Linear_Regression_Task2_200070030.ipynb

{
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  {
   "cell_type": "markdown",
   "id": "89223f98",
   "metadata": {},
   "source": [
    "### Importing useful libraries \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "26f77ebe",
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   "outputs": [],
   "source": [
    "# This Python 3 environment comes with many helpful analytics libraries installed\n",
    "# For example, here's several helpful packages to load in\n",
    "import numpy as np   # linear algebra\n",
    "import matplotlib.pyplot as plt # data visualization\n",
    "import pandas as pd  # data processing, CSV file I/O (e.g. pd.read_csv)\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31c8220d",
   "metadata": {},
   "source": [
    "### Loading the dataset \n",
    "#### For implementation we will be using house prediction dataset . The dataset can be found [here](https://github.com/vrinda01go/Hellofoss/blob/main/Room_price_data.csv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1c5d873a",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"Hostel_Linear-Dataset.csv\")  #import text file "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "1ca9aba0",
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Price</th>\n",
       "      <th>Hostel No.</th>\n",
       "      <th>Occupancy</th>\n",
       "      <th>Room Size</th>\n",
       "      <th>Floor</th>\n",
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       "    Price  Hostel No.  Occupancy  Room Size  Floor\n",
       "0  2540.0           3          1        686      8\n",
       "1  2900.0           3          2        966      5\n",
       "2     NaN           3          1        788      8\n",
       "3  2362.0           3          2        924      2\n",
       "4     NaN           3          2       1098      5"
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   "source": [
    "df.head()"
   ]
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  {
   "cell_type": "markdown",
   "id": "af08f245",
   "metadata": {},
   "source": [
    "# Visualizing and Cleaning the data\n",
    "\n",
    "We will now be removing the nan values and identical values from the dataset\n",
    "\n",
    "For seeing if there are nan values in the dataset we will use the isna() function and then to remove them we will use the dropna() function. We will need to set additional parameters like rows and columns in the dropna function depending on the number of nan values present for each column\n",
    "\n",
    "Using the sum() function with isna() function we can get to know the number of missing values in each column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "2fd4babb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Price         1531\n",
       "Hostel No.       0\n",
       "Occupancy        0\n",
       "Room Size        0\n",
       "Floor            0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum()"
   ]
  },
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   "cell_type": "markdown",
   "id": "83ef03c3",
   "metadata": {},
   "source": [
    "After this we will proceed to remove the nan values \n",
    "\n",
    "Since there are not many nan values in the column 'Price' as compared to the number of rows we will remove the rows which have nan values. \n",
    "\n",
    "Reseting the index after removing the nan values and dropping the old index will also be important"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "b65e4503",
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       "<p>4817 rows × 5 columns</p>\n",
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      "text/plain": [
       "       Price  Hostel No.  Occupancy  Room Size  Floor\n",
       "0     2540.0           3          1        686      8\n",
       "1     2900.0           3          2        966      5\n",
       "2     2362.0           3          2        924      2\n",
       "3     1432.0           2          1        706      3\n",
       "4     1702.0           2          2       1038      3\n",
       "...      ...         ...        ...        ...    ...\n",
       "4812  1624.0           2          1        674      3\n",
       "4813  1470.0           2          1        626      3\n",
