Linear_Regression.ipynb

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        "<a href=\"https://colab.research.google.com/github/Demon-Sheriff/Linear-Alg_ML_fs/blob/master/Linear_Regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "metadata": {
        "id": "gXyA0-UBTlj3"
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      "source": [
        "# Implementing linear regression from scratch using gradient descent."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# import the libraries for data preprocessing...\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import seaborn as sns\n",
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "N_AoEbZzTxhx"
      },
      "execution_count": 3,
      "outputs": []
    },
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      "cell_type": "code",
      "source": [
        "import kagglehub\n",
        "\n",
        "# Download latest version\n",
        "path = kagglehub.dataset_download(\"camnugent/california-housing-prices\")\n",
        "\n",
        "print(\"Path to dataset files:\", path)"
      ],
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        "outputId": "6dc5cfd3-6ab7-4d5f-b694-55c720626d97"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Warning: Looks like you're using an outdated `kagglehub` version, please consider updating (latest version: 0.3.4)\n",
            "Downloading from https://www.kaggle.com/api/v1/datasets/download/camnugent/california-housing-prices?dataset_version_number=1...\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 400k/400k [00:00<00:00, 62.1MB/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting files...\n",
            "Path to dataset files: /root/.cache/kagglehub/datasets/camnugent/california-housing-prices/versions/1\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\n"
          ]
        }
      ]
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      "cell_type": "code",
      "source": [
        "path = '/content/sample_data/california_housing_train.csv'\n",
        "df = pd.read_csv(path)\n",
        "df.head()\n",
        "\n",
        "# load the testing data\n",
        "test_path = '/content/sample_data/california_housing_test.csv'\n",
        "test_df = pd.read_csv(test_path)\n",
        "test_df.head()"
      ],
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      "execution_count": 5,
      "outputs": [
        {
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          "data": {
            "text/plain": [
              "   longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
              "0    -122.05     37.37                27.0       3885.0           661.0   \n",
              "1    -118.30     34.26                43.0       1510.0           310.0   \n",
              "2    -117.81     33.78                27.0       3589.0           507.0   \n",
              "3    -118.36     33.82                28.0         67.0            15.0   \n",
              "4    -119.67     36.33                19.0       1241.0           244.0   \n",
              "\n",
              "   population  households  median_income  median_house_value  \n",
              "0      1537.0       606.0         6.6085            344700.0  \n",
              "1       809.0       277.0         3.5990            176500.0  \n",
              "2      1484.0       495.0         5.7934            270500.0  \n",
              "3        49.0        11.0         6.1359            330000.0  \n",
              "4       850.0       237.0         2.9375             81700.0  "
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              "      <th></th>\n",
              "      <th>longitude</th>\n",
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              "      <td>37.37</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-118.30</td>\n",
              "      <td>34.26</td>\n",
              "      <td>43.0</td>\n",
              "      <td>1510.0</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
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              "      <td>6.1359</td>\n",
              "      <td>330000.0</td>\n",
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              "      <th>4</th>\n",
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              "      <td>36.33</td>\n",
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              "summary": "{\n  \"name\": \"test_df\",\n  \"rows\": 3000,\n  \"fields\": [\n    {\n      \"column\": \"longitude\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.9949362939550161,\n        \"min\": -124.18,\n        \"max\": -114.49,\n        \"num_unique_values\": 607,\n        \"samples\": [\n          -121.15,\n          -121.46,\n          -121.02\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"latitude\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2.1296695233438325,\n        \"min\": 32.56,\n        \"max\": 41.92,\n        \"num_unique_values\": 587,\n        \"samples\": [\n          40.17,\n          33.69,\n          39.61\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"housing_median_age\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 12.555395554955755,\n        \"min\": 1.0,\n        \"max\": 52.0,\n        \"num_unique_values\": 52,\n        \"samples\": [\n          14.0,\n          49.0,\n          7.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"total_rooms\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2155.59333162558,\n        \"min\": 6.0,\n        \"max\": 30450.0,\n        \"num_unique_values\": 2215,\n        \"samples\": [\n          1961.0,\n          1807.0,\n          680.