true_main.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fb92c6ea",
   "metadata": {},
   "source": [
    "## TP Matematica Superior K3052 - Santiago Ozan\n",
    "\n",
    "Este trabajo practico esta desarrollado en python usando librerias de pandas y matplotlib\n",
    "\n",
    "https://github.com/santi12386/TP_Mat_Sup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "c907e553",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "b7989e3c",
   "metadata": {},
   "outputs": [],
   "source": [
    "datos_matrix = np.matrix('0.2 0.6 1.2 1.9 2.8 3.5 3.7 4.3 4.9 5.7 6.1 6.5; 2.36 2.55 2.89 3.34 3.98 4.87 5.65 6.83 7.92 9.44 11.04 12.89')\n",
    "datos_matrix\n",
    "\n",
    "datos = pd.DataFrame(datos_matrix)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "997659ab",
   "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>X</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.2</td>\n",
       "      <td>2.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.6</td>\n",
       "      <td>2.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.2</td>\n",
       "      <td>2.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.9</td>\n",
       "      <td>3.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.8</td>\n",
       "      <td>3.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3.5</td>\n",
       "      <td>4.87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.7</td>\n",
       "      <td>5.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4.3</td>\n",
       "      <td>6.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.9</td>\n",
       "      <td>7.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5.7</td>\n",
       "      <td>9.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>6.1</td>\n",
       "      <td>11.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>6.5</td>\n",
       "      <td>12.89</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      X      Y\n",
       "0   0.2   2.36\n",
       "1   0.6   2.55\n",
       "2   1.2   2.89\n",
       "3   1.9   3.34\n",
       "4   2.8   3.98\n",
       "5   3.5   4.87\n",
       "6   3.7   5.65\n",
       "7   4.3   6.83\n",
       "8   4.9   7.92\n",
       "9   5.7   9.44\n",
       "10  6.1  11.04\n",
       "11  6.5  12.89"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aux = pd.DataFrame(np.asarray(datos).transpose())\n",
    "datos_dataframe = aux.rename(columns={0: \"X\", 1: \"Y\"})\n",
    "datos_dataframe"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad66bd0b",
   "metadata": {},
   "source": [
    "# Punto a)\n",
    "Grafico de la nube de puntos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "28d26455",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f53529c8190>]"
      ]
     },
     "execution_count": 38,
     "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": [
    "plt.plot(datos_dataframe['X'], datos_dataframe['Y'], 'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab15a697",
   "metadata": {},
   "source": [
    "# Punto b)\n",
    "\n",
    "Recta de minimos cuadrados:\n",
    "\n",
    "Expresion aproximante:\n",
    "$$P(x)=A_1*x+A_2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "480cbdf3",
   "metadata": {},
   "source": [
    "Sistema de ecuaciones normales:\n",
    "$$A_1\\sum_{n=0}^{11}{x_i}^2+A_2\\sum_{n=0}^{11}{x_i} =\\sum_{n=0}^{11}{f({x_i}){x_i}}$$\n",
    "\n",
    "$$A_1\\sum_{n=0}^{11}{x_i}+A_2*n=\\sum_{n=0}^{11}{f({x_i})}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "3ea6e7ba",
   "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>Xi</th>\n",
       "      <th>Yi</th>\n",
       "      <th>Xi^2</th>\n",
       "      <th>Xi Yi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.2</td>\n",
       "      <td>2.36</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.6</td>\n",
       "      <td>2.55</td>\n",
       "      <td>0.36</td>\n",
       "      <td>1.530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.2</td>\n",
       "      <td>2.89</td>\n",
       "      <td>1.44</td>\n",
       "      <td>3.468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.9</td>\n",
       "      <td>3.34</td>\n",
       "      <td>3.61</td>\n",
       "      <td>6.346</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.8</td>\n",
       "      <td>3.98</td>\n",
       "      <td>7.84</td>\n",
       "      <td>11.144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3.5</td>\n",
       "      <td>4.87</td>\n",
       "      <td>12.25</td>\n",
       "      <td>17.045</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.7</td>\n",
       "      <td>5.65</td>\n",
       "      <td>13.69</td>\n",
       "      <td>20.905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4.3</td>\n",
       "      <td>6.83</td>\n",
       "      <td>18.49</td>\n",
       "      <td>29.369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.9</td>\n",
       "      <td>7.92</td>\n",
       "      <td>24.01</td>\n",
       "      <td>38.808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5.7</td>\n",
       "      <td>9.44</td>\n",
       "      <td>32.49</td>\n",
       "      <td>53.808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>6.1</td>\n",
       "      <td>11.04</td>\n",
       "      <td>37.21</td>\n",
       "      <td>67.344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>6.5</td>\n",
       "      <td>12.89</td>\n",
       "      <td>42.25</td>\n",
       "      <td>83.785</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Xi     Yi   Xi^2   Xi Yi\n",
       "0   0.2   2.36   0.04   0.472\n",
       "1   0.6   2.55   0.36   1.530\n",
       "2   1.2   2.89   1.44   3.468\n",
       "3   1.9   3.34   3.61   6.346\n",
       "4   2.8   3.98   7.84  11.144\n",
       "5   3.5   4.87  12.25  17.045\n",
       "6   3.7   5.65  13.69  20.905\n",
       "7   4.3   6.83  18.49  29.369\n",
       "8   4.9   7.92  24.01  38.808\n",
       "9   5.7   9.44  32.49  53.808\n",
       "10  6.1  11.04  37.21  67.344\n",
