linear_regression_by_kirshna.ipynb

{
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  {
   "cell_type": "code",
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   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from sklearn.datasets import load_boston\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\Lenovo\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\sklearn\\utils\\deprecation.py:87: FutureWarning: Function load_boston is deprecated; `load_boston` is deprecated in 1.0 and will be removed in 1.2.\n",
      "\n",
      "    The Boston housing prices dataset has an ethical problem. You can refer to\n",
      "    the documentation of this function for further details.\n",
      "\n",
      "    The scikit-learn maintainers therefore strongly discourage the use of this\n",
      "    dataset unless the purpose of the code is to study and educate about\n",
      "    ethical issues in data science and machine learning.\n",
      "\n",
      "    In this special case, you can fetch the dataset from the original\n",
      "    source::\n",
      "\n",
      "        import pandas as pd\n",
      "        import numpy as np\n",
      "\n",
      "        data_url = \"http://lib.stat.cmu.edu/datasets/boston\"\n",
      "        raw_df = pd.read_csv(data_url, sep=\"\\s+\", skiprows=22, header=None)\n",
      "        data = np.hstack([raw_df.values[::2, :], raw_df.values[1::2, :2]])\n",
      "        target = raw_df.values[1::2, 2]\n",
      "\n",
      "    Alternative datasets include the California housing dataset (i.e.\n",
      "    :func:`~sklearn.datasets.fetch_california_housing`) and the Ames housing\n",
      "    dataset. You can load the datasets as follows::\n",
      "\n",
      "        from sklearn.datasets import fetch_california_housing\n",
      "        housing = fetch_california_housing()\n",
      "\n",
      "    for the California housing dataset and::\n",
      "\n",
      "        from sklearn.datasets import fetch_openml\n",
      "        housing = fetch_openml(name=\"house_prices\", as_frame=True)\n",
      "\n",
      "    for the Ames housing dataset.\n",
      "  warnings.warn(msg, category=FutureWarning)\n"
     ]
    },
    {
     "data": {
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       "{'data': array([[6.3200e-03, 1.8000e+01, 2.3100e+00, ..., 1.5300e+01, 3.9690e+02,\n",
       "         4.9800e+00],\n",
       "        [2.7310e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9690e+02,\n",
       "         9.1400e+00],\n",
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       "         4.0300e+00],\n",
       "        ...,\n",
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       "         5.6400e+00],\n",
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       "         6.4800e+00],\n",
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       "         7.8800e+00]]),\n",
       " 'target': array([24. , 21.6, 34.7, 33.4, 36.2, 28.7, 22.9, 27.1, 16.5, 18.9, 15. ,\n",
       "        18.9, 21.7, 20.4, 18.2, 19.9, 23.1, 17.5, 20.2, 18.2, 13.6, 19.6,\n",
       "        15.2, 14.5, 15.6, 13.9, 16.6, 14.8, 18.4, 21. , 12.7, 14.5, 13.2,\n",
       "        13.1, 13.5, 18.9, 20. , 21. , 24.7, 30.8, 34.9, 26.6, 25.3, 24.7,\n",
       "        21.2, 19.3, 20. , 16.6, 14.4, 19.4, 19.7, 20.5, 25. , 23.4, 18.9,\n",
       "        35.4, 24.7, 31.6, 23.3, 19.6, 18.7, 16. , 22.2, 25. , 33. , 23.5,\n",
       "        19.4, 22. , 17.4, 20.9, 24.2, 21.7, 22.8, 23.4, 24.1, 21.4, 20. ,\n",
       "        20.8, 21.2, 20.3, 28. , 23.9, 24.8, 22.9, 23.9, 26.6, 22.5, 22.2,\n",
       "        23.6, 28.7, 22.6, 22. , 22.9, 25. , 20.6, 28.4, 21.4, 38.7, 43.8,\n",
       "        33.2, 27.5, 26.5, 18.6, 19.3, 20.1, 19.5, 19.5, 20.4, 19.8, 19.4,\n",
       "        21.7, 22.8, 18.8, 18.7, 18.5, 18.3, 21.2, 19.2, 20.4, 19.3, 22. ,\n",
       "        20.3, 20.5, 17.3, 18.8, 21.4, 15.7, 16.2, 18. , 14.3, 19.2, 19.6,\n",
       "        23. , 18.4, 15.6, 18.1, 17.4, 17.1, 13.3, 17.8, 14. , 14.4, 13.4,\n",
       "        15.6, 11.8, 13.8, 15.6, 14.6, 17.8, 15.4, 21.5, 19.6, 15.3, 19.4,\n",
       "        17. , 15.6, 13.1, 41.3, 24.3, 23.3, 27. , 50. , 50. , 50. , 22.7,\n",
       "        25. , 50. , 23.8, 23.8, 22.3, 17.4, 19.1, 23.1, 23.6, 22.6, 29.4,\n",