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"total_bedrooms\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 415.6543681363232,\n        \"min\": 2.0,\n        \"max\": 5419.0,\n        \"num_unique_values\": 1055,\n        \"samples\": [\n          532.0,\n          764.0,\n          2162.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"population\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1030.5430124122422,\n        \"min\": 5.0,\n        \"max\": 11935.0,\n        \"num_unique_values\": 1802,\n        \"samples\": [\n          947.0,\n          1140.0,\n          2019.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"households\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 365.42270980552604,\n        \"min\": 2.0,\n        \"max\": 4930.0,\n        \"num_unique_values\": 1026,\n        \"samples\": [\n          646.0,\n          629.0,\n          504.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"median_income\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.854511729691481,\n        \"min\": 0.4999,\n        \"max\": 15.0001,\n        \"num_unique_values\": 2578,\n        \"samples\": [\n          1.725,\n          0.7403,\n          2.6964\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"median_house_value\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 113119.68746964433,\n        \"min\": 22500.0,\n        \"max\": 500001.0,\n        \"num_unique_values\": 1784,\n        \"samples\": [\n          71900.0,\n          63000.0,\n          115800.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
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          "metadata": {},
          "execution_count": 5
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    {
      "cell_type": "code",
      "source": [
        "# some feature engineering...\n",
        "df.describe()"
      ],
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          "height": 300
        },
        "id": "0GmXWfm1YQuR",
        "outputId": "34cdbc93-c045-422d-e0eb-6255741a3740"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "          longitude      latitude  housing_median_age   total_rooms  \\\n",
              "count  17000.000000  17000.000000        17000.000000  17000.000000   \n",
              "mean    -119.562108     35.625225           28.589353   2643.664412   \n",
              "std        2.005166      2.137340           12.586937   2179.947071   \n",
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              "max     -114.310000     41.950000           52.000000  37937.000000   \n",
              "\n",
              "       total_bedrooms    population    households  median_income  \\\n",
              "count    17000.000000  17000.000000  17000.000000   17000.000000   \n",
              "mean       539.410824   1429.573941    501.221941       3.883578   \n",
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              "      <td>1.000000</td>\n",
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              "      <td>0.499900</td>\n",
              "      <td>14999.000000</td>\n",
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              "      <th>25%</th>\n",
              "      <td>-121.790000</td>\n",
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              "      <td>1167.000000</td>\n",
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              "      <td>648.250000</td>\n",
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              "summary": "{\n  \"name\": \"df\",\n  \"rows\": 8,\n  \"fields\": [\n    {\n      \"column\": \"longitude\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 6046.6451651071675,\n        \"min\": -124.35,\n        \"max\": 17000.0,\n        \"num_unique_values\": 8,\n        \"samples\": [\n          -119.5621082352941,\n          -118.49,\n          17000.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"latitude\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 5999.40166383228,\n        \"min\": 2.1373397946570734,\n        \"max\": 17000.0,\n        \"num_unique_values\": 8,\n        \"samples\": [\n          35.62522470588235,\n          34.25,\n          17000.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"housing_median_age\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 6001.428368089024,\n        \"min\": 1.0,\n        \"max\": 17000.0,\n        \"num_unique_values\": 8,\n        \"samples\": [\n          28.58935294117647,\n          29.0,\n          17000.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"total_rooms\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 13113.353227786365,\n        \"min\": 2.0,\n        \"max\": 37937.0,\n        \"num_unique_values\": 8,\n        \"samples\": [\n          2643.664411764706,\n          2127.0,\n          17000.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"total_bedrooms\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 5959.238771737063,\n        \"min\": 1.0,\n        \"max\": 17000.0,\n        \"num_unique_values\": 8,\n        \"samples\": [\n          539.4108235294118,\n          434.0,\n          17000.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"population\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 12740.640658201448,\n        \"min\": 3.0,\n        \"max\": 35682.0,\n        \"num_unique_values\": 8,\n        \"samples\": [\n          1429.5739411764705,\n          1167.0,\n          17000.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"households\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 5942.738122392389,\n        \"min\": 1.0,\n        \"max\": 17000.0,\n        \"num_unique_values\": 8,\n        \"samples\": [\n          501.2219411764706,\n          409.0,\n          17000.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"median_income\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 6008.784464952051,\n        \"min\": 0.4999,\n        \"max\": 17000.0,\n        \"num_unique_values\": 8,\n        \"samples\": [\n          3.8835781000000007,\n          3.5446,\n          17000.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"median_house_value\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 156700.95757149634,\n        \"min\": 14999.0,\n        \"max\": 500001.0,\n        \"num_unique_values\": 8,\n        \"samples\": [\n          207300.91235294117,\n          180400.0,\n          17000.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
