Regression_Linear,_ridge_and_lasso.ipynb

{
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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>NX</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",
       "      <th>MEDV</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</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1</td>\n",
       "      <td>296</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>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</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>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</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>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</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>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</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
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      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS     NX     RM   AGE     DIS  RAD  TAX  PTRATIO  \\\n",
       "0  0.00632  18.0   2.31     0  0.538  6.575  65.2  4.0900    1  296     15.3   \n",
       "1  0.02731   0.0   7.07     0  0.469  6.421  78.9  4.9671    2  242     17.8   \n",
       "2  0.02729   0.0   7.07     0  0.469  7.185  61.1  4.9671    2  242     17.8   \n",
       "3  0.03237   0.0   2.18     0  0.458  6.998  45.8  6.0622    3  222     18.7   \n",
       "4  0.06905   0.0   2.18     0  0.458  7.147  54.2  6.0622    3  222     18.7   \n",
       "\n",
       "        B  LSTAT  MEDV  \n",
       "0  396.90   4.98  24.0  \n",
       "1  396.90   9.14  21.6  \n",
       "2  392.83   4.03  34.7  \n",
       "3  394.63   2.94  33.4  \n",
       "4  396.90   5.33  36.2  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "boston = pd.read_csv(\"boston.csv\")\n",
    "\n",
    "boston.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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    {
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       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NX</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",
       "      <th>MEDV</th>\n",
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       "      <th>501</th>\n",
       "      <td>0.06263</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
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       "      <td>0.573</td>\n",
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       "      <td>21.0</td>\n",
       "      <td>391.99</td>\n",
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       "      <th>502</th>\n",
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       "      <td>76.7</td>\n",
       "      <td>2.2875</td>\n",
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       "      <td>9.08</td>\n",
       "      <td>20.6</td>\n",
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       "      <th>503</th>\n",
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       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.976</td>\n",
       "      <td>91.0</td>\n",
       "      <td>2.1675</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
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       "      <td>396.90</td>\n",
       "      <td>5.64</td>\n",
       "      <td>23.9</td>\n",
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       "    <tr>\n",
       "      <th>504</th>\n",
       "      <td>0.10959</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.794</td>\n",
       "      <td>89.3</td>\n",
       "      <td>2.3889</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>393.45</td>\n",
       "      <td>6.48</td>\n",
       "      <td>22.0</td>\n",
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       "      <th>505</th>\n",
       "      <td>0.04741</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.030</td>\n",
       "      <td>80.8</td>\n",
       "      <td>2.5050</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>7.88</td>\n",
       "      <td>11.9</td>\n",
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      "text/plain": [
       "        CRIM   ZN  INDUS  CHAS     NX     RM   AGE     DIS  RAD  TAX  PTRATIO  \\\n",
       "501  0.06263  0.0  11.93     0  0.573  6.593  69.1  2.4786    1  273     21.0   \n",
       "502  0.04527  0.0  11.93     0  0.573  6.120  76.7  2.2875    1  273     21.0   \n",
       "503  0.06076  0.0  11.93     0  0.573  6.976  91.0  2.1675    1  273     21.0   \n",
       "504  0.10959  0.0  11.93     0  0.573  6.794  89.3  2.3889    1  273     21.0   \n",
       "505  0.04741  0.0  11.93     0  0.573  6.030  80.8  2.5050    1  273     21.0   \n",
       "\n",
       "          B  LSTAT  MEDV  \n",
       "501  391.99   9.67  22.4  \n",
       "502  396.90   9.08  20.6  \n",
       "503  396.90   5.64  23.9  \n",
       "504  393.45   6.48  22.0  \n",
       "505  396.90   7.88  11.9  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "OR_am4LeZSi4",
    "outputId": "c8b5303a-689c-4421-cc67-0d1797ac1a0b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506, 14)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "df-8lJitZTrf"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 506 entries, 0 to 505\n",
      "Data columns (total 14 columns):\n",
      " #   Column   Non-Null Count  Dtype  \n",
      "---  ------   --------------  -----  \n",
      " 0   CRIM     506 non-null    float64\n",
      " 1   ZN       506 non-null    float64\n",
      " 2   INDUS    506 non-null    float64\n",
      " 3   CHAS     506 non-null    int64  \n",
      " 4   NX       506 non-null    float64\n",
