Feature_Engineering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d2aeabdf",
   "metadata": {},
   "source": [
    "## DATA INTERPOLATION"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d648dcb0",
   "metadata": {},
   "source": [
    "- It is the process of estimating values within dataset based on known values "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "860781cf",
   "metadata": {},
   "source": [
    "## Types of data interpolation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "416fe955",
   "metadata": {},
   "source": [
    "**1) Linear Interpolation.**\n",
    "**2) Cubic Interpolation with scipy.**\n",
    "**3) Polynomial Interpolation.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81cb878d",
   "metadata": {},
   "source": [
    "### 1. Linear Interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "133f9c83",
   "metadata": {},
   "outputs": [],
   "source": [
    "# importing lib\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c8772f9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating array\n",
    "x = np.array([1,2,3,4,5])\n",
    "y = np.array([2,4,6,8,10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "7c44769e",
   "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": [
    "# assuming x and y are defined as arrays or lists\n",
    "sns.scatterplot(x=x, y=y, color='blue')\n",
    "plt.title('Scatter plot with Seaborn and Matplotlib')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "078e08e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.        ,  2.88888889,  3.77777778,  4.66666667,  5.55555556,\n",
       "        6.44444444,  7.33333333,  8.22222222,  9.11111111, 10.        ])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# interpolation\n",
    "x_new = np.linspace(1,5,10) # create new x values \n",
    "y_interp = np.interp(x_new,x,y)\n",
    "y_interp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5bb8ac71",
   "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": [
    "# visualization after linear interpolation\n",
    "sns.scatterplot(x=x_new,y=y_interp)\n",
    "plt.title(\"With linear interpolation\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90ccf638",
   "metadata": {},
   "source": [
    "## 2. Cubic Interpolation Using Scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "798fc3ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating array\n",
    "x = np.array([1,2,3,4,5])\n",
