{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![CDS 411 logo](../../img/cds-411-logo.png)\n",
    "\n",
    "# Class 14: Data-driven modeling II\n",
    "\n",
    "---\n",
    "\n",
    "![CC BY-SA 4.0 license](../../img/cc-by-sa.png)\n",
    "\n",
    "This notebook is licensed under a [Creative Commons Attribution-ShareAlike 4.0 International License](http://creativecommons.org/licenses/by-sa/4.0/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Load packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "cell_style": "split",
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from pathlib import Path\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Key questions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*   What is the connection between *computational science* and *data science*? \n",
    "\n",
    "*   Where can we interface data-driven modeling and rule-based modeling?\n",
    "\n",
    "*   How can we apply the tools of data science to problems in the traditional sciences?\n",
    "\n",
    "*   How can we use our tools to improve scientific reproducibility?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Motivating example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A researcher is investigating an energy-based model (a common type of rules-based model) that describes the interactions between a one-dimensional chain of vectors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![One-dimensional chain of vectors](../../img/1d_vector_chain.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*   The vectors are represented by arrows and their rotational planes are represented by the oval shapes.\n",
    "\n",
    "*   The vectors all sit in-plane and the planes are all parallel, meaning both the planes and vectors are perpendicular to the horizontal line that travels through each of the ovals.\n",
    "\n",
    "*   The relative angle between any two neighboring vectors is always equal to $\\theta{}$, such that the relative angle between vectors that are second nearest-neighbors is $2\\theta{}$, and so on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The energy-based model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The energy-based model for the interactions between one vector and all the others is as follows:\n",
    "\n",
    "\\begin{equation}\n",
    "E(\\theta{})=\\sum_{n}J_{n}\\cos\\left(n\\theta{}\\right)\n",
    "\\end{equation}\n",
    "\n",
    "The summation over $n$ is taken over all vectors neighboring a reference vector and is, in principle, infinite."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The minimum energy is special\n",
    "\n",
    "*   When working with energy-based models, you often look for parameter values that *minimize the energy*, possibly subject to certain constraints\n",
