P5_Class_Prep_GradientDescent_4_Final.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ef802080",
   "metadata": {},
   "source": [
    "## <font color = darkblue> This is a demonstration of Gradient Descent\n",
    "- The program creates a hypothetical example of a simple linear regression problem\n",
    "- It iteratively updates weight using GD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cdf09c0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ------------------------\n",
    "# Importing dependencies\n",
    "# ------------------------\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import SGDRegressor\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore') \n",
    "sns.set(rc={'figure.figsize':(11,8)})\n",
    "# pd.set_option('display.float_format', lambda x: '%.2f' % x)\n",
    "pd.options.display.float_format = '{:.2f}'.format\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f903bc80",
   "metadata": {},
   "source": [
    "## GD on a Simple Linear Regression (SLR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9f951d5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# ---------------------------------------------------------\n",
    "# MSE function\n",
    "# An alternative is to use sklearn.metrics.mean_squared_error\n",
    "# ---------------------------------------------------------\n",
    "\n",
    "def mse(x, y, b0, b1):\n",
    "    y_predicted = b0 + b1*x\n",
    "    error = y - y_predicted\n",
    "    squared_error = error**2\n",
    "    mse = np.mean(squared_error)\n",
    "    return mse\n",
    "\n",
    "# ---------------------------------------------------------\n",
    "# Gradient function\n",
    "# This calculates the GD adjustment at each step\n",
    "# ---------------------------------------------------------\n",
    "def gradients(x, y, b0, b1):\n",
    "    N = len(x)\n",
    "    b0_gradient = -2*np.sum(y - (b0 + b1*x))/N\n",
    "    b1_gradient = -2*np.sum(x*(y - (b0 + b1*x)))/N\n",
    "    return b0_gradient, b1_gradient\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "542dddeb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 100)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# -----------------------------\n",
    "# Initialize the coefficients\n",
    "# -----------------------------\n",
    "b0 = 0\n",
    "b1 = 0\n",
    "\n",
    "# ----------------------------------------------------------\n",
    "# Learning  rate\n",
    "# The speed at which the cost comes does the parabolic cost function\n",