       "11  6.5  12.89  42.25  83.785"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>Xi</th>\n",
       "      <th>Yi</th>\n",
       "      <th>Xi^2</th>\n",
       "      <th>Xi Yi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>41.4</td>\n",
       "      <td>73.76</td>\n",
       "      <td>193.68</td>\n",
       "      <td>334.024</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Xi     Yi    Xi^2    Xi Yi\n",
       "0  41.4  73.76  193.68  334.024"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xi_2 = pow(datos_dataframe['X'], 2)\n",
    "xi_yi = datos_dataframe['X']*datos_dataframe['Y']\n",
    "\n",
    "tabla1 = pd.concat([datos_dataframe['X'], datos_dataframe['Y'], xi_2, xi_yi], axis=1)\n",
    "tabla1.columns = ['Xi', 'Yi', 'Xi^2', 'Xi Yi']\n",
    "\n",
    "tabla1_sums = pd.DataFrame([sum(tabla1['Xi']), sum(tabla1['Yi']), sum(tabla1['Xi^2']), sum(tabla1['Xi Yi'])]).transpose()\n",
    "tabla1_sums.columns=['Xi', 'Yi', 'Xi^2', 'Xi Yi']\n",
    "\n",
    "display(tabla1, tabla1_sums)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4421ed95",
   "metadata": {},
   "source": [
    "Planteo de las ecuaciones normales:\n",
    "\n",
    "$$A_1*193.68+A_2*41.4=334.024$$\n",
    "$$A_1*41.4+A_2*12=73.76$$\n",
    "\n",
    "$$A_1=\\frac{334.024-A_2*41.4}{193.68}$$\n",
    "\n",
    "$$A_2=\\frac{73.76-A_1*41.4}{12}$$\n",
    "\n",
    "Formulas de Jacobi\n",
    "$$A_1^{k+1}=-A_2^k*(41.4/193.68)+(334.024/193.68)$$\n",
    "\n",
    "$$A_2^{k+1}=-A_1^k*(41.4/12)+(73.76/12)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "5fdbf5cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'T de Jacobi'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.213755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-3.45</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      0         1\n",
       "0  0.00 -0.213755\n",
       "1 -3.45  0.000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'C'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.724618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6.146667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0\n",
       "0  1.724618\n",
       "1  6.146667"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'A Inicial'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0\n",
       "0  0\n",
       "1  0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'A a las 100 iteraciones'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.564444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.749333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0\n",
       "0  1.564444\n",
       "1  0.749333"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T_Jacobi = np.matrix([[0, -41.4/193.68],[-41.4/12, 0]])\n",
    "display(\"T de Jacobi\", pd.DataFrame(T_Jacobi))\n",
    "C_Jacobi = np.matrix([[334.024/193.68],[73.76/12]])\n",
    "display(\"C\", pd.DataFrame(C_Jacobi))\n",
    "\n",
    "A_Jacobi = np.matrix([[0],[0]])\n",
    "A_Jacobi_anterior = A_Jacobi\n",
    "display(\"A Inicial\", pd.DataFrame(A_Jacobi))\n",
    "\n",
    "for i in range(0,100):\n",
    "    A_Jacobi = T_Jacobi*A_Jacobi_anterior+C_Jacobi\n",
    "    A_Jacobi_anterior = A_Jacobi\n",
    "display(\"A a las 100 iteraciones\" ,pd.DataFrame(A_Jacobi))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb650b49",
   "metadata": {},
   "source": [
    "Recta aproximante hallada:\n",
    "$$P(x)=1.564444*x+0.749333$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9de4145",
   "metadata": {},
   "source": [
    "Graficos - Recta de minimos cuadrados hallada por aproximacion + nube de puntos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "08f038a9",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5352a0be20>]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAD4CAYAAAD1jb0+AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAAAdpUlEQVR4nO3deXRV1fnG8e/LoMYxWqI/iFoUadQKGo1DpY5IoYo0YOtQB6pYHFqqViPG1lmBNs51HhEFaUUmJwbFgVoKhkGDQhzqRIIlDkGQCCG8vz92sIggSe5w7kmez1qs5B5u7nkXi/Ww2efde5u7IyIi8dMq6gJERKRpFOAiIjGlABcRiSkFuIhITCnARURiqk06b9auXTvv2LFjOm8pIhJ7s2fP/tTdc9a/ntYA79ixI6Wlpem8pYhI7JnZhxu6rikUEZGYUoCLiMSUAlxEJKYU4CIiMaUAFxGJqbR2oYiItDTj51ZQMrmcyuoaOmRnUdQzj8L83KR8tgJcRCRFxs+toHhsGTW1dQBUVNdQPLYMICkhrikUEZEUKZlc/k14r1VTW0fJ5PKkfL4CXEQkRSqraxp1vbEU4CIiKdIhO6tR1xtLAS4ikiJFPfPIatv6W9ey2ramqGdeUj5fDzFFRFJk7YNKdaGIiMRQYX5u0gJ7fZpCERGJKQW4iEhMKcBFRGJKAS4iElMKcBGRmFKAi4jElAJcRCSmNhngZvaQmS0xs/nrXCsxs4Vm9oaZjTOz7JRWKSIi39GQEfhwoNd616YC+7h7V+BtoDjJdYmIyCZsMsDd/RXg8/WuTXH31fUv/w3snILaRETkeyRjDvws4LmN/aaZDTSzUjMrraqqSsLtREQEEgxwM/sTsBoYubH3uPt97l7g7gU5OTmJ3E5ERNbR5M2szKw/0Bvo7u6evJJERKQhmhTgZtYLGAwc4e4rkluSiIg0REPaCB8HZgB5ZrbIzAYAdwDbAFPNbJ6Z3ZPiOkVEZD2bHIG7+ykbuPxgCmoREZFG0EpMEZGYUoCLiMSUAlxEJKYU4CIiMaUAFxGJKQW4iEhMNXklpohIczV+bgUlk8uprK6hQ3YWRT3zKMzPjbqs71CAi4isY/zcCorHllFTWwdARXUNxWPLADIuxDWFIiKyjpLJ5d+E91o1tXWUTC6PqKKNU4CLiKyjsrqmUdejpAAXEVlHh+ysRl3fpOXLoaQEapL/D4ACXERkHUU988hq2/pb17LatqaoZ17jPmj1arj3XthjD7j0Unj22SRWGSjARUTWUZify9B+XcjNzsKA3Owshvbr0vAHmO4wbhzssw+cey507gz/+heccELSa1UXiojIegrzc5vWcfLqq2G0/a9/wZ57woQJcPzxYJb8ItEIXEQkcQsXQt++8NOfwvvvw333QVkZ9OmTsvAGBbiISNMtXgznnBOmS154Aa67Dt55B377W2iT+gkOTaGIiDTWsmWhs+Smm2DVKjj/fLjiCkjzwe0KcBGRhlq1KkyPXHstVFXBSSfBDTdAp06RlKMpFBGRTXGHf/wD9t4bBg2CH/8YZs2C0aMjC29QgIuIfL+XX4ZDDgmj7awseOYZmDYNDjww6soU4CIiG/Tmm6EF8MgjobISHnoI5s2DY49NaWdJYyjARUTWVVEBAwZA164wfToMGwZvvw1nngmtW2/659NIDzFFRACWLg1hfeutsGYNXHAB/OlP8IMfRF3ZRm1yBG5mD5nZEjObv861Hcxsqpm9U/91+9SWKSKSIitXhtDu1CkEeL9+YWHOzTdndHhDw6ZQhgO91rt2GfCCu3cGXqh/LSISH2vWwKhRYcn7RRdBfj7Mng0jR8Juu0VdXYNsMsDd/RXg8/Uu/wJ4pP77R4DC5JYlIpJCa7tITj0VttsOJk2CqVNh//2jrqxRmvoQcyd3XwxQ/3XHjb3RzAaaWamZlVZVVTXxdiIiSfD669CrF3TvDp9+CiNGwJw50LNn1JU1Scq7UNz9PncvcPeCnDQvMxURAeCjj6B//zBNMmsW3HgjlJfD6adDq/g24zW1C+W/Ztbe3RebWXtgSTKLEhFJii++gKFD4fbbw+tLLoHiYti+efRdNPWfnolA//rv+wMTklOOiEgSfP11GGV36hS+nnxy6OX+61+bTXhDw9oIHwdmAHlmtsjMBgDDgB5m9g7Qo/61iEi06urg0UchLw+KisIS+HnzYPhw2HXXqKtLuk1Oobj7KRv5re5JrkVEpGncYcoUGDw4PKgsKAihfdRRUVeWUlqJKSLxNmcODB7M+IpaSrpfTGWv7emQnUVR9o+afX9zfB+/ikjL9v778OtfwwEHMH7p5hT3uZiKrXbAMSqqv6Z4bBnj51ZEXWVKKcBFJF4+/TSsnNxzTxg/HoqLKSm8kJr14qymto6SyeXR1JgmCnARiYeamrBXSadOoS3w9NPD+ZNDhlD55coN/khldU2ai0wvBbiIZLa6Onj4YejcOfRwH3EEvPEGPPAA5OYC0CE7a4M/urHrzYUCXEQyk3s4/Wa//eCss0JYv/wyTJwYjjRbR1HPPLLafnuv7qy2rSnqmZfGgtNPAS4imWfWrNAC2Lt3WJTzxBPw73/D4Ydv8O2F+bkM7deF3OwsDMjNzmJovy4U5uemt+40UxuhiGSO996Dyy8PBwjn5MAdd8DAgdC27SZ/tDA/t9kH9voU4CISvaoquO46uPtu2GwzuPLKsG/JNttEXVlGU4CLSHS++gpuuSXsUbJiBZx9Nlx1FbRvH3VlsaAAF5H0W706dJZcdRUsXgx9+8KQIaG3WxpMAS4i6eMeukguuyycO3nooTBmTPgqjaYuFBFJjxkzQhdJYWEI8nHj4J//VHgnQAEuIqlVXh5Oej/0UHj3XbjnHpg/PwS5WdTVxZoCXERS45NP4LzzwqKbqVPh2mtDgJ9zDrTR7G0y6E9RRJJr2bJwCs5NN8HKlXDuuaEtcMeNnn0uTaQAF5HkqK2F+++Ha66BJUvgl78MnSWdO0ddWbOlABeRxLjD2LFho6l33gkPKidOhIMPjrqyZk9z4CLSdNOnh4eTv/xlWEH51FPw0ksK7zRRgItI4731FvTpE0bbH30EDz4YzqLs3VudJWmkABeRhqushN/+Frp0CVu7DhkSpk3OOgtat970z0tSaQ5cRDZt6dKwX8ktt4Rl8IMGwZ//DO3aRV1Zi6YAF5GNW7UqLLy57rpwFuUpp8D118Puu0ddmaApFBHZkDVrYPRo2GsvuOAC6NoVSkth1CiFdwZJKMDN7CIze9PM5pvZ42a2RbIKE5GITJsGBx0URttbbw3PPQfPPw8HHBB1ZbKeJge4meUCfwAK3H0foDVwcrIKE5E0e+MNOPZY6N49LMQZPhzmzIFevb7TWTJ+bgXdhk1jt8ueoduwaYyfWxFNzS1conPgbYAsM6sFtgQqEy9JRNLq44/hiitgxAjYbrvwsHLQINhiw/+hHj+3guKxZdTU1gFQUV1D8dgygBZ3pFnUmjwCd/cK4EbgI2AxsNTdp6z/PjMbaGalZlZaVVXV9EpFJLmqq2HwYPjRj+Dxx+GPfwxnUhYVbTS8AUoml38T3mvV1NZRMrk8xQXL+hKZQtke+AWwG9AB2MrMTlv/fe5+n7sXuHtBTk5O0ysVkeRYuRJuvhk6dYKSkrCKsrw8bEC1ww6b/PHK6ppGXZfUSeQh5jHA++5e5e61wFhAO7OLZKo1a+CxxyAvDy6+GAoKwhz3o49Cx44N/pgO2VmNui6pk0iAfwQcYmZbmpkB3YEFySlLRJLq+edDYJ9+ehhlT50KkyfDfvs1+qOKeuaR1fbbqy6z2ramqGdekoqVhkpkDnwmMAaYA5TVf9Z9SapLRJJh7lz42c+gRw/4/HMYOTL0cx9zTJM/sjA/l6H9upCbnYUBudlZDO3XRQ8wI2DunrabFRQUeGlpadruJ9JiffBB6CwZORK23z4sez//fNh886grkyYws9nuXrD+dS2lF2lOPv8cbrgB7rgDWrWCSy8NJ8BnZ0ddmaSAAlykOaipgb/9LewOuGwZ9O8fzqDceeeoK5MUUoCLxFldXegiueIKWLQIjjsOhg2DffaJujJJA21mJRJH7vDss5CfD2eeCe3bh5Nwnn5a4d2CKMBF4qa0NOxXctxxsGIF/OMfMHMmHHFE1JVJminAReLivffg5JPhwAOhrAxuvz0cbfarX+kYsxZKc+Aima6qKhyocM890LZtaAksKoJtt426MomYAlwkU61YEY4w+8tf4KuvYMAAuPpq6NAh6sokQyjARTLN6tVhL+6rrgqHCPfpEzpL9tor6sokw2gOXCRTuMNTT8G++4aT33/4Q5g+HSZMUHjLBmkELpIJZs4M89rTp4f9uZ98Evr2bfDDyfFzKyiZXE5ldQ0dsrMo6pmnvUlaAI3ARaL09tthP+5DDgnf3303zJ8P/fo1KryLx5ZRUV2D878TcnTMWfOnABeJwn//C7/7Hfz4xzBpUng4+e67cO65odOkEXRCTsulKRSRdFq+PJyGU1IS9i855xy48krYaacmf6ROyGm5NAIXSYfa2tDHvcceobukZ8+wCOfOOxMKb9AJOS2ZAlwkldxh3LiwP8l554UHlDNmwJgx4fsk0Ak5LZcCXCRVXn0VunULDyTbtIGJE+Hll8MDyyTSCTktl+bARZJt4cJwiMKECWHV5P33w29+E0I8RQrzcxXYLZBG4CLJUlkJAweGzpJp08LJOO+8A2efndLwlpZLf6tEEvXll6Gr5Oabw8PK3/0uHLCQkxN1ZdLMKcBFmqq2Fu69NxxdVlUFJ50URt2dOkVdmbQQmkIRaSz3cIjC3nvDoEFhymTWLBg9WuEtaaUAF2mMtV0kJ50EW2wBzzwT5rsPPDDqyqQFSijAzSzbzMaY2UIzW2BmP0lWYSIZZf586N0bjjwyPKx8+GGYNw+OPVan4UhkEp0Dvw2Y5O6/NLPNgC2TUJNI5li0KKycHD4cttkmHK4waBBkaZWjRK/JAW5m2wKHA78BcPdVwKrklCUSserqENa33gpr1sCFF8Lll8MPfhBxYSL/k8gUyu5AFfCwmc01swfMbKv132RmA82s1MxKq6qqEridSBqsXBmOMevUKZyCc8IJUF4ON92k8JaMk0iAtwH2B+5293zgK+Cy9d/k7ve5e4G7F+SoL1Yy1Zo1MGoU7Lkn/PGPcMABMGcOPPYYdOwYdXUiG5RIgC8CFrn7zPrXYwiBLhIvzz8PBQVw6qmQnQ1TpoRf+flRVybyvZo8B+7un5jZx2aW5+7lQHfgreSVJpJi8+bB4MEhrH/4wzDaPuUUaJVYd62ON5N0SbQLZRAwsr4D5T/AmYmXJJJiH34Ylro/9lgYcd94Y1j+vsUWCX/02uPN1p6Qs/Z4M0AhLkmXUIC7+zygIDmliKTYF1/AkCFw++2hd7uoKOwauP32SbvF9x1vpgCXZNNeKNL8ff013HFH2Kdk6VI444ywf8muuyb9VjreTNJJS+ml+aqrgxEjIC8vjLYPOSTMew8fnpLwBh1vJumlAJfmxx0mTw6tgP37h21dX3gBnnsOunZN6a11vJmkkwJcmpc5c6BHD+jVK+zT/fjjYafAo49Oy+11vJmkk+bApXl4/334059CYLdrB7fdBueeC5ttlvZSdLyZpIsCXOLt00/Dw8k77wzHll1+OVx6KWy3XdSViaScAlziacWKMMoeNgyWL4ezzoKrr4ZcjXyl5VCAS7zU1cEjj8CVV0JFBRx/fAjxvfeOujKRtNNDTIkHd3j6adh3XxgwAHbeGV55BSZOVHhLi6UAl8w3cyYcdVQYba9cCU88ATNmwGGHRV2ZSKQ0hSKZ6913w0PJJ54Ivdx33AEDB0LbtpGVpI2qJJMowCXzLFkSlrrfey9svnmY777kknCkWYS0UZVkGk2hSOb46iu47rpwGs4998DZZ4dR+DXXRB7e8P0bVYlEQSNwid7q1fDQQ+Hw4E8+gb59YejQsIdJBtFGVZJpNAKX6LjD+PHQpQucc04Yeb/6Kowdm3HhDdqoSjKPAlyisbaLpG/f8HrcOJg+HQ49NNq6voc2qpJMowCX9Covh379QlC/9154UFlWBoWF4ZCFDKaNqiTTaA5c0uOTT8LDyPvvh6ys8LDyootgq62irqxRtFGVZBIFuKTWsmXhzMmbbgqLcM47L5xHueOOUVcmEnsKcEmN2tow2r7mmtDXfeKJYdfAPfaIujKRZkMBLsnlDk8+GVZQvvMOHHEEPPUUHHRQ1JWJNDt6iCnJ88or8JOfwK9+FQ5SePppePFFhbdIiijAJXFvvQV9+oTR9qJFYVHO66/DccdlfGeJSJwpwKXpKirCcvcuXeDll2HIEHj7bTjzTGjdetM/LyIJSXgO3MxaA6VAhbv3TrwkyXhLl8Jf/wq33BKWwf/hD+E8ynbtUnpb7QQo8m3JeIh5AbAA2DYJnyWZbNWqsMnUtdfCZ5/BKafA9dfD7run/NbaCVDkuxKaQjGznYHjgAeSU45kpDVrYPRo2GsvuOAC2G8/KC2FUaPSEt6gnQBFNiTROfBbgUuBNRt7g5kNNLNSMyutqqpK8HaSdi++CAcfHEbb22wDkybB1KlwwAFpLUM7AYp8V5MD3Mx6A0vcffb3vc/d73P3AncvyMnJaertJN3KyuDYY+Hoo+G//4URI2DOHOjZM5LOEu0EKPJdiYzAuwF9zOwDYDRwtJk9lpSqJDoffwy/+U04PHjGDCgpCZ0lp58OraJrWtJOgCLf1eSHmO5eDBQDmNmRwCXuflpyypK0q64Ohyjcdlt4ffHFUFwMO+wQaVlrrX1QqS4Ukf/RUvqW7uuv4c47wz4l1dVhpH3ddbDrrlFX9h3aCVDk25IS4O7+EvBSMj5L0mTNGhg5Ev78Z/joozC3/Ze/hKkTEYkFrcRsiaZMgf33hzPOCItvnn8+dJcovEViRQHeksydCz16hNH20qWhj/u116B796grE5Em0Bx4S/DBB2GqZOTI8FDy5pvh/PNh880BLVEXiSsFeHP22Wfh4eSdd4YWwMsug8GDITv7m7doibpIfGkKpTmqqQkPJDt1Cm2Bp54aDlcYOvRb4Q1aoi4SZxqBNyd1dfDoo+HMyUWLwn7cw4bBPvts9Ee0RF0kvjQCbw7c4dlnIT8/7MXdvj289FI4Eed7whu0RF0kzhTgcffaa2G/kuOOgxUr4O9/h5kzw+k4DaAl6iLxpQCPq/feg5NPDudNvvkm/O1v4WizE09s1GZThfm5DO3XhdzsLAzIzc5iaL8ueoApEgOaA49Yo1v4qqrCUvd77oG2bcN89yWXwLZNP09DS9RF4kkBHqFGtfB99RXcemvoLlmxAgYMgKuvDvPdItIiaQolQg1q4Vu9Gu6/Hzp3DotxuneH+fPh3nsV3iItnAI8Qt/bwucOEydC164wcCB07AjTp8O4cbDnnuktVEQykgI8Qhtt4ctqBYcfDr/4RejtHjsWXn0VfvrTNFcoIplMAR6hDbbwraml6O9/CSsn77orTJf07RvJMWYiktn0EHM96dzY6ZtTZp59i8ovV9LhyyqK/j2awpOOgoufhq23Tsl9RaR5UICvI+0bOy1fTuGE+ym88cZwMs4558CkEbDTTsm/l4g0O5pCWUfaNnaqrQ193HvsAddcA716hUU4d96p8BaRBms2I/BkTH2kfGMn99BFUlwcTno/7DAYPx4OOSQ5ny8iLUqzGIGvnfqoqK7B+d/Ux/i5FY36nJRu7PTqq9CtG5xwArRuDRMmwMsvK7xFpMmaRYAna+ojJRs7LVgAhYWhBfDDD+GBB+CNN6BPH3WWiEhCmsUUSrKmPr7pCklGF0plZVjq/uCDoZvkhhvgwgthyy0b/1kiIhvQLAK8Q3YWFRsI66ZMfSS8sdOXX0JJSTh3srYWfv/7sOFUu3ZN/0wRkQ1o8hSKme1iZi+a2QIze9PMLkhmYY2REXtar1oVtnTt1Amuvz5MkSxcGI40U3iLSAokMgJfDVzs7nPMbBtgtplNdfe3klRbgyV16qOx3OGJJ+Dyy8Me3UcfHXYMLChI/b1FpEVrcoC7+2Jgcf33y8xsAZALpD3AIaI9rV96CS69NJyK06ULPPcc9Oyph5MikhZJ6UIxs45APjAzGZ+X8crKwhFmRx0FixfD8OEwd25YkKPwFpE0STjAzWxr4EngQnf/cgO/P9DMSs2stKqqKtHbRWvRIjjrLNh339DXPWxYWJDTv3/o7RYRSaOEAtzM2hLCe6S7j93Qe9z9PncvcPeCnJycRG4XnerqsHqyc2cYORIuuijMdw8eDFk6vV1EotHkOXAzM+BBYIG735y8kjLIypVw993hDMovvoBTTw3fd+wYdWUiIgmNwLsBpwNHm9m8+l/HJqmuaK1ZA6NGhZNvLroIDjgAZs+GRx9VeItIxkikC+WfQPN7Yvf882FqZM4c2G8/mDIFevSIuioRke9oFnuhJMXrr4cukh494LPPwmh79myFt4hkLAX4hx/CGWdAfn7o577pJigvh9NOg1b64xGRzNUs9kJpks8/hyFDwvL3Vq3CgpzLLoPs7KgrExFpkJYX4F9/HUJ7yBBYujT0cF97LeyyS9SViYg0SsuZI6irgxEjIC8vjLYPPTTMez/8sMJbRGKp+Qe4O0yaBPvvH0bbO+4I06bBM8+E/UtERGKqeQf47NlwzDHw85/DsmUwejTMnBn2MBERibnmGeD/+Q/8+tdhS9c33gh7ci9cCCedpM4SEWk2mtdDzE8/DYcp3HUXtGkT9ugePBi23TbqykREkq55BPiKFXDrreEgheXLYcCAcB5lhw5RVyYikjLxDvC6OnjkkXDmZGVlOMZs6FDYe++oKxMRSbl4Tgi7w9NPQ9euYbS9yy7wyiswYYLCW0RajPgF+KxZcOSRcPzx4dT3MWNgxgw47LCoKxMRSav4BPi778KJJ8LBB4eOkrvugjffhBNO0DFmItIixSPAr78e9toLnn0WrroqhPl550HbtlFXJiISmXg8xOzYEc4+O4T3//1f1NWIiGSEeAT4aaeFXyIi8o14TKGIiMh3KMBFRGJKAS4iElMKcBGRmFKAi4jElAJcRCSmFOAiIjGlABcRiSlz9/TdzKwK+LCJP94O+DSJ5aSTao9GXGuPa92g2lPlh+6es/7FtAZ4Isys1N0Loq6jKVR7NOJae1zrBtWebppCERGJKQW4iEhMxSnA74u6gASo9mjEtfa41g2qPa1iMwcuIiLfFqcRuIiIrEMBLiISU7EIcDPrZWblZvaumV0WdT0NZWYPmdkSM5sfdS2NYWa7mNmLZrbAzN40swuirqmhzGwLM5tlZq/X135N1DU1lpm1NrO5ZvZ01LU0hpl9YGZlZjbPzEqjrqcxzCzbzMaY2cL6v/c/ibqmhsj4OXAzaw28DfQAFgGvAae4+1uRFtYAZnY4sBwY4e77RF1PQ5lZe6C9u88xs22A2UBhTP7MDdjK3ZebWVvgn8AF7v7viEtrMDP7I1AAbOvuvaOup6HM7AOgwN0zdTHMRpnZI8B0d3/AzDYDtnT36ojL2qQ4jMAPAt519/+4+ypgNPCLiGtqEHd/Bfg86joay90Xu/uc+u+XAQuA3GirahgPlte/bFv/K7NHKesws52B44AHoq6lpTCzbYHDgQcB3H1VHMIb4hHgucDH67xeREzCpDkws45APjAz4lIarH4KYh6wBJjq7rGpHbgVuBRYE3EdTeHAFDObbWYDoy6mEXYHqoCH66euHjCzraIuqiHiEOC2gWuxGVHFmZltDTwJXOjuX0ZdT0O5e5277wfsDBxkZrGYvjKz3sASd58ddS1N1M3d9wd+DvyufgoxDtoA+wN3u3s+8BUQi2dtcQjwRcAu67zeGaiMqJYWo37++ElgpLuPjbqepqj/b/BLQK9oK2mwbkCf+rnk0cDRZvZYtCU1nLtX1n9dAowjTH/GwSJg0Tr/UxtDCPSMF4cAfw3obGa71T9cOBmYGHFNzVr9g8AHgQXufnPU9TSGmeWYWXb991nAMcDCSItqIHcvdved3b0j4e/5NHc/LeKyGsTMtqp/4E399MPPgFh0X7n7J8DHZpZXf6k7kPEP7CH81yGjuftqM/s9MBloDTzk7m9GXFaDmNnjwJFAOzNbBFzl7g9GW1WDdANOB8rq55IBLnf3Z6MrqcHaA4/Udy+1Av7h7rFqx4upnYBx4d9+2gCj3H1StCU1yiBgZP0g8T/AmRHX0yAZ30YoIiIbFocpFBER2QAFuIhITCnARURiSgEuIhJTCnARkZhSgIuIxJQCXEQkpv4fsSOox6VE51gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,6.5,100)\n",
    "y = 1.564444*x+0.749333\n",
    "\n",
    "plt.plot(x, y, '-r', label='P(x)=1.564444*x+0.749333')\n",
    "plt.plot(datos_dataframe['X'], datos_dataframe['Y'], 'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bf02f22",
   "metadata": {},
   "source": [
    "# Punto c\n",
    "\n",
    "Parabola de minimos cuadrados\n",
    "\n",
    "Expresion aproximante:\n",
    "$$P(x)=A_1*x^2+A_2x+A_3$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28bfdbf9",
   "metadata": {},
   "source": [
    "Sistema de ecuaciones normales:\n",
    "$$A_1\\sum_{n=0}^{11}{x_i}^4+A_2\\sum_{n=0}^{11}{x_i}^3+A_3\\sum_{n=0}^{11}{x_i}^2=\\sum_{n=0}^{11}{f({x_i}){x_i}^2}$$\n",
    "$$A_1\\sum_{n=0}^{11}{x_i}^3+A_2\\sum_{n=0}^{11}{x_i}^2+A_3\\sum_{n=0}^{11}{x_i}=\\sum_{n=0}^{11}{f({x_i}){x_i}}$$\n",
    "$$A_1\\sum_{n=0}^{11}{x_i}^2+A_2\\sum_{n=0}^{11}{x_i}+A_3*n=\\sum_{n=0}^{11}{f({x_i})}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "6151716c",
   "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>Xi</th>\n",
       "      <th>Yi</th>\n",
       "      <th>Xi^2</th>\n",
       "      <th>Xi^3</th>\n",
       "      <th>Xi^4</th>\n",
       "      <th>Xi Yi</th>\n",
       "      <th>Xi^2 Yi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.2</td>\n",
       "      <td>2.36</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.0016</td>\n",
       "      <td>0.472</td>\n",
       "      <td>0.0944</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.6</td>\n",
       "      <td>2.55</td>\n",
       "      <td>0.36</td>\n",
       "      <td>0.216</td>\n",
       "      <td>0.1296</td>\n",
       "      <td>1.530</td>\n",
       "      <td>0.9180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.2</td>\n",
       "      <td>2.89</td>\n",
       "      <td>1.44</td>\n",
       "      <td>1.728</td>\n",
       "      <td>2.0736</td>\n",
       "      <td>3.468</td>\n",
       "      <td>4.1616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.9</td>\n",
       "      <td>3.34</td>\n",
       "      <td>3.61</td>\n",
       "      <td>6.859</td>\n",
       "      <td>13.0321</td>\n",
       "      <td>6.346</td>\n",
       "      <td>12.0574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.8</td>\n",
       "      <td>3.98</td>\n",
       "      <td>7.84</td>\n",
       "      <td>21.952</td>\n",
       "      <td>61.4656</td>\n",
       "      <td>11.144</td>\n",
       "      <td>31.2032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3.5</td>\n",
       "      <td>4.87</td>\n",
       "      <td>12.25</td>\n",
       "      <td>42.875</td>\n",
       "      <td>150.0625</td>\n",
       "      <td>17.045</td>\n",
       "      <td>59.6575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.7</td>\n",
       "      <td>5.65</td>\n",
       "      <td>13.69</td>\n",
       "      <td>50.653</td>\n",
       "      <td>187.4161</td>\n",
       "      <td>20.905</td>\n",
       "      <td>77.3485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4.3</td>\n",
       "      <td>6.83</td>\n",
       "      <td>18.49</td>\n",
       "      <td>79.507</td>\n",
       "      <td>341.8801</td>\n",
       "      <td>29.369</td>\n",
       "      <td>126.2867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.9</td>\n",
       "      <td>7.92</td>\n",
       "      <td>24.01</td>\n",
       "      <td>117.649</td>\n",
       "      <td>576.4801</td>\n",
       "      <td>38.808</td>\n",
       "      <td>190.1592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5.7</td>\n",
       "      <td>9.44</td>\n",
       "      <td>32.49</td>\n",
       "      <td>185.193</td>\n",
       "      <td>1055.6001</td>\n",
       "      <td>53.808</td>\n",
       "      <td>306.7056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>6.1</td>\n",
       "      <td>11.04</td>\n",
       "      <td>37.21</td>\n",
       "      <td>226.981</td>\n",
       "      <td>1384.5841</td>\n",
       "      <td>67.344</td>\n",