       "        23.2, 24.6, 29.9, 37.2, 39.8, 36.2, 37.9, 32.5, 26.4, 29.6, 50. ,\n",
       "        32. , 29.8, 34.9, 37. , 30.5, 36.4, 31.1, 29.1, 50. , 33.3, 30.3,\n",
       "        34.6, 34.9, 32.9, 24.1, 42.3, 48.5, 50. , 22.6, 24.4, 22.5, 24.4,\n",
       "        20. , 21.7, 19.3, 22.4, 28.1, 23.7, 25. , 23.3, 28.7, 21.5, 23. ,\n",
       "        26.7, 21.7, 27.5, 30.1, 44.8, 50. , 37.6, 31.6, 46.7, 31.5, 24.3,\n",
       "        31.7, 41.7, 48.3, 29. , 24. , 25.1, 31.5, 23.7, 23.3, 22. , 20.1,\n",
       "        22.2, 23.7, 17.6, 18.5, 24.3, 20.5, 24.5, 26.2, 24.4, 24.8, 29.6,\n",
       "        42.8, 21.9, 20.9, 44. , 50. , 36. , 30.1, 33.8, 43.1, 48.8, 31. ,\n",
       "        36.5, 22.8, 30.7, 50. , 43.5, 20.7, 21.1, 25.2, 24.4, 35.2, 32.4,\n",
       "        32. , 33.2, 33.1, 29.1, 35.1, 45.4, 35.4, 46. , 50. , 32.2, 22. ,\n",
       "        20.1, 23.2, 22.3, 24.8, 28.5, 37.3, 27.9, 23.9, 21.7, 28.6, 27.1,\n",
       "        20.3, 22.5, 29. , 24.8, 22. , 26.4, 33.1, 36.1, 28.4, 33.4, 28.2,\n",
       "        22.8, 20.3, 16.1, 22.1, 19.4, 21.6, 23.8, 16.2, 17.8, 19.8, 23.1,\n",
       "        21. , 23.8, 23.1, 20.4, 18.5, 25. , 24.6, 23. , 22.2, 19.3, 22.6,\n",
       "        19.8, 17.1, 19.4, 22.2, 20.7, 21.1, 19.5, 18.5, 20.6, 19. , 18.7,\n",
       "        32.7, 16.5, 23.9, 31.2, 17.5, 17.2, 23.1, 24.5, 26.6, 22.9, 24.1,\n",
       "        18.6, 30.1, 18.2, 20.6, 17.8, 21.7, 22.7, 22.6, 25. , 19.9, 20.8,\n",
       "        16.8, 21.9, 27.5, 21.9, 23.1, 50. , 50. , 50. , 50. , 50. , 13.8,\n",
       "        13.8, 15. , 13.9, 13.3, 13.1, 10.2, 10.4, 10.9, 11.3, 12.3,  8.8,\n",
       "         7.2, 10.5,  7.4, 10.2, 11.5, 15.1, 23.2,  9.7, 13.8, 12.7, 13.1,\n",
       "        12.5,  8.5,  5. ,  6.3,  5.6,  7.2, 12.1,  8.3,  8.5,  5. , 11.9,\n",
       "        27.9, 17.2, 27.5, 15. , 17.2, 17.9, 16.3,  7. ,  7.2,  7.5, 10.4,\n",
       "         8.8,  8.4, 16.7, 14.2, 20.8, 13.4, 11.7,  8.3, 10.2, 10.9, 11. ,\n",
       "         9.5, 14.5, 14.1, 16.1, 14.3, 11.7, 13.4,  9.6,  8.7,  8.4, 12.8,\n",
       "        10.5, 17.1, 18.4, 15.4, 10.8, 11.8, 14.9, 12.6, 14.1, 13. , 13.4,\n",
       "        15.2, 16.1, 17.8, 14.9, 14.1, 12.7, 13.5, 14.9, 20. , 16.4, 17.7,\n",
       "        19.5, 20.2, 21.4, 19.9, 19. , 19.1, 19.1, 20.1, 19.9, 19.6, 23.2,\n",
       "        29.8, 13.8, 13.3, 16.7, 12. , 14.6, 21.4, 23. , 23.7, 25. , 21.8,\n",
       "        20.6, 21.2, 19.1, 20.6, 15.2,  7. ,  8.1, 13.6, 20.1, 21.8, 24.5,\n",
       "        23.1, 19.7, 18.3, 21.2, 17.5, 16.8, 22.4, 20.6, 23.9, 22. , 11.9]),\n",
       " 'feature_names': array(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD',\n",
       "        'TAX', 'PTRATIO', 'B', 'LSTAT'], dtype='<U7'),\n",
       " 'DESCR': \".. _boston_dataset:\\n\\nBoston house prices dataset\\n---------------------------\\n\\n**Data Set Characteristics:**  \\n\\n    :Number of Instances: 506 \\n\\n    :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.\\n\\n    :Attribute Information (in order):\\n        - CRIM     per capita crime rate by town\\n        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\\n        - INDUS    proportion of non-retail business acres per town\\n        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\\n        - NOX      nitric oxides concentration (parts per 10 million)\\n        - RM       average number of rooms per dwelling\\n        - AGE      proportion of owner-occupied units built prior to 1940\\n        - DIS      weighted distances to five Boston employment centres\\n        - RAD      index of accessibility to radial highways\\n        - TAX      full-value property-tax rate per $10,000\\n        - PTRATIO  pupil-teacher ratio by town\\n        - B        1000(Bk - 0.63)^2 where Bk is the proportion of black people by town\\n        - LSTAT    % lower status of the population\\n        - MEDV     Median value of owner-occupied homes in $1000's\\n\\n    :Missing Attribute Values: None\\n\\n    :Creator: Harrison, D. and Rubinfeld, D.L.\\n\\nThis is a copy of UCI ML housing dataset.\\nhttps://archive.ics.uci.edu/ml/machine-learning-databases/housing/\\n\\n\\nThis dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\\n\\nThe Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\\nprices and the demand for clean air', J. Environ. Economics & Management,\\nvol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\\n...', Wiley, 1980.   N.B. Various transformations are used in the table on\\npages 244-261 of the latter.\\n\\nThe Boston house-price data has been used in many machine learning papers that address regression\\nproblems.   \\n     \\n.. topic:: References\\n\\n   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\\n   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\\n\",\n",