    "# ----------------------------------------------------------\n",
    "lr = 0.01\n",
    "\n",
    "# ----------------------------------------------------------\n",
    "# Lists for storing Loss and coefficients\n",
    "# ----------------------------------------------------------\n",
    "loss = []\n",
    "b0_list = []\n",
    "b1_list = []\n",
    "\n",
    "# ---------------------------------------------\n",
    "# Generating simple linear regression data \n",
    "# Note that the coeficients are 3(beta 0) and 2 (beta 1)\n",
    "# ---------------------------------------------\n",
    "\n",
    "x = np.arange(0,10,0.1)\n",
    "y = 2*x + 3 + np.random.normal(0,2,len(x))\n",
    "\n",
    "\n",
    "len(x), len(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ee3bd0cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x216 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --------------------------------------------------\n",
    "# Repeated descent of the gradient through iterations\n",
    "# --------------------------------------------------\n",
    "\n",
    "for i in range(1000):\n",
    "    b0_gradient, b1_gradient = gradients(x, y, b0, b1)\n",
    "\n",
    "# -----------------------------------    \n",
    "#     Adjusting the coefficients\n",
    "# -----------------------------------    \n",
    "    b0 = b0 - lr*b0_gradient\n",
    "    b1 = b1 - lr*b1_gradient\n",
    "\n",
    "# -----------------------------------    \n",
    "# appending coefficients and the loss values \n",
    "# -----------------------------------    \n",
    "    loss.append(mse(x, y, b0, b1))\n",
    "    b0_list.append(b0)\n",
    "    b1_list.append (b1)\n",
    "    \n",
    "\n",
    "# ------------------------------------    \n",
    "# Stacking the above three in a df    \n",
    "# ------------------------------------    \n",
    "\n",
    "ndf = pd.DataFrame()\n",
    "ndf[\"loss\"]= loss\n",
    "ndf[\"b0\"]= b0_list\n",
    "ndf[\"b1\"]= b1_list\n",
    "\n",
    "n2df= ndf.stack().reset_index()\n",
    "n2df.columns = ['index', 'metric', 'value']\n",
    "\n",
    "# ------------------------------------    \n",
    "# Create a grid of plots\n",
    "# ------------------------------------    \n",
    "grid = sns.FacetGrid(n2df, col=\"metric\", hue=\"metric\", palette=\"Wistia\")\n",
    "\n",
    "grid.map(sns.relplot, \"index\", \"value\", kind=\"line\")\n",
    "\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d0dd3d4",