      " 5   RM       506 non-null    float64\n",
      " 6   AGE      506 non-null    float64\n",
      " 7   DIS      506 non-null    float64\n",
      " 8   RAD      506 non-null    int64  \n",
      " 9   TAX      506 non-null    int64  \n",
      " 10  PTRATIO  506 non-null    float64\n",
      " 11  B        506 non-null    float64\n",
      " 12  LSTAT    506 non-null    float64\n",
      " 13  MEDV     506 non-null    float64\n",
      "dtypes: float64(11), int64(3)\n",
      "memory usage: 55.5 KB\n"
     ]
    }
   ],
   "source": [
    "boston.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "1pI5-i11ZWKU"
   },
   "outputs": [],
   "source": [
    "x = boston.drop(\"MEDV\", axis=1).values #input factors\n",
    "\n",
    "y = boston[\"MEDV\"].values\n",
    "#values method converts a datafarme into array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "6zBUcchYZxZ9"
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "scaler = StandardScaler()#instantiation\n",
    "\n",
    "xs = scaler.fit_transform(x) #result is in form of array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "ivM6gu-4anZU"
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(xs, y, test_size=0.3,\\\n",
    "                                                    random_state=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VTnWshcNxvZ4"
   },
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "jQ1IblG-cnGV"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(354, 13)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "_qs20eu7cqhJ"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(152, 13)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 74
    },
    "id": "_eXhkL0Bcs03",
    "outputId": "089cdb3c-69e6-4be6-d691-3f1588f22e6c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "#instantiate regression\n",
    "model = LinearRegression()\n",
    "\n",
    "model.fit(x_train,y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nvPrR_3Pe2p0"
   },
   "source": [
    "y = a + bx, simple linear regression\n",
    "\n",
    "y = a + bx1 +cx2 +dx3+ .......\n",
    "\n",
    "y = 5 + 1.5 x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "kNmUKdBZepr9",
    "outputId": "f023fef6-6f36-4794-df74-20ba9a7643a0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.589670302295588"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "4yRyjNuDfMEw",
    "outputId": "0f7d3eb0-0d61-42bf-dde5-738c327644d9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.84677953,  1.41623312,  0.40553633,  0.61902108, -2.48543003,\n",
       "        1.96244469,  0.10052138, -3.18967316,  2.67519835, -1.89922198,\n",
       "       -2.17462796,  0.58828654, -4.05806653])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "wij8sn7EfaZ1",
    "outputId": "0c9d63b5-c23b-4f39-f003-5ec47f6e7a3e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NX', 'RM', 'AGE', 'DIS', 'RAD', 'TAX',\n",
       "       'PTRATIO', 'B', 'LSTAT'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "o = boston.drop(\"MEDV\", axis=1)\n",
    "o.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 457
    },
    "id": "uPUkdRuvfvXM",
    "outputId": "d527ab67-5e6d-4c8a-a64a-7815cd360a97"
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    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>-0.846780</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>1.416233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>0.405536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>0.619021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NX</th>\n",
       "      <td>-2.485430</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>1.962445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>0.100521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>-3.189673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>2.675198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>-1.899222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>-2.174628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.588287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>-4.058067</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                0\n",
       "CRIM    -0.846780\n",
       "ZN       1.416233\n",
       "INDUS    0.405536\n",
       "CHAS     0.619021\n",
       "NX      -2.485430\n",
       "RM       1.962445\n",
       "AGE      0.100521\n",
       "DIS     -3.189673\n",
       "RAD      2.675198\n",
       "TAX     -1.899222\n",
       "PTRATIO -2.174628\n",
       "B        0.588287\n",
       "LSTAT   -4.058067"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(model.coef_,index=o.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "id": "2gt0c5Raf8Fc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7836295385076292"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#r squared:  coeff of determination\n",
    "\n",
    "model.score(x_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "id": "RlWNzTCTiISW"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.453237437198149"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#margin of error: RMSE\n",
    "\n",
    "y_pred = model.predict(x_test)\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from math import sqrt\n",
    "\n",
    "mse = mean_squared_error(y_test,y_pred)\n",
    "rmse = sqrt(mse)\n",
    "rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "id": "i0HE6wtkjeK0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7103879080674731"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#r squared train data\n",