       " 'filename': 'boston_house_prices.csv',\n",
       " 'data_module': 'sklearn.datasets.data'}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = load_boston()\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = pd.DataFrame(df.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "          0     1      2    3      4      5     6       7    8      9     10  \\\n",
       "0    0.00632  18.0   2.31  0.0  0.538  6.575  65.2  4.0900  1.0  296.0  15.3   \n",
       "1    0.02731   0.0   7.07  0.0  0.469  6.421  78.9  4.9671  2.0  242.0  17.8   \n",
       "2    0.02729   0.0   7.07  0.0  0.469  7.185  61.1  4.9671  2.0  242.0  17.8   \n",
       "3    0.03237   0.0   2.18  0.0  0.458  6.998  45.8  6.0622  3.0  222.0  18.7   \n",
       "4    0.06905   0.0   2.18  0.0  0.458  7.147  54.2  6.0622  3.0  222.0  18.7   \n",
       "..       ...   ...    ...  ...    ...    ...   ...     ...  ...    ...   ...   \n",
       "501  0.06263   0.0  11.93  0.0  0.573  6.593  69.1  2.4786  1.0  273.0  21.0   \n",
       "502  0.04527   0.0  11.93  0.0  0.573  6.120  76.7  2.2875  1.0  273.0  21.0   \n",
       "503  0.06076   0.0  11.93  0.0  0.573  6.976  91.0  2.1675  1.0  273.0  21.0   \n",
       "504  0.10959   0.0  11.93  0.0  0.573  6.794  89.3  2.3889  1.0  273.0  21.0   \n",
       "505  0.04741   0.0  11.93  0.0  0.573  6.030  80.8  2.5050  1.0  273.0  21.0   \n",
       "\n",
       "         11    12  \n",
       "0    396.90  4.98  \n",
       "1    396.90  9.14  \n",
       "2    392.83  4.03  \n",
       "3    394.63  2.94  \n",
       "4    396.90  5.33  \n",
       "..      ...   ...  \n",
       "501  391.99  9.67  \n",
       "502  396.90  9.08  \n",
       "503  396.90  5.64  \n",
       "504  393.45  6.48  \n",
       "505  396.90  7.88  \n",
       "\n",
       "[506 rows x 13 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset.columns = df.feature_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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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>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.02985</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.430</td>\n",
       "      <td>58.7</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.12</td>\n",
       "      <td>5.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.08829</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>6.012</td>\n",
       "      <td>66.6</td>\n",
       "      <td>5.5605</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>395.60</td>\n",
       "      <td>12.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.14455</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>6.172</td>\n",
       "      <td>96.1</td>\n",
       "      <td>5.9505</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>396.90</td>\n",
       "      <td>19.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.21124</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>5.631</td>\n",
       "      <td>100.0</td>\n",
       "      <td>6.0821</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>386.63</td>\n",
       "      <td>29.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.17004</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>6.004</td>\n",
       "      <td>85.9</td>\n",
       "      <td>6.5921</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>386.71</td>\n",
       "      <td>17.10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM    AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575   65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421   78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185   61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998   45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147   54.2  6.0622  3.0  222.0   \n",