       "4814  1020.0           3          2       1006      3\n",
       "4815  2400.0           2          2        938      1\n",
       "4816   950.0           3          2       1053      2\n",
       "\n",
       "[4817 rows x 5 columns]"
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   "source": [
    "df=df.dropna().reset_index()\n",
    "df=df[['Price','Hostel No.','Occupancy','Room Size','Floor']]\n",
    "df"
   ]
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   "cell_type": "markdown",
   "id": "40784889",
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   "source": [
    "Now we can use the drop_duplicate function to remove the duplicate values\n",
    "\n",
    "This function has a parameter calle 'keep' where we specifiy to drop and which value to keep\n",
    "\n",
    "For this excercise we will keep the first values and drop the rest of the duplicates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "75fa3dc8",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "       Price  Hostel No.  Occupancy  Room Size  Floor\n",
       "0     2540.0           3          1        686      8\n",
       "1     2900.0           3          2        966      5\n",
       "2     2362.0           3          2        924      2\n",
       "3     1432.0           2          1        706      3\n",
       "4     1702.0           2          2       1038      3\n",
       "...      ...         ...        ...        ...    ...\n",
       "4812  1624.0           2          1        674      3\n",
       "4813  1470.0           2          1        626      3\n",
       "4814  1020.0           3          2       1006      3\n",
       "4815  2400.0           2          2        938      1\n",
       "4816   950.0           3          2       1053      2\n",
       "\n",
       "[4815 rows x 5 columns]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
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   "source": [
    "df=df.drop_duplicates()\n",
    "df"
   ]
  },
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   "cell_type": "markdown",
   "id": "a007a33f",
   "metadata": {},
   "source": [
    "For visualizing the data we will first start with looking at the distribution of different columns to see if there are enough number for each category in every column and dropping them if the data is biased for one category more than the other"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "b325df62",
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAEICAYAAACzliQjAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAT6ElEQVR4nO3df6zd9X3f8edrdsovBzAivXNsFlPJooO4S8MVo0WKrkc33CYN/DE0R2nmTHSWJpqRjmmDrVs0aV74o1TpktLNCmlcgbhyTCZbTdIFuVhZtBAWk7SOcRBucIiNY6eDODFipGbv/XG+TFfX19e+59x7zz3+PB/S0Tnn8/31Okf3vs73fM+vVBWSpDb8jWEHkCQtHktfkhpi6UtSQyx9SWqIpS9JDbH0Jakhlr40gyRrk1SS5cPOIs0nS1/NS3I4yWtJTr15At4+7FzSQrD0pZ5fr6oVb56AlxZiIz5z0LBZ+tJ5SPL2JLuTvJzkUJJ/OmXaRUk+keSl7vSJJBd10yaSHEnyr5P8APijod0ICXCvQzo/jwEH6B32+XngiSTfrao9wL8FbgbeBRSwC/gd4N91y/5N4CrgHbijpSGL372j1iU5DFwNnO6G9gIfBV4A3gKsAg4DV1bVT7plPg6sqqoPJ/lL4CNV9cVu2m3Af62qtUkmgC8Dl1fV/1mcWySdnXsdUs8dVXVld7pj2rS3Ay+/Wfid7wGrp0z/3rRpU18I/qGFr6XC0pfO7SXgqiRvnTL2t4CjU6a/Y9q0qS8E+3RaS4alL51DVX0f+J/Ax5NcnOQXgLuAR7tZHgN+J8nbklwN/HvgkeGklWbnC7nS+fkA8F/o7cG/Anysqp7opv1H4HLgL7rrn+vGpCXHF3IlqSEe3pGkhlj6ktQQS1+SGmLpS1JDlvy7d66++upau3ZtX8u++uqrXHbZZfMbaIGMUlYYrbyjlBVGK+8oZYXRyjto1n379v1VVb3tjAlVtaRPN954Y/XrySef7HvZxTZKWatGK+8oZa0arbyjlLVqtPIOmhX4Rs3QqR7ekaSGWPqS1BBLX5IaYulLUkMsfUlqyDlLP8lnkpxI8u0pY1cleSLJ8935yinT7u9+Tu657sck3hy/Mcn+btp/TpL5vzmSpNmcz57+Z4GN08buA/ZU1TpgT3edJNcDm4AbumUeSrKsW+YPgS3Auu40fZ2SpAV2ztKvqq8AL08bvh3Y3l3eDtwxZXyyql6vqheAQ8BNSVbR+7m4r3XvH/3jKctIkhZJv5/IHauqYwBVdSzJz3bjq4Gnpsx3pBv76+7y9PEZJdlC71kBY2Nj7N27t6+Qp06d6nvZxTZKWWG08o5SVhitvKOUFUYr70Jlne+vYZjpOH3NMj6jqtoGbAMYHx+viYmJvsLs3buXfpddbPOVde19Xxg8zHm4d/0bPPjVV///9cMPvHdRttuPUfo7gNHKO0pZYbTyLlTWft+9c7w7ZEN3fqIbPwJcM2W+NfR+aehId3n6uCRpEfVb+ruBzd3lzcCuKeObklyU5Fp6L9g+3R0K+kmSm7t37fzjKctIkhbJOQ/vJHkMmACuTnIE+BjwALAjyV3Ai8CdAFV1IMkO4FngNHB3Vb3Rreqf0Xsn0CXAl7qTJGkRnbP0q+oDZ5l061nm3wpsnWH8G8A755ROkjSv/ESuJDXE0pekhlj6ktQQS1+SGrLkfyN3FPXzAal715/mw4v0wSpJ7XJPX5IaYulLUkMsfUlqiKUvSQ3xhVyNvHO9cL5QL5Iv5W8Wlc7GPX1JaoilL0kNsfQlqSGWviQ1xNKXpIZY+pLUEEtfkhpi6UtSQyx9SWqIpS9JDbH0JakhF/R37+w/etIfJpGkKdzTl6SGWPqS1BBLX5IaYulLUkMsfUlqiKUvSQ2x9CWpIZa+JDXE0pekhlj6ktSQgUo/yW8nOZDk20keS3JxkquSPJHk+e585ZT5709yKMlzSW4bPL4kaS76Lv0kq4F/DoxX1TuBZcAm4D5gT1WtA/Z010lyfTf9BmAj8FCSZYPFlyTNxaCHd5YDlyRZDlwKvATcDmzvpm8H7ugu3w5MVtXrVfUCcAi4acDtS5LmoO/Sr6qjwO8CLwLHgJNV9WVgrKqOdfMcA362W2Q18P0pqzjSjUmSFkmqqr8Fe8fqHwf+EfAj4HPATuBTVXXllPleqaqVSf4A+FpVPdKNPwx8saoen2HdW4AtAGNjYzdOTk72lfHEyyc5/lpfiy66sUsYmaxwZt71q68YWpb9R0/OOn2h7tuFus2nTp1ixYoVC7Lu+TZKWWG08g6adcOGDfuqanz6+CDfp/8rwAtV9UOAJJ8Hfhk4nmRVVR1Lsgo40c1/BLhmyvJr6B0OOkNVbQO2AYyPj9fExERfAT/56C4e3D8aPxlw7/rTI5MVzsx7+IMTQ8tyrt9MWKj7dqFu8969e+n3b36xjVJWGK28C5V1kGP6LwI3J7k0SYBbgYPAbmBzN89mYFd3eTewKclFSa4F1gFPD7B9SdIc9b37U1VfT7ITeAY4DXyT3t75CmBHkrvoPTDc2c1/IMkO4Nlu/rur6o0B80uS5mCg57xV9THgY9OGX6e31z/T/FuBrYNsU5LUPz+RK0kNsfQlqSGWviQ1xNKXpIZY+pLUEEtfkhpi6UtSQyx9SWqIpS9JDbH0Jakhlr4kNcTSl6SGWPqS1BBLX5IaYulLUkMsfUlqiKUvSQ2x9CWpIZa+JDXE0pekhlj6ktQQS1+SGmLpS1JDLH1JaoilL0kNsfQlqSGWviQ1xNKXpIZY+pLUEEtfkhpi6UtSQyx9SWqIpS9JDRmo9JNcmWRnku8kOZjkl5JcleSJJM935yunzH9/kkNJnkty2+DxJUlzMeie/u8Df1pVPw/8HeAgcB+wp6rWAXu66yS5HtgE3ABsBB5KsmzA7UuS5qDv0k9yOfAe4GGAqvppVf0IuB3Y3s22Hbiju3w7MFlVr1fVC8Ah4KZ+ty9JmrtUVX8LJu8CtgHP0tvL3wfcAxytqiunzPdKVa1M8ingqap6pBt/GPhSVe2cYd1bgC0AY2NjN05OTvaV8cTLJzn+Wl+LLrqxSxiZrHBm3vWrrxhalv1HT846faHu24W6zadOnWLFihULsu75NkpZYbTyDpp1w4YN+6pqfPr48gEyLQfeDXykqr6e5PfpDuWcRWYYm/ERp6q20XtAYXx8vCYmJvoK+MlHd/Hg/kFu4uK5d/3pkckKZ+Y9/MGJoWX58H1fmHX6Qt23C3Wb9+7dS79/84ttlLLCaOVdqKyDHNM/Ahypqq9313fSexA4nmQVQHd+Ysr810xZfg3w0gDblyTNUd+lX1U/AL6f5Lpu6FZ6h3p2A5u7sc3Aru7ybmBTkouSXAusA57ud/uSpLkb9DnvR4BHk/wM8F3gn9B7INmR5C7gReBOgKo6kGQHvQeG08DdVfXGgNuXJM3BQKVfVd8CznihgN5e/0zzbwW2DrJNSVL//ESuJDXE0pekhlj6ktQQS1+SGmLpS1JDLH1JaoilL0kNsfQlqSGWviQ1xNKXpIZY+pLUEEtfkhpi6UtSQyx9SWqIpS9JDbH0Jakhlr4kNcTSl6SGWPqS1BBLX5IaYulLUkMsfUlqiKUvSQ2x9CWpIZa+JDXE0pekhlj6ktQQS1+SGmLpS1JDLH1JaoilL0kNsfQlqSGWviQ1ZODST7IsyTeT/El3/aokTyR5vjtfOWXe+5McSvJcktsG3bYkaW7mY0//HuDglOv3AXuqah2wp7tOkuuBTcANwEbgoSTL5mH7kqTzNFDpJ1kDvBf49JTh24Ht3eXtwB1Txier6vWqegE4BNw0yPYlSXOTqup/4WQn8HHgrcC/rKr3JflRVV05ZZ5Xqmplkk8BT1XVI934w8CXqmrnDOvdAmwBGBsbu3FycrKvfCdePsnx1/padNGNXcLIZIUz865ffcXQsuw/enLW6Qt13y7UbT516hQrVqxYkHXPt1HKCqOVd9CsGzZs2FdV49PHl/e7wiTvA05U1b4kE+ezyAxjMz7iVNU2YBvA+Ph4TUycz+rP9MlHd/Hg/r5v4qK6d/3pkckKZ+Y9/MGJoWX58H1fmHX6Qt23C3Wb9+7dS79/84ttlLLCaOVdqKyD/CfcArw/ya8BFwOXJ3kEOJ5kVVUdS7IKONHNfwS4Zsrya4CXBti+JGmO+j6mX1X3V9WaqlpL7wXaP6uq3wB2A5u72TYDu7rLu4FNSS5Kci2wDni67+SSpDlbiOMJDwA7ktwFvAjcCVBVB5LsAJ4FTgN3V9UbC7B9SdJZzEvpV9VeYG93+X8Dt55lvq3A1vnYpiRp7vxEriQ1xNKXpIZY+pLUEEtfkhpi6UtSQyx9SWqIpS9JDbH0Jakho/MNX5I0BGvP8YV+C+WzGy9bkPW6py9JDXFPX+rTQu0B3rv+9Dm/LvrwA+9dkG3rwueeviQ1xNKXpIZ4eEfSkjdfh9LO59DZhc49fUlqiHv6ks7b9D1u95xHj3v6ktQQS1+SGmLpS1JDLH1JaoilL0kNsfQlqSGWviQ1xNKXpIZY+pLUEEtfkhpi6UtSQyx9SWqIpS9JDbH0Jakhlr4kNcTSl6SG9F36Sa5J8mSSg0kOJLmnG78qyRNJnu/OV05Z5v4kh5I8l+S2+bgBkqTzN8ie/mng3qr628DNwN1JrgfuA/ZU1TpgT3edbtom4AZgI/BQkmWDhJckzU3fpV9Vx6rqme7yT4CDwGrgdmB7N9t24I7u8u3AZFW9XlUvAIeAm/rdviRp7lJVg68kWQt8BXgn8GJVXTll2itVtTLJp4CnquqRbvxh4EtVtXOG9W0BtgCMjY3dODk52VeuEy+f5PhrfS266MYuYWSywpl516++YmhZ9h89Oev0Ub9vZzKs+3v6fX0h3rdLxbVXLGPFihV9L79hw4Z9VTU+fXzgH0ZPsgJ4HPhoVf04yVlnnWFsxkecqtoGbAMYHx+viYmJvrJ98tFdPLh/NH77/d71p0cmK5yZ9/AHJ4aW5Vw/zD3q9+1MhnV/T7+vL8T7dqn47MbL6Lf7ZjPQu3eSvIVe4T9aVZ/vho8nWdVNXwWc6MaPANdMWXwN8NIg25ckzc0g794J8DBwsKp+b8qk3cDm7vJmYNeU8U1JLkpyLbAOeLrf7UuS5m6Q5zm3AB8C9if5Vjf2b4AHgB1J7gJeBO4EqKoDSXYAz9J758/dVfXGANuXJM1R36VfVV9l5uP0ALeeZZmtwNZ+tylJGoyfyJWkhlj6ktQQS1+SGmLpS1JDLH1JaoilL0kNsfQlqSGWviQ1xNKXpIZY+pLUEEtfkhpi6UtSQyx9SWqIpS9JDbH0Jakhlr4kNcTSl6SGWPqS1BBLX5IaYulLUkMsfUlqiKUvSQ2x9CWpIZa+JDXE0pekhlj6ktQQS1+SGmLpS1JDLH1JaoilL0kNsfQlqSGWviQ1xNKXpIYseukn2ZjkuSSHkty32NuXpJYtauknWQb8AfCrwPXAB5Jcv5gZJKlli72nfxNwqKq+W1U/BSaB2xc5gyQ1K1W1eBtL/iGwsap+s7v+IeDvVtVvTZtvC7Clu3od8Fyfm7wa+Ks+l11so5QVRivvKGWF0co7SllhtPIOmvUdVfW26YPLB1hhPzLD2BmPOlW1Ddg28MaSb1TV+KDrWQyjlBVGK+8oZYXRyjtKWWG08i5U1sU+vHMEuGbK9TXAS4ucQZKatdil/7+AdUmuTfIzwCZg9yJnkKRmLerhnao6neS3gP8OLAM+U1UHFnCTAx8iWkSjlBVGK+8oZYXRyjtKWWG08i5I1kV9IVeSNFx+IleSGmLpS1JDLsjST/KZJCeSfHvYWc4lyTVJnkxyMMmBJPcMO9PZJLk4ydNJ/rzL+h+Gnel8JFmW5JtJ/mTYWWaT5HCS/Um+leQbw85zLkmuTLIzyXe6v99fGnammSS5rrtP3zz9OMlHh51rNkl+u/sf+3aSx5JcPG/rvhCP6Sd5D3AK+OOqeuew88wmySpgVVU9k+StwD7gjqp6dsjRzpAkwGVVdSrJW4CvAvdU1VNDjjarJP8CGAcur6r3DTvP2SQ5DIxX1Uh8eCjJduB/VNWnu3fjXVpVPxpyrFl1XwVzlN6HQr837DwzSbKa3v/W9VX1WpIdwBer6rPzsf4Lck+/qr4CvDzsHOejqo