       "      <td>410.7984</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>6.5</td>\n",
       "      <td>12.89</td>\n",
       "      <td>42.25</td>\n",
       "      <td>274.625</td>\n",
       "      <td>1785.0625</td>\n",
       "      <td>83.785</td>\n",
       "      <td>544.6025</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Xi     Yi   Xi^2     Xi^3       Xi^4   Xi Yi   Xi^2 Yi\n",
       "0   0.2   2.36   0.04    0.008     0.0016   0.472    0.0944\n",
       "1   0.6   2.55   0.36    0.216     0.1296   1.530    0.9180\n",
       "2   1.2   2.89   1.44    1.728     2.0736   3.468    4.1616\n",
       "3   1.9   3.34   3.61    6.859    13.0321   6.346   12.0574\n",
       "4   2.8   3.98   7.84   21.952    61.4656  11.144   31.2032\n",
       "5   3.5   4.87  12.25   42.875   150.0625  17.045   59.6575\n",
       "6   3.7   5.65  13.69   50.653   187.4161  20.905   77.3485\n",
       "7   4.3   6.83  18.49   79.507   341.8801  29.369  126.2867\n",
       "8   4.9   7.92  24.01  117.649   576.4801  38.808  190.1592\n",
       "9   5.7   9.44  32.49  185.193  1055.6001  53.808  306.7056\n",
       "10  6.1  11.04  37.21  226.981  1384.5841  67.344  410.7984\n",
       "11  6.5  12.89  42.25  274.625  1785.0625  83.785  544.6025"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>Xi</th>\n",
       "      <th>Yi</th>\n",
       "      <th>Xi^2</th>\n",
       "      <th>Xi^3</th>\n",
       "      <th>Xi^4</th>\n",
       "      <th>Xi Yi</th>\n",
       "      <th>Xi^2 Yi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>41.4</td>\n",
       "      <td>73.76</td>\n",
       "      <td>193.68</td>\n",
       "      <td>1008.246</td>\n",
       "      <td>5557.788</td>\n",
       "      <td>334.024</td>\n",
       "      <td>1763.993</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Xi     Yi    Xi^2      Xi^3      Xi^4    Xi Yi   Xi^2 Yi\n",
       "0  41.4  73.76  193.68  1008.246  5557.788  334.024  1763.993"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xi_2 = pow(datos_dataframe['X'], 2)\n",
    "xi_3 = pow(datos_dataframe['X'], 3)\n",
    "xi_4 = pow(datos_dataframe['X'], 4)\n",
    "xi_yi = datos_dataframe['X']*datos_dataframe['Y']\n",
    "xi_2_yi = xi_2*datos_dataframe['Y']\n",
    "\n",
    "tabla2 = pd.concat([datos_dataframe['X'], datos_dataframe['Y'], xi_2, xi_3, xi_4, xi_yi, xi_2_yi], axis=1)\n",
    "tabla2.columns = ['Xi', 'Yi', 'Xi^2', 'Xi^3', 'Xi^4', 'Xi Yi', 'Xi^2 Yi']\n",
    "    \n",
    "tabla2_sums = pd.DataFrame([sum(tabla2['Xi']), sum(tabla2['Yi']), sum(tabla2['Xi^2']), sum(tabla2['Xi^3']), sum(tabla2['Xi^4']), sum(tabla2['Xi Yi']), sum(tabla2['Xi^2 Yi'])]).transpose()\n",
    "tabla2_sums.columns=['Xi', 'Yi', 'Xi^2', 'Xi^3', 'Xi^4', 'Xi Yi', 'Xi^2 Yi']\n",
    "display(tabla2, tabla2_sums)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5255c21",
   "metadata": {},
   "source": [
    "Planteo del sistema:\n",
    "\n",
    "$$A_1*5557.788+A_2*1008.246+A_3*193.68=1763.993$$\n",
    "\n",
    "$$A_1*1008.246+A_2*193.68+A_3*41.4=334.024$$\n",
    "$$A_1*193.68+A_2*41.4+A_3*12=73.76$$\n",
    "\n",
    "Ecuaciones de Gauss-Seidel\n",
    "\n",
    "$$A_1^{K+1}=A_2^k*(-1008.246/5557.788)A_3^k*(-193.68/5557.788)+(1763.993/5557.788)$$\n",
    "\n",
    "$$A_2^{K+1}=A_1^{K+1}*(-1008.246/193.68)+A_3^k*(-41.4/193.68)+(334.024/193.68)$$\n",
    "\n",
    "$$A_3^{K+1}=A_1^{K+1}*(-193.68/12)+A_2^{K+1}*(-41.4/12)+(73.76/12)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bc775a2",
   "metadata": {},
   "source": [
    "Polinomio aproximante:\n",
    "$$P(x)=0.255529618189472*x^2-0.143398273502509x+2.51714300600557$$\n",
    "\n",
    "Graficos - Parabola de minimos cuadrados hallada por aproximacion + nube de puntos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "4c0247bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5352a77850>]"
      ]
     },
     "execution_count": 43,
     "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": [
    "x = np.linspace(0,6.5,100)\n",
    "y = 0.255529618189472*pow(x,2)-0.143398273502509*x+2.51714300600557\n",
    "\n",
    "plt.plot(x, y, '-r', label='P(x)=0.255529618189472*x^2-0.143398273502509x+2.51714300600557')\n",
    "\n",
    "plt.plot(datos_dataframe['X'], datos_dataframe['Y'], 'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e9ed7b8",
   "metadata": {},
   "source": [
    "# Punto d)\n",
    "\n",
    "Modelo:\n",
    "$$y =\\frac{a}{x+b}$$\n",
    "\n",
    "Cambio de variables:\n",
    "$$\\frac{1}{y}=\\frac{x}{a}+\\frac{b}{a}$$\n",
    "   \n",
    "$$Y=\\frac{1}{y}; A_1=\\frac{1}{a}; A_2=\\frac{b}{a}$$\n",
    "\n",
    "Ecuacion lineal propuesta\n",
    "$$Y=A_1*x+A_2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "54f36653",
   "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>xi</th>\n",
       "      <th>Yi</th>\n",
       "      <th>xi^2</th>\n",
       "      <th>xi Yi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.423729</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.084746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.6</td>\n",
       "      <td>0.392157</td>\n",
       "      <td>0.36</td>\n",
       "      <td>0.235294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.2</td>\n",
       "      <td>0.346021</td>\n",
       "      <td>1.44</td>\n",
       "      <td>0.415225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.9</td>\n",
       "      <td>0.299401</td>\n",
       "      <td>3.61</td>\n",
       "      <td>0.568862</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.8</td>\n",
       "      <td>0.251256</td>\n",
       "      <td>7.84</td>\n",
       "      <td>0.703518</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3.5</td>\n",
       "      <td>0.205339</td>\n",
       "      <td>12.25</td>\n",
       "      <td>0.718686</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.7</td>\n",
       "      <td>0.176991</td>\n",
       "      <td>13.69</td>\n",
       "      <td>0.654867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4.3</td>\n",