   "metadata": {},
   "source": [
    "## <font color = darkblue> The same demonstration with multiple linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "4befe27c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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79cgjj+j555/X9u3b9frrr/d6fyejrokpBQD26TJwly9frscee0xFRUUaMmSIli9friVLlvS6wZdfflkzZszQkCFDlJmZqRUrVmjChAm93t/JqGtuWUchP5vHowNIvC4DNxQKaezYse3fT506VfF4vNcN7tq1S/F4XDfffLNmzZqlv/zlLyosLOz1/k5GbXNUhXmZrKMAwBZdDu0yMjJUX1/fHkqffPLJSTUYj8e1efNmPfHEE8rLy9Mtt9yiNWvWqKysrFvbFxfn96pdv7/gmPdCcaOB/XOO+7NUkcq1n4hb+yW5t2/0q2tdBu4tt9yi7373uzp48KDuuOMObdy4Uffdd1+vGxw4cKBKSko0YMAASdLFF1+srVu3djtwa2oCsizTozb9/gJVVzce8/6BQ83Kz0o/7s9SQWf9SnVu7Zfk3r7RryO36UyXgTtt2jSNHj1aGzdulGVZmj9/vsaMGdOjAo7e309/+lM1NDSoX79++sc//qGLLrqo1/s7GfXNUZ3mz3OkbQDe02Xg1tXVqbCwUDNmzDjivaKiol41OGHCBN1www265pprFI1G9ZWvfEXf+ta3erWvk1XbHNGEvCJH2gbgPV0G7uTJk485qeT3+/X3v/+9143Onj1bs2fP7vX2fcEYo/rmqE7hkjAANukycHfs2NH+OhKJaN26dfr0008TWpQdAuGYYpZRUR43PQCwR49u7c3KylJZWZk2btyYqHpsc/guM0a4AOzRrTncNsYYbdu2TQ0NDYmsyRZtK4VxlxkAu3R7DteYlkuxiouLdffddye8sERrG+EWMqUAwCY9msN1k7bA5aQZALt0GrgrV6484YbXX399nxdjpzqWZgRgs04D98MPP7SzDtvVNkWV5pMKcghcAPboNHB/+ctf2lmH7eqboyrMzVRaGgvXALBHl3O4b7/9tv7whz+oublZxhhZlqU9e/botddes6G8xKltjrDwOABbdXkd7uLFi3XeeecpEAho5syZys/P1/Tp0+2oLaEaWke4AGCXLke4Pp9PN910k2prazV69GjNnDnTsbUP+lJDKCp/QY7TZQDwkC5HuHl5LatpjRgxQjt37lROTo7S0lL/2ZMNwZj65/KkBwD26TJxJkyYoB/96Ee67bbbNG/ePFVUVCgjI/WDqiEYVX+mFADYqMuhalVVlc444wyNGjVKd999tyzL0oMPPmhHbQljWUaBcEwFOal/4ACQOroM3MmTJ+vVV1/VN77xDe3YsUM33nijRo8ebUdtCRMIx2SMGOECsFWXgXv11Vdr1apV+t3vfqf6+nrNmTNH8+fPt6O2hGkIttzWW0DgArBRt89+hUIhRSIRGWOUnp6eyJoSrjEUkyROmgGwVZeJs3LlSq1evVqRSESzZ8/WqlWrNHDgQDtqS5i2EW5/busFYKMuA3fbtm1avHixLrjgAjvqsUV74DLCBWCjLhMn1a9IOJ7DUwqMcAHYJ/XvYOiF9pNmTCkAsJFHAzemNJ/ULzu1T/4BSC0eDdyoCnIyj3n8OwAkkmcDlxNmAOzmycBtDMW46QGA7TwZuCxcA8AJngzcxlBM/Vm4BoDNPBm4DcEoUwoAbOe5wDXGcNIMgCM8F7jhmKVo3LCOAgDbeS5wD6+jQOACsJcHA5elGQE4w3OB2xhiHQUAzvBc4LI0IwCneDBwW6YU8hnhArCZ5wK3KdwSuDyxF4DdPBe4gXDbCJfABWAvzwVuUyimjDSfsjM813UADvNc6gTCMfXLzmAtXAC281zgNoXjTCcAcITnAjcQivFoHQCO8FzgNoVjys9mhAvAfp4L3EA4pn5MKQBwgPcCN8QIF4AzvBm4jHABOMDRwF22bJkWLlxoa5vM4QJwimOB++abb2rNmjW2thmNWQrHLPUjcAE4wJHAraur04oVK3TzzTfb2m5ThNt6ATjHkeS55557dPvtt2v//v093ra4OL9Xbfr9BWqubpIkDRmYL7+/oFf7STZu6cfR3Novyb19o19dsz1wn3nmGQ0dOlQlJSVavXp1j7evqQnIskyPtvH7C1Rd3ajP9jdIkkwkpurqxh63nWza+uU2bu2X5N6+0a8jt+mM7YH74osvqrq6WrNmzVJ9fb2am5v1i1/8QosWLUp424FQXJK4DheAI2xPnpUrV7a/Xr16tTZt2mRL2EqshQvAWZ66DrdtLVyuUgDgBEeTp6ysTGVlZba