    "\n",
    "*   For this model, the constraints are the interaction parameters $J_{n}$\n",
    "\n",
    "*   Thus, we may ask this question of the model: for a given set of interaction parameters $J_{n}$, what value of $\\theta{}$ minimizes the energy?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The model terms\n",
    "\n",
    "The model may feel a bit abstract when written in the more compact summation notation. Let's dig into this further to better understand what's going on by writing out the first few terms in the summation. Here's how we'll proceed:\n",
    "\n",
    "*   Select a vector from our diagram to use as a reference point. We'll go with the one with angle $\\varphi{}_{0}$? We'll label that $n=0$.\n",
    "\n",
    "*   Expand the sum by systematically iterating through the vector's neighbors. A good practice is to start with the closest neighbors and move outward."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**First neighbors**\n",
    "\n",
    "\\begin{equation}\n",
    "E(\\theta{})=J_{-1}\\cos\\left(-\\theta{}\\right)+J_{1}\\cos\\left(\\theta{}\\right)=\\left(J_{-1}+J_{1}\\right)\\cos\\left(\\theta{}\\right)+\\dots{}\n",
    "\\end{equation}\n",
    "\n",
    "If we assume that the interaction parameter $J$ only depends on distance, not whether the neighbor is to the left or to the right, then we simplify to\n",
    "\n",
    "\\begin{equation}\n",
    "E(\\theta{})=2J_{1}\\cos\\left(\\theta\\right)+\\dots{}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**First and second neighbors**\n",
    "\n",
    "\\begin{equation}\n",
    "E(\\theta{})=2J_{1}\\cos\\left(\\theta{}\\right)+2J_{2}\\cos\\left(2\\theta{}\\right)+\\dots{}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**First, second, and third neighbors**\n",
    "\n",
    "\\begin{equation}\n",
    "E(\\theta{})=2J_{1}\\cos\\left(\\theta{}\\right)+2J_{2}\\cos\\left(2\\theta{}\\right)+2J_{3}\\cos\\left(3\\theta{}\\right)+\\dots{}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You probably get the point as to how this continues."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What does this have to do with data-driven modeling?\n",
    "\n",
    "*   As of right now, we simply have a formula that depends on a single variable $\\theta{}$ and the unspecified interaction parameters $J_{n}$.\n",
    "\n",
    "*   If we had no data available, then we could systematically sweep the interaction parameters and investigate how the value for $\\theta{}$ that minimizes the energy changes.\n",
    "\n",
    "*   If we did have data available, then we could try and find the interaction parameters $J_{n}$ that best reproduce the data trends\n",
    "\n",