       "5  0.02985   0.0   2.18   0.0  0.458  6.430   58.7  6.0622  3.0  222.0   \n",
       "6  0.08829  12.5   7.87   0.0  0.524  6.012   66.6  5.5605  5.0  311.0   \n",
       "7  0.14455  12.5   7.87   0.0  0.524  6.172   96.1  5.9505  5.0  311.0   \n",
       "8  0.21124  12.5   7.87   0.0  0.524  5.631  100.0  6.0821  5.0  311.0   \n",
       "9  0.17004  12.5   7.87   0.0  0.524  6.004   85.9  6.5921  5.0  311.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  \n",
       "0     15.3  396.90   4.98  \n",
       "1     17.8  396.90   9.14  \n",
       "2     17.8  392.83   4.03  \n",
       "3     18.7  394.63   2.94  \n",
       "4     18.7  396.90   5.33  \n",
       "5     18.7  394.12   5.21  \n",
       "6     15.2  395.60  12.43  \n",
       "7     15.2  396.90  19.15  \n",
       "8     15.2  386.63  29.93  \n",
       "9     15.2  386.71  17.10  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "## independent and dependent features\n",
    "X = dataset\n",
    "y = df.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([24. , 21.6, 34.7, 33.4, 36.2, 28.7, 22.9, 27.1, 16.5, 18.9, 15. ,\n",
       "       18.9, 21.7, 20.4, 18.2, 19.9, 23.1, 17.5, 20.2, 18.2, 13.6, 19.6,\n",
       "       15.2, 14.5, 15.6, 13.9, 16.6, 14.8, 18.4, 21. , 12.7, 14.5, 13.2,\n",
       "       13.1, 13.5, 18.9, 20. , 21. , 24.7, 30.8, 34.9, 26.6, 25.3, 24.7,\n",
       "       21.2, 19.3, 20. , 16.6, 14.4, 19.4, 19.7, 20.5, 25. , 23.4, 18.9,\n",
       "       35.4, 24.7, 31.6, 23.3, 19.6, 18.7, 16. , 22.2, 25. , 33. , 23.5,\n",
       "       19.4, 22. , 17.4, 20.9, 24.2, 21.7, 22.8, 23.4, 24.1, 21.4, 20. ,\n",
       "       20.8, 21.2, 20.3, 28. , 23.9, 24.8, 22.9, 23.9, 26.6, 22.5, 22.2,\n",
       "       23.6, 28.7, 22.6, 22. , 22.9, 25. , 20.6, 28.4, 21.4, 38.7, 43.8,\n",
       "       33.2, 27.5, 26.5, 18.6, 19.3, 20.1, 19.5, 19.5, 20.4, 19.8, 19.4,\n",
       "       21.7, 22.8, 18.8, 18.7, 18.5, 18.3, 21.2, 19.2, 20.4, 19.3, 22. ,\n",
       "       20.3, 20.5, 17.3, 18.8, 21.4, 15.7, 16.2, 18. , 14.3, 19.2, 19.6,\n",
       "       23. , 18.4, 15.6, 18.1, 17.4, 17.1, 13.3, 17.8, 14. , 14.4, 13.4,\n",
       "       15.6, 11.8, 13.8, 15.6, 14.6, 17.8, 15.4, 21.5, 19.6, 15.3, 19.4,\n",
       "       17. , 15.6, 13.1, 41.3, 24.3, 23.3, 27. , 50. , 50. , 50. , 22.7,\n",
       "       25. , 50. , 23.8, 23.8, 22.3, 17.4, 19.1, 23.1, 23.6, 22.6, 29.4,\n",
       "       23.2, 24.6, 29.9, 37.2, 39.8, 36.2, 37.9, 32.5, 26.4, 29.6, 50. ,\n",
       "       32. , 29.8, 34.9, 37. , 30.5, 36.4, 31.1, 29.1, 50. , 33.3, 30.3,\n",
       "       34.6, 34.9, 32.9, 24.1, 42.3, 48.5, 50. , 22.6, 24.4, 22.5, 24.4,\n",
       "       20. , 21.7, 19.3, 22.4, 28.1, 23.7, 25. , 23.3, 28.7, 21.5, 23. ,\n",
       "       26.7, 21.7, 27.5, 30.1, 44.8, 50. , 37.6, 31.6, 46.7, 31.5, 24.3,\n",
       "       31.7, 41.7, 48.3, 29. , 24. , 25.1, 31.5, 23.7, 23.3, 22. , 20.1,\n",
       "       22.2, 23.7, 17.6, 18.5, 24.3, 20.5, 24.5, 26.2, 24.4, 24.8, 29.6,\n",
       "       42.8, 21.9, 20.9, 44. , 50. , 36. , 30.1, 33.8, 43.1, 48.8, 31. ,\n",
       "       36.5, 22.8, 30.7, 50. , 43.5, 20.7, 21.1, 25.2, 24.4, 35.2, 32.4,\n",
       "       32. , 33.2, 33.1, 29.1, 35.1, 45.4, 35.4, 46. , 50. , 32.2, 22. ,\n",
       "       20.1, 23.2, 22.3, 24.8, 28.5, 37.3, 27.9, 23.9, 21.7, 28.6, 27.1,\n",
       "       20.3, 22.5, 29. , 24.8, 22. , 26.4, 33.1, 36.1, 28.4, 33.4, 28.2,\n",
       "       22.8, 20.3, 16.1, 22.1, 19.4, 21.6, 23.8, 16.2, 17.8, 19.8, 23.1,\n",
       "       21. , 23.8, 23.1, 20.4, 18.5, 25. , 24.6, 23. , 22.2, 19.3, 22.6,\n",
       "       19.8, 17.1, 19.4, 22.2, 20.7, 21.1, 19.5, 18.5, 20.6, 19. , 18.7,\n",
       "       32.7, 16.5, 23.9, 31.2, 17.5, 17.2, 23.1, 24.5, 26.6, 22.9, 24.1,\n",
       "       18.6, 30.1, 18.2, 20.6, 17.8, 21.7, 22.7, 22.6, 25. , 19.9, 20.8,\n",
       "       16.8, 21.9, 27.5, 21.9, 23.1, 50. , 50. , 50. , 50. , 50. , 13.8,\n",
       "       13.8, 15. , 13.9, 13.3, 13.1, 10.2, 10.4, 10.9, 11.3, 12.3,  8.8,\n",
       "        7.2, 10.5,  7.4, 10.2, 11.5, 15.1, 23.2,  9.7, 13.8, 12.7, 13.1,\n",
       "       12.5,  8.5,  5. ,  6.3,  5.6,  7.2, 12.1,  8.3,  8.5,  5. , 11.9,\n",
       "       27.9, 17.2, 27.5, 15. , 17.2, 17.9, 16.3,  7. ,  7.2,  7.5, 10.4,\n",
       "        8.8,  8.4, 16.7, 14.2, 20.8, 13.4, 11.7,  8.3, 10.2, 10.9, 11. ,\n",