    "model.score(x_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "id": "J0Zqq8lUkh_8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.849055005805464"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#margin of error: RMSE\n",
    "\n",
    "y_pred_train = model.predict(x_train)\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from math import sqrt\n",
    "\n",
    "mse = mean_squared_error(y_train,y_pred_train)\n",
    "rmse = sqrt(mse)\n",
    "rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "id": "NAG4D3M8ktPV"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>MEDV</td>       <th>  R-squared:         </th> <td>   0.741</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.734</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   108.1</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 08 Aug 2023</td> <th>  Prob (F-statistic):</th> <td>6.72e-135</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>10:02:17</td>     <th>  Log-Likelihood:    </th> <td> -1498.8</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3026.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   492</td>      <th>  BIC:               </th> <td>   3085.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    13</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   36.4595</td> <td>    5.103</td> <td>    7.144</td> <td> 0.000</td> <td>   26.432</td> <td>   46.487</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CRIM</th>      <td>   -0.1080</td> <td>    0.033</td> <td>   -3.287</td> <td> 0.001</td> <td>   -0.173</td> <td>   -0.043</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ZN</th>        <td>    0.0464</td> <td>    0.014</td> <td>    3.382</td> <td> 0.001</td> <td>    0.019</td> <td>    0.073</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CHAS</th>      <td>    2.6867</td> <td>    0.862</td> <td>    3.118</td> <td> 0.002</td> <td>    0.994</td> <td>    4.380</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AGE</th>       <td>    0.0007</td> <td>    0.013</td> <td>    0.052</td> <td> 0.958</td> <td>   -0.025</td> <td>    0.027</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>INDUS</th>     <td>    0.0206</td> <td>    0.061</td> <td>    0.334</td> <td> 0.738</td> <td>   -0.100</td> <td>    0.141</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NX</th>        <td>  -17.7666</td> <td>    3.820</td> <td>   -4.651</td> <td> 0.000</td> <td>  -25.272</td> <td>  -10.262</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RM</th>        <td>    3.8099</td> <td>    0.418</td> <td>    9.116</td> <td> 0.000</td> <td>    2.989</td> <td>    4.631</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>DIS</th>       <td>   -1.4756</td> <td>    0.199</td> <td>   -7.398</td> <td> 0.000</td> <td>   -1.867</td> <td>   -1.084</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RAD</th>       <td>    0.3060</td> <td>    0.066</td> <td>    4.613</td> <td> 0.000</td> <td>    0.176</td> <td>    0.436</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TAX</th>       <td>   -0.0123</td> <td>    0.004</td> <td>   -3.280</td> <td> 0.001</td> <td>   -0.020</td> <td>   -0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PTRATIO</th>   <td>   -0.9527</td> <td>    0.131</td> <td>   -7.283</td> <td> 0.000</td> <td>   -1.210</td> <td>   -0.696</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>B</th>         <td>    0.0093</td> <td>    0.003</td> <td>    3.467</td> <td> 0.001</td> <td>    0.004</td> <td>    0.015</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>LSTAT</th>     <td>   -0.5248</td> <td>    0.051</td> <td>  -10.347</td> <td> 0.000</td> <td>   -0.624</td> <td>   -0.425</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>178.041</td> <th>  Durbin-Watson:     </th> <td>   1.078</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 783.126</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.521</td>  <th>  Prob(JB):          </th> <td>8.84e-171</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 8.281</td>  <th>  Cond. No.          </th> <td>1.51e+04</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.51e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   MEDV   R-squared:                       0.741\n",
       "Model:                            OLS   Adj. R-squared:                  0.734\n",
       "Method:                 Least Squares   F-statistic:                     108.1\n",
       "Date:                Tue, 08 Aug 2023   Prob (F-statistic):          6.72e-135\n",
       "Time:                        10:02:17   Log-Likelihood:                -1498.8\n",
       "No. Observations:                 506   AIC:                             3026.\n",
       "Df Residuals:                     492   BIC:                             3085.\n",
       "Df Model:                          13                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     36.4595      5.103      7.144      0.000      26.432      46.487\n",
       "CRIM          -0.1080      0.033     -3.287      0.001      -0.173      -0.043\n",
       "ZN             0.0464      0.014      3.382      0.001       0.019       0.073\n",
       "CHAS           2.6867      0.862      3.118      0.002       0.994       4.380\n",
       "AGE            0.0007      0.013      0.052      0.958      -0.025       0.027\n",
       "INDUS          0.0206      0.061      0.334      0.738      -0.100       0.141\n",
       "NX           -17.7666      3.820     -4.651      0.000     -25.272     -10.262\n",
       "RM             3.8099      0.418      9.116      0.000       2.989       4.631\n",
       "DIS           -1.4756      0.199     -7.398      0.000      -1.867      -1.084\n",