5V1TPd5Z8AB4HVw001s+o51V19S3da0nsNSdYA7wU+PewsF5IklwPvAR4GqKqfLvXC79wK/OVSLfwplgOXJFkOXMo8fp7pgiz9UZVkLfCLwNeHHOWsukMl3wJOAE9U1ZLN2vkE8K+A/zvkHOejgC8n2dd9FclS9nPAD4E/6g6dfTrJZcMOdR42AY8NO8Rsquoo8LvAi8Ax4GRVfXm+1m/pLxFJVgCPAx+tqh8PO8/ZVNUbVfUuep+mvinJkj18luR9wImq2jfsLOfplqp6N71vob27O0y5VC0H3g38YVX9IvAqsKS/Kr07BPV+4HPDzjKbJCvpfRHltcDbgcuS/MZ8rd/SXwK64+OPA49W1eeHned8dE/l9wIbh5tkVrcA7++OlU8Cfy/JI8ONdHZV9VJ3fgL4b/S+lXapOgIcmfJMbye9B4Gl7FeBZ6rq+LCDnMOvAC9U1Q+r6q+BzwO/PF8rt/SHrHtx9GHgYFX93rDzzCbJ25Jc2V2+hN4f53eGGmoWVXV/Va2pqrX0ntb/WVXN2x7TfEpyWfdCPt1hkn8ALNl3n1XVD4DvJ7muG7oVWHJvPpjmAyzxQzudF4Gbk1za9cOt9F7rmxcXZOkneQz4GnBdkiNJ7hp2plncAnyI3l7om28p+7VhhzqLVcCTSf6C3vcoPVFVS/ptkCNkDPhqkj8Hnga+UFV/OuRM5/IR4NHu7+FdwH8abpyzS3Ip8Pfp7TUvad2zp53AM8B+ej09b1/JcEG+ZVOSNLMLck9fkjQzS1+SGmLpS1JDLH1JaoilL0kNsfQlqSGWviQ15P8BgbuTkpp6QBAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "columns = df.columns\n",
    "for column in columns:\n",
    "    df.hist(column)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9811a731",
   "metadata": {},
   "source": [
    "We can clearly notice that for the Occupancy column the (occupancy) = 4 has a really low set of data points as compared to others. Hence we can proceed in dropping those rows where the occupancy is 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "825783c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "df.drop(df[df[\"Occupancy\"]==4].index,inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "30c64310",
   "metadata": {},
   "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>Price</th>\n",
       "      <th>Hostel No.</th>\n",
       "      <th>Occupancy</th>\n",
       "      <th>Room Size</th>\n",
       "      <th>Floor</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2540.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>686</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2900.0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>966</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2362.0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>924</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1432.0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>706</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1702.0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1038</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Price  Hostel No.  Occupancy  Room Size  Floor\n",
       "0  2540.0           3          1        686      8\n",
       "1  2900.0           3          2        966      5\n",
       "2  2362.0           3          2        924      2\n",
       "3  1432.0           2          1        706      3\n",
       "4  1702.0           2          2       1038      3"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f333875b",
   "metadata": {},
   "source": [
    "We will now write the columns between categorical and numerical\n",
    "\n",
    "categorical = Hostel No, occupancy, floor\n",
    "\n",
    "Numerical = price, occupancy, roomsize, floor, hostel No.\n",
    "\n",
    "Remember that we can treat Hostel Number and occupancy as numerical or categorical. For this notebook we will treat them as categorical for data visualization and numerical for the regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f34ca6a",
   "metadata": {},
   "source": [
    "We will also plot the scatter plots and the correlation map to analyse the relation ships between different numerical columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "f4a3ab6e",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "categorical = ['Hostel No.', 'Occupancy', 'Floor']\n",
    "numerical = [ 'Price', 'Room Size']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "df2b588a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for column1 in numerical:\n",
    "    for column2 in numerical:\n",
    "        if(column1 != column2):\n",
    "            sns.scatterplot(x=df[column1],y=df[column2])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "625b89a8",
   "metadata": {},
   "source": [
    "We can notice that there are no linear relation present between the numerical columns. Hence no need to drop anything"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a7f95fa",
   "metadata": {},
   "source": [