       "      <td>0.146413</td>\n",
       "      <td>18.49</td>\n",
       "      <td>0.629575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.9</td>\n",
       "      <td>0.126263</td>\n",
       "      <td>24.01</td>\n",
       "      <td>0.618687</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5.7</td>\n",
       "      <td>0.105932</td>\n",
       "      <td>32.49</td>\n",
       "      <td>0.603814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>6.1</td>\n",
       "      <td>0.090580</td>\n",
       "      <td>37.21</td>\n",
       "      <td>0.552536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>6.5</td>\n",
       "      <td>0.077580</td>\n",
       "      <td>42.25</td>\n",
       "      <td>0.504267</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     xi        Yi   xi^2     xi Yi\n",
       "0   0.2  0.423729   0.04  0.084746\n",
       "1   0.6  0.392157   0.36  0.235294\n",
       "2   1.2  0.346021   1.44  0.415225\n",
       "3   1.9  0.299401   3.61  0.568862\n",
       "4   2.8  0.251256   7.84  0.703518\n",
       "5   3.5  0.205339  12.25  0.718686\n",
       "6   3.7  0.176991  13.69  0.654867\n",
       "7   4.3  0.146413  18.49  0.629575\n",
       "8   4.9  0.126263  24.01  0.618687\n",
       "9   5.7  0.105932  32.49  0.603814\n",
       "10  6.1  0.090580  37.21  0.552536\n",
       "11  6.5  0.077580  42.25  0.504267"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>xi</th>\n",
       "      <th>Yi</th>\n",
       "      <th>xi^2</th>\n",
       "      <th>xi Yi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>41.4</td>\n",
       "      <td>2.641661</td>\n",
       "      <td>193.68</td>\n",
       "      <td>6.290077</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     xi        Yi    xi^2     xi Yi\n",
       "0  41.4  2.641661  193.68  6.290077"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Yi = 1/datos_dataframe['Y']\n",
    "xi_2 = pow(datos_dataframe['X'], 2)\n",
    "xi_Yi = datos_dataframe['X']*Yi\n",
    "\n",
    "tabla1 = pd.concat([datos_dataframe['X'], Yi, xi_2, xi_Yi], axis=1)\n",
    "tabla1.columns = ['xi', 'Yi', 'xi^2', 'xi Yi']\n",
    "\n",
    "tabla1_sums = pd.DataFrame([sum(tabla1['xi']), sum(tabla1['Yi']), sum(tabla1['xi^2']), sum(tabla1['xi Yi'])]).transpose()\n",
    "tabla1_sums.columns=['xi', 'Yi', 'xi^2', 'xi Yi']\n",
    "\n",
    "display(tabla1, tabla1_sums)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e64c92db",
   "metadata": {},
   "source": [
    "Sistema de ecuaciones normales:\n",
    "$$A_1\\sum_{n=0}^{11}{x_i}^2+A_2\\sum_{n=0}^{11}{x_i} =\\sum_{n=0}^{11}{f({x_i}){x_i}}$$\n",
    "\n",
    "$$A_1\\sum_{n=0}^{11}{x_i}+A_2*n=\\sum_{n=0}^{11}{f({x_i})}$$\n",
    "\n",
    "Planteo de las ecuaciones normales\n",
    "\n",
    "$$A_1*193.68+A_2*41.4=6.290077$$\n",
    "$$A_1*41.4+A_2*12=2.641661$$\n",
    "\n",
    "$$A_1=\\frac{6.290077-A_2*41.4}{193.68}$$\n",
    "$$A_2=\\frac{2.641661-A_1*41.4}{12}$$\n",
    "\n",
    "Ecuaciones de Jacobi\n",
    "$$A_1^{k+1}=-A_2^k*(41.4/193.68)+(6.290077/193.68)$$\n",
    "$$A_2^{k+1}=-A_1^k*(41.4/12)+(2.641661/12)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "2e445127",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'T de Jacobi'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.213755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-3.45</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      0         1\n",
       "0  0.00 -0.213755\n",
       "1 -3.45  0.000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'C'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.032477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.220138</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0\n",
       "0  0.032477\n",
       "1  0.220138"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'A Inicial'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0\n",
       "0  0\n",
       "1  0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'A a las 100 iteraciones'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.055529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.411714</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0\n",
       "0 -0.055529\n",
       "1  0.411714"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T_Jacobi = np.matrix([[0, -(41.4/193.68)],[-(41.4/12), 0]])\n",
    "display(\"T de Jacobi\", pd.DataFrame(T_Jacobi))\n",
    "C_Jacobi = np.matrix([[(6.290077/193.68)],[(2.641661/12)]])\n",
    "display(\"C\", pd.DataFrame(C_Jacobi))\n",
    "\n",
    "A_Jacobi = np.matrix([[0],[0]])\n",
    "A_Jacobi_anterior = A_Jacobi\n",
    "display(\"A Inicial\", pd.DataFrame(A_Jacobi))\n",
    "\n",
    "for i in range(0,100):\n",
    "    A_Jacobi = T_Jacobi*A_Jacobi_anterior+C_Jacobi\n",
    "    A_Jacobi_anterior = A_Jacobi\n",
    "\n",
    "display(\"A a las 100 iteraciones\" ,pd.DataFrame(A_Jacobi))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17b9ca65",
   "metadata": {},
   "source": [
    "Recordando:\n",
    "$$Y=\\frac{1}{y}; A_1=\\frac{1}{a}; A_2=\\frac{b}{a}$$\n",
    "\n",
    "Valores de a y b calculados\n",
    "$$-0.055529=\\frac{1}{a}$$\n",
    "\n",
    "$$0.411714=\\frac{b}{a}$$\n",
    "\n",
    "$$a=-18.008608; b=-7.414396$$\n",
    "\n",
    "Funcion aproximante:\n",
    "$$y=\\frac{-18.008608}{x-7.414396}$$\n",
    "\n",
    "Graficos - aproximacion por modelo + nube de puntos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "18ab930e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f53528eb0a0>]"
      ]
     },
     "execution_count": 46,
     "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": [
    "x = np.linspace(0,6.5,100)\n",
    "y = (-18.008608114678815)/(x-7.41439)\n",
    "plt.plot(x, y, '-r', label='P(x)=(-18.008608114678815/x)+2.428870')\n",
    "\n",
    "plt.plot(datos_dataframe['X'], datos_dataframe['Y'], 'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "887e7ff9",
   "metadata": {},
   "source": [
    "# Punto e)\n",
    "\n",
    "Modelo:\\n\",\n",
