Non-Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = pd.read_csv('https://apmonitor.com/che263/uploads/Main/heart_rate.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>Time (sec)</th>\n",
       "      <th>Heart Rate (BPM)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>241.000000</td>\n",
       "      <td>241.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>600.000000</td>\n",
       "      <td>142.983402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>348.574478</td>\n",
       "      <td>11.387115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>103.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>300.000000</td>\n",
       "      <td>138.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>600.000000</td>\n",
       "      <td>147.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>900.000000</td>\n",
       "      <td>151.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1200.000000</td>\n",
       "      <td>154.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Time (sec)  Heart Rate (BPM)\n",
       "count   241.000000        241.000000\n",
       "mean    600.000000        142.983402\n",
       "std     348.574478         11.387115\n",
       "min       0.000000        103.000000\n",
       "25%     300.000000        138.000000\n",
       "50%     600.000000        147.000000\n",
       "75%     900.000000        151.000000\n",
       "max    1200.000000        154.000000"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def bpm(t,c0,c1,c2,c3):\n",
    "    return c0+c1*t-c2*np.exp(-c3*t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = [150,0.01,90,0.01]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17899ae78d0>]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "n = len(x['Time (sec)'])\n",
    "y = np.empty(n)\n",
    "for i in range(n):\n",
    "    y[i] = bpm(x['Time (sec)'][i],g[0],g[1],g[2],g[3])\n",
    "\n",
    "plt.plot(x['Time (sec)'],x['Heart Rate (BPM)'])\n",
    "plt.plot(x['Time (sec)'],y,'r-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import curve_fit\n",
    "t = x['Time (sec)']\n",
    "hr = x['Heart Rate (BPM)']\n",
    "c,cov = curve_fit(bpm,t,hr,g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.42373197e+02 9.24806139e-03 4.00292041e+01 6.84029133e-03]\n"
     ]
    }
   ],
   "source": [
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x178a1561ac8>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "n = len(x['Time (sec)'])\n",
    "y = np.empty(n)\n",
    "for i in range(n):\n",
    "    y[i] = bpm(x['Time (sec)'][i],c[0],c[1],c[2],c[3])\n",
    "\n",
    "plt.plot(x['Time (sec)'],x['Heart Rate (BPM)'])\n",
    "plt.plot(x['Time (sec)'],y,'r-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2:  0.9929887696706108\n"
     ]
    }
   ],
   "source": [
    "# Calculating the R^2 value\n",
    "from sklearn.metrics import r2_score\n",
    "print('R^2: ',r2_score(y,hr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}