    "Now we will plot box plots of categorical and numerical columns to get more information about the number of outliers and the distrubtion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "e73f0769",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAD4CAYAAADsKpHdAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAW80lEQVR4nO3df3Dc9Z3f8efbNuHIAIdlDoVaTEwnnmtsp1eKSmndXDWlllwuV7kzoXWm1J7C1COZpmnaucZq07m/GJO5m6NHepLGVygm5EJcevW6CZztcU6XNsOPmksaLHMcbrgQgYHEhhyZ9DjLfveP/chd5LWNtNLuWno+Znb03ff3+9n9aOdrvfz5fH9sZCaSJC1pdQckSe3BQJAkAQaCJKkwECRJgIEgSSqWtboDs3XttdfmqlWrWt2NBePtt9/mmmuuaXU3pHO4b86t55577keZ+XP11l2ygbBq1SoOHz7c6m4sGJVKhf7+/lZ3QzqH++bciojvn2+dU0aSJMBAkCQVBoIkCTAQJEmFgSBJAt5HIETEQxHxZkQcqan9WkT8UUR8NyL+W0RcU7NuKCKORcSLEdFXU785Ip4v6x6IiCj1yyPiq6X+TESsmttfUdKlqK+vjyVLlrBp0yaWLFlCX1/fxRupIe9nhPAwsHFa7SCwLjP/MvDHwBBARKwBNgNrS5vhiFha2owA24DV5TH1mncDb2XmR4D7gS/M9peRtDD09fVx4MABBgYGePTRRxkYGODAgQOGwjy7aCBk5jeBk9NqBzJzsjx9Gugqy/3AY5n5bma+DBwDbomI64GrM/OprN5v+xFgU02b3WX5ceC2qdGDpMXp4MGDDA4OMjw8zJVXXsnw8DCDg4McPHiw1V1b0ObiGMJdwJNleSXwg5p1E6W2sixPr7+nTQmZHwMr5qBfki5RmcnOnTvfU9u5cyd+f8v8auhK5Yj4d8Ak8OWpUp3N8gL1C7Wp937bqE470dnZydjY2Ey6q4vw81Q72bJlC5/97GeB6r55//33n13W/Jh1IETEVuATwG35/2N7ArihZrMu4LVS76pTr20zERHLgJ9l2hTVlMzcBewC6O7uzp6entl2X9NUKhX8PNUuent72bdvHytXrmT9+vXs37+fffv20dvb6346j2YVCBGxEfgc8Lcz86c1q/YBvxMRvwH8BaoHj5/NzNMR8U5E3Ao8A2wBvljTZivwFPBJ4BvpuFBa1Pbv309fXx+jo6OMjIwQEfT29rJ///5Wd21Bu2ggRMRXgB7g2oiYAH6V6llFlwMHy/HfpzNzIDPHI2IPcJTqVNI9mXm6vNQg1TOWrqB6zGHquMODwJci4hjVkcHmufnVJF3Kpv74e3O75rloIGTmp+qUH7zA9vcC99apHwbW1an/GXDHxfohSZpfXqksSQIMBEltyiuVm89AkNR2vFK5NS7Zb0yTtHDVXqlcqVQYHh4GYHR0tMU9W9gcIUhqO16p3BoGgqS2ExEMDQ29pzY0NIS3OZtfThlJajsbNmxgZGQEgPXr17N9+3ZGRkbo7e1tcc8WNgNBUtvxSuXWcMpIUls6fPjw2WMGmcnhw4db3KOFz0CQ1HZWrFjByZMnWbt2LaOjo6xdu5aTJ0+yYoV3xp9PBoKktjMVBkeOHOFDH/oQR44cORsKmj8GgqS29MQTT1zwueaegSCpLd1+++0XfK65ZyBIajsdHR2Mj4+zbt06Xn/9ddatW8f4+DgdHR2t7tqC5mmnktrOiRMnWLFiBePj4wwMDADVkDhx4kSLe7awOUKQ1JZOnDhBZrJ3714y0zBoAgNBkgQYCJKkwkCQJAEGgiSpMBAkSYCBIEkqDARJEmAgSJKKiwZCRDwUEW9GxJGaWkdEHIyIl8rP5TXrhiLiWES8GBF9NfWbI+L5su6BKN+FFxGXR8RXS/2ZiFg1x7+jpEtQX18fS5YsYdOmTSxZsoS+vr6LN1JD3s8I4WFg47TaDuBQZq4GDpXnRMQaYDOwtrQZjoilpc0IsA1YXR5Tr3k38FZmfgS4H/jCbH8ZSQtDX18fBw4cYGBggEcffZSBgQEOHDhgKMyziwZCZn4TmH4T8n5gd1neDWyqqT+Wme9m5svAMeCWiLgeuDozn8rqVyA9Mq3N1Gs9DtwWfpO2tKgdPHiQwcFBhoeHufLKKxkeHmZwcJCDBw+2umsL2mxvbteZmccBMvN4RFxX6iuBp2u2myi1U2V5en2qzQ/Ka01GxI+BFcCPpr9pRGyjOsqgs7OTsbGxWXZf9fh5ql1kJrfffvvZfXJsbIzbb7+dkZER99N5NNd3O633P/u8QP1Cbc4tZu4CdgF0d3dnT0/PLLqoeiqVCn6eahcRwRNPPMHw8PDZfXP79u1EhPvpPJptILwREdeX0cH1wJulPgHcULNdF/BaqXfVqde2mYiIZcDPcu4UlaRFZMOGDYyMjACwfv16tm/fzsjICL29vS3u2cI229NO9wFby/JWoFJT31zOHLqR6sHjZ8v00jsRcWs5PrBlWpup1/ok8I1ynEHSIrV//356e3sZHR3lzjvvZHR0lN7eXvbv39/qri1oFx0hRMRXgB7g2oiYAH4VuA/YExF3A68AdwBk5nhE7AGOApPAPZl5urzUINUzlq4AniwPgAeBL0XEMaojg81z8ptJuqRN/fGvVCr09/e3uDeLw0UDITM/dZ5Vt51n+3uBe+vUDwPr6tT/jBIokqTW8UplSRJgIEiSCgNBkgQYCJKkwkCQJAEGgiSpMBAkSYCBIEkqDARJbckvyGk+A0FS2/ELclpjrm9/LUkNq/2CnEqlwvDwMACjo6Mt7tnC5ghBUtvJTHbu3Pme2s6dO/FGyPPLEYKkthMRrFu3jldffZXMJCJYuXIlfrvu/HKEIKntLF++nImJCdasWcPo6Chr1qxhYmKC5cuXt7prC5ojBElt56233qKrq4ujR48yMDBARNDV1cWrr77a6q4taI4QJLWdzOTIkSOcOXOGvXv3cubMGY4cOeIxhHnmCEFS2/EYQms4QpDUdqaOIUyNCDLTYwhNYCBIajsnT56cUV1zw0CQ1JbuuusuMpO9e/eSmdx1112t7tKCZyBIkgAPKktqUw899BAPPfRQq7uxqDhCkNR2Ojo6ZlTX3DAQJLWdqQvTpk4znbow7a233mpxzxa2hgIhIj4bEeMRcSQivhIRPxMRHRFxMCJeKj+X12w/FBHHIuLFiOirqd8cEc+XdQ+EJxtLi5oXprXGrAMhIlYC/wLozsx1wFJgM7ADOJSZq4FD5TkRsaasXwtsBIYjYml5uRFgG7C6PDbOtl+SLn0RwdDQ0HtqQ0NDXpg2zxqdMloGXBERy4APAq8B/cDusn43sKks9wOPZea7mfkycAy4JSKuB67OzKeyGv+P1LSRtAht2LCBkZERtm/fzk9+8hO2b9/OyMgIGzZsaHXXFrRZn2WUma9GxK8DrwD/FziQmQciojMzj5dtjkfEdaXJSuDpmpeYKLVTZXl6/RwRsY3qSILOzk7GxsZm233V4eepdjE0NMTJkycZGRlhZGQEgO7uboaGhtxP59GsA6EcG+gHbgTeBv5LRNx5oSZ1anmB+rnFzF3ALoDu7u7s6emZQY91IZVKBT9PtZOOjg4i4uy9jDo6OtxH51kjU0Z/F3g5M3+YmaeA3wX+JvBGmQai/HyzbD8B3FDTvovqFNNEWZ5el7RITX2ncu29jPxO5fnXSCC8AtwaER8sZwXdBrwA7AO2lm22ApWyvA/YHBGXR8SNVA8eP1uml96JiFvL62ypaSNpETpw4MCM6pobjRxDeCYiHgf+EJgEvk11OudKYE9E3E01NO4o249HxB7gaNn+nsw8XV5uEHgYuAJ4sjwkLXKDg4OsX7+eb33rW2ePJWj+xKV6Xm93d3cePny41d1YMCqVCv39/a3uhgRUTzudOn5QW8tMr0VoUEQ8l5nd9dZ5pbKktjT9D79BMP8MBEkSYCBIkgoDQZIEGAiS2tjatWsZHR1l7dq1re7KouAX5EhqW+Pj4wwMDLS6G4uGIwRJEmAgSJIKA0GSBBgIkqTCQJAkAQaCJKkwECRJgIEgSSoMBEkSYCBIkgoDQZIEGAiSpMJAkCQBBoIkqTAQJEmAgSBJKgwESRJgIEiSioYCISKuiYjHI+KPIuKFiPgbEdEREQcj4qXyc3nN9kMRcSwiXoyIvpr6zRHxfFn3QEREI/2SJM1coyOE3wR+LzP/EvALwAvADuBQZq4GDpXnRMQaYDOwFtgIDEfE0vI6I8A2YHV5bGywX5KkGZp1IETE1cAvAg8CZOafZ+bbQD+wu2y2G9hUlvuBxzLz3cx8GTgG3BIR1wNXZ+ZTmZnAIzVtJElNsqyBtn8R+CHwnyPiF4DngM8AnZl5HCAzj0fEdWX7lcDTNe0nSu1UWZ5eP0dEbKM6kqCzs5OxsbEGuq/p/Dx1KXA/nT+NBMIy4K8Cn87MZyLiNynTQ+dR77hAXqB+bjFzF7ALoLu7O3t6embUYZ1fpVLBz1OXAvfT+dPIMYQJYCIznynPH6caEG+UaSDKzzdrtr+hpn0X8Fqpd9WpS5KaaNaBkJmvAz+IiJ8vpduAo8A+YGupbQUqZXkfsDkiLo+IG6kePH62TC+9ExG3lrOLttS0kSQ1SSNTRgCfBr4cER8Avgf8U6ohsyci7gZeAe4AyMzxiNhDNTQmgXsy83R5nUHgYeAK4MnykCQ1UUOBkJnfAbrrrLrtPNvfC9xbp34YWNdIXyRJjfFKZUkSYCBIkgoDQZIEGAiSpMJAkCQBBoIkqTAQJEmAgSBJKgwESRJgIEiSCgNBkgQYCJKkwkCQJAEGgiSpMBAkSYCBIEkqDARJEmAgSJIKA0GSBBgIkqTCQJAkAQaCJKkwECRJgIEgSSoaDoSIWBoR346Ir5XnHRFxMCJeKj+X12w7FBHHIuLFiOirqd8cEc+XdQ9ERDTaL0nSzMzFCOEzwAs1z3cAhzJzNXCoPCci1gCbgbXARmA4IpaWNiPANmB1eWycg35JuoRExNnHXGynmWsoECKiC/gl4D/VlPuB3WV5N7Cppv5YZr6bmS8Dx4BbIuJ64OrMfCozE3ikpo2kRSIzzz7mYjvN3LIG2/8H4N8AV9XUOjPzOEBmHo+I60p9JfB0zXYTpXaqLE+vnyMitlEdSdDZ2cnY2FiD3VctP0+1i6VLl3L69Om6dffT+TPrQIiITwBvZuZzEdHzfprUqeUF6ucWM3cBuwC6u7uzp+f9vK3ej0qlgp+n2sXk5CSXXXYZk5OTZ2vLli3j1KlTLezVwtfIlNF64O9HxJ8AjwF/JyIeBd4o00CUn2+W7SeAG2radwGvlXpXnbqkRezUqVNkJh/+3NfITMOgCWYdCJk5lJldmbmK6sHib2TmncA+YGvZbCtQKcv7gM0RcXlE3Ej14PGzZXrpnYi4tZxdtKWmjSSpSRo9hlDPfcCeiLgbeAW4AyAzxyNiD3AUmATuycypScJB4GHgCuDJ8pAkNdGcBEJmjgFjZfkEcNt5trsXuLdO/TCwbi76IkmaHa9UliQBBoIkqTAQJEmAgSBJKgwESRJgIEiSCgNBkgQYCJKkwkCQJAEGgiSpMBAkSYCBIEkqDARJEmAgSJIKA0GSBBgIkqTCQJAkAQaCJKkwECRJgIEgSSqWtboDkhaXVTu+3pQ2f3LfL824zWJnIEhqupn8sa5UKvT398/o9WcTIHLKSJJUGAiSJKCBQIiIGyLi9yPihYgYj4jPlHpHRByMiJfKz+U1bYYi4lhEvBgRfTX1myPi+bLugYiIxn4tSdJMNTJCmAT+dWZ+FLgVuCci1gA7gEOZuRo4VJ5T1m0G1gIbgeGIWFpeawTYBqwuj40N9EuSNAuzDoTMPJ6Zf1iW3wFeAFYC/cDustluYFNZ7gcey8x3M/Nl4BhwS0RcD1ydmU9lZgKP1LSRJDXJnJxlFBGrgJuAZ4DOzDwO1dCIiOvKZiuBp2uaTZTaqbI8vV7vfbZRHUnQ2dnJ2NjYXHRfhZ+nmmWm+9ps9k3355lrOBAi4krgvwL/MjP/9ALT//VW5AXq5xYzdwG7ALq7u7Onp2fG/VV9lUoFP081xe99fUb72qz2zRm+h6oaOssoIi6jGgZfzszfLeU3yjQQ5eebpT4B3FDTvAt4rdS76tQlSU3UyFlGATwIvJCZv1Gzah+wtSxvBSo19c0RcXlE3Ej14PGzZXrpnYi4tbzmlpo2kqQmaWTKaD3wT4DnI+I7pfZvgfuAPRFxN/AKcAdAZo5HxB7gKNUzlO7JzNOl3SDwMHAF8GR5SJKaaNaBkJn/k/rz/wC3nafNvcC9deqHgXWz7YskqXHey0hSU1310R18bPeOGbX5/O7Pz/A9ALy53UwZCJKa6p0X7vPmdm3KexlJkgADQZJUOGUkqS3M5p6W1bvdaK44QpDUFjKz7uPDn/vaeddpbhkIkiTAKSNJLTDTs4A8a6g5HCFIkgBHCJJaYCbXIaza8fUZbT/VRjPnCEGSBDhCkNRkM711xVUfZca3uvDWFbNjIEhqqpneusIpo+ZxykiSBDhCkNQCnnbangwESU01m+mfmbbR7DhlJEkCDARJUmEgSJIAjyFIahMXuv11fKF+3Tuezi1HCJLawvlucb13715vf90kBoIkCTAQJEmFgSBJAtooECJiY0S8GBHHImJmd7KSJDWsLQIhIpYCvwX8PWAN8KmIWNPaXknS4tIWgQDcAhzLzO9l5p8DjwH9Le6TJC0q7XIdwkrgBzXPJ4C/Pn2jiNgGbAPo7OxkbGysKZ271Hz6+5+eVbvP7/78jLb/4oe/OKv3kWbKf+vN0S6BUO+KlHNOMs7MXcAugO7u7uzp6Znnbl2anuf5GbepVCr09zsoU/upVCr4b7052mXKaAK4oeZ5F/Bai/oiSYtSuwTC/wJWR8SNEfEBYDOwr8V9kqRFpS2mjDJzMiL+ObAfWAo8lJnjLe6WJC0qbREIAJn5BPBEq/shSYtVu0wZSZJazECQJAEGgiSpMBAkSQDEpfolExHxQ+D7re7HAnIT8O1Wd0Kqw31zbn04M3+u3opLNhA0tyIiM/P832EotYj7ZvM4ZSRJAgwESVJhIGjKT1rdAek83DebxGMIkiTAEYIkqTAQJEmAgbBgRUROe/xaRHw3Ipwj1Jyps5/9gya+94+nvfcrpT4ZEUeb1Y+FxEBYwDIzah6/MlevGxEr5uq1dOmb2seofsvhV5vxnhHx74GrgV8u7/2LwOOlP8syc00z+rHQGAiLVERsnva/q8pF6pMRcaaMMH7U0s6rXf2Uckv9iPj6tP3okxepZ0Scrqn/fs3yZJ33+lvl5x8AZOb/yMx/VV7rTEQcj4hD00cwZf1/nFZ/ZJ4/l0uGZxktUNOnhjIzIuK7wMfK8hlgMjM/EBFHgLUXqU9S/fKiv5KZ/7vpv5Da0tRVxBFxFfCnwP/JzI+U/e87mXlT2XciM5depH46M5dFxE+BK4BfASrAHwNbMvNLNe879X5QHZm8kpmryrozwBuZeX3N9qcBat7rtzNzW0R8E/i4V0JXOUJYwGqnjOqsDmCkbLcOICI+cYE6wCnDQNOVP7BTf5xvmtpfMvOmUhsFlpyvXvNSz5Wf3yvb/XpmvlRqm2vfMzPfKW3/ADgFfPg8Iwki4o2y7TUR8fFS/mel3x+v12axMhBU69RF6mea1RFdOsp/OH65PH2jgZeaugCt3n72M3XeNzOzJzMvB75BdQT7HhHxVeA6YFsJkQ9O9fki/2FalAyExesMMAhQppLIzP0XqEvnlZlfo/qd6FdQ/qcfEYfL6gHgTNnmnPps3i8idkRE7X751+ps8wngHwJjmfnbpZ/7y7rXy8+IiP8+mz4sRAbC4vWPgcvKsPljwL6L1KULysyNZXGc6vej31z2o6XAPyrrzlefqWuA3pqDxVcBvzVtm6ljDj21B5WB+4HO8vwM0DfLPiw4HlSWJAGOECRJhYEgSQIMBElSYSBIkgADQZJUGAiSJMBAkCQV/w8yDQED3g506QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for c in categorical:\n",
    "    for n in numerical:\n",
    "        df.boxplot(column=[c,n])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a74d69fd",
   "metadata": {},
   "source": [
    "Now that we have analysed our data we can proceed to normalixing our data and regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77d8c6ba",
   "metadata": {},
   "source": [
