Linear Regression Single-variable/Linear Regression.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression With One Variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:yellow\">Sample problem of predicting per-capita income of Canada</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below table represents the head of the year and per-capita income."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "   year          PCI\n0  1970  3399.299037\n1  1971  3768.297935\n2  1972  4251.175484\n3  1973  4804.463248\n4  1974  5576.514583",
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     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Problem Statement**: Given above data build a machine learning model that can predict percapitaIncome based on year\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Per-capita Income can be represented as following equation,\n",
    "\n",
    "Per-capita Income = m * (year) + b\n",
    "\n",
    "Generic form of same equation is, y=mx+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn import linear_model\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "<class 'pandas.core.frame.DataFrame'>\nRangeIndex: 47 entries, 0 to 46\nData columns (total 3 columns):\n #   Column                   Non-Null Count  Dtype  \n---  ------                   --------------  -----  \n 0   year                     47 non-null     int64  \n 1   per capita income (US$)  47 non-null     float64\n 2   PCI                      47 non-null     float64\ndtypes: float64(2), int64(1)\nmemory usage: 1.2 KB\n"
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "   year          PCI\n0  1970  3399.299037\n1  1971  3768.297935\n2  1972  4251.175484\n3  1973  4804.463248\n4  1974  5576.514583",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>year</th>\n      <th>PCI</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1970</td>\n      <td>3399.299037</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1971</td>\n      <td>3768.297935</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1972</td>\n      <td>4251.175484</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1973</td>\n      <td>4804.463248</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1974</td>\n      <td>5576.514583</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "df = pd.read_csv('canada_per_capita_income.csv')\n",
    "new='PCI'\n",
    "df['PCI']=(df['per capita income (US$)'])\n",
    "df.info()\n",
    "del df['per capita income (US$)']\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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     "output_type": "execute_result",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "plt.xlabel('year')\n",
    "plt.ylabel('per-capita income')\n",
    "plt.scatter(df.year,df.PCI,color='red',marker='+')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "   year\n0  1970\n1  1971\n2  1972\n3  1973\n4  1974",
      "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>year</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1970</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1971</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1972</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1973</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1974</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "new_df = df.drop('PCI',axis='columns')\n",
    "new_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0    3399.299037\n1    3768.297935\n2    4251.175484\n3    4804.463248\n4    5576.514583\nName: PCI, dtype: float64"
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "price = df.PCI\n",
    "price.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "# Create linear regression object\n",
    "reg = linear_model.LinearRegression()\n",
    "reg.fit(new_df,price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(1) Predict Per-capita income for 2018**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([41288.69409442])"
     },
     "metadata": {},
     "execution_count": 32
    }
   ],
   "source": [
    "reg.predict([[2020]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([828.46507522])"
     },
     "metadata": {},
     "execution_count": 26
    }
   ],
   "source": [
    "reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "-1632210.7578554575"
     },
     "metadata": {},
     "execution_count": 27
    }
   ],
   "source": [
    "reg.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Y = m * X + b (m is coefficient and b is intercept)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "39631.76393850264"
     },
     "metadata": {},
     "execution_count": 28
    }
   ],
   "source": [
    "2018*828.46507522  -1632210.7578554575"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(1) Predict per-capita income for the year 1969**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([42117.15916964])"
     },
     "metadata": {},
     "execution_count": 31
    }
   ],
   "source": [
    "reg.predict([[2021]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x1d6332ffdf0>]"
     },
     "metadata": {},
     "execution_count": 43
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "plt.xlabel('year')\n",
    "plt.ylabel('per-capita income')\n",
    "# plt.scatter(df.year,df.PCI,color='red',marker='+')\n",
    "plt.plot(df.year,reg.predict(df[['PCI']]),color=\"blue\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}