1Fwi1XqVA4AJwgDdHuDmsFgbAft4K3FBMaT4pN5PABWA/TwVuE097AOAgTwVuIMzCNQCc46nAbQrFuEIBgGM8FbiBcIxrcAE4xlOB2zaHCwBO8FTgBkJxrsEF4BhPBW4TzzMD4CBPBW6Apz0AcJBnAjduGQUjceVlcdMDAGd4JnBD0dalGRnhAnCIZwK3OdwSuLmMcAE4xDuB2/o8s7xsAheAMzwUuC0j3LwsphQAOMM7gRtuC1xGuACc4Z3AZUoBgMM8FLhMKQBwlgcDlxEuAGd4J3DDTCkAcJZnAjfIlAIAh3kmcJsjcWWk+ZSZzuN1ADjDO4Ebjik3K53nmQFwjGcCtykSVx7rKABwkGcCtzkc4woFAI7yTuCyNCMAhxG4AGATzwRuMBJjDheAozwTuM1hRrgAnOWdwGVKAYDDPBS4MeUypQDAQZ4IXGMMI1wAjvNE4AYjcRnDSmEAnOWJwG1qWymMhWsAOMgTgcvSjACSgScC9/AIl8AF4BxvBG6IKQUAzvNG4DKlACAJeCRweZ4ZAOd5I3CZUgCQBLwRuK1TCrmMcAE4yFOByxwuACd5JnB9Pikng8AF4BxPBG5zKKbczHSlpfEASQDOceQs0sMPP6z169dLkqZOnaq77roroe01tT6xFwCcZPsIt7y8XG+88YbWrFmj5557Tu+9955efvnlhLbJAyQBJAPbR7h+v18LFy5UVlaWJGnMmDHat29fQtsMRuLKIXABOMz2wB03blz764qKCq1fv15PPfVUt7cvLs7vcZvBSFwFuVny+wt6vG2yc2OfJPf2S3Jv3+hX1xy7E2Dnzp2aN2+e7rrrLp122mnd3q6mJiDLMj1qKxiJKcMnVVc39rDK5Ob3F7iuT5J7+yW5t2/068htOuPIVQpbtmzR97//ff34xz/WlVdemfD2gpG4cjKZUgDgLNtHuPv379f8+fO1YsUKlZSU2NJmcySuoYU5trQFAJ2xPXAfffRRhcNhLV26tP29OXPm6Oqrr05Ym8FITDmZnrjkGEASsz1wFy9erMWLF9vaJlMKAJKBJ4Z9wUicGx8AOM71gWtZhhEugKTg+sANxVoWH2eEC8Bp7g/ciCVJnDQD4DjXp1Ao2jrCZUoBgMM8E7jM4QJwmusDN9gWuMzhAnCY+wM3wpQCgOTg+sANMcIFkCTcH7itVynkcpUCAIe5PoWCnDQDkCRcH7hcpQAgWbg+cNtPmjGHC8Bhrg9cbnwAkCw8ELiW0tN8ykj3OV0KAI9zfeAGoy1LM/p8BC4AZ7k+cEOshQsgSbg+cIPRuPKyHXs4MQC0c33gMsIFkCzcH7hRAhdAcnB94AajlnKzmFIA4DzXBy4jXADJwvWBG4zElccIF0AScH3gMsIFkCzcH7iRuHKzCVwAznN/4EYtRrgAkoKrA9cY03prL3O4AJzn6sANRVue9pDHCBdAEnB54LathcsIF4DzPBG4jHABJANXBy5PewCQTFwduG1zuLmsFgYgCbg6cNvWHD+lX5azhQCAXB64nx9aoP8z93x9aWyx06UAgLsD1+fzafLYYh6vAyApuDpwASCZELgAYBMCFwBsQuACgE0IXACwCYELADYhcAHAJgQuANiEwAUAmxC4AGCTlFtGKy2td7fp9na7ZEe/Uo9b+0a/uuYzxpg+2xsAoFNMKQCATQhcALAJgQsANiFwAcAmBC4A2ITABQCbELgAYBMCFwBsQuACgE1cHbgvvPCCZsyYoenTp+vJJ590upxeCQQCuvzyy7Vnzx5JUnl5uWbOnKnp06drxYoV7Z97//33VVZWpksuuUR33323YrGYUyV36eGHH1ZpaalKS0u1fPlySe7olyT95je/0YwZM1RaWqqVK1dKck/fJGnZsmVauHChJPf063vf+55KS0s1a9YszZo1S++++27i+mZc6sCBA2batGmmtrbWNDU1mZkzZ5qdO3c6XVaPvPPOO+byyy8348ePN5999pkJBoNm6tSpZvfu3SYajZq5c+ea1157zRhjTGlpqXn77beNMcb8x3/8h3nyyScdrLxzGzduNFdddZUJh8MmEomYa6+91rzwwgsp3y9jjHnrrbfMnDlzTDQaNcFg0EybNs28//77ruibMcaUl5ebCy64wPz0pz91xd+iMcZYlmWmTJliotFo+3uJ7JtrR7jl5eWaPHmyioqKlJeXp0suuUQbNmxwuqweWbVqle69914NGjRIkrR161aNHDlSw4cPV0ZGhmbOnKkNGzZo7969CoVCOvfccyVJZWVlSdtXv9+vhQsXKisrS5mZmRozZowqKipSvl+S9KUvfUmPP/64MjIyVFNTo3g8roaGBlf0ra6uTitWrNDNN98syR1/i5L0ySefSJLmzp2rb37zm/rzn/+c0L65NnCrqqrk9/vbvx80aJAqKysdrKjnlixZovPPP7/9+876dPT7fr8/afs6bty49j/YiooKrV+/Xj6fL+X71SYzM1MPPfSQSktLVVJS4op/M0m65