Linear_Regression_Task2_20b030018.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "89223f98",
   "metadata": {},
   "source": [
    "### Importing useful libraries \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "26f77ebe",
   "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)\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": 126,
   "id": "1c5d873a",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"Hostel_Linear-Dataset.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "1ca9aba0",
   "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>NaN</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>788</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</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>4</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>1098</td>\n",
       "      <td>5</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     NaN           3          1        788      8\n",
       "3  2362.0           3          2        924      2\n",
       "4     NaN           3          2       1098      5"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "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": 128,
   "id": "2fd4babb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1531"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"Price\"].isna().sum()\n",
    "# Since only Price column values is null in between"
   ]
  },
  {
   "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": 129,
   "id": "b65e4503",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<bound method NDFrame.head of        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",
       "5002  1624.0           2          1        674      3\n",
       "5003  1470.0           2          1        626      3\n",
       "5004  1020.0           3          2       1006      3\n",
       "5005  2400.0           2          2        938      1\n",
       "5006   950.0           3          2       1053      2\n",
       "\n",
       "[5007 rows x 5 columns]>"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.dropna(how = \"any\", subset = [\"Price\"], axis=0)\n",
    "df = df.reset_index(drop = True)\n",
    "df.head"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40784889",
   "metadata": {},
   "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": 130,
   "id": "75fa3dc8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<bound method NDFrame.head of        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",
       "5000  1624.0           2          1        674      3\n",
       "5001  1470.0           2          1        626      3\n",
       "5002  1020.0           3          2       1006      3\n",
       "5003  2400.0           2          2        938      1\n",
       "5004   950.0           3          2       1053      2\n",
       "\n",
       "[5005 rows x 5 columns]>"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.drop_duplicates()\n",
    "df = df.reset_index(drop = True)\n",
    "df.head"
   ]
  },
  {
   "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": 132,
   "id": "b325df62",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NuLSq3j3UZzuwva3+LPDENLs6G/juEg93lFZbPbD6arKelW211QMLq+lnquqnptuw4t7IraqdwM4T9UnycFVtHtGQltxqqwdWX03Ws7Kttnpg6Woa9Ru5h4DzhtbPbW2SpBEYdeg/BGxKcn6S1wLXAfeMeAyS1K2Rnt6pqqNJ3g08AJwC7Kqqx+exqxOe/hlDq60eWH01Wc/KttrqgSWqaaRv5EqSlpdfwyBJHTH0JakjYxf64/A1DknOS/KFJF9P8niSX23tZyV5MMn+9nN9a0+SD7WaHk1y0dC+trX++5NsW66a2lhOSfIXSe5t6+cn+Uob9x+1N+dJcmpbP9C2bxzax62t/YkkVyxTKcfGsi7JnyT5ZpJvJHnjOM9Rkn/W/t4eS/KpJKeN2xwl2ZXkhSSPDbUt2pwkuTjJvvY7H0qSZajn37a/uUeTfDbJuqFt0z72M+XeTPN7QlU1NjcGb/4+CbwOeC3wNeCC5R7XNOPcAFzUln8S+J/ABcC/AXa09h3A+9vy1cDngQBbgK+09rOAp9rP9W15/TLW9c+BTwL3tvW7geva8oeBf9KW/ynw4bZ8HfBHbfmCNmenAue3uTxlGeu5C3hXW34tsG5c5wg4B/gWcPrQ3Nw0bnME/D3gIuCxobZFmxPgz1vftN+9ahnquRxY05bfP1TPtI89J8i9meb3hGMa9R/nAh/ANwIPDK3fCty63OOaw7g/x+D7hp4ANrS2DcATbfkjwPVD/Z9o268HPjLU/qp+I67hXGAP8PeBe9s/mu8O/fH+eG4YXJ31xra8pvXL1Pka7rcM9ZzJICQzpX0s54hB6D/Tgm5Nm6MrxnGOgI1TQnJR5qRt++ZQ+6v6jaqeKdt+GfhEW572sWeG3DvRv8ET3cbt9M6xP+xjnm1tK1Z72fxzwFeAiap6rm36NjDRlmeqayXV+++B3wB+1Nb/OvD9qjra1ofH9uNxt+2HW/+VVM/5wHeA/9JOWf3nJGcwpnNUVYeADwB/CTzH4DF/hPGeo2MWa07OactT25fTOxi84oCTr+dE/wZnNG6hP1aSrAU+DfxaVf1geFsNnprH4nrZJL8IvFBVjyz3WBbRGgYvu++sqp8DXmZw6uDHxmyO1jP48sLzgZ8GzgCuXNZBLYFxmpPZJHkvcBT4xCjvd9xCf2y+xiHJaxgE/ieq6jOt+fkkG9r2DcALrX2mulZKvT8P/FKSg8BuBqd4/gOwLsmxD/gNj+3H427bzwS+x8qpBwZHRc9W1Vfa+p8weBIY1zn6B8C3quo7VfVXwGcYzNs4z9ExizUnh9ry1PaRS3IT8IvADe2JDE6+nu8x8/zOaNxCfyy+xqFdEfBR4BtV9cGhTfcAx64k2MbgXP+x9hvb1QhbgMPt5ewDwOVJ1rcjuctb20hV1a1VdW5VbWTwmP9ZVd0AfAF4S+s2tZ5jdb6l9a/Wfl27cuR8YBODN9ZGrqq+DTyT5Gdb02UMvuJ7LOeIwWmdLUn+Wvv7O1bP2M7RkEWZk7btB0m2tMfoxqF9jUySKxmcKv2lqnplaNNMj/20udfma6b5ndko36BZpDdFrmZwNcyTwHuXezwzjPEXGLwEfRT4artdzeAc3B5gP/CnwFmtfxj85zJPAvuAzUP7egdwoN3evgJqm+T/X73zuvZHeQD4Y+DU1n5aWz/Qtr9u6Pff2+p8giW+cmIOtbwBeLjN039lcKXH2M4R8K+BbwKPAX/A4CqQsZoj4FMM3pP4Kwavxt65mHMCbG6Pz5PA7zHljfwR1XOAwTn6Y9nw4dkee2bIvZnm90Q3v4ZBkjoybqd3JEkLYOhLUkcMfUnqiKEvSR0x9CWpI4a+JHXE0Jekjvw/fjBWe9sqHTEAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "columns = df.columns\n",