    "*   Causality and rules-based models: Depending on your rules-based model was derived, its parameters may be used to quantify real-world processes and help to establish causal mechanisms that are responsible for generating the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following data comes from \"first principles\" simulations of a physical system whose behavior strongly resembles the energy-based model we just discussed. For the purposes of our discussion, we will treat this data the same way we would treat data collected in a controlled laboratory experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "vector_sim_csv_path = Path(\"../../data/vectorsim/vector_sim_data.csv\")\n",
    "vector_sim_df = pd.read_csv(vector_sim_csv_path)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The CSV file only contains the results of two simulation runs. There are more, but this is enough to illustrate the overall point.\n",
    "\n",
    "We visualize the data to get an idea of what we're dealing with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rN8aiLI488kjmzJnDfffdxxdffIHP5+Oll17ioosuqvc5PXr0qPk+NTWVjIwMsrOzawIfQL9+3sDdsrKy1iteRETix58Ch/8W0nvVvb/XCDjgHAW+BKLQFyMbt4datX1zPfPMM1xxxRU89thjHHDAAQwZMoS77rqLSCTSIsfXDF0RkXasQ1e4eAEMOxZMVaTwBWDUFPjVvJ+2SULQ5d0Y6ZbWtNXJm9q+uTp27MiNN97IjTfeyHfffcczzzzDzTffTCgU4txzz41JDSIi0kb5UrwlWc7+O+zYCFs3eD8HOnqBz1HoSyT6bcRIzsBu7JWegtlDO4O3fEvOwG6tXtOyZcvIzs7mjTfeAGDvvffmuuuuIzs7m8WLF7f664uISDvg+L2ZvB33gox9oUMX8PkV+BKQevpiJOBzOG/MAO5fsKLBdhY479ABMZnEMWzYMDp16sSVV17Jhg0bGDBgAHl5eRQWFvLLX/6y1V9fREREYkcxPIYuyR3EhOE9AXbr8av+ecLwnlycOygm9TiOw2uvvcYxxxzDTTfdxKmnnsqLL77InXfeybRp02JSg4iIiMSGSeaB9saYLKCoqKiIrKysOtusXLkS13XrXb6kqUIRl0fzVjHn428p27rzHTnOO3RAzJZqaStWr16N4zgMHjw43qWIiIjEVXFxMaNGjQIYZa0tburzdXk3xgI+h2kTBnNx7qCEv/euiIiItB8KfXES8DmMyeyx54YiIiIiLUBdSyIiIiJJQKFPREREJAno8q6IiEiyCe8Aa7019nyxuRmAxJ9Cn4iISLJwI1CxAT57BraXQ78DYOTPvACoe+S2ewp9IiIiycC6sOA2+OA+7/tqnXrDuS9Ar30V/No5jekTERFp78KV8Nmz8P69Owc+gK3r4alTwEbiU5vEjEKfiIhIe+dPhY8erH//th/h0zleOJR2S6FPRESkvQtth9LPG27z7aLY1CJxo9An9Vq9ejX9+vXjpZdeapHjzZ07l9zcXLp27cqAAQM444wzWLZsWYscW0REGuALeDN1G5KSDiTvrVmTgUKf1GvgwIHMnz+fE088MepjvfTSS0yZMoXBgwfz9NNPc/fdd1NcXMykSZMoKytrgWpFRKRB++7h3/Ls/wJHy7e0Z5q9Gy+REGbNx96U+bTu2P6HJuRaSSNHjmyR49x2222MGzeO2bNn12wbNmwY48aN48033+T8889vkdcREZG6GDj6Jvh6PgS37r576EQYdHjsy5KYUk9frEVCOO//L4EH9yfw9KkE/nmh9/XBA3De/1+IhGJazubNm7nqqqsYPHgwPXr0YNy4cbz66qsArFq1itTUVJ588kkAFi5cSGpqKo8//jjHHHNMzWXaW2+9lY0bNzJt2jT69etHr169mDx5MsuXL695nZycHC699NKdXrs6UP74448xOlsRkSTl+KDbPjD1bRhyNBjjbe/QDcZdCWf/3VurT9o19fTFUiSE/4Vf4Kz4Nxaz876KDfjfuxP3+08IT5kds16/Sy+9lLy8PG6//Xb69u3L3/72N84880zmzZvHwIED63zOrbfeyi233MJ///d/8+STT3L77bcze/ZsJkyYwBNPPMHatWv5wx/+wK9+9Svef/99AB599NHdjvPuu+8CcNRRR7Xa+YmISBV/CvQcBue9CDs2wY7N0KWvN4wvAa80SctT6Ish56MHcFb8GwCzy2DZ6p+dr9/G+egB3COuiUlN8+bNY+