       "        9.5, 14.5, 14.1, 16.1, 14.3, 11.7, 13.4,  9.6,  8.7,  8.4, 12.8,\n",
       "       10.5, 17.1, 18.4, 15.4, 10.8, 11.8, 14.9, 12.6, 14.1, 13. , 13.4,\n",
       "       15.2, 16.1, 17.8, 14.9, 14.1, 12.7, 13.5, 14.9, 20. , 16.4, 17.7,\n",
       "       19.5, 20.2, 21.4, 19.9, 19. , 19.1, 19.1, 20.1, 19.9, 19.6, 23.2,\n",
       "       29.8, 13.8, 13.3, 16.7, 12. , 14.6, 21.4, 23. , 23.7, 25. , 21.8,\n",
       "       20.6, 21.2, 19.1, 20.6, 15.2,  7. ,  8.1, 13.6, 20.1, 21.8, 24.5,\n",
       "       23.1, 19.7, 18.3, 21.2, 17.5, 16.8, 22.4, 20.6, 23.9, 22. , 11.9])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "## train test split\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train,X_test, y_train,y_test = train_test_split(X,y,test_size=0.3 , random_state=42)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.02985</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.430</td>\n",
       "      <td>58.7</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.12</td>\n",
       "      <td>5.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>116</th>\n",
       "      <td>0.13158</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10.01</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.547</td>\n",
       "      <td>6.176</td>\n",
       "      <td>72.5</td>\n",
       "      <td>2.7301</td>\n",
       "      <td>6.0</td>\n",
       "      <td>432.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>393.30</td>\n",
       "      <td>12.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>0.17142</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.91</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.448</td>\n",
       "      <td>5.682</td>\n",
       "      <td>33.8</td>\n",
       "      <td>5.1004</td>\n",
       "      <td>3.0</td>\n",
       "      <td>233.0</td>\n",
       "      <td>17.9</td>\n",
       "      <td>396.90</td>\n",
       "      <td>10.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.05393</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>5.935</td>\n",
       "      <td>29.3</td>\n",
       "      <td>4.4986</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>386.85</td>\n",
       "      <td>6.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>468</th>\n",
       "      <td>15.57570</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.580</td>\n",
       "      <td>5.926</td>\n",
       "      <td>71.0</td>\n",
       "      <td>2.9084</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>368.74</td>\n",
       "      <td>18.13</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",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>106</th>\n",
       "      <td>0.17120</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.56</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.520</td>\n",
       "      <td>5.836</td>\n",
       "      <td>91.9</td>\n",
       "      <td>2.2110</td>\n",
       "      <td>5.0</td>\n",
       "      <td>384.0</td>\n",
       "      <td>20.9</td>\n",
       "      <td>395.67</td>\n",
       "      <td>18.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>270</th>\n",
       "      <td>0.29916</td>\n",
       "      <td>20.0</td>\n",
       "      <td>6.96</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.464</td>\n",
       "      <td>5.856</td>\n",
       "      <td>42.1</td>\n",
       "      <td>4.4290</td>\n",
       "      <td>3.0</td>\n",
       "      <td>223.0</td>\n",
       "      <td>18.6</td>\n",
       "      <td>388.65</td>\n",
       "      <td>13.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>348</th>\n",
       "      <td>0.01501</td>\n",
       "      <td>80.0</td>\n",
       "      <td>2.01</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.435</td>\n",
       "      <td>6.635</td>\n",
       "      <td>29.7</td>\n",
       "      <td>8.3440</td>\n",
       "      <td>4.0</td>\n",
       "      <td>280.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>390.94</td>\n",
       "      <td>5.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>435</th>\n",
       "      <td>11.16040</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.740</td>\n",
       "      <td>6.629</td>\n",
       "      <td>94.6</td>\n",