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          },
          "metadata": {},
          "execution_count": 8
        }
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    },
    {
      "cell_type": "code",
      "source": [
        "df.isna().sum()"
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          "height": 366
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        "id": "Mxa_hMNfY976",
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      },
      "execution_count": 10,
      "outputs": [
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          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "longitude             0\n",
              "latitude              0\n",
              "housing_median_age    0\n",
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              "population            0\n",
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              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>households</th>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>median_income</th>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>median_house_value</th>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div><br><label><b>dtype:</b> int64</label>"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# The data looks good with no null values"
      ],
      "metadata": {
        "id": "IK5BsqRDZEwm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# selecting the target and segregating it from the features.\n",
        "y = df['median_house_value']\n",
        "X = df.drop('median_house_value', axis=1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "id": "OkO6QGmnZL2U",
        "outputId": "af7783f2-6d3b-4a40-e81e-bc0091962794"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
              "0        -114.31     34.19                15.0       5612.0          1283.0   \n",
              "1        -114.47     34.40                19.0       7650.0          1901.0   \n",
              "2        -114.56     33.69                17.0        720.0           174.0   \n",
              "3        -114.57     33.64                14.0       1501.0           337.0   \n",
              "4        -114.57     33.57                20.0       1454.0           326.0   \n",
              "...          ...       ...                 ...          ...             ...   \n",
              "16995    -124.26     40.58                52.0       2217.0           394.0   \n",
              "16996    -124.27     40.69                36.0       2349.0           528.0   \n",
              "16997    -124.30     41.84                17.0       2677.0           531.0   \n",
              "16998    -124.30     41.80                19.0       2672.0           552.0   \n",
              "16999    -124.35     40.54                52.0       1820.0           300.0   \n",
              "\n",
              "       population  households  median_income  \n",
              "0          1015.0       472.0         1.4936  \n",
              "1          1129.0       463.0         1.8200  \n",
              "2           333.0       117.0         1.6509  \n",
              "3           515.0       226.0         3.1917  \n",
              "4           624.0       262.0         1.9250  \n",
              "...           ...         ...            ...  \n",
              "16995       907.0       369.0         2.3571  \n",
              "16996      1194.0       465.0         2.5179  \n",
              "16997      1244.0       456.0         3.0313  \n",
              "16998      1298.0       478.0         1.9797  \n",
              "16999       806.0       270.0         3.0147  \n",
              "\n",
              "[17000 rows x 8 columns]"
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              "      <th></th>\n",
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              "      <td>34.19</td>\n",
              "      <td>15.0</td>\n",
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              "      <td>1283.0</td>\n",
              "      <td>1015.0</td>\n",
              "      <td>472.0</td>\n",
              "      <td>1.4936</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-114.47</td>\n",
              "      <td>34.40</td>\n",
              "      <td>19.0</td>\n",
              "      <td>7650.0</td>\n",
              "      <td>1901.0</td>\n",
              "      <td>1129.0</td>\n",
              "      <td>463.0</td>\n",
              "      <td>1.8200</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-114.56</td>\n",
              "      <td>33.69</td>\n",
              "      <td>17.0</td>\n",
              "      <td>720.0</td>\n",
              "      <td>174.0</td>\n",
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              "      <td>117.0</td>\n",
              "      <td>1.6509</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-114.57</td>\n",