557dPvtt6t///6S3PG3KEkNDQ0qKSnRb3/7Wz322GN6+umntW/fvoT1zbWBa1mWfL7Dy6oZY474PhV11qdU7OvOnTs1d+5c3XXXXRo+fLhr+iVJCxYs0Jtvvqn9+/eroqIi5fv2zDPPaOjQoSopKWl/zy1/i+edd56WL1+ugoICDRgwQLNnz9ZDDz2UsL6l3Hq43TVkyBBt3ry5/fvq6ur2/zVPVUOGDFF1dXX79219Ovr9gwcPJnVft2zZogULFmjRokUqLS3Vpk2bXNGvjz/+WJFIRGeeeaZyc3M1ffp0bdiwQenp6e2fScW+vfjii6qurtasWbNUX1+v5uZm7d27N+X7JUmbN29WNBptP5gYYzRs2LCE/T26doT75S9/WW+++aYOHTqkYDCol156SRdeeKHTZZ2UCRMm6NNPP9WuXbsUj8e1bt06XXjhhRo2bJiys7O1ZcsWSdLatWuTtq/79+/X/Pnz9cADD6i0tFSSO/olSXv27NHixYsViUQUiUT0t7/9TXPmzEn5vq1cuVLr1q3T2rVrtWDBAn3961/XH//4x5TvlyQ1NjZq+fLlCofDCgQCWrNmje64446E9c21I9zBgwfr9ttv17XXXqtoNKrZs2frC1/4gtNlnZTs7GwtXbpUt956q8LhsKZOnapLL71UkvTAAw9o8eLFCgQCGj9+vK699lqHqz2+Rx99VOFwWEuXLm1/b86cOSnfL0maOnWqtm7dqiuuuELp6emaPn26SktLNWDAgJTv29Hc8LcoSdOmTdO7776rK664QpZl6ZprrtF5552XsL7xxAcAsIlrpxQAINkQuABgEwIXAGxC4AKATQhcALAJgQvX+Pe//60FCxZ0+/OHDh3SGWeckcCKgCNxWRg869ChQyopKdEHH3zgdCnwCNfe+ADveeutt3T//ffr7LPPVn5+vj744AMdOHBAZ5xxhpYtW6Z+/frppZde0ooVK5Sbm6uzzz77iO2feeYZPfXUU7IsS0VFRfrZz36mUaNG6frrr9f48eN11113qby8XAsXLtTq1as1cOBAh3qKVEXgwpW2bdumxx9/XD6fT9/5zne0YcMGTZ06VYsWLdLTTz+tsWPH6ve//3375zdt2qTnnntOTz75pHJzc/XGG2/ohz/8odavX69f/epXuvLKKzVx4kTdd999evDBBwlb9AqBC1f66le/qqysLEnS6aefrvr6em3ZskWnn366xo4dK0m66qqr9Otf/1qS9Nprr2nXrl2aM2dO+z4aGhpUV1enQYMG6f7779cPfvAD3XrrrZo0aZL9HYIrELhwpZycnPbXPp9PbacqOp6yyMg4/OdvWZZmzZqln/zkJ+3fV1VVqbCwUJL00UcfaeDAgdq6dasd5cOluEoBnjFp0iR99NFH2rFjhyRp9erV7T+bMmWK/vrXv6qqqkqS9NRTT+m6666T1PJ0g8cff1zPPvusGhsb9ac//cn+4uEKjHDhGQMGDNADDzygO++8U5mZmUdMDUyZMkU33nij5s6dK5/Pp/z8fD388MNqamrSHXfcocWLF2vw4MFaunSpvv3tb2vSpEk666yzHOwNUhGXhQGATZhSAACbELgAYBMCFwBsQuACgE0IXACwCYELADYhcAHAJgQuANjk/wPaPVaWTh+mWQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def gradients(x1,x2, y, b0, b1, b2):\n",
    "    N = len(x1)\n",
    "    b0_gradient = -2*np.sum(y - (b0 + b1*x1 + b2*x2))/N\n",
    "    b1_gradient = -2*np.sum(x1*(y - (b0 + b1*x1+ b2*x2)))/N\n",
    "    b2_gradient = -2*np.sum(x2*(y - (b0 + b1*x1+ b2*x2)))/N\n",
    "    return b0_gradient, b1_gradient, b2_gradient\n",
    "\n",
    "def mse(x1, x2,y, b0, b1,b2):\n",
    "    y_predicted = b0 + b1*x1 + b2*x2\n",
    "    error = y - y_predicted\n",
    "    squared_error = error**2\n",
    "    mse = np.mean(squared_error)\n",
    "    return mse\n",
    "\n",
    "# Initialize the coefficients\n",
    "b0, b1, b2 = 0,0,0\n",
    "\n",
    "# Learning  rate\n",
    "lr = 0.0001\n",
    "\n",
    "# Lists for loss and coefficients\n",
    "loss, b0_list,b1_list,b2_list = [],[],[],[]\n",
