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February 19, 2023 06:02
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Linear regression - Coefficient estimates
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| " Unnamed: 0 TV radio newspaper sales\n", | |
| "0 1 230.1 37.8 69.2 22.1\n", | |
| "1 2 44.5 39.3 45.1 10.4\n", | |
| "2 3 17.2 45.9 69.3 9.3\n", | |
| "3 4 151.5 41.3 58.5 18.5\n", | |
| "4 5 180.8 10.8 58.4 12.9\n", | |
| ".. ... ... ... ... ...\n", | |
| "195 196 38.2 3.7 13.8 7.6\n", | |
| "196 197 94.2 4.9 8.1 9.7\n", | |
| "197 198 177.0 9.3 6.4 12.8\n", | |
| "198 199 283.6 42.0 66.2 25.5\n", | |
| "199 200 232.1 8.6 8.7 13.4\n", | |
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| " <th></th>\n", | |
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| " <th>TV</th>\n", | |
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| " <th>0</th>\n", | |
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| " <th>1</th>\n", | |
| " <td>2</td>\n", | |
| " <td>44.5</td>\n", | |
| " <td>39.3</td>\n", | |
| " <td>45.1</td>\n", | |
| " <td>10.4</td>\n", | |
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| " <tr>\n", | |
| " <th>2</th>\n", | |
| " <td>3</td>\n", | |
| " <td>17.2</td>\n", | |
| " <td>45.9</td>\n", | |
| " <td>69.3</td>\n", | |
| " <td>9.3</td>\n", | |
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| " <tr>\n", | |
| " <th>3</th>\n", | |
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| " <td>151.5</td>\n", | |
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| " <th>4</th>\n", | |
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| " <td>180.8</td>\n", | |
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| " <th>195</th>\n", | |
| " <td>196</td>\n", | |
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| " <td>12.8</td>\n", | |
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| " <th>198</th>\n", | |
| " <td>199</td>\n", | |
| " <td>283.6</td>\n", | |
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| " <td>25.5</td>\n", | |
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| "metadata": {}, | |
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| "source": [ | |
| "import pandas as pd\n", | |
| "\n", | |
| "data = pd.read_csv('https://www.statlearning.com/s/Advertising.csv')\n", | |
| "\n", | |
| "data" | |
| ] | |
| }, | |
| { | |
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| "source": [ | |
| "X = data['TV']\n", | |
| "\n", | |
| "Y = data['sales']\n", | |
| "\n", | |
| "X.mean()" | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "Gpkb9hZfCa7M", | |
| "outputId": "252b7aba-a3a3-44e4-9ec9-6d5a3f6f769f" | |
| }, | |
| "execution_count": 68, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "147.0425" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 68 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "#Linear regression\n", | |
| "\n", | |
| "## Coefficient estimates\n", | |
| "\n", | |
| "" | |
| ], | |
| "metadata": { | |
| "id": "4higIj6GObKs" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "def beta1(x, y):\n", | |
| " mean_x = X.mean()\n", | |
| " mean_y = Y.mean()\n", | |
| " return ((X - mean_x) * (Y - mean_y)).sum() / ((X - mean_x) ** 2).sum()\n", | |
| "\n", | |
| "def beta0(X, Y):\n", | |
| " return Y.mean() - beta1(X, Y) * X.mean()\n", | |
| "\n", | |
| "print('b0 = ', beta0(X, Y))\n", | |
| "print('b1 = ', beta1(X, Y))\n" | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "JaFhhfKWJHja", | |
| "outputId": "64bf6dcb-eed4-4469-df60-0315563db22c" | |
| }, | |
| "execution_count": 74, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "b0 = 7.0325935491276965\n", | |
| "b1 = 0.047536640433019736\n" | |
| ] | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "b0 = beta0(X, Y)\n", | |
| "b1 = beta1(X, Y)\n", | |
| "\n", | |
| "sales = b0 + b1 * X\n", | |
| "\n", | |
| "sales" | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "WUcDBTceNWtn", | |
| "outputId": "5d19ca7c-f133-463e-88b8-7035797c509f" | |
| }, | |
| "execution_count": 70, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "0 17.970775\n", | |
| "1 9.147974\n", | |
| "2 7.850224\n", | |
| "3 14.234395\n", | |
| "4 15.627218\n", | |
| " ... \n", | |
| "195 8.848493\n", | |
| "196 11.510545\n", | |
| "197 15.446579\n", | |
| "198 20.513985\n", | |
| "199 18.065848\n", | |
| "Name: TV, Length: 200, dtype: float64" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 70 | |
| } | |
| ] | |
| } | |
| ] | |
| } |
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