rUqVxwwQUATJw4kdNPP53ly5fXG/ruvfdeTjvtNADGjx/P3Llz6dmzJ7NmzcJUfXpcu3YtM2bMoKKigvT09N2OsXHjRq655hqmTJnC6NGjW+nsRERkJ9XhLq2795CkotAXK5EQvk8ew2J2C3y1WQy+T/6Ge9iVMfnkdeSRRzJnzhz23ntvJk2axMiRI2tm665atarO5/To0aPm+9TUVDIyMsjOzq4JfAD9+vUDoKysbLfQFwwGOfvss3FdlwceeKCFz0hERETqojF9MWLWfIyp2NBg4AOvx89UlHqTPGLgmWee4YorruCxxx7jgAMOYMiQIdx1111EIi2zMrvdZYyItZaLLrqIJUuW8PLLL9OzZ88WeR0RERFpmEJfrGwvb932zdSxY0duvPFGCgsLWblyJZdddhkzZszgzjvvbJXXu+aaa3j99dd59dVXW2xmsIiIiOyZQl+sNHXsRAzGWixbtozs7GzeeOMNAPbee2+uu+46srOzWbx4cYu/3p/+9CdmzZrFCy+8wMEHH9zixxcREZH6aUxfjNj+h2LTe0FF2R7H9JHey1u3r5UNGzaMTp06ceWVV7JhwwYGDBhAXl4ehYWF/PKXv2zR15o9ezY333wzV199NSkpKXzwwQc77T/8cK0PJSIi0poU+mLFFyBy0FT87zV82dRgCR/0q5hM4nAch9dee43p06dz0003sXHjRgYNGsSdd97JtGnT6p3I0Rxz5swBvJm/99577277Kyt1k28REZHWZHYdaJ9MjDFZQFFRURFZWVl1tlm5ciWu69a7fEmTREL4X7wA5+u3d5vFW/2zO/TYmK7Tl+hWr16N4zgMHjw43qWIiIjEVXFxMaNGjQIYZa0tburzNaYvlnwBwlNmEz7yBkjvtfO+9F6Ej7xBgU9ERERahS7vxpovgHvENbiHXdkm7r0rIiIi7YNCX7z4Ath9NHlBREREYkOXd0VERESSgEJfIyTzZJd405+9iIhIy1Do2wNjDK7rxruMpOW67k739BUREZHmUejbg0AgQCQSabF70UrjVf+5BwKa4CIiIhIthb496NKlCwBlZWW61BhD1lrKysqAn34HIiIi0nyavbsHnTt3pmPHjmzZsoWKigp8Pp8uN7Yyay2RSATXdenYsSOdO3eOd0kiIiJtnkLfHhhj6N+/P+Xl5WzdulW9fTHi9/vp1KkT3bt3V8gWkeQW3gEWby1XxxfvaqQNU+hrBL/fT69evejVq9eeG4uIiLQE68KmNVD4Dwhtg8zxkHkkREJazF+aRaFPREQk0bgReO238NkcqL7C9N49kLEfnP8SdNxLwU+aTBM5REREEkm4Ehb+CT596qfAV630c5jzcwU+aRaFPhERkURiHPjPo/XvX18MJXleb6BIEyRU6DPG+I0xVxtjvjDGbDPGrDDG3GGMSa/VZoAx5gVjzEZjzHZjzEfGmPHxrFtERKTFlK+CbT823GbVe97YPpEmSLQxfQ8D5wC3AJ8C+wL/A+wN/MIY4wfeBLoCVwJbgd8B84wxo621y+NRtIiISIvxd2hEmzTQygbSRAkT+owxnYFfAndYa++q2vy2MWYv4EZjzEXAMUAWMNFau6DqeW8Da4DLgKtjXriIiEhL6jYAeo+C9UV17zcGss8Af2ps65I2L5Eu71YA/YE/7rJ9K144TQPGAkHgneqd1totQD5waGzKFBERaUXhIBx7qze2ry4H/gK67h3bmqRdSJjQZ611rbXrrLXbjTE+Y0y6MeZY4Frgb9baTUAfoMzuvkJyKZAR65pFRERanD/FW4/v3BegT/ZP29N7woTfw8n31R8IRRqQMJd3d7EE7zIuwFvAr6u+TwHqGrkaqdpXL2NMBrDr6spDoqhRRESkdfgCMCgXLnvfW6A5vAO67eMt2KzAJ82UqKHvTKA7MA64GfhfvIkbDdnT/dGmATPq2pGfn8+6devo378/mZmZ5OXl1eybOHEihYWFlJaWAjBixAjS09MpKCgAID09nbFjx5Kfn09FRQUAOTk5VFRUsGzZMgAyMjLIzs5m/vz5NcfNzc2lpKSENWvWAJCZmUlGRgaLFi0CICUlhdzcXAoKCigvLwdg1KhRABQVeeM8unfvTk5ODnl5eQSDQQDGjBlDaWkpJSUlADonnZPOSeekc2ov59TZkpf3fvs6p/b4e2rFc8rPzycaJtHvJWuMuQG4HRiAN6v3FGtt713aPAPkWGv3beA49fX0vVJUVERWVlYdzxIRERFJDMXFxdVhdJS1tripz0+Ynj5jTB/gVOB1a+23tXYtxRt7uA+wAdjLGBOw1ta+zNsbWNvQ8a21pXhj/2q/ZkuULiIiIpLwEmlgQCrwF+DcXbbvX/X1G+AjwAecUL3TGNMFOAxvBq+IiIiI1CFhevqstd8YY54HbqrqgfsEL/DdCDxlrf3eGFMKFAOzjDG/B37AW5zZAn+NT+UiIiIiiS+RevoAzgduAy4EXgEuwhvPNxXAWhsGjgcWAvcCz+IF1+OstaviUK+IiIhIm5AwPX0A1togcEfVo742a4AzYlaUiIiISDuQaD19IiIiItIKFPpEREREkoBCn4iIiEgSUOgTERERSQIKfSIiIiJJQKFPREREJAko9ImIiIgkAYU+ERERkSSg0CciIiKSBBT6RERERJKAQp+IiIhIElDoExEREUkCCn0iIiIiSUChT0RERCQJ+ONdgIiISLtgLYQrve/9KWDUryKJRaFPREQkGtb1At6GZfDFK174GzEZ+o4GNwKOL94VigAKfSIiIs3nuuAG