       "RAD            0.3060      0.066      4.613      0.000       0.176       0.436\n",
       "TAX           -0.0123      0.004     -3.280      0.001      -0.020      -0.005\n",
       "PTRATIO       -0.9527      0.131     -7.283      0.000      -1.210      -0.696\n",
       "B              0.0093      0.003      3.467      0.001       0.004       0.015\n",
       "LSTAT         -0.5248      0.051    -10.347      0.000      -0.624      -0.425\n",
       "==============================================================================\n",
       "Omnibus:                      178.041   Durbin-Watson:                   1.078\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              783.126\n",
       "Skew:                           1.521   Prob(JB):                    8.84e-171\n",
       "Kurtosis:                       8.281   Cond. No.                     1.51e+04\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.51e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.formula.api as smf\n",
    "\n",
    "reg_all = smf.ols(formula = 'MEDV ~ CRIM + ZN + CHAS + AGE + INDUS + NX + RM \\\n",
    "+ DIS + RAD + TAX + PTRATIO + B + LSTAT', data=boston).fit()\n",
    "reg_all.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "id": "zjsgX9WGoUm0"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>MEDV</td>       <th>  R-squared:         </th> <td>   0.741</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.735</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   128.2</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 08 Aug 2023</td> <th>  Prob (F-statistic):</th> <td>5.54e-137</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>10:02:37</td>     <th>  Log-Likelihood:    </th> <td> -1498.9</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3022.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   494</td>      <th>  BIC:               </th> <td>   3072.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    11</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   36.3411</td> <td>    5.067</td> <td>    7.171</td> <td> 0.000</td> <td>   26.385</td> <td>   46.298</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CRIM</th>      <td>   -0.1084</td> <td>    0.033</td> <td>   -3.307</td> <td> 0.001</td> <td>   -0.173</td> <td>   -0.044</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ZN</th>        <td>    0.0458</td> <td>    0.014</td> <td>    3.390</td> <td> 0.001</td> <td>    0.019</td> <td>    0.072</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CHAS</th>      <td>    2.7187</td> <td>    0.854</td> <td>    3.183</td> <td> 0.002</td> <td>    1.040</td> <td>    4.397</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NX</th>        <td>  -17.3760</td> <td>    3.535</td> <td>   -4.915</td> <td> 0.000</td> <td>  -24.322</td> <td>  -10.430</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RM</th>        <td>    3.8016</td> <td>    0.406</td> <td>    9.356</td> <td> 0.000</td> <td>    3.003</td> <td>    4.600</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>DIS</th>       <td>   -1.4927</td> <td>    0.186</td> <td>   -8.037</td> <td> 0.000</td> <td>   -1.858</td> <td>   -1.128</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RAD</th>       <td>    0.2996</td> <td>    0.063</td> <td>    4.726</td> <td> 0.000</td> <td>    0.175</td> <td>    0.424</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TAX</th>       <td>   -0.0118</td> <td>    0.003</td> <td>   -3.493</td> <td> 0.001</td> <td>   -0.018</td> <td>   -0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PTRATIO</th>   <td>   -0.9465</td> <td>    0.129</td> <td>   -7.334</td> <td> 0.000</td> <td>   -1.200</td> <td>   -0.693</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>B</th>         <td>    0.0093</td> <td>    0.003</td> <td>    3.475</td> <td> 0.001</td> <td>    0.004</td> <td>    0.015</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>LSTAT</th>     <td>   -0.5226</td> <td>    0.047</td> <td>  -11.019</td> <td> 0.000</td> <td>   -0.616</td> <td>   -0.429</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>178.430</td> <th>  Durbin-Watson:     </th> <td>   1.078</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 787.785</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.523</td>  <th>  Prob(JB):          </th> <td>8.60e-172</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 8.300</td>  <th>  Cond. No.          </th> <td>1.47e+04</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.47e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   MEDV   R-squared:                       0.741\n",
       "Model:                            OLS   Adj. R-squared:                  0.735\n",
       "Method:                 Least Squares   F-statistic:                     128.2\n",
       "Date:                Tue, 08 Aug 2023   Prob (F-statistic):          5.54e-137\n",
       "Time:                        10:02:37   Log-Likelihood:                -1498.9\n",
       "No. Observations:                 506   AIC:                             3022.\n",
       "Df Residuals:                     494   BIC:                             3072.\n",
       "Df Model:                          11                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     36.3411      5.067      7.171      0.000      26.385      46.298\n",
       "CRIM          -0.1084      0.033     -3.307      0.001      -0.173      -0.044\n",
       "ZN             0.0458      0.014      3.390      0.001       0.019       0.072\n",
       "CHAS           2.7187      0.854      3.183      0.002       1.040       4.397\n",
