Linear-regression.ipynb

{
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   "source": [
    "#importing all libraries required\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "69fee00c-5552-4c10-9390-2084bc62b326",
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   "outputs": [],
   "source": [
    "data = pd.read_csv(\"score.csv\")"
   ]
  },
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   "execution_count": 9,
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Hours</th>\n",
       "      <th>Scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.5</td>\n",
       "      <td>21</td>\n",
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       "      <th>1</th>\n",
       "      <td>5.1</td>\n",
       "      <td>47</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.2</td>\n",
       "      <td>27</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8.5</td>\n",
       "      <td>75</td>\n",
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       "      <th>4</th>\n",
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       "      <td>30</td>\n",
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       "      <th>5</th>\n",
       "      <td>1.5</td>\n",
       "      <td>20</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>9.2</td>\n",
       "      <td>88</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.5</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8.3</td>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2.7</td>\n",
       "      <td>25</td>\n",
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      "text/plain": [
       "   Hours  Scores\n",
       "0    2.5      21\n",
       "1    5.1      47\n",
       "2    3.2      27\n",
       "3    8.5      75\n",
       "4    3.5      30\n",
       "5    1.5      20\n",
       "6    9.2      88\n",
       "7    5.5      60\n",
       "8    8.3      81\n",
       "9    2.7      25"
      ]
     },
     "execution_count": 9,
     "metadata": {},
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   ],
   "source": [
    "data.head(10)"
   ]
  },
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       "(array([[2.5],\n",
       "        [5.1],\n",
       "        [3.2],\n",
       "        [8.5],\n",
       "        [3.5],\n",
       "        [1.5],\n",
       "        [9.2],\n",
       "        [5.5],\n",
       "        [8.3],\n",
       "        [2.7],\n",
       "        [7.7],\n",
       "        [5.9],\n",
       "        [4.5],\n",
       "        [3.3],\n",
       "        [1.1],\n",
       "        [8.9],\n",
       "        [2.5],\n",
       "        [1.9],\n",
       "        [6.1],\n",
       "        [7.4],\n",
       "        [2.7],\n",
       "        [4.8],\n",
       "        [3.8],\n",
       "        [6.9],\n",
       "        [7.8]]),\n",
       " array([21, 47, 27, 75, 30, 20, 88, 60, 81, 25, 85, 62, 41, 42, 17, 95, 30,\n",
       "        24, 67, 69, 30, 54, 35, 76, 86], dtype=int64))"
      ]
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   "source": [
    "#preparing the data\n",
    "#iloc is slicing \n",
    "x = data.iloc[:,:-1].values #hours\n",
    "y= data.iloc[:, 1].values #score\n",
    "\n",
    "x, y\n",
    "#now the data has been splited"
   ]
  },
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   "execution_count": null,
   "id": "7b6e944a-4457-4990-83e3-1e48b1c15493",
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       "      <th></th>\n",
       "      <th>Hours</th>\n",
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       "      <td>3.2</td>\n",
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       "      <td>8.5</td>\n",
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       "      <th>6</th>\n",
       "      <td>9.2</td>\n",
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       "      <td>5.5</td>\n",
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       "      <td>8.3</td>\n",
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       "      <th>9</th>\n",
       "      <td>2.7</td>\n",
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       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>7.7</td>\n",
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       "      <th>11</th>\n",
       "      <td>5.9</td>\n",
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       "      <th>12</th>\n",
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       "      <td>3.3</td>\n",
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       "      <th>14</th>\n",
       "      <td>1.1</td>\n",
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       "      <th>15</th>\n",
       "      <td>8.9</td>\n",
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       "      <th>16</th>\n",
       "      <td>2.5</td>\n",
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       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1.9</td>\n",
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       "      <th>18</th>\n",
       "      <td>6.1</td>\n",
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       "      <th>19</th>\n",
       "      <td>7.4</td>\n",
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       "      <td>2.7</td>\n",
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       "      <td>4.8</td>\n",
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       "      <th>22</th>\n",
       "      <td>3.8</td>\n",
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       "      <th>23</th>\n",
       "      <td>6.9</td>\n",
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       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>7.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Hours\n",
       "0     2.5\n",
       "1     5.1\n",
       "2     3.2\n",
       "3     8.5\n",
       "4     3.5\n",
       "5     1.5\n",
       "6     9.2\n",
       "7     5.5\n",
       "8     8.3\n",
       "9     2.7\n",
       "10    7.7\n",
       "11    5.9\n",
       "12    4.5\n",
       "13    3.3\n",
       "14    1.1\n",
       "15    8.9\n",
       "16    2.5\n",
       "17    1.9\n",
       "18    6.1\n",
       "19    7.4\n",
       "20    2.7\n",
       "21    4.8\n",
       "22    3.8\n",
       "23    6.9\n",
       "24    7.8"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# there will be be 2 things: test annd train \n",
    "# wew want all rows means : and the which column? mention it after column\n",
    "# -1 mean that all columns to be selected \n",
    "x= data.iloc[:, :-1]\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5904b724-3698-42aa-ad9e-1d07863582bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "regressor = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "02f261c3-f454-4011-86ab-3389aabae489",
   "metadata": {},
   "outputs": [],
   "source": [
    "# test should be less than train part\n",
    "# test< train size\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "74f5bdd9-61f4-48f6-8dc4-7286e7a4e2b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "#this function divides data into two parts\n",
    "#20% of data will be reserved for evaluation and then 80% of data will be trained \n",