       "      <td>2.1247</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>109.85</td>\n",
       "      <td>23.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>102</th>\n",
       "      <td>0.22876</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.56</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.520</td>\n",
       "      <td>6.405</td>\n",
       "      <td>85.4</td>\n",
       "      <td>2.7147</td>\n",
       "      <td>5.0</td>\n",
       "      <td>384.0</td>\n",
       "      <td>20.9</td>\n",
       "      <td>70.80</td>\n",
       "      <td>10.63</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>354 rows × 13 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS   RAD    TAX  \\\n",
       "5     0.02985   0.0   2.18   0.0  0.458  6.430  58.7  6.0622   3.0  222.0   \n",
       "116   0.13158   0.0  10.01   0.0  0.547  6.176  72.5  2.7301   6.0  432.0   \n",
       "45    0.17142   0.0   6.91   0.0  0.448  5.682  33.8  5.1004   3.0  233.0   \n",
       "16    1.05393   0.0   8.14   0.0  0.538  5.935  29.3  4.4986   4.0  307.0   \n",
       "468  15.57570   0.0  18.10   0.0  0.580  5.926  71.0  2.9084  24.0  666.0   \n",
       "..        ...   ...    ...   ...    ...    ...   ...     ...   ...    ...   \n",
       "106   0.17120   0.0   8.56   0.0  0.520  5.836  91.9  2.2110   5.0  384.0   \n",
       "270   0.29916  20.0   6.96   0.0  0.464  5.856  42.1  4.4290   3.0  223.0   \n",
       "348   0.01501  80.0   2.01   0.0  0.435  6.635  29.7  8.3440   4.0  280.0   \n",
       "435  11.16040   0.0  18.10   0.0  0.740  6.629  94.6  2.1247  24.0  666.0   \n",
       "102   0.22876   0.0   8.56   0.0  0.520  6.405  85.4  2.7147   5.0  384.0   \n",
       "\n",
       "     PTRATIO       B  LSTAT  \n",
       "5       18.7  394.12   5.21  \n",
       "116     17.8  393.30  12.04  \n",
       "45      17.9  396.90  10.21  \n",
       "16      21.0  386.85   6.58  \n",
       "468     20.2  368.74  18.13  \n",
       "..       ...     ...    ...  \n",
       "106     20.9  395.67  18.66  \n",
       "270     18.6  388.65  13.00  \n",
       "348     17.0  390.94   5.99  \n",
       "435     20.2  109.85  23.27  \n",
       "102     20.9   70.80  10.63  \n",
       "\n",
       "[354 rows x 13 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
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       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>173</th>\n",
       "      <td>0.09178</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.05</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.510</td>\n",
       "      <td>6.416</td>\n",
       "      <td>84.1</td>\n",
       "      <td>2.6463</td>\n",
       "      <td>5.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>16.6</td>\n",
       "      <td>395.50</td>\n",
       "      <td>9.04</td>\n",
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       "    <tr>\n",
       "      <th>274</th>\n",
       "      <td>0.05644</td>\n",
       "      <td>40.0</td>\n",
       "      <td>6.41</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.447</td>\n",
       "      <td>6.758</td>\n",
       "      <td>32.9</td>\n",
       "      <td>4.0776</td>\n",
       "      <td>4.0</td>\n",
       "      <td>254.0</td>\n",
       "      <td>17.6</td>\n",
       "      <td>396.90</td>\n",
       "      <td>3.53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>491</th>\n",
       "      <td>0.10574</td>\n",
       "      <td>0.0</td>\n",
       "      <td>27.74</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.609</td>\n",
       "      <td>5.983</td>\n",
       "      <td>98.8</td>\n",
       "      <td>1.8681</td>\n",
       "      <td>4.0</td>\n",
       "      <td>711.0</td>\n",
       "      <td>20.1</td>\n",
       "      <td>390.11</td>\n",
       "      <td>18.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>0.09164</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10.81</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.413</td>\n",
       "      <td>6.065</td>\n",
       "      <td>7.8</td>\n",
       "      <td>5.2873</td>\n",
       "      <td>4.0</td>\n",
       "      <td>305.0</td>\n",
       "      <td>19.2</td>\n",
       "      <td>390.91</td>\n",
       "      <td>5.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>452</th>\n",