       "NX           -17.3760      3.535     -4.915      0.000     -24.322     -10.430\n",
       "RM             3.8016      0.406      9.356      0.000       3.003       4.600\n",
       "DIS           -1.4927      0.186     -8.037      0.000      -1.858      -1.128\n",
       "RAD            0.2996      0.063      4.726      0.000       0.175       0.424\n",
       "TAX           -0.0118      0.003     -3.493      0.001      -0.018      -0.005\n",
       "PTRATIO       -0.9465      0.129     -7.334      0.000      -1.200      -0.693\n",
       "B              0.0093      0.003      3.475      0.001       0.004       0.015\n",
       "LSTAT         -0.5226      0.047    -11.019      0.000      -0.616      -0.429\n",
       "==============================================================================\n",
       "Omnibus:                      178.430   Durbin-Watson:                   1.078\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              787.785\n",
       "Skew:                           1.523   Prob(JB):                    8.60e-172\n",
       "Kurtosis:                       8.300   Cond. No.                     1.47e+04\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.47e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_all = smf.ols(formula = 'MEDV ~ CRIM + ZN + CHAS + NX + RM \\\n",
    "+ DIS + RAD + TAX + PTRATIO + B + LSTAT', data=boston).fit()\n",
    "reg_all.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "ZgVvRkzJpGcX"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_JNUmQDscBwo"
   },
   "source": [
    "**RIDGE REGRESSION**\n",
    "\n",
    "Without cross validation and tuning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 206
    },
    "id": "c0QWwNXxcEOG",
    "outputId": "22504ae9-9c65-4434-d8bf-604ca00f06a9"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\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>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NX</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",
       "      <th>MEDV</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</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1</td>\n",
       "      <td>296</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</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</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</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</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</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</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</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</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS     NX     RM   AGE     DIS  RAD  TAX  PTRATIO  \\\n",
       "0  0.00632  18.0   2.31     0  0.538  6.575  65.2  4.0900    1  296     15.3   \n",
       "1  0.02731   0.0   7.07     0  0.469  6.421  78.9  4.9671    2  242     17.8   \n",
       "2  0.02729   0.0   7.07     0  0.469  7.185  61.1  4.9671    2  242     17.8   \n",
       "3  0.03237   0.0   2.18     0  0.458  6.998  45.8  6.0622    3  222     18.7   \n",
       "4  0.06905   0.0   2.18     0  0.458  7.147  54.2  6.0622    3  222     18.7   \n",
       "\n",
       "        B  LSTAT  MEDV  \n",
       "0  396.90   4.98  24.0  \n",
       "1  396.90   9.14  21.6  \n",
       "2  392.83   4.03  34.7  \n",
       "3  394.63   2.94  33.4  \n",
       "4  396.90   5.33  36.2  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "boston = pd.read_csv(\"boston.csv\")\n",
    "\n",
    "boston.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "id": "FCRUBF5mdFYo"
   },
   "outputs": [],
   "source": [
    "x = boston.drop(\"MEDV\", axis=1).values #input factors\n",
    "\n",
    "y = boston[\"MEDV\"].values\n",
    "#values method converts a datafarme into array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 74
    },
    "id": "BXqpBNUEgEAR",
    "outputId": "413631d8-41ac-498f-bc88-8c4781c0193a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=1)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import RepeatedKFold\n",
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(x,y,test_size=0.3,random_state=1)\n",
    "\n",
    "#instantiate the model\n",
    "model = Ridge(alpha=1)\n",
    "\n",
    "model.fit(x_train,y_train)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "QziMOrx_3qIy",
    "outputId": "261eaa57-2b23-47d1-ce7d-f3b91569c1d6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7890510666829776"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#r squared\n",
    "model.score(x_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "li_4RZD24BKl",
    "outputId": "1bfb8137-52bc-44d3-a57d-e0d18353ceab"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.397091798887489"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = model.predict(x_test)\n",
    "\n",
    "#margin of error\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "mse = mean_squared_error(y_test, y_pred)\n",
    "rmse = mse ** 0.5\n",
    "rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "sqsbJJE540Cl",
    "outputId": "be1b54a8-f797-400f-85cb-681fcd1a90ff"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.882557479143369"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#overfitting\n",
    "y_pred_train = model.predict(x_train)\n",
    "\n",
    "#margin of error\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "mse = mean_squared_error(y_train, y_pred_train)\n",
    "rmse = mse ** 0.5\n",
    "rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "PdPyVGb_5LuU",