    "\n",
    "# ---------------------------------------------\n",
    "# Generating multiple linear regression data \n",
    "# ---------------------------------------------\n",
    "\n",
    "x1 = np.arange(0,10,0.1)\n",
    "x2 = np.arange(10,20,0.1)\n",
    "y = 7+5*x1 + 10*x2  + np.random.normal(0,2,len(x1))\n",
    "\n",
    "# # Creating a list of the above three\n",
    "# listofcols = [y,x1,x2]\n",
    "\n",
    "# # creating df\n",
    "# df = pd.DataFrame(listofcols).transpose()\n",
    "\n",
    "# # Name the columns\n",
    "# df.columns = ['y', 'x1', 'x2']\n",
    "\n",
    "# # # # --------------------------------------------------\n",
    "# # # # Iterations and repeated descent of the gradient\n",
    "# # # # --------------------------------------------------\n",
    "\n",
    "for i in range(500):\n",
    "    b0_gradient, b1_gradient, b2_gradient = gradients(x1,x2, y, b0, b1, b2)\n",
    "#     Adjusting the coefficients\n",
    "    b0 = b0 - lr*b0_gradient\n",
    "    b1 = b1 - lr*b1_gradient\n",
    "    b2 = b2 - lr*b2_gradient\n",
    "#     print(b0, b1, b2)\n",
    "\n",
    "    \n",
    "# # appending coefficients and the loss values \n",
    "    loss.append(mse(x1,x2, y, b0, b1,b2))\n",
    "    b0_list.append(b0)\n",
    "    b1_list.append (b1)\n",
    "    b2_list.append (b2)\n",
    "\n",
    "# print(loss)    \n",
    "\n",
    "# # # ------------------------------------    \n",
    "# # # Stacking the above three in a df    \n",
    "# # # ------------------------------------    \n",
    "\n",
    "ndf = pd.DataFrame()\n",
    "ndf[\"loss\"]= loss\n",
    "ndf[\"b0\"]= b0_list\n",
    "ndf[\"b1\"]= b1_list\n",
    "ndf[\"b2\"]= b2_list\n",
    "n2df= ndf.stack().reset_index()\n",
    "n2df.columns = ['index', 'metric', 'value']\n",
    "\n",
    "# # # # ------------------------------------    \n",
    "# # # # Create a grid of plots\n",
    "# # # # ------------------------------------    \n",
    "grid = sns.FacetGrid(n2df, col=\"metric\", hue=\"metric\", palette=\"Blues\")\n",
    "\n",
    "grid.map(sns.relplot, \"index\", \"value\", kind=\"line\")\n",
    "\n",
    "plt.show()\n",
    "# ndf"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "735774e4",
   "metadata": {},
   "source": [
    "## <font color = darkred> Repeat the above demonstration for MLR with four independent features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "29b1f1e8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}