4flfwPJ5P21/9w7IHA9nPwv+NHDU6yfxp3ehiIhIs1l49YqdA1+1koXwz4tjX5JIPRT6REREmmt7ORT9s/79y96ALd/Hrh6RBij0iYiINNe3i8AN17/fWijJ876KxJlCn4iISHOlpDeiTUcwpvVrEdkDhT4REZHm2udw6Nij/v0pnWDYcbGrR6QBCn0iIiLNZS1M+H39+3Ov0ZItkjC0ZIuIiEhz+VPg4KkQSIf37obyEm971wFwxO/g4Au1SLMkDIU+ERGRaDg+yD4dDjwXfizxFmvukQmRkAKfJBSFPhERkWj5U72vPTJ33yaSIPQRRERERCQJKPSJiIiIJAGFPhEREZEkoNAnIiIikgQU+kRERESSgEKfiIiISBJQ6BMRERFJAgp9IiIiIklAoU9EREQkCSj0iYiIiCQBhT4RERGRJKDQJyIiIpIEFPpEREREkoBCn4iIiEgSUOgTERERSQIKfSIiIiJJQKFPREREJAko9ImIiIgkAYU+ERERkSTgj3cBIiIiMRUJQXgHfPsx+FNhwBiwFvwp8a5MpFUp9ImISPKIhOGtG+DTOV7wA+i4Fxx5HYy5FIwugEn7pdAnIiLJwbrwyq9h6fM7b9/2gxcEfQE48Hyv90+kHdJHGhERSQ6bv4fCf9S//717wFFfiLRfCn0iItL+RYLwxave2L36bFkLpZ/HriaRGFPoExGR9s8CbqQR7dxWL0UkXhT6RESk/fOnwPATGm7TsQdk7BebekTiQKFPRESSw15DYPik+veP/U3Dl39F2jiFPhERSRIWzpgNI38Gxvy02d8Bjvgd5F6ttfqkXUuoaUrGGAe4BrgY2AdYC7wCzLDWbqxqMwD4M3AMkAp8BtxgrV0Yl6JFRKRtMI63HMt/zfZm8q5YAL5U2HeyF/y0Rp+0cwkV+oD7gEuBu4D3gf2AW4F9gUnGGD/wJtAVuBLYCvwOmGeMGW2tXR6XqkVEpG2oDnZd+8MB53k9frV7/UTasYQJfcaYXsBvgDustTdVbZ5njPEBdxtj9gGyqh4TrbULqp73NrAGuAy4OvaVi4hIm+SoZ0+SS1TveGPM/i1VCF7v3bPAi7tsr140qQcwFggC71TvtNZuAfKBQ1uwFhEREZF2JdqPOZ8aY4qMMddXjbVrNmvt19ba86y1n+6y6yhgPVAM9AHKrN1telUpkBHN64uIiIi0Z9GGvkuAlcAMoMQY864xZqoxpmv0pYEx5iC8sXu3WmuDQAoQqqNppGpfQ8fKMMZk1X4AQ1qiThEREZFEF9WYPmvtLGCWMSYNOB44BbgDeNAYMxeYA7xhra0rqDWoqufwFeAt4C+NKWcP+6fhhdPd5Ofns27dOvr3709mZiZ5eXk1+yZOnEhhYSGlpaUAjBgxgvT0dAoKCgBIT09n7Nix5OfnU1FRAUBOTg4VFRUsW7YMgIyMDLKzs5k/f37NcXNzcykpKWHNmjUAZGZmkpGRwaJFiwBISUkhNzeXgoICysvLARg1ahQARUVFAHTv3p2cnBzy8vIIBoMAjBkzhtLSUkpKSgB0TjonnZPOSeekc9I5tZNzys/PJxpm9yulURzMmI54we92YFDV5h+BB4DbrG3c/W2MMT2qx6hzAAAgAElEQVTwZu9uBY6y1lZUbX8EOMVa23uX9s8AOdbafRs4ZgbQa5fNQ4BXioqKyMrKakxpIiIiInFRXFxcHUZHWWuLm/r8qGfvVgW9k4AzgBOAAPAv4DrgPeBsvGVX+gK/buTxXsfruTuhOvBV2QDsZYwJ7NJ72BtvTb96WWtL8cb+1X6tPZUjIiIi0i5EO3v3Bbwg9hwwHLgZGGCtPdla+6K1doO19gHgFuCcRhzPD/wDb8LGsdbaH3Zp8hHgwwuX1c/pAhyGN4NXREREROoQbU/fkcCjwOw6Zt3Wlgc81YjjzQKOxbsjx2BjzOBa+zbhje8rxhtH+HvgB7zFmS3w16aXLyIiIpIcog19/ay14T01stZ+AnzSiONdUPX1iTr2LbTWTjDGHI93G7Z78WbsFgDHWWtXNapiERERkSQUbeh7ZA/j4rYDXwBPWWs37elg1to9DrKz1q7BGz8oIiIiIo0UbegbAYwByvFm2lbrDHQHvsdby+8GY8yR1tqVUb6eiIiIiDRDtIszzwXeBfpbazOrH8CAqu334M3aXQv8KcrXEhEREZFmijb0/Rq411pbWXujtXY73ri7adbaMuBu4IgoX0tEREREmina0NcL6FbPvi5A/6rvfwTSo3wtEREREWmmaEPfx8BtxphRtTcaY/bDW5D546pNx9T6XkRERERiLNqJHJcDbwNLjDErgfVAT2Bo1fe/McZ0w5vM8fMoX0tEREREmimq0GetLaxaQPliIAfIAJYB9wFPWGt3ABhj9q26DZqIiIiIxEGzQ5/xFujLBZZaa+9vqK0Cn4iIiEh8NXtMn7XWAm8AB7RcOSIiIiLSGqKdyPERcFhLFCIiIiIirSfaiRwrgBnGmD7AD3Xst9ba/4nyNUREREQkStGGvkuqvl5Rz34LKPSJiIiIxFm0s3ejvTwsIiIiIjEQbU8fAMYYBxgO7AV8Zq2tMMY41lq3JY4vIiJJyI2AMbDxW1idD2ndYchRYC34U+JdnUibE3XoM8ZMB34HdMe7nHuIMeZ74B1jzPHW2m+ifQ0REUkykTAEt8ALU2HF/J+2d+wBx9wKB5wNTov0W4gkjaguzxpj/gBMBx4FTgMMgLV2HbAKuDPK+kREJBk5Djx5ys6BD2Dbj/Dq5bDsLQgH41ObSBsV7Zi