    "outputId": "f752a297-30bc-4be0-b6e3-47f4dd80344f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38.95161909934214"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "NBToU1585XkD",
    "outputId": "f2451535-a0f3-4329-b555-6ddb1e469b2b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-8.99352520e-02,  6.20345865e-02,  1.21404325e-02,  2.23426149e+00,\n",
       "       -1.12838152e+01,  2.89618901e+00, -4.81458007e-03, -1.36998976e+00,\n",
       "        2.83653073e-01, -1.22828776e-02, -8.84229846e-01,  7.09753443e-03,\n",
       "       -5.80033848e-01])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "23KECHI45hkG",
    "outputId": "0e00eca6-a85d-49b9-c58f-6b2ef1cf9ce9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NX', 'RM', 'AGE', 'DIS', 'RAD', 'TAX',\n",
       "       'PTRATIO', 'B', 'LSTAT'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "o = boston.drop(\"MEDV\", axis=1)\n",
    "o.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "id": "Y6WMZtsJ50sK"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>-0.089935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>0.062035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>0.012140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>2.234261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NX</th>\n",
       "      <td>-11.283815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>2.896189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>-0.004815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>-1.369990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>0.283653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>-0.012283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>-0.884230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.007098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>-0.580034</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0\n",
       "CRIM     -0.089935\n",
       "ZN        0.062035\n",
       "INDUS     0.012140\n",
       "CHAS      2.234261\n",
       "NX      -11.283815\n",
       "RM        2.896189\n",
       "AGE      -0.004815\n",
       "DIS      -1.369990\n",
       "RAD       0.283653\n",
       "TAX      -0.012283\n",
       "PTRATIO  -0.884230\n",
       "B         0.007098\n",
       "LSTAT    -0.580034"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(model.coef_, index=o.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "X3N6jpMuS_lm"
   },
   "source": [
    "**Ridge Regression**\n",
    "\n",
    "With crossvalidation and tuning\n",
    "\n",
    "RidgeCV: gridsearch is inbuilt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 248
    },
    "id": "CuAjkSM758-i",
    "outputId": "78f26540-dade-4db8-a9a8-11e32a14d26d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RidgeCV(alphas=array([0.1 , 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 ,\n",
       "       0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 , 0.31,\n",
       "       0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4 , 0.41, 0.42,\n",
       "       0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5 , 0.51, 0.52, 0.53,\n",
       "       0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6 , 0.61, 0.62, 0.63, 0.64,\n",
       "       0.65, 0.66, 0.67, 0.68, 0.69, 0.7 , 0.71, 0.72, 0.73, 0.74, 0.75,\n",
       "       0.76, 0.77, 0.78, 0.79, 0.8 , 0.81, 0.82, 0.83, 0.84, 0.85, 0.86,\n",
       "       0.87, 0.88, 0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97,\n",
       "       0.98, 0.99]),\n",
       "        cv=RepeatedKFold(n_repeats=3, n_splits=10, random_state=1),\n",
       "        scoring='neg_mean_absolute_error')"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import RidgeCV\n",
    "from numpy import arange\n",
    "\n",
    "#instantiate repeated k fold\n",
    "rcv = RepeatedKFold(n_splits=10,n_repeats=3,random_state=1)\n",
    "\n",
    "#instantiate ridgecv\n",
    "model = RidgeCV(alphas=arange(0.1, 1, 0.01), cv=rcv, scoring='neg_mean_absolute_error')\n",
    "\n",
    "model.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "U3JDcilvWV3f",
    "outputId": "66156b9f-dad7-4878-b463-636cf68269ac"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5799999999999997"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# summarize chosen configuration\n",
    "model.alpha_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "2I1ywghcWy1F",
    "outputId": "0fb708e5-1290-4c15-8630-c2d3e52c2acd"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7883167600760095"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#rsquared\n",
    "model.score(x_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "vq38HpfkW_VL",
    "outputId": "9e3dc9a9-92cd-41ae-e5c3-b54c8c33abfc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.4047382196086"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = model.predict(x_test)\n",
    "\n",
    "mse = mean_squared_error(y_test,y_pred)\n",
    "rmse = mse ** 0.5\n",
    "rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "6rPslgSUXNo2",
    "outputId": "ce263cd0-4afa-4519-ff7a-bd392021940a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.866642733557797"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#overfitting\n",
    "y_pred_train = model.predict(x_train)\n",
    "\n",
    "mse = mean_squared_error(y_train,y_pred_train)\n",
    "rmse = mse ** 0.5\n",
    "rmse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NONBLWqvX6rk"
   },
   "source": [
    "Linear regression\n",
    "\n",
    "R = 78.36, rmse = 4.45\n",
    "\n",
    "Ridge without cv and tuning\n",
    "\n",
    "R = 78.9, rmse=4.40\n",
    "\n",
    "Ridge with cv and tuning\n",