    "### Importing useful libraries \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "fffac537",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This Python 3 environment comes with many helpful analytics libraries installed\n",
    "# For example, here's several helpful packages to load in\n",
    "import numpy as np   # linear algebra\n",
    "import matplotlib.pyplot as plt # data visualization\n",
    "import pandas as pd  # data processing, CSV file I/O (e.g. pd.read_csv)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04cd7e4e",
   "metadata": {},
   "source": [
    "### Loading the dataset \n",
    "#### For implementation we will be using house prediction dataset . The dataset can be found [here](https://github.com/vrinda01go/Hellofoss/blob/main/Insti_data.csv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "id": "4ac8e74b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/bh/j3nhmrx97nx0q5lw7s_6w2tw0000gn/T/ipykernel_28064/176543688.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  df['Room Size']=df['Room Size']/max(df['Room Size']) #To normalize room size data\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[2.54000000e+03, 3.00000000e+00, 1.00000000e+00, 4.90350250e-01,\n",
       "        8.00000000e+00],\n",
       "       [2.90000000e+03, 3.00000000e+00, 2.00000000e+00, 6.90493209e-01,\n",
       "        5.00000000e+00],\n",
       "       [2.36200000e+03, 3.00000000e+00, 2.00000000e+00, 6.60471766e-01,\n",
       "        2.00000000e+00],\n",
       "       ...,\n",
       "       [1.02000000e+03, 3.00000000e+00, 2.00000000e+00, 7.19085061e-01,\n",
       "        3.00000000e+00],\n",
       "       [2.40000000e+03, 2.00000000e+00, 2.00000000e+00, 6.70478914e-01,\n",
       "        1.00000000e+00],\n",
       "       [9.50000000e+02, 3.00000000e+00, 2.00000000e+00, 7.52680486e-01,\n",
       "        2.00000000e+00]])"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Room Size']=df['Room Size']/max(df['Room Size']) #To normalize room size data\n",
    "data = np.array(df, dtype=float)\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "627a5a3a",
   "metadata": {},
   "source": [
    "#### Since our dataset has four features i.e Hostel No. , Occupancy, Room Size and Floor ,our hypothesis function becomes\n",
    "### hθ(x) = θ0 + θ1x1 + θ2x2 +θ3x3 + θ4x4\n",
    "#### where x1 ,x2,x3 and x4 are the two features (i.e. size of house and number of rooms)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58fdf0fe",
   "metadata": {},
   "source": [
    "### So Your task is to define hypothesis function having 4 features and a corresponding cost function "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "34dc5643",
   "metadata": {},
   "outputs": [],
   "source": [
    "def hypotheses_fn(theta,X):\n",
    "    return X.dot(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "6fae141b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(theta,X,Y):\n",
    "    pred=hypotheses_fn(theta,X)\n",
    "    return (1/(2*len(Y))) * np.sum(np.square(pred-Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "178eb11f",
   "metadata": {},
   "source": [
    "### Gradient Descent \n",
    "#### So we have our hypothesis function and we have a way of measuring how well it fits into the data. Now we need to estimate the parameters in the hypothesis function. That's where gradient descent comes in.\n",
    "### Your next task is to define gradient descent function having some specific value of learning rate and number of epochs.\n",
    "#### Note that learning rate should be neither very high nor very low .Why?\n",
    "#### Check out exact reason [here](https://towardsdatascience.com/understanding-learning-rates-and-how-it-improves-performance-in-deep-learning-d0d4059c1c10)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "167b5bdc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(theta,X,Y,learning_rate,iterations):\n",
    "    len_y=len(Y)\n",
    "    costs=[]\n",
    "    for i in range(iterations):\n",
    "        pred=hypotheses_fn(theta,X)\n",
    "        theta-=(1/len_y)*learning_rate*(X.T.dot((pred-Y)))\n",
    "        costs.append(cost(theta,X,Y))\n",
    "        \n",
    "    plt.plot(costs)\n",
    "    plt.title(\"Costs changing with each epoch\")\n",
    "    plt.xlabel(\"Epoch\")\n",