              "      <td>33.64</td>\n",
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              "      <td>1501.0</td>\n",
              "      <td>337.0</td>\n",
              "      <td>515.0</td>\n",
              "      <td>226.0</td>\n",
              "      <td>3.1917</td>\n",
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              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-114.57</td>\n",
              "      <td>33.57</td>\n",
              "      <td>20.0</td>\n",
              "      <td>1454.0</td>\n",
              "      <td>326.0</td>\n",
              "      <td>624.0</td>\n",
              "      <td>262.0</td>\n",
              "      <td>1.9250</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
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              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
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              "      <th>16995</th>\n",
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              "      <td>52.0</td>\n",
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              "      <td>394.0</td>\n",
              "      <td>907.0</td>\n",
              "      <td>369.0</td>\n",
              "      <td>2.3571</td>\n",
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              "      <td>40.69</td>\n",
              "      <td>36.0</td>\n",
              "      <td>2349.0</td>\n",
              "      <td>528.0</td>\n",
              "      <td>1194.0</td>\n",
              "      <td>465.0</td>\n",
              "      <td>2.5179</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16997</th>\n",
              "      <td>-124.30</td>\n",
              "      <td>41.84</td>\n",
              "      <td>17.0</td>\n",
              "      <td>2677.0</td>\n",
              "      <td>531.0</td>\n",
              "      <td>1244.0</td>\n",
              "      <td>456.0</td>\n",
              "      <td>3.0313</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16998</th>\n",
              "      <td>-124.30</td>\n",
              "      <td>41.80</td>\n",
              "      <td>19.0</td>\n",
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              "      <td>478.0</td>\n",
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              "    <tr>\n",
              "      <th>16999</th>\n",
              "      <td>-124.35</td>\n",
              "      <td>40.54</td>\n",
              "      <td>52.0</td>\n",
              "      <td>1820.0</td>\n",
              "      <td>300.0</td>\n",
              "      <td>806.0</td>\n",
              "      <td>270.0</td>\n",
              "      <td>3.0147</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>17000 rows × 8 columns</p>\n",
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              "type": "dataframe",
              "variable_name": "X",
              "summary": "{\n  \"name\": \"X\",\n  \"rows\": 17000,\n  \"fields\": [\n    {\n      \"column\": \"longitude\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2.005166408426173,\n        \"min\": -124.35,\n        \"max\": -114.31,\n        \"num_unique_values\": 827,\n        \"samples\": [\n          -117.56,\n          -123.32,\n          -118.26\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"latitude\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2.1373397946570734,\n        \"min\": 32.54,\n        \"max\": 41.95,\n        \"num_unique_values\": 840,\n        \"samples\": [\n          38.44,\n          40.79,\n          32.69\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"housing_median_age\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 12.586936981660335,\n        \"min\": 1.0,\n        \"max\": 52.0,\n        \"num_unique_values\": 52,\n        \"samples\": [\n          23.0,\n          52.0,\n          47.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"total_rooms\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2179.947071452768,\n        \"min\": 2.0,\n        \"max\": 37937.0,\n        \"num_unique_values\": 5533,\n        \"samples\": [\n          3564.0,\n          6955.0,\n          5451.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"total_bedrooms\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 421.49945157986514,\n        \"min\": 1.0,\n        \"max\": 6445.0,\n        \"num_unique_values\": 1848,\n        \"samples\": [\n          729.0,\n          719.0,\n          2075.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"population\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1147.852959159525,\n        \"min\": 3.0,\n        \"max\": 35682.0,\n        \"num_unique_values\": 3683,\n        \"samples\": [\n          249.0,\n          1735.0,\n          235.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"households\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 384.52084085590013,\n        \"min\": 1.0,\n        \"max\": 6082.0,\n        \"num_unique_values\": 1740,\n        \"samples\": [\n          390.0,\n          1089.0,\n          1351.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"median_income\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.908156518379093,\n        \"min\": 0.4999,\n        \"max\": 15.0001,\n        \"num_unique_values\": 11175,\n        \"samples\": [\n          7.2655,\n          5.6293,\n          4.2262\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.model_selection import train_test_split"
      ],
      "metadata": {
        "id": "dRSuT0u1W74d"
      },
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# so first lets start coding up linear regression using gradient descent..."