    "\n",
    "R = 78.83, rmse = 4.4047"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "x9wKijP5XY26",
    "outputId": "9148592f-77e2-4641-fb76-694cc05193e5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-9.22605745e-02,  6.16667500e-02,  2.50763986e-02,  2.30126902e+00,\n",
       "       -1.40928582e+01,  2.87272384e+00, -2.54431729e-03, -1.41037774e+00,\n",
       "        2.90013469e-01, -1.19966062e-02, -9.17381421e-01,  6.92039959e-03,\n",
       "       -5.76631711e-01])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 457
    },
    "id": "YGcuvnQ7Y0dE",
    "outputId": "dc401da8-2338-4973-93f7-decabcc4a7ab"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>-0.092261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>0.061667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>0.025076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>2.301269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NX</th>\n",
       "      <td>-14.092858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>2.872724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>-0.002544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>-1.410378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>0.290013</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>-0.011997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>-0.917381</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.006920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>-0.576632</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0\n",
       "CRIM     -0.092261\n",
       "ZN        0.061667\n",
       "INDUS     0.025076\n",
       "CHAS      2.301269\n",
       "NX      -14.092858\n",
       "RM        2.872724\n",
       "AGE      -0.002544\n",
       "DIS      -1.410378\n",
       "RAD       0.290013\n",
       "TAX      -0.011997\n",
       "PTRATIO  -0.917381\n",
       "B         0.006920\n",
       "LSTAT    -0.576632"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(model.coef_, index=o.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "e9PcrsWsZ035"
   },
   "source": [
    "**Lasso Regression**\n",
    "\n",
    "without cv and tuning\n",
    "\n",
    "ridge (L2) = SSR + lambda * slope square\n",
    "\n",
    "lasso (L1) = SSR + lambda * |slope|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "id": "xZAEI555Y9EO"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lasso(alpha=1)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "#instantiate lasso\n",
    "model = Lasso(alpha=1)\n",
    "\n",
    "model.fit(x_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "id": "ddYwMrRqbNHj"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6694782854622285"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#r squared\n",
    "model.score(x_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "id": "vJgLp4EebYRF"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.503980216349544"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = model.predict(x_test)\n",
    "\n",
    "mse = mean_squared_error(y_test,y_pred)\n",
    "rmse = mse ** 0.5\n",
    "rmse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Zqx9UnGqcK-A"
   },
   "source": [
    "**Lasso with cross validation and tuning**\n",
    "\n",
    "LassoCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "id": "wjrpxYZhbsq6"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3825.9654070020806, tolerance: 2.481023952830189\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3937.4085336641947, tolerance: 2.714946632075472\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3590.481940172951, tolerance: 2.5934341886792454\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3842.8859757629434, tolerance: 2.5396811477987424\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3847.4322311063806, tolerance: 2.575585109717869\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3307.5544828355232, tolerance: 2.5445537429467087\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3825.7045764854993, tolerance: 2.6257198871473357\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3752.1493001462586, tolerance: 2.6378354545454545\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3660.9379501162475, tolerance: 2.5574387460815045\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3629.2195126185143, tolerance: 2.5908931786833858\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3819.904751723614, tolerance: 2.547803311320755\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3651.842822423645, tolerance: 2.5357410345911946\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3722.113247945519, tolerance: 2.5606194591194966\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3654.18882932383, tolerance: 2.398980355345912\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3447.576667714755, tolerance: 2.6355054545454544\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3740.3689654481714, tolerance: 2.5433020877742947\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3853.35573419086, tolerance: 2.732188815047022\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3931.0372351075566, tolerance: 2.7137653354231976\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3548.382144533538, tolerance: 2.5430743510971787\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3810.3819219572542, tolerance: 2.649187755485894\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3137.9519502847143, tolerance: 2.48150084591195\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3927.4657985642043, tolerance: 2.5627118867924534\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3884.2778156086024, tolerance: 