    "$$y =a*b^x $$\n",
    "\n",
    "Cambio de variables:\n",
    "$$\\ln{y}=\\ln{a}+\\ln{b}*x$$\n",
    "\n",
    "$$Y=\\ln{y}; A_1=\\ln{b}; A_2=\\ln{a}$$\n",
    "\n",
    "Ecuacion lineal propuesta\n",
    "$$Y=A_1*x+A_2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "dfc3de0e",
   "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>xi</th>\n",
       "      <th>Yi</th>\n",
       "      <th>xi^2</th>\n",
       "      <th>xi Yi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.858662</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.171732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.6</td>\n",
       "      <td>0.936093</td>\n",
       "      <td>0.36</td>\n",
       "      <td>0.561656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.2</td>\n",
       "      <td>1.061257</td>\n",
       "      <td>1.44</td>\n",
       "      <td>1.273508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.9</td>\n",
       "      <td>1.205971</td>\n",
       "      <td>3.61</td>\n",
       "      <td>2.291345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.8</td>\n",
       "      <td>1.381282</td>\n",
       "      <td>7.84</td>\n",
       "      <td>3.867589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3.5</td>\n",
       "      <td>1.583094</td>\n",
       "      <td>12.25</td>\n",
       "      <td>5.540829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.7</td>\n",
       "      <td>1.731656</td>\n",
       "      <td>13.69</td>\n",
       "      <td>6.407126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4.3</td>\n",
       "      <td>1.921325</td>\n",
       "      <td>18.49</td>\n",
       "      <td>8.261696</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.9</td>\n",
       "      <td>2.069391</td>\n",
       "      <td>24.01</td>\n",
       "      <td>10.140017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5.7</td>\n",
       "      <td>2.244956</td>\n",
       "      <td>32.49</td>\n",
       "      <td>12.796249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>6.1</td>\n",
       "      <td>2.401525</td>\n",
       "      <td>37.21</td>\n",
       "      <td>14.649303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>6.5</td>\n",
       "      <td>2.556452</td>\n",
       "      <td>42.25</td>\n",
       "      <td>16.616937</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     xi        Yi   xi^2      xi Yi\n",
       "0   0.2  0.858662   0.04   0.171732\n",
       "1   0.6  0.936093   0.36   0.561656\n",
       "2   1.2  1.061257   1.44   1.273508\n",
       "3   1.9  1.205971   3.61   2.291345\n",
       "4   2.8  1.381282   7.84   3.867589\n",
       "5   3.5  1.583094  12.25   5.540829\n",
       "6   3.7  1.731656  13.69   6.407126\n",
       "7   4.3  1.921325  18.49   8.261696\n",
       "8   4.9  2.069391  24.01  10.140017\n",
       "9   5.7  2.244956  32.49  12.796249\n",
       "10  6.1  2.401525  37.21  14.649303\n",
       "11  6.5  2.556452  42.25  16.616937"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>xi</th>\n",
       "      <th>Yi</th>\n",
       "      <th>xi^2</th>\n",
       "      <th>xi Yi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>41.4</td>\n",
       "      <td>19.951662</td>\n",
       "      <td>193.68</td>\n",
       "      <td>82.577986</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     xi         Yi    xi^2      xi Yi\n",
       "0  41.4  19.951662  193.68  82.577986"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Yi = np.log(datos_dataframe['Y'])\n",
    "xi_2 = pow(datos_dataframe['X'], 2)\n",
    "xi_Yi = datos_dataframe['X']*Yi\n",
    "\n",
    "tabla1 = pd.concat([datos_dataframe['X'], Yi, xi_2, xi_Yi], axis=1)\n",
    "tabla1.columns = ['xi', 'Yi', 'xi^2', 'xi Yi']\n",
    "\n",
    "tabla1_sums = pd.DataFrame([sum(tabla1['xi']), sum(tabla1['Yi']), sum(tabla1['xi^2']), sum(tabla1['xi Yi'])]).transpose()\n",
    "tabla1_sums.columns=['xi', 'Yi', 'xi^2', 'xi Yi']\n",
    "\n",
    "display(tabla1, tabla1_sums)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a3c94a4",
   "metadata": {},
   "source": [
    "Sistema de ecuaciones normales:\n",
    "$$A_1\\sum_{n=0}^{11}{x_i}^2+A_2\\sum_{n=0}^{11}{x_i} =\\sum_{n=0}^{11}{f({x_i}){x_i}}$$\n",
    "\n",
    "$$A_1\\sum_{n=0}^{11}{x_i}+A_2*n=\\sum_{n=0}^{11}{f({x_i})}$$\n",
    "\n",
    "Planteo de ecuaciones normales\n",
    "$$A_1*193.68+A_2*41.4=82.577986$$\n",
    "$$A_1*41.4+A_2*12=19.951662$$\n",
    "\n",
    "$$A_1=\\frac{82.577986-A_2*41.4}{193.68}$$\n",
    "$$A_2=\\frac{19.951662-A_1*41.4}{12}$$\n",
    "\n",
    "Ecuaciones de Jacobi\\n\",\n",
    "$$A_1^{k+1}=-A_2^k*(41.4/193.68)+(82.577986/193.68)$$\n",
    "$$A_2^{k+1}=-A_1^k*(41.4/12)+(19.951662/12)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "8f398de1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'T de Jacobi'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.213755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-3.45</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      0         1\n",
       "0  0.00 -0.213755\n",
       "1 -3.45  0.000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'C'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.426363</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.662638</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0\n",
       "0  0.426363\n",
       "1  1.662638"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'A Inicial'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0\n",
       "0  0\n",
       "1  0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'A a las 100 iteraciones'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.270300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.730104</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0\n",
       "0  0.270300\n",
       "1  0.730104"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T_Jacobi = np.matrix([[0, -(41.4/193.68)],[-(41.4/12), 0]])\n",
    "display(\"T de Jacobi\", pd.DataFrame(T_Jacobi))\n",