    "y = np.array([2,8,27,64,125])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "fb3a8ef7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEICAYAAACktLTqAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAWpklEQVR4nO3dfZRkdX3n8fenAbUVH+BMgy0PGRM7rCDR4fQiuyQuLBrxEQ9HNrgqozHLyR52o5vsGsAc0Rw1nuwmYdckmzMHjUNElJgxEo66shMVza6YAfEBEZsowjgt04LP9qo43/3j3pGiqJ5+qO6umTvv1zl1qu7vPvy+9avuT926dasqVYUkqVvGRl2AJGn1Ge6S1EGGuyR1kOEuSR1kuEtSBxnuktRBhrt+JsmvJLl9H/M3Jqkkh65nXcNKcmeSZy4wb5/3eR/bvDTJFcNXt/aSvCHJu4ZY/9YkZ6xeRVoPhnuHJbkkyQf72mYWaDu/qj5RVSf0tC8YimtQ6zuTvGk9+urVf5+Xsd5bquo3lrLssOG6ngY9DlV1UlV9bEQlaYUM9267ATg9ySEASR4PHAac0tf2pHZZ7YcOtFdK2j8Y7t32jzRh/rR2+hnAR4Hb+9r+qap2JTkjyU6AJH8FHA/8XZLvJ3ltz3ZfmuSuJN9M8rq9jUkenuTyJLvay+VJHt7Oe0WST/YW1x7ieVKSC4GXAq9t+/q7QXcmyUlJrk9yX5J7klzatj9ob7P3fvT450m+mORbSf4yySMGLZvkuCTbkswluTfJny5Qy8/2xnsOV23uH5ckZwOXAr/W3rfPtu2PTfL2JLNJvp7kTT1PuK9I8g9J/iTJfcAbetreluQ7Sb6U5Kyeep6Q5Np2bO5I8u8G1d0u+9dJvtFu54YkJ7XtAx+H3ldwizzGZyTZmeR3kuxu79srF6pDa8tw77Cq+jFwI02A015/AvhkX9tD9tqr6uXAXcALqurwqvrDntm/DJwAnAW8PsmT2/bXAafRPHE8FTgV+L0l1LkFuAr4w7avF/Qvk+TRwP8GPgw8gebVxvbFtt3jpcCzgV8AfnFQXW24Xgd8DdgIHAO8Zxl9PGRcqurDwFuA97b37antsluB+9v7sQn4VaD3MM/Tga8ARwFv7mvbAFwGbEtyZDvvamAnzdi8GHhLb/j3+RAw1W77ZpqxX9LjwOKP8eOBx9KM3auAP0tyxAJ1aA0Z7t33cR4I8l+hCfdP9LV9fJnbfGNVzVfVZ4HP0vyTQxOgv19Vu6tqDngj8PJhiu/xfOAbVfVHVfX/qup7VXXjMtb/06q6u6ruownLlwxY5lSacPwvVfWDtp9PDlhuIQuNy4MkORp4DvCatp/dwJ8A5/cstquq3lZV91fVfNu2G7i8qn5SVe+leQX2vCTH0Tyx/G5b8y3AFSww9lX1jnb8fgS8AXhqkscu8T4u9hj/pJ3/k6r6IPB9mic8rTOP5XXfDcBF7d7TRFXNJLkH2Nq2PYXlH2//Rs/tHwKHt7efQLPXu9fX2rbVcBzwT0Osf3fP7YXqOg74WlXdv8I+FhqXfj9Hc7hsNsnetrG+Gu/uXwn4ej34m/723o8nAPdV1ff65k33b6B9dfJm4DxgAtjTztoAfGeBenst9hjf2zd++xoHrSH33Lvv/9K8TL4Q+AeAqvousKtt21VVX11g3eV+ZegumuDa6/i2DeAHwCP3zmjfyF1OX3fTHFIZ5EHbpjk00O+4Berq7+P4NXgDs/++3Q38CNhQVY9rL4+pqpP2sQ7AMel5NuCB+7ELOLI9dNU77+sDtvFvgXOAZ9L8XWxs2/dud7HHYV+PsfYjhnvHtS/pdwC/TXM4Zq9Ptm372mu/B/j5ZXR3NfB7SSaSbABeD+w9BfCzwElJnta+mfmGZfZ1HfD4JK9p39R7dJKnt/NuAZ6b5Mj2SeM1A9a/KMmx7THqS4H3Dljm08As8NYkj0ryiCSnL3anl+AeYGOSMYCqmgU+AvxRksckGUvyC0n+1SLbOQr4rSSHJTkPeDLwwaq6G/g/wB+0Nf8SzfHuqwZs49E0Tyz30jwhvmVArft6HPb1GGs/YrgfHD5OEwy9x48/0bbtK9z/gOYf+dtJ/vMS+nkTzRPJ54DP07xZ9yaAqvoy8Ps0b4rO9NUC8HbgxLavv+3fcHvI4VnAC2gOf8wAZ7az/4rmyeNOmtAcFNzvbud9pb085Jz6qvppu/0n0byZvBP4tSXc78X8dXt9b5Kb29sXAA8Dvgh8C3gfMLnIdm6keSP0mzSHVl5cVfe2815Csxe+C3g/cFlVXT9gG1fSHEr5etv3p/rm7/NxYB+PsfYv8cc6pP1fklcAv1FVvzzqWnRgcM9dkjrIcJekDvKwjCR1kHvuktRB+8WHmDZs2FAbN24cdRmSdEC56aabvllVE4Pm7RfhvnHjRnbs2DHqMiTpgJLkawvN87CMJHWQ4S5JHWS4S1IHGe6S1EGGuyR10H5xtowkHWz27IGZGZidhclJmJqCsVXc3XbPXZLW2Z49sG0bbNoEZ57ZXG/b1rSvFsNdktbZzAxccAHMtz+gOD/fTM/MrF4fhrskrbPZ2QeCfa/5+aZ9tRjukrTOJidhfPzBbePjTftqMdwlaZ1NTcGVVz4Q8OPjzfTU1Or14dkykrTOxsbg3HPh5JPX7mwZw12SRmBsDE44obmsyfYXWyDJO5LsTvKFnrb/muRLST6X5P1JHtcz75IkdyS5Pcmz16ZsSdK+LOVFwDuBs/vargeeUlW/BHwZuAQgyYnA+cBJ7Tp/nuSQVatWkrQki4Z7Vd0A3NfX9pGqur+d/BRwbHv7HOA9VfWjqvoqcAdw6irWK0lagtU4fP/rwIfa28cAd/fM29m2PUSSC5PsSLJjbm5uFcqQJO01VLgneR1wP3DV3qYBiw38Be6q2lJV01U1PTEx8FeiJEkrtOKzZZJsBp4PnFVVewN8J3Bcz2LHArtWXp4kaSVWtOee5Gzgd4EXVtUPe2ZdC5yf5OFJnghMAZ8evkxJ0nIsuuee5GrgDGBDkp3AZTRnxzwcuD4JwKeq6jer6tYk1wBfpDlcc1FV/XStipckDZYHjqiMzvT0dO3YsWPUZUjSASXJTVU1PWie3y0jSR1kuEtSBxnuktRBhrskdZDhLkkdZLhLUgcZ7pLUQYa7JHWQ4S5JHWS4S1IHGe6S1EGGuyR1kOEuSR1kuEtSBxnuktRBhrskdZDhLkkdZLhLUgcZ7pLUQYa7JHWQ4S5JHWS4S1IHGe6S1EGLhnuSdyTZneQLPW1HJrk+yUx7fUTPvEuS3JHk9iTPXqvCJUkLW8qe+zuBs/vaLga2V9UUsL2dJsmJwPnASe06f57kkFWrVpK0JIuGe1XdANzX13wOsLW9vRV4UU/7e6rqR1X1VeAO4NTVKVWStFQrPeZ+dFXNArTXR7XtxwB39yy3s217iCQXJtmRZMfc3NwKy5AkDbLab6hmQFsNWrCqtlTVdFVNT0xMrHIZknRwW2m435NkEqC93t227wSO61nuWGDXysuTJK3ESsP9WmBze3sz8IGe9vOTPDzJE4Ep4NPDlShJWq5DF1sgydXAGcCGJDuBy4C3AtckeRVwF3AeQFXdmuQa4IvA/cBFVfXTNapdkrSARcO9ql6ywKyzFlj+zcCbhylKkjQcP6EqSR1kuEtSBxnuktRBhrskdZDhLkkdZLhLUgcZ7pLUQYa7JHWQ4S5JHWS4S1IHGe6S1EGGuyR1kOEuSR1kuEtSBxnuktRBhrskdZDhLkkdZLhLUgcZ7pLUQYa7JHWQ4S5JHWS4S1IHGe6S1EFDhXuS/5Tk1iRfSHJ1kkckOTLJ9Ulm2usjVqtYSdLSrDjckxwD/BYwXVVPAQ4BzgcuBrZX1RSwvZ2WJK2jYQ/LHAqMJzkUeCSwCzgH2NrO3wq8aMg+JEnLtOJwr6qvA/8NuAuYBb5TVR8Bjq6q2XaZWeCo1ShUkrR0wxyWOYJmL/2JwBOARyV52TLWvzDJjiQ75ubmVlqGJGmAYQ7LPBP4alXNVdVPgG3AvwTuSTIJ0F7vHrRyVW2pqumqmp6YmBiiDElSv2HC/S7gtCSPTBLgLOA24Fpgc7vMZuADw5UoSVquQ1e6YlXdmOR9wM3A/cBngC3A4cA1SV5F8wRw3moUKklauhWHO0BVXQZc1tf8I5q9eEnSiPgJVUnqIMNdkjrIcJekDjLcJamDDHdJ6iDDXZI6yHCXpA4y3CWpgwx3Seogw12SOshwl6QOMtwlqYMMd0nqIMNdkjrIcJekDjLcJamDDHdJ6qChfolJkvbaswdmZmB2FiYnYWoKxtx9HBmHXtLQ9uyBbdtg0yY488zmetu2pl2jYbhLGtrMDFxwAczPN9Pz8830zMxo6zqYGe6ShjY7+0Cw7zU/37RrNAx3SUObnITx8Qe3jY837RoNw13S0Kam4MorHwj48fFmempqtHUdzDxbRtLQxsbg3HPh5JM9W2Z/MVS4J3kccAXwFKCAXwduB94LbATuBP5NVX1rmH4k7f/GxuCEE5qLRm/Y59X/Dny4qv4Z8FTgNuBiYHtVTQHb22lJ0jpacbgneQzwDODtAFX146r6NnAOsLVdbCvwouFKlCQt1zB77j8PzAF/meQzSa5I8ijg6KqaBWivjxq0cpILk+xIsmNubm6IMiRJ/YYJ90OBU4D/WVWbgB+wjEMwVbWlqqaranpiYmKIMiRJ/YYJ953Azqq6sZ1+H03Y35NkEqC93j1ciZKk5VpxuFfVN4C7k+x9b/ws4IvAtcDmtm0z8IGhKpQkLduw57n/R+CqJA8DvgK8kuYJ45okrwLuAs4bsg9J0jINFe