    "    plt.ylabel(\"Cost\")\n",
    "    plt.show()\n",
    "        \n",
    "    return theta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "724e407a",
   "metadata": {},
   "source": [
    "### Now we want to visualize how our cost function varies with number of epochs .So your next task is to plot graph of updated costs vs number of epochs "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e82f6ebf",
   "metadata": {},
   "source": [
    "#### After plotting above graph you will notice that your cost function decreases with epochs.\n",
    "#### Perfect! This is all what we wanted to seek by doing linear regression. \n",
    "\n",
    "#### Now it's time to test our model on some test data. \n",
    "\n",
    "#### For this you will define a test function that will take as input Hostel No. , Occupancy, Room Size , Floor and the final theta vector that was returned by our linear regression model and will give us the price of the house. Compute it for any set of features given and final value of theta as given by gradient descent function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "c522bca3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=data[:,1:]\n",
    "X=np.c_[np.ones((len(X),1)),X]\n",
    "Y=data[:,0]\n",
    "theta=np.zeros(5)\n",
    "theta_ideal=gradient_descent(theta,X,Y,0.001,200)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "947f35b1",
   "metadata": {},
   "source": [
    "#### Now since we have defined all required functions , we can call functions one by one and get our final results .\n",
    "#### Your final task is to use all functions defined above and predict the price of room for some input combinations to check how well your model works."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06e54ef5",
   "metadata": {},
   "source": [
    "#### You can try playing with different values of alpha and epochs and see which combination gives most accurate results but do lookout for overfitting \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "3fc631fd",
   "metadata": {},
   "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>Predicted values</th>\n",
       "      <th>Actual values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3457.990337</td>\n",
       "      <td>2540.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2555.206555</td>\n",
       "      <td>2900.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1522.488370</td>\n",
       "      <td>2362.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1578.342395</td>\n",
       "      <td>1432.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1708.619272</td>\n",
       "      <td>1702.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4810</th>\n",
       "      <td>1577.246480</td>\n",
       "      <td>1624.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4811</th>\n",
       "      <td>1575.602607</td>\n",
       "      <td>1470.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4812</th>\n",
       "      <td>1869.056585</td>\n",
       "      <td>1020.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4813</th>\n",
       "      <td>1017.674673</td>\n",
       "      <td>2400.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4814</th>\n",
       "      <td>1526.906278</td>\n",
       "      <td>950.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>4815 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Predicted values  Actual values\n",
       "0          3457.990337         2540.0\n",
       "1          2555.206555         2900.0\n",
       "2          1522.488370         2362.0\n",
       "3          1578.342395         1432.0\n",
       "4          1708.619272         1702.0\n",
       "...                ...            ...\n",
       "4810       1577.246480         1624.0\n",
       "4811       1575.602607         1470.0\n",
       "4812       1869.056585         1020.0\n",
       "4813       1017.674673         2400.0\n",
       "4814       1526.906278          950.0\n",
       "\n",
       "[4815 rows x 2 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def test(X,Y):\n",
    "    display(pd.DataFrame({\"Predicted values\":X.dot(theta_ideal),\"Actual values\":Y}))\n",
    "\n",
    "test(X,Y)"
   ]
  }
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