      ],
      "metadata": {
        "id": "AsKuoHaKVFsi"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**The basic idea is to select some `num_iterations` which is basically jargon for `epocs` in ML lingo and keep minimising the cost function...**\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ],
      "metadata": {
        "id": "Cp_cZSKJVkZ0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**The cost function that we are going up with is standard `MSE` function and the learning rate `α` which is our hyperparameter (something that we set ourselves)**\n",
        "\n"
      ],
      "metadata": {
        "id": "pCo95r6CWHE-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# But we will need a gradient descent function too...\n",
        "\n",
        "# Initialize parameters\n",
        "def initialize_parameters(n_features):\n",
        "    weights = np.zeros(n_features)\n",
        "    bias = 0\n",
        "    return weights, bias\n",
        "\n",
        "# Predict function\n",
        "def predict(X, weights, bias):\n",
        "    return np.dot(X, weights) + bias\n",
        "\n",
        "# Cost function (Mean Squared Error)\n",
        "def compute_cost(y, y_pred):\n",
        "    m = len(y)\n",
        "    cost = (1 / (2 * m)) * np.sum((y_pred - y) ** 2)\n",
        "    return cost\n",
        "\n",
        "# Gradient Descent\n",
        "def gradient_descent(X, y, weights, bias, learning_rate, epochs):\n",
        "    m = len(y)\n",
        "    for epoch in range(epochs):\n",
        "        # Make predictions\n",
        "        y_pred = predict(X, weights, bias)\n",
        "\n",
        "        # Calculate gradients\n",
        "        dw = (1 / m) * np.dot(X.T, (y_pred - y))\n",
        "        db = (1 / m) * np.sum(y_pred - y)\n",
        "\n",
        "        # Update parameters\n",
        "        weights -= learning_rate * dw\n",
        "        bias -= learning_rate * db\n",
        "\n",
        "        # Optional: Calculate cost to monitor progress\n",
        "        if epoch % 100 == 0:  # adjust frequency as desired\n",
        "            cost = compute_cost(y, y_pred)\n",
        "            print(f\"Epoch {epoch}, Cost: {cost}\")\n",
        "\n",
        "    return weights, bias\n"
      ],
      "metadata": {
        "id": "WdihfuazhJR1"
      },
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "![image.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "4Cy1-AqYfGWh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# okay here we go..\n",
        "\n",
        "def linear_regression(X, y, num_iterations = 1000, learning_rate = 0.01):\n",
        "\n",
        "  # start off with w vector as 0 vector\n",
        "  w = np.zeros(X.shape[1])\n",
        "  # start off with the bias as 0 (scalar value)\n",
        "  b = 0\n",
        "\n",
        "  # convert X into numpy array for vectorized operations.\n",
        "  X = X.values\n",
        "  y = y.values # I AM NOT SURE AS TO WHY THIS STEP IS BEING DONE... YET\n",
        "\n",
        "  n = len(y)\n",
        "\n",
        "  for _ in range(num_iterations):\n",
        "\n",
        "    # calculate the error -> how do we do that ? well it is expected val - predicted value\n",
        "    y_pred = predict(X, w, b) # predicted value\n",
        "    errors = (y - y_pred) ** 2\n",
        "\n",
        "    # update w and b by calculating w_gradient and b_gradient respectively.\n",
        "    w_gradient = np.dot(X.T, errors) * (1/n)\n",
        "    b_gradient = np.mean(errors)\n",
        "\n",
        "    # update step\n",
        "    w -= learning_rate * w_gradient\n",
        "    b -= learning_rate * b_gradient\n",
        "\n",
        "    # calculate cost to monitor progress\n",
        "    if num_iterations % 50 == 0:  # adjust frequency as desired\n",
        "        cost = compute_cost(y, y_pred)\n",
        "        print(f\"epoch {num_iterations}, Cost: {cost}\")\n",
        "\n",
        "  print(f\"Final weights: {w}\")\n",
        "  print(f\"Final bias: {b}\")\n",
        "  return w, b\n"
      ],
      "metadata": {
        "id": "-6N99ngJWEnl"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# moment of truth...\n"
      ],
      "metadata": {
        "id": "mHB0isYCaQ2N"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}