    "C_Jacobi = np.matrix([[(82.577986/193.68)],[(19.951662/12)]])\n",
    "display(\"C\", pd.DataFrame(C_Jacobi))\n",
    "\n",
    "A_Jacobi = np.matrix([[0],[0]])\n",
    "A_Jacobi_anterior = A_Jacobi\n",
    "display(\"A Inicial\", pd.DataFrame(A_Jacobi))\n",
    "\n",
    "for i in range(0,100):\n",
    "    A_Jacobi = T_Jacobi*A_Jacobi_anterior+C_Jacobi\n",
    "    A_Jacobi_anterior = A_Jacobi\n",
    "\n",
    "display(\"A a las 100 iteraciones\" ,pd.DataFrame(A_Jacobi))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43098f4e",
   "metadata": {},
   "source": [
    "Cambio de variables:\n",
    "\n",
    "$$A_1=0.270300=\\ln{b}; A_2=0.730104=\\ln{a}$$\n",
    "\n",
    "$$a=e^{0.730104}=2.075296; b=e^{0.270300}=1.310357$$\n",
    "\n",
    "Funcion aproximante:\n",
    "$$y=2.075296*1.310357^x$$\n",
    "\n",
    "Graficos - aproximacion por modelo + nube de puntos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "74fe5e37",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5352957640>]"
      ]
     },
     "execution_count": 49,
     "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": [
    "x = np.linspace(0,6.5,100)\n",
    "y = 2.075296*(pow(1.310357,x))\n",
    "plt.plot(x, y, '-r', label='P(x)=(-18.008608114678815/x)+2.428870')\n",
    "\n",
    "plt.plot(datos_dataframe['X'], datos_dataframe['Y'], 'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea8380cc",
   "metadata": {},
   "source": [
    "# Punto f)\n",
    "\n",
    "Por descarte podemos decir que la funcion del punto d) no es adecuada ya que presenta una asintota horizontal en x~=7.41439, luego se mantiene cercana a 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "27baf20f",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f53527cf0d0>]"
      ]
     },
     "execution_count": 50,
     "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": [
    "x = np.linspace(0,10,100)\n",
    "y = (-18.008608114678815)/(x-7.41439)\n",
    "plt.plot(x, y, '-r', label='P(x)=(-18.008608114678815/x)+2.428870')\n",
    "\n",
    "plt.plot(datos_dataframe['X'], datos_dataframe['Y'], 'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "226d9cf8",
   "metadata": {},
   "source": [
    "Tambien podemos descartar la recta de minimos cuadrados, ya que tenemos la parabola disponible y esta presenta un error menor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "9b20412e",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f53537fb1f0>]"
      ]
     },
     "execution_count": 51,
     "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": [
    "x = np.linspace(0,6.5,100)\n",
    "\n",
    "y = 0.255529618189472*pow(x,2)-0.143398273502509*x+2.51714300600557\n",
    "\n",
    "plt.plot(x, y, '-g')\n",
    "\n",
    "x = np.linspace(0,6.5,100)\n",
    "\n",
    "y = 1.564444*x+0.749333\n",
    "\n",
    "plt.plot(x, y, '-r', label='P(x)=1.564444*x+0.749333')\n",
    "\n",
    "plt.plot(datos_dataframe['X'], datos_dataframe['Y'], 'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d07c7f9f",
   "metadata": {},
   "source": [
    "Esto nos deja con la parabola de minimos cuadrados y el modelo exponencial.\n",
    "\n",
    "Al graficar ambos en un rango mas amplio, vemos que la exponencial crece mucho mas rapido que la parabola. Al alejarse del rango dado, vemos que la exponencial alcanza niveles absurdos (> 10^100 para 1 millon de subscriptores) mientras que la parabola se mantiene en amplitudes razonables.\n",
    "\n",
    "Ademas, el modelo exponencial fue calculado \"linealmente\" a traves de un cambio de variable, por lo que termina siendo inferior al modelo de parabola.\n",
    "\n",
    "Por lo tanto, el modelo que mejor se adapta en este caso es el de parabolas de minimos cuadrados.\n",
    "\n",
    "en el caso de los 20k subscriptores, ya no podemos basarnos en lo arrojado por la estimacion ya que se sale demasiado del rango original (200; 6500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "60477d20",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'exponencial: 3000 subscriptores -> 46692 visitas'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'exponencial: 7000 subscriptores -> 137659 visitas'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'exponencial: 20000 subscriptores -> 4622455 visitas'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'parabola: 3000 subscriptores -> 43867 visitas'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'parabola: 7000 subscriptores -> 140343 visitas'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'parabola: 20000 subscriptores -> 1018610 visitas'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5352873b50>]"
      ]
     },
     "execution_count": 52,
     "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": [
    "x = np.linspace(0,20, 100)\n",
    "\n",
    "y = 0.255529618189472*pow(x,2)-0.143398273502509*x+2.51714300600557\n",
    "display (\"exponencial: 3000 subscriptores -> %d visitas\" %(10000*(2.075296*(pow(1.310357,3)))))\n",
    "display (\"exponencial: 7000 subscriptores -> %d visitas\" %(10000*(2.075296*(pow(1.310357,7)))))\n",
    "display (\"exponencial: 20000 subscriptores -> %d visitas\" %(10000*(2.075296*(pow(1.310357,20)))))\n",
    "display (\"parabola: 3000 subscriptores -> %d visitas\" %(10000*(0.255529618189472*pow(3,2)-0.143398273502509*3+2.51714300600557)))\n",
    "display (\"parabola: 7000 subscriptores -> %d visitas\" %(10000*(0.255529618189472*pow(7,2)-0.143398273502509*7+2.51714300600557)))\n",
    "display (\"parabola: 20000 subscriptores -> %d visitas\" %(10000*(0.255529618189472*pow(20,2)-0.143398273502509*20+2.51714300600557)))\n",
    "plt.plot(x, y, '-g',label='P(x)=0.255529618189472*x^2-0.143398273502509x+2.51714300600557')\n",
    "         \n",
    "y = 2.075296*(pow(1.310357,x))\n",
    "plt.plot(x, y, '-r', label='P(x)=(-18.008608114678815/x)+2.428870')"
   ]
  }
 ],
 "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": "3.10.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}