2.5951948459119496\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3701.8334613057414, tolerance: 2.527523798742138\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3760.729464259275, tolerance: 2.4719744388714737\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3514.588409985641, tolerance: 2.544758971786834\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3688.720714768311, tolerance: 2.571974275862069\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3927.4501817254677, tolerance: 2.7185748150470217\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3911.802443054072, tolerance: 2.661431272727273\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: UserWarning: Coordinate descent with alpha=0 may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:633: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 3777.2147124630646, tolerance: 2.7179846520376176\n",
      "  model = cd_fast.enet_coordinate_descent_gram(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:1714: UserWarning: With alpha=0, this algorithm does not converge well. You are advised to use the LinearRegression estimator\n",
      "  model.fit(X, y)\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:647: UserWarning: Coordinate descent with no regularization may lead to unexpected results and is discouraged.\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "C:\\Users\\Yashika Batra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:647: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 4.162e+03, tolerance: 2.874e+00 Linear regression models with null weight for the l1 regularization term are more efficiently fitted using one of the solvers implemented in sklearn.linear_model.Ridge/RidgeCV instead.\n",
      "  model = cd_fast.enet_coordinate_descent(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LassoCV(alphas=array([0.  , 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 ,\n",
       "       0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 , 0.21,\n",
       "       0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 , 0.31, 0.32,\n",
       "       0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4 , 0.41, 0.42, 0.43,\n",
       "       0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5 , 0.51, 0.52, 0.53, 0.54,\n",
       "       0.55, 0.56, 0.57, 0.58, 0.59, 0.6 , 0.61, 0.62, 0.63, 0.64, 0.65,\n",
       "       0.66, 0.67, 0.68, 0.69, 0.7 , 0.71, 0.72, 0.73, 0.74, 0.75, 0.76,\n",
       "       0.77, 0.78, 0.79, 0.8 , 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87,\n",
       "       0.88, 0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98,\n",
       "       0.99]),\n",
       "        cv=RepeatedKFold(n_repeats=3, n_splits=10, random_state=1))"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LassoCV\n",
    "\n",
    "#instantiate repeated k fold\n",
    "rcv = RepeatedKFold(n_splits=10,n_repeats=3,random_state=1)\n",
    "\n",
    "model = LassoCV(alphas=arange(0,1,0.01),\\\n",
    "                cv=rcv)#default scoring is r squared\n",
    "\n",
    "model.fit(x_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "id": "NMxejSFieJ9N"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.alpha_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "alpha 1 means model is same as traditional linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "id": "tG8yrxngeOQ2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7836295385076293"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(x_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "id": "6aGRZQw6fJ4E"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.453237437198148"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = model.predict(x_test)\n",
    "\n",
    "mse = mean_squared_error(y_test,y_pred)\n",
    "rmse = mse ** 0.5\n",
    "rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "id": "MBIwN2e3eZ6P"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>-0.098542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>0.060784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>0.059172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>2.439560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NX</th>\n",
       "      <td>-21.469965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>2.795814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>0.003575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>-1.516272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>0.307542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>-0.011280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>-1.005466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.006450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>-0.568835</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0\n",
       "CRIM     -0.098542\n",
       "ZN        0.060784\n",
       "INDUS     0.059172\n",
       "CHAS      2.439560\n",
       "NX      -21.469965\n",
       "RM        2.795814\n",
       "AGE       0.003575\n",
       "DIS      -1.516272\n",
       "RAD       0.307542\n",
       "TAX      -0.011280\n",
       "PTRATIO  -1.005466\n",
       "B         0.006450\n",
       "LSTAT    -0.568835"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(model.coef_,index=o.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dZHAuRlPe_be"
   },
   "source": [
    "Ridge with cv and tuning\n",
    "\n",
    "R = 78.83, rmse=4.4047\n",
    "\n",
    "Lasso with cv and tuning\n",
    "\n",
    "R= 77.9, rmse = 4.49"
   ]
  }
 ],
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