_time": "2023-06-04T13:48:29.167559300Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qReeEg_UlJit",
        "outputId": "cf6cdcac-d566-45f7-ffd7-251b66bc5a15"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Artinya, terdapat 82.34% variasi Y yang dapat dijelaskan oleh model regresi yang memuat X2, X1_2, dan X3_12 (X2, X1, X3)."
      ],
      "metadata": {
        "collapsed": false,
        "id": "sN0U3W2LlJit"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## MSE\n",
        "Merupakan salah satu metrik evakuasi yang umum digunakan dalam regresi untuk mengukur prediksi model regresi dengan nilai sebenarnya dari variabel dependen.\n",
        "Secara matematis, rumus MSE dapat dinyatakan sebagai berikut:\n",
        "\n",
        "MSE = (1/n) * Σ(y - y_pred)^2\n",
        "\n",
        "Di mana:\n",
        "\n",
        "n adalah jumlah total observasi dalam dataset.\n",
        ">\n",
        "y adalah nilai observasi sebenarnya dari variabel dependen.\n",
        ">\n",
        "y_pred adalah nilai prediksi yang dihasilkan oleh model regresi."
      ],
      "metadata": {
        "collapsed": false,
        "id": "RnbBnIeglJit"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [],
      "source": [
        "Y_pred = []\n",
        "for i in range(len(df)):\n",
        "    Y_pred.append(b[0] + b[1] * df['X2'][i] + b[2] * df['X1'][i] + b[3] * df['X3'][i])"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.066480500Z",
          "start_time": "2023-06-04T13:48:29.184157700Z"
        },
        "id": "dpdUI7DxlJit"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Skor MSE\n",
        "\n",
        "----\n",
        "Didapatkan skor MSE yang mengindikasikan tingkat kesalahan rata-rata kuadrat antara nilai prediksi dan nilai sebenarnya dari model regresi yang telah dibuat adalah sebesar 19.1066"
      ],
      "metadata": {
        "id": "-mWyBdXYqF9E"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "19.106582887305798"
            ]
          },
          "metadata": {},
          "execution_count": 131
        }
      ],
      "source": [
        "# Mencari nilai MSE\n",
        "def MSE(Y, Y_pred):\n",
        "    return np.sum((Y - Y_pred)**2) / len(Y)\n",
        "\n",
        "MSE = MSE(Y, Y_pred)\n",
        "MSE"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.066480500Z",
          "start_time": "2023-06-04T13:48:29.216670300Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5WPcnAjGlJiu",
        "outputId": "c9d27aa2-b405-4ddf-fc70-4a670d7fe24e"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Visualisasi nilai error\n",
        "\n",
        "\n",
        "---\n",
        "Didapatkan hasil bahwa nilai yang diprekdiksi kurang lebih sama dengan nilai yang sebenarnya. Sehingga diketahui bahwa model yang dibangun efektif dalam melakukan prediksi nilai\n"
      ],
      "metadata": {
        "id": "0uu6lBOWrxJC"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f7377b82e60>"
            ]
          },
          "metadata": {},
          "execution_count": 132
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Membuat plot error MSE\n",
        "plt.figure(figsize=(10, 5))\n",
        "plt.plot(Y, label='Y')\n",
        "plt.plot(Y_pred, label='Y_pred')\n",
        "plt.legend()"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2023-06-04T13:48:30.887623200Z",
          "start_time": "2023-06-04T13:48:29.245314300Z"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 462
        },
        "id": "ydewmv_IlJiu",
        "outputId": "f4380afb-4644-4028-bee7-b73515bd9f4a"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Kesimpulan\n",
        "1. Variabel independen yang masuk ke model antara lain: X1 (Export), X2 (Import), dan X3 (Industrial production growth rate)\n",
        "2. Variabel X1 (Export), X2 (Import), dan X3 (Industrial production growth rate) memiliki hubungan yang signifikan dengan variabel dependen Y (GDP). Dalam model regresi, ketiga variabel ini memiliki pengaruh yang cukup penting terhadap perubahan nilai GDP pada suatu negara.\n",
        "3. Variabel independen X4 (Investment) dan X5 (Unemployment rate) tidak memiliki pengaruh signifikan dalam menjelaskan variasi nilai GDP dalam model regresi ini."
      ],
      "metadata": {
        "id": "GFmIAjgNsJvO"
      }
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.11.0"
    },
    "colab": {
      "provenance": [],
      "toc_visible": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}