5VdQswPWDWWcNsV5I0HD8/JkkdZLhLUgcZ7pLUQYa7JHWQ4S5JHWS4S1IHGe6S1EGGuyR1kOEuSR1kuEtSBxnuktRBhrskdZDhLkkdZLhLUgcZ7pLUQYa7JHWQ4S5JHWS4S1IHGe6S1EGGuyR1kOEuSR1kuEtSBxnuktRBQ4d7kkOSfCbJde30kUmuTzLTXh8xfJmSpOVYjT33VwO39UxfDGyvqilgezstSVpHQ4V7kmOB5wFX9DSfA2xtb28FXjRMH5Kk5Rt2z/1y4LXAnp62o6tqFqC9PmrQikkuTLIjyY65ubkhy5Ak9VpxuCd5PrC7qm5ayfpVtaWqpqtqemJiYqVlSJIGOHSIdU8HXpjkucAjgMckeRdwT5LJqppNMgnsXo1CJUlLt+I996q6pKqOraqNwPnA31fVy4Brgc3tYpuBDwxdpSRpWdbiPPe3As9KMgM8q52WJK2jYQ7L/ExVfQz4WHv7XuCs1diuJGll/ISqJHWQ4S5JHWS4S1IHGe6S1EGGuyR1kOEuSR1kuEtSBxnuktRBhrskdZDhLkkdZLhLUgcZ7pLUQavyxWFSF+3ZAzMzMDsLk5MwNQVj7g7pAOGfqjTAnj2wbRts2gRnntlcb9vWtEsHAsNdGmBmBi64AObnm+n5+WZ6Zma0dUlLZbhLA8zOPhDse83PN+3SgcBwlwaYnITx8Qe3jY837dKBwHCXBpiagiuvfCDgx8eb6amp0dYlLZVny0gDjI3BuefCySd7towOTIa7tICxMTjhhOYiHWjcD5GkDjLcJamDDHdJ6qAVh3uS45J8NMltSW5N8uq2/cgk1yeZaa+PWL1yJUlLMcye+/3A71TVk4HTgIuSnAhcDGyvqilgezstSVpHKw73qpqtqpvb298DbgOOAc4BtraLbQVeNGSNkqRlWpVj7kk2ApuAG4Gjq2oWmicA4KgF1rkwyY4kO+bm5lajDElSa+hwT3I48DfAa6rqu0tdr6q2VNV0VU1PTEwMW4YkqcdQ4Z7kMJpgv6qqtrXN9ySZbOdPAruHK1GStFzDnC0T4O3AbVX1xz2zrgU2t7c3Ax9YeXmSpJUY5usHTgdeDnw+yS1t26XAW4FrkrwKuAs4b6gKJUnLtuJwr6pPAllg9lkr3a4kaXh+QlWSOshwl6QOMtwlqYMMd0nqIMNdkjrIcJekDjLcJamDDHdJ6iDDXZI6yHCXpA4a5rtldIDZswdmZmB2FiYnYWoKxnx6lzrJf+2DxJ49sG0bbNoEZ57ZXG/b1rRL6h7D/SAxMwMXXADz8830/HwzPTMz2rokrQ3D/SAxO/tAsO81P9+0S+oew/0gMTkJ4+MPbhsfb9oldY/hfpCYmoIrr3wg4MfHm+mpqdHWJWlteLbMQWJsDM49F04+2bNlpIOB4X4QGRuDE05oLpK6zf02Seogw12SOuiAPizjJy4labADNgr9xKUkLeyADXc/cSlJC1uzcE9ydpLbk9yR5OLV3r6fuJSkha1JuCc5BPgz4DnAicBLkpy4mn34iUtJWtha7bmfCtxRVV+pqh8D7wHOWc0O/MSlJC1src6WOQa4u2d6J/D03gWSXAhcCHD88ccvuwM/cSlJC1urcM+AtnrQRNUWYAvA9PR0DVh+UX7iUpIGW6v93J3AcT3TxwK71qgvSVKftQr3fwSmkjwxycOA84Fr16gvSVKfNTksU1X3J/kPwP8CDgHeUVW3rkVfkqSHWrOvH6iqDwIfXKvtS5IW5rklktRBqVrRiSqrW0QyB3xtiE1sAL65SuWsJutaHutaHutani7W9XNVNTFoxn4R7sNKsqOqpkddRz/rWh7rWh7rWp6DrS4Py0hSBxnuktRBXQn3LaMuYAHWtTzWtTzWtTwHVV2dOOYuSXqwruy5S5J6GO6S1EEHTLgneUeS3Um+sMD8JPkf7S8/fS7JKftJXWck+U6SW9rL69ehpuOSfDTJbUluTfLqAcus+3gtsa5RjNcjknw6yWfbut44YJlR/X0tpbZ1H7O230OSfCbJdQPmjWS8llDXSMaq7fvOJJ9v+90xYP7qjllVHRAX4BnAKcAXFpj/XOBDNF83fBpw435S1xnAdes8VpPAKe3tRwNfBk4c9Xgtsa5RjFeAw9vbhwE3AqeNeryWUdu6j1nb728D7x7U96jGawl1jWSs2r7vBDbsY/6qjtkBs+deVTcA9+1jkXOAK6vxKeBxSdb8R/eWUNe6q6rZqrq5vf094DaaH1Dpte7jtcS61l07Bt9vJw9rL/1nGozq72spta27JMcCzwOuWGCRkYzXEuran63qmB0w4b4Eg379aeTB0foX7cvqDyU5aT07TrIR2ESzx9drpOO1j7pgBOPVvpS/BdgNXF9V+814LaE2WP8xuxx4LbBngfmjGq/L2XddMLr/xwI+kuSmNL9E129Vx6xL4b7orz+NyM003//wVOBtwN+uV8dJDgf+BnhNVX23f/aAVdZlvBapayTjVVU/raqn0fywzKlJntK3yMjGawm1reuYJXk+sLuqbtrXYgPa1nS8lljXyP4fgdOr6hTgOcBFSZ7RN39Vx6xL4b5f/vpTVX1378vqar4G+bAkG9a63ySH0QToVVW1bcAiIxmvxeoa1Xj19P9t4GPA2X2zRv73tVBtIxiz04EXJrkTeA/wr5O8q2+ZUYzXonWN8u+rqna117uB9wOn9i2yqmPWpXC/Frigfcf5NOA7VTU76qKSPD5J2tun0oz5vWvcZ4C3A7dV1R8vsNi6j9dS6hrReE0keVx7exx4JvClvsVG8ve1lNrWe8yq6pKqOraqNtL8ytrfV9XL+hZb9/FaSl2j+Ptq+3pUkkfvvQ38KtB/ht2qjtma/VjHaktyNc073RuS7AQuo3lziar6C5ofBnkucAfwQ+CV+0ldLwb+fZL7gXng/GrfGl9DpwMvBz7fHqsFuBQ4vqeuUYzXUuoaxXhNAluTHELzz35NVV2X5Dd76hrJ39cSaxvFmD3EfjJei9U1qrE6Gnh/+7xyKPDuqvrwWo6ZXz8gSR3UpcMykqSW4S5JHWS4S1IHGe6S1EGGuyR1kOEuSR1kuEtSB/1/F8c3dlNU+fYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualization\n",
    "sns.scatterplot(x=x, y=y, color ='blue')\n",
    "plt.title('Without cubic interpolation')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2b84245c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# interpolation\n",
    "from scipy.interpolate import interp1d\n",
    "f = interp1d(x,y,kind='cubic')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "9362aaaf",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_new = np.linspace(1,5,10)\n",
    "y_interpt = f(x_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b62c183a",
   "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": [
    "# visualization after cubic interpolation\n",
    "sns.scatterplot(x=x_new,y=y_interpt)\n",
    "plt.title(\"With cubic interpolation\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62af2d82",
   "metadata": {},
   "source": [
    "## 3. Polynomial Interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "55f99184",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create sample array\n",
    "x = np.array([1,2,3,4,5])\n",
    "y = np.array([1,4,9,16,25])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "96350b8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "p = np.polyfit(x,y,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "035fc958",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_new = np.linspace(1,5,10)\n",
    "y_interpt = np.polyval(p,x_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "bbbc0971",
   "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": [
    "# visualization after polynomial interpolation\n",
    "sns.scatterplot(x=x_new,y=y_interpt)\n",
    "plt.title(\"With polynomial interpolation\")\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}