       "      <td>5.09017</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.713</td>\n",
       "      <td>6.297</td>\n",
       "      <td>91.8</td>\n",
       "      <td>2.3682</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>385.09</td>\n",
       "      <td>17.27</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",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>441</th>\n",
       "      <td>9.72418</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.740</td>\n",
       "      <td>6.406</td>\n",
       "      <td>97.2</td>\n",
       "      <td>2.0651</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>385.96</td>\n",
       "      <td>19.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.98843</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>5.813</td>\n",
       "      <td>100.0</td>\n",
       "      <td>4.0952</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>394.54</td>\n",
       "      <td>19.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>225</th>\n",
       "      <td>0.52693</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.20</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.504</td>\n",
       "      <td>8.725</td>\n",
       "      <td>83.0</td>\n",
       "      <td>2.8944</td>\n",
       "      <td>8.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>17.4</td>\n",
       "      <td>382.00</td>\n",
       "      <td>4.63</td>\n",
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       "    <tr>\n",
       "      <th>433</th>\n",
       "      <td>5.58107</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.713</td>\n",
       "      <td>6.436</td>\n",
       "      <td>87.9</td>\n",
       "      <td>2.3158</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>100.19</td>\n",
       "      <td>16.22</td>\n",
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       "    <tr>\n",
       "      <th>447</th>\n",
       "      <td>9.92485</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.740</td>\n",
       "      <td>6.251</td>\n",
       "      <td>96.6</td>\n",
       "      <td>2.1980</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>388.52</td>\n",
       "      <td>16.44</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>152 rows × 13 columns</p>\n",
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      ],
      "text/plain": [
       "        CRIM    ZN  INDUS  CHAS    NOX     RM    AGE     DIS   RAD    TAX  \\\n",
       "173  0.09178   0.0   4.05   0.0  0.510  6.416   84.1  2.6463   5.0  296.0   \n",
       "274  0.05644  40.0   6.41   1.0  0.447  6.758   32.9  4.0776   4.0  254.0   \n",
       "491  0.10574   0.0  27.74   0.0  0.609  5.983   98.8  1.8681   4.0  711.0   \n",
       "72   0.09164   0.0  10.81   0.0  0.413  6.065    7.8  5.2873   4.0  305.0   \n",
       "452  5.09017   0.0  18.10   0.0  0.713  6.297   91.8  2.3682  24.0  666.0   \n",
       "..       ...   ...    ...   ...    ...    ...    ...     ...   ...    ...   \n",
       "441  9.72418   0.0  18.10   0.0  0.740  6.406   97.2  2.0651  24.0  666.0   \n",
       "23   0.98843   0.0   8.14   0.0  0.538  5.813  100.0  4.0952   4.0  307.0   \n",
       "225  0.52693   0.0   6.20   0.0  0.504  8.725   83.0  2.8944   8.0  307.0   \n",
       "433  5.58107   0.0  18.10   0.0  0.713  6.436   87.9  2.3158  24.0  666.0   \n",
       "447  9.92485   0.0  18.10   0.0  0.740  6.251   96.6  2.1980  24.0  666.0   \n",
       "\n",
       "     PTRATIO       B  LSTAT  \n",
       "173     16.6  395.50   9.04  \n",
       "274     17.6  396.90   3.53  \n",
       "491     20.1  390.11  18.07  \n",
       "72      19.2  390.91   5.52  \n",
       "452     20.2  385.09  17.27  \n",
       "..       ...     ...    ...  \n",
       "441     20.2  385.96  19.52  \n",
       "23      21.0  394.54  19.88  \n",
       "225     17.4  382.00   4.63  \n",
       "433     20.2  100.19  16.22  \n",
       "447     20.2  388.52  16.44  \n",
       "\n",
       "[152 rows x 13 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Standarizing the dataset\n",
    "## we used standardScaler for standardized our dataset\n",
    "## Remember we use fit_transform for input x_train\n",