    "for i in range(len(columns)):\n",
    "    df.hist(columns[i])"
   ]
  },
  {
   "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": null,
   "id": "825783c0",
   "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": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df[(df[['Occupancy']] != 4).all(axis=1)]\n",
    "df = df.reset_index(drop = True)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": 113,
     "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": null,
   "id": "f4a3ab6e",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "categorical = ['Hostel No.', 'Occupancy', 'Floor']\n",
    "numerical = [ 'Price', 'Room Size']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "df2b588a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "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": null,
   "id": "e73f0769",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x720 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], figsize = (15, 10))"
   ]
  },
  {
   "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": null,
   "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": null,
   "id": "4ac8e74b",
   "metadata": {},
   "outputs": [
    {
     "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": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Room Size'] = df['Room Size'] / max(df['Room Size']) #normalization\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": null,
   "id": "34dc5643",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define and complete hypothesis function\n",
    "def hypothesis(x, theta):\n",
    "   return x.dot(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6fae141b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define and complete cost function\n",
    "def cost(x, y, theta):\n",
    "    return np.sum(np.square(hypothesis(x, theta) - y)) / (2 * len(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": null,
   "id": "167b5bdc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(x, y, theta, n, iter):\n",
    "    val = []\n",
    "    epochs = []\n",
    "    m = len(y)\n",
    "    for i in range(iter):\n",
    "        theta -= (n/m) * x.T.dot((hypothesis(x, theta) - y))\n",
    "        val += [cost(x, y, theta)]\n",
    "        epochs += [i]\n",
    "    plt.xlabel(\"Epochs\")\n",
    "    plt.ylabel(\"Costs\")\n",
    "    plt.title(\"cost function variation w.r.t number of epochs\")\n",
    "    plt.plot(epochs, val)\n",
    "    plt.show()\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": null,
   "id": "c522bca3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compare(x, y, final_theta):\n",
    "    print(pd.DataFrame({\"Original\": y, \"Predicted\": hypothesis(x, final_theta)}))"
   ]
  },
  {
   "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": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1., 1.])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial_theta = np.ones((5))\n",
    "initial_theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3fc631fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      Original    Predicted\n",
      "0       2540.0  3157.640354\n",
      "1       2900.0  2355.231485\n",
      "2       2362.0  1419.383807\n",
      "3       1432.0  1452.015287\n",
      "4       1702.0  1585.789114\n",
      "...        ...          ...\n",
      "4810    1624.0  1450.943224\n",
      "4811    1470.0  1449.335130\n",
      "4812    1020.0  1733.611166\n",
      "4813    2400.0   959.478522\n",
      "4814     950.0  1423.705560\n",
      "\n",
      "[4815 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "x = data[:, 1:]\n",
    "x = np.c_[np.ones((len(x), 1)), x]\n",
    "y = data[:, 0]\n",
    "final_theta = gradient_descent(x, y, initial_theta, 0.0001, 1000)\n",
    "compare(x, y, final_theta)"
   ]
  }
 ],
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