    "x_train, x_test, y_train, y_test = train_test_split(x,y,test_size =0.2, random_state = 42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "3287ae21-df45-4f23-9409-c1ab40c4a5af",
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       "      <th>Hours</th>\n",
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       "      <th>9</th>\n",
       "      <td>2.7</td>\n",
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       "      <td>5.1</td>\n",
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       "      <th>22</th>\n",
       "      <td>3.8</td>\n",
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       "      <td>1.5</td>\n",
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       "      <td>3.2</td>\n",
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       "      <td>4.5</td>\n",
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       "      <td>8.9</td>\n",
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       "      <td>3.5</td>\n",
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       "      <th>20</th>\n",
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       "      <th>18</th>\n",
       "      <td>6.1</td>\n",
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       "      <th>24</th>\n",
       "      <td>7.8</td>\n",
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       "      <td>5.5</td>\n",
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       "      <td>7.7</td>\n",
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       "      <th>14</th>\n",
       "      <td>1.1</td>\n",
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       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>7.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>9.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "    Hours\n",
       "9     2.7\n",
       "13    3.3\n",
       "1     5.1\n",
       "22    3.8\n",
       "5     1.5\n",
       "2     3.2\n",
       "12    4.5\n",
       "15    8.9\n",
       "3     8.5\n",
       "4     3.5\n",
       "20    2.7\n",
       "17    1.9\n",
       "21    4.8\n",
       "18    6.1\n",
       "24    7.8\n",
       "7     5.5\n",
       "10    7.7\n",
       "14    1.1\n",
       "19    7.4\n",
       "6     9.2"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "80b8be13-6f3d-42ee-b063-7715b2418da1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([25, 42, 47, 35, 20, 27, 41, 95, 75, 30, 30, 24, 54, 67, 86, 60, 85,\n",
       "       17, 69, 88], dtype=int64)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train"
   ]
  },
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   "execution_count": 15,
   "id": "28602798-5757-4699-8b32-b32d036de8bc",
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       "      <td>8.3</td>\n",
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       "    Hours\n",
       "8     8.3\n",
       "16    2.5\n",
       "0     2.5\n",
       "23    6.9\n",
       "11    5.9"
      ]
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     "execution_count": 15,
     "metadata": {},
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   ],
   "source": [
    "x_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "631b8419-6126-4d73-a307-0ebf2027d680",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([81, 30, 21, 76, 62], dtype=int64)"
      ]
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     "execution_count": 24,
     "metadata": {},
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    "y_test"
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   "cell_type": "code",
   "execution_count": 16,
   "id": "9fc91d53-6d17-4fa0-b8a9-502e2551656a",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete.\n"
     ]
    }
   ],
   "source": [
    "regressor.fit(x_train, y_train)\n",
    "print(\"Training complete.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d0e8b2c8-c88e-4c4a-bd71-c890f4c76746",
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   "outputs": [
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       "      <th>Hours</th>\n",
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       "      <th>8</th>\n",
       "      <td>8.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>6.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>5.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Hours\n",
       "8     8.3\n",
       "16    2.5\n",
       "0     2.5\n",
       "23    6.9\n",
       "11    5.9"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "4f07ee58-f81f-4f76-90bb-313a09c47f5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([83.18814104, 27.03208774, 27.03208774, 69.63323162, 59.95115347])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regressor.predict(x_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "3aa612ee-f27d-4103-a39a-238524dbb7fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x16ecd6e0c10>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "af7a1dce-6a68-4ba2-b07f-df3595e7db74",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the calculated parameters are : Theta_1:  9.682078154455697 theta_2:  2.826892353899737\n"
     ]
    }
   ],
   "source": [
    "print(\"the calculated parameters are : Theta_1: \", regressor.coef_[0], \"theta_2: \", regressor.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d9d71861-211c-4c94-b2a0-358f3c6a7e42",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Hours\n",
      "8     8.3\n",
      "16    2.5\n",
      "0     2.5\n",
      "23    6.9\n",
      "11    5.9\n"
     ]
    }
   ],
   "source": [
    "#making predictions:\n",
    "print(x_test)\n",
    "y_pred = regressor.predict(x_test) #predicting the score\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6f7eb609-8f8e-44d3-8f34-c4733988bc49",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "        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>Actual</th>\n",
       "      <th>Predicted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>81</td>\n",
       "      <td>83.188141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>30</td>\n",
       "      <td>27.032088</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21</td>\n",
       "      <td>27.032088</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>76</td>\n",
       "      <td>69.633232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>62</td>\n",
       "      <td>59.951153</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Actual  Predicted\n",
       "0      81  83.188141\n",
       "1      30  27.032088\n",
       "2      21  27.032088\n",
       "3      76  69.633232\n",
       "4      62  59.951153"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df= pd.DataFrame({\"Actual\": y_test, \"Predicted\": y_pred})\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d71c190e-9d63-4c7d-8498-e50e3118f308",
   "metadata": {},
   "source": [
    "Comparing the actual and predicted errors\n",
    "and evalutaing the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cda7f8b8-521d-40a9-a815-d3dcbc76a066",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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