    "## and transform() for output X_test\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = scaler.fit_transform(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_test = scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "## hyper-parameter tune??\n",
    "## cross validation?? we divide data into parts and train the parts of data and find the accuracy of each data and we find the mean accuracy\n",
    "from sklearn.linear_model import LinearRegression\n",
    "## cross validation\n",
    "from sklearn.model_selection import cross_val_score\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LinearRegression</label><div class=\"sk-toggleable__content\"><pre>LinearRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regression = LinearRegression()\n",
    "regression.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean_square_error = cross_val_score(regression ,X_train , y_train , scoring='neg_mean_squared_error',cv=10 )\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-25.550660791660796"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(mean_square_error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "## prediction on test data\n",
    "reg_pred = regression.predict(X_test)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([28.64896005, 36.49501384, 15.4111932 , 25.40321303, 18.85527988,\n",
       "       23.14668944, 17.3921241 , 14.07859899, 23.03692679, 20.59943345,\n",
       "       24.82286159, 18.53057049, -6.86543527, 21.80172334, 19.22571177,\n",
       "       26.19191985, 20.27733882,  5.61596432, 40.44887974, 17.57695918,\n",
       "       27.44319095, 30.1715964 , 10.94055823, 24.02083139, 18.07693812,\n",
       "       15.934748  , 23.12614028, 14.56052142, 22.33482544, 19.3257627 ,\n",
       "       22.16564973, 25.19476081, 25.31372473, 18.51345025, 16.6223286 ,\n",
       "       17.50268505, 30.94992991, 20.19201752, 23.90440431, 24.86975466,\n",
       "       13.93767876, 31.82504715, 42.56978796, 17.62323805, 27.01963242,\n",
       "       17.19006621, 13.80594006, 26.10356557, 20.31516118, 30.08649576,\n",
       "       21.3124053 , 34.15739602, 15.60444981, 26.11247588, 39.31613646,\n",
       "       22.99282065, 18.95764781, 33.05555669, 24.85114223, 12.91729352,\n",
       "       22.68101452, 30.80336295, 31.63522027, 16.29833689, 21.07379993,\n",
       "       16.57699669, 20.36362023, 26.15615896, 31.06833034, 11.98679953,\n",
       "       20.42550472, 27.55676301, 10.94316981, 16.82660609, 23.92909733,\n",
       "        5.28065815, 21.43504661, 41.33684993, 18.22211675,  9.48269245,\n",
       "       21.19857446, 12.95001331, 21.64822797,  9.3845568 , 23.06060014,\n",
       "       31.95762512, 19.16662892, 25.59942257, 29.35043558, 20.13138581,\n",
       "       25.57297369,  5.42970803, 20.23169356, 15.1949595 , 14.03241742,\n",
       "       20.91078077, 24.82249135, -0.47712079, 13.70520524, 15.69525576,\n",
       "       22.06972676, 24.64152943, 10.7382866 , 19.68622564, 23.63678009,\n",
       "       12.07974981, 18.47894211, 25.52713393, 20.93461307, 24.6955941 ,\n",
       "        7.59054562, 19.01046053, 21.9444339 , 27.22319977, 32.18608828,\n",
       "       15.27826455, 34.39190421, 12.96314168, 21.01681316, 28.57880911,\n",
       "       15.86300844, 24.85124135,  3.37937111, 23.90465773, 25.81792146,\n",
       "       23.11020547, 25.33489201, 33.35545176, 20.60724498, 38.4772665 ,\n",
       "       13.97398533, 25.21923987, 17.80946626, 20.63437371,  9.80267398,\n",
       "       21.07953576, 22.3378417 , 32.32381854, 31.48694863, 15.46621287,\n",
       "       16.86242766, 28.99330526, 24.95467894, 16.73633557,  6.12858395,\n",
       "       26.65990044, 23.34007187, 17.40367164, 13.38594123, 39.98342478,\n",
       "       16.68286302, 18.28561759])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x1cf626de290>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.displot(reg_pred - y_test, kind='kde')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "score = r2_score(reg_pred , y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6693702691495593"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.4 64-bit",
   "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": "3.10.4"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "8c3d4d9970fc5c09c50d9318a9c7fbf4d0159e4b28833276f5678ee22bded273"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}