8i4EZ1tobgLm77HsYODbK44uISLKJhGHFO7B2Sf1t3rtbl3hFmija0JcB1Pe3MgykR3l8ERFJNm4Ylr3RcJu1n8GOTbGpR6SdiDb0LQHOqWffFKAwyuOLiIiISAuINvTNAM4xxizAu9RrgQnGmFnABcAdUR5fRESSjc8P+57UcJt+OdCha2zqEWknogp91tp/AacC/YGH8CZy3AP8DLjIWvtS1BWKiEhycfwweLwX7OpiDIy/HiKayCHSFFEvrmytnWutHQ4MA3KBA4C+1trHoz22iIgkKWvhF6/A8OO9kFetUwac+lcYegz4NJFDpClabJEja+0KvHvxioiIRMfxQUo6nP0sbF4L3y2GDt1g0BHeos0+rdEn0lRR/a0xxnQG/gBMAHpRtU5fLdZaOySa1xARkSTl+LyvXff2HrtuF5Emifaj0l+AM4G3gS+iL0dEREREWkO0oe8E4Fpr7f0tUYyIiIiItI5oJ3JYoLglChERERGR1hNt6Hse+K+WKEREREREWk+0l3fXADcZY3oAS+vYb621/xPla4iIiIhIlKINfbdVff151WNXFlDoExEREYmzqEKftdYBMMb4gOHAXsBn1tqtxhiftTbSAjWKiIiISJSiviOHMWY6UAoUAe8Cw40xfYAiY8zAaI8vIiIiItGLKvQZY/4ATAcexbu86wBYa9cBq4C7oqxPRERERFpAtGP6LgZmWGv/VHWJt7aHgceiPL6IiIiItIBoL+9mAEvq2RcG0qM8voiIiIi0gGhD3xLgnHr2TQEKozy+iIiIiLSAaC/vzgDeMMb0x1uo2QITjDHTgAuA06M8voiIiIi0gKh6+qy1/wJOBfoDDwEGuAf4GXCRtfalqCsUERERkahF29OHtXYuMNcYMwToA2wBirVGn4iIiEjiiDr0VbPWrgBWtNTxRERERKTlRL04s4iIiIgkPoU+ERERkSSg0CciIiLSTBHXEnHdmp+DYbeB1vHVYmP6RERERFpKMOyS4ndq/Rwhxb/rzb+ax3UtjmOiPk4o4vL595v563sr+M+qcjoEHCaP6sul44fQKdW/U/2JQKFPREREEoa1Fmvhuf+sZk7+N5SUVdC7Swf+6+ABXHrkYHw+g99pepgKR1z8Pofl67dQsLqcHukpHDUiA2tpVjgLRVzmLv2ea55fgmt/2v7X91byz0+/4+Vp4+jdtUOzam0tCn0iIiKSMCxw2ZxP+Nfn62u2rSnfzr1vL+ffX6znH5cdRlMzWijiUl4R5LI5BRSsLq/Z3q1jgOkn7sepB/TD72vaQUMRlxv/WbRT4Ku2YUslN71SzKO/OLhphbayxImfIiIiktTCEZcFX5TuFPhqW7pmE7M/XEUw3LSlgI2BMx/J3ynwAWzcFuK6F5bw/tdlhCKNH4sXiri8/Ol3bA/VX8e7y0rZvCPUpDpbm0KfiIiIJATHMTz3n9UNtvnH4jVNGtsXiri8WbiOkrKKOvdbCw8u+Bp/E8b4RVzL2k07GmzjWijbUtnoY8aCQp+IiLSMcHCXnxPrPzxJfI4xlG0NNtimbGvT3leutbyzrLTBNou/KaeyCbNufY5hcM/0BtsEfIY+XTs0+pixoNAnIiLRsy4UvQiPHAV/3BseOBA+fABC28ENx7s6aSNCEZdhGZ0abDM0oxPW1jGQrj7WC5MNMWbPbWoL+BxOHN2PrmmBetucMKovaSktM9u4pSj0iYhIdKwLr1wOL18G3xdAcCv8uBIW3AZ/mwSRxBrXJInL5xguPDyzwTa/HDeIcF2zJxo45qT9ejfYZtyQvfD7mr6Ey/8750BS65hVMqRXOreekoVD9MvCtCSFPhERaT43Aqvz4bOn696/donX46dLvdIIjjEM79OJ35+wb537zx0zkBOy+xJowkxbv8/h6JG9Gdm3c537fY7htxOH4TYhSIK3zMuhmXvx7rUTmHpEJvv378qYzB7cekoWr1+ZS3qqv0XWAmxJWrJFRESaz7rwyeMNt/n0aRh/fWzqkTbP7zhMzc1k4sjePPHhKkrKttK3axrnjhnI/gO6NekybDVrLc9dchhXP/8ZC74spfrqcP/uacw4eT8OHNi9yUu2gBf8+nZL4/rj961Z62/XRaUTiUKfiIg0n+OHLXUvr1Fjy9rY1CLtht9xGNIrnZtP2o+AzxB2LY4xzQp84PX2dUo1PHr+wZRuqaT4+010T0/hwAHdCEVsk3oO61I75CVq4AOFPhERiUYkBD2HQcnC+tv0HB67eiQudr9lWvS9XcYYUvxeyAs0Y7zdrnxVl1r7dO2w06za6tdIBgkZR40xw40xfzTGfFvHvgHGmBeMMRuNMduNMR8ZY8bHo04RkaTnC8CYy7zpj/U55CKN6WunIq4lGHb52wclHH3Pu+x381uc+EAeLxaswbW2abNspdUlVOgzxhxrjPkQWAZcB/TfZb8feBMYA1wJnAuEgXnGGH2UFBGJNWOgRyZM+mPdwW/UFDjoAvCnxr42aXUR13LWI/nc+eaXrCyrYFswQvH3m/n9Pwv5zdMFKPIllkS7vHsk8BVwU9X3N++y/zggC5horV0AYIx5G1gDXAZcHbtSRUQE8Mb1HXIJDD4aFj0MZcugU2/IuQAGjweTUP0L0kKCYZen8lftdmuzam8WrWPhsg3kDuvZrEkS0vISKvRZa2+q/t4Yk1tHk7FAEHin1nO2GGPygUNbv0IREamTzw+9RsDku8CX4i3lglXga8dS/A7P/2dNg22e/Xg140f0ilFFsicJFfoaoQ9QZncfJFCKd8m3XsaYDGDXd96QFqxNRCS5GeMFPgAnse5EIK2jdEvD959dv3lHs2fcSstra6EvBahrafdI1b6GTANm1LUjPz+fdevW0b9/fzIzM8nLy6vZN3HiRAoLCykt9e7bN2LECNLT0ykoKAAgPT2dsWPHkp+fT0WFdzPnnJwcKioqWLZsGQAZGRlkZ2czf/78muPm5uZSUlLCmjXep6TMzEwyMjJYtGiRd6IpKeTm5lJQUEB5udd1PmrUKACKiooA6N69Ozk5OeTl5REMevcqHDNmDKWlpZSUlADonHROOiedk85J59Rq53TVfkF2hCK89I3Xo3vaPt79a1dvNTy9wseUvbfWHLutnFMi/57y8/OJhknUmTXGmFuAGdZaU2vbE8AEa+2gXdo+AYy31tZ775YGevpeKSoqIisrq2UKFxERSQKhsMubRWu58rnP6m3z6uWHM2rvrurtayHFxcXVYXSUtba4qc9vaz19QSCtju0pQIPrAVhrS/EuA9cwehOKiEiScV1LyHVxjMF1LamB5l2KD/gdTtq/H+9//QPPL95thTWuPW44Wf0U+BJJWwt9G4C9jDEBa23ty7y9AS35LiIi0gBrLZ9+u5HnF3/Lxm0h9uvXhV+M3YdOqX4CzVhM2TGGO6dkMyVnb55etJr1m3cwqGc6vxw3iOG9O9csiCyJoa2Fvo8AH3AC8CqAMaYLcBhwfxzrEhERSWiua7nyuU+Zu/SnPpJ5xet46J2vefi8gzh8aM9m3UXDMYaDB/XgoH28+9eGIi5+x+hqWgJqa3Pp3wKKgVnGmKnGmFOB1wAL/DWulYmIiCSoynCEWe+v3Cnw/bTP5ddPf8L2YLjZx/c5pmYtvoDPUeBLUG0q9Flrw8DxwELgXuBZvN7K46y1q+JYmoiISMJK9ft48qNv6t2/I+Ty9KLVVIYiMaxKYi1hL+9aa28Bbqlj+xrgjFjXIyIi0lZtD0ZYU769wTZfrtuiHrp2rk319ImIiEjTpfgd0vYwS7d7egqJuoybtAyFPhERkXbOtZaT9+/XYJuzDhnQrIkc0nbotysiItLO+R3DtZOG07tLap37zzxkACP6dNbl3XZOoU9ERKSdM8bQPS2F16/I5dwxA0lP8S71Ds3oxO2njeKOn2drEeUkkLATOURERKTlBPwOe3VK4ZafZXH7admEIi4Bn0Mw7CrwJQmFPhERkSRhjCHg8wJeoGpdPY3jSx76TYuIiIgkAYU+ERERkSSg0CciIpKggmG35vuIa4m4bgOtRRqmMX0iIsnGWnDD3mN7OaT1AMcHjh80oD8hBMMuG7cFeejdFbxRuJYdoQiHZPbg0iOHkDOwW819bkWaQqFPRCSZREJQuQXm3QjFL0F4BwTSIPsMOO42CKSDT/81xFM44rJu0w5OfegDfqwI1myf/0UpC74s5Y7TsplyUP+aiRgijaV3jIhIMolUwqyJsORZL/ABhLZDwZPw2HFe75/ElTGGm18p2inwVbMWbnmtmMqwLvNK0yn0iYgki3AlLPor/Liy7v0bvoSCJ7x2EjebtodY+NWGevfvCLm8VLCGkIKfNJFCn4hIsvCnQtGLDbcpfMFrJ3HzY0Ul1jbcZv2WSiJ7aiSyC4U+EZFkEqxoeH/lltjUIfXq0zWN1D0smDwsoxM+R5NupGkU+kREkoUbhr0ParhN/0O8yR4SNx38DieO7lvv/u4dA0zO7quJHNJkeseIiCQNB8ZdUf+yLI4Pxl3uLd0iceM4hpk/y2LfPp1329cxxcdfzjtoj5d/Reqiv9kiIsnCcaD3KDj5/+D1qyFSa3aovwOc8v+gxxCt1RdnjjGkBXy8dsURvPzpd8xdupbtoQiHDOrBheMG0SUtoPvlSrMo9ImIJBNfAPY/C0aeDJ8+BZu+hW6DIOd8L/j5AvGuUKBm8eVTDtib0w/qjzGGynCEVL8vzpVJW6bQJyKSbHwBSOsGh14C1gXjaMZugqrdo6fAJ9FS6BMRSVYKeiJJRYMCRERERJKAevpERESiFHFdwFB7Coxrbc3YPJFEoNAnIiIShVDEpfj7zTww/yveXVaKBY4Y2pMrjx7GAQO7aT09SRgKfSIiIs0UDLt8uKKMi2YvJuz+tHhe3ldlfPB1Gf93zoEcO7KPlliRhKB3oYiISDMFfIbpLxftFPiquRZueeVzHP1PKwlCb0UREZFmKli9kTXl2+vdv2FrJe9/VRbDikTqp9AnIiLSTGVbKxvVxuq+aZIAFPpERESaKatvlz22yd67G0a3tpMEoNAnIiLSTP26p3H40L3q3X/ggG6M6NM5hhWJ1E+hT0Qk0YVrXUK0LkRC8atFduJay/1nHciQXum77evfPY2HzsshFHHjUJnI7rRki4hIonLDXsBb9DAseRa2/QAZ+8GYy2DECd49cyWu/I5Dt7QA8646ktcL1/L25+txreXofXvzs/37YQxap08ShkKfiEiiCgfhb5Ng3dKftpW85z0OuxyO+x8FvwRQfdeNyaP6Mjm7LwDWorX5JOHoHSkikojClZB3z86Br7aPHoT1n3vpQhJCwO8Q8HkPBT5JRHpXiogkIn8qfPpUw20W/w0iwdjUIyJtnkKfiEgisi5sLW24zebvwPHFph4RafMU+kREEpFxoPughtvsNQTcSEzKaU9CYZftwQiLV/3I0jUbibiWYFgzbKX900QOEZFEFK6Egy6Ef8+oe78xcOgl3mVgabSIa7lr3jKeWfQNFUEvMPfuksrvjhnOGQcPwOdoEWVpv9TTJyKSiPypMO5yGDpx933GwKQ7oUv/2NfVhrmu5caXCnk0b2VN4ANYv7mSG/5ZyIufrFGPn7Rr6ukTEUlUxgfnvABfzvUmdWwrg4wsGPtr6DkCfPonvCk2bKnkH4u/rXf/ff9ezukHK0hL+6V/MUREEpUx3mPECTDyJG+cXyQEjt/bLo0Wiri8UbQWt4EVbr7ftIPl67awbyPupyvSFin0iYgkOl+g7u+l0ay1hCJ7XtMw1FAqFGnjNKZPRETavYDP4agRvRps0zUtwIjenWNUkUjsKfSJiEi7Z4xhWO/O5A7rWW+bX44bFLuCROJAoU9ERJJCxLU8fN5BjB++c4+f3zFcMG4Qvz1mmG6fJu2axvSJiLQ0N+LdUUMTLhKKzzF0CPh44sJDWFlWwXvLN5Diczghuy9d0wI4+l1JO6fQJyLSUiIhCO+Az1+Byi0w6Ajokw2RsJZXSRDViy8P6dWJgT06Ygz4HfXuSXLQv0IiIi3BuvD+nyHvf73gV23AGDjrGUjr5vX8ScII+BT2JLnoHS8iEq1wJXwyG965fefAB/DtInjyFG+NPRGRONK/QiIi0fIF4IP769+/vghWLvTG+omIxIlCn4hItLash/KShtt8/W+IBGNTj4hIHRT6RESi1ZhJGrqThojEmUKfiEi00ntB3wMabpN1GvhTY1NPOxRxXVyrW6SJREOhT0QkWuEgHPWH+tfkG3oM9N1fkzmaKBxxAfhy7Wae+/hb5i5dy45QhFDVdhFpmja5foAx5lTgFmBfYCswF7jaWvtjPOuqixsJgxsGx4ejyzsi7ZM/BYYcBWc8CW/fBOWrqranwuizYPLdYK0Wam6CcMRl4/YQlz71CZ98U16zPT3Fx7WTRvCLwwbVrLknIo3T5kKfMeZw4EXgZeAmYCDwx6qvR8extJ244UqM44ev/oVTtgzbeW9s1imAwfhTmn3ccMTFcYPe/x9YTCCViAt+rTclEl++AAyfBCNPgnVFENzqLczs76A7czSD4xjOfiSfr0q37rS9Ihhh5muf07NTKpOy+ui2aSJN0OZCH/Bb4FvgDGutC2CM2QLMNsaMttYujWt1gA1XwtolmOd/gdmyFgAD8Oa1uCfdDyNPwjSx189aC5EgJlSJ+fRJnHVLoEM3Qvufh7/faMIRt/nBL1wJjg9bvhr8KZiu/b3LVVGEU5GkVD1mr+/o+NbRxoUjLguXb9gt8NX20Ltfc/L+/WJYlUjb1xZD31hgXnXgq/J21ddDgbiHPnZswpnzc+82TLtu/+dU3IsWQJ9sjONr9CFNJERk9SJ8z53t9SBUCXz8COx/Nr5THyLi2iZf7rDWxXxwP3z8V0xFmbexz2jsMbdgMo+MasZhKOwSqPoUXvt7kYQQCYPjeLdOsy4E0rwlVXz6sBNvYdfyzpelDbb5Yu0WNm4L0q2jfl8ijdUW/xfuA+z6r0H1zxkxrmU3NlyJWfTX3QNfNTeC88F9QONnobmuxQ3v2C3w1VjyLOQ/jOM2bQ0w60Ywr1/j3UWgOvABrFuKefp07MqFXo9fE4XCLuHgDgJ+h+APqwn+sJqA3yEc3EEorAHYkgAiQfi+AOZMgdt7w+194NGj4au3vTG4EndOIz7AakyfSNO0xdAXAEK1N1hrq5e5r/cjnzEmwxiTVfsBDGnp4ow/FVblNdyo5D1vvF9jRSoxBbPrDnzVr/vxI95rN4HZsg4+ebzundbF/HtGky/xhiIufsfiFL8IDxxIyv9lk/J/2fDgwThfvobfsTUz8kTiIhyEkjx4/ARYscCbYAHw3Sfw3Dne7dQioYaPIa0q4DNMzu7bYJucgd3plNoWL1aJxE97+xvTUPfZNGBGXTvy8/NZt24d/fv3JzMzk7y8n0LbxIkTKSwspLTU60wcMWIE6enpFBQUAJCens7YsWPJz8+noqICgJzU/lR0d1jW+2cAZGwpJPu7Z5i/7x3eQX1+coNBSkpKWLNmDQCZmZlkZGSwaNEiAFJSUsjNzaWgoIDy8h9hS3dGdc4GoGjvcwDovq2EnNWPkDdsOkFfOvz734wZO5bS0lJKSry7A9R7Tks/o3T1VzDij4xY/yrplespGHixd07BUsau/DP56cdS8fY8cPzk5ORQUVHBsmXLvHPKyCA7O5v58+fXHDc3N5eSFV+zZsXnsHUTmU4mGSlbWTT4d945Fa7i8MrZLDWjKd+0CYBRo0Z551RU5J1T9+7k5OSQl5dHMOj1Mo4ZM2bnc+rbh8yB/chbVFD1KzfN+z019pwa/Xsqb/45tdR7T+fUuHMqL2FU+kjvnHb9+/T1JoKbFwKmbZ1TO/o9LfnsMyrKy5l5sOXZr71/1k/bx/uwuHqr4dmVPqYO3cGCBQvazDm1x9+Tzin255Sfn080jG1ji10aY4LAn62119falgJUAr+31t5Zz/MygF67bB4CvFJUVERWVlaL1OeGKjGfzsa8cV39jcZcij32tkbP4rWhHZi3p8PHj9bfyJ8KN37vzRJsTJ3B7Tgf/BkW/qnhdr/5GKfXiEYds6bWe4ZB5ea6G3TcC3vNsiZPZCES9GZELrgNVlb1zvTJhnG/hVE/hyaMj6z7+GFvXJfPr7XU2rt1hfDwEQ23mTILsqZ4Y/4kLiKupTIc4foXlvJm0TrCrvd/Vf/uaUw/cT+OGZmhVQsk6RQXF1eH0VHW2uKmPr8t9vRtwBvXV1vvqq9r63uStbaUXcYCmlZYQsEJpGIPPB/y/wI/rty9QVp37OFXNWnZFuNPwR54Pqah0Jd1GtZaGntG1gkQ2ScXHw2EvrTumB6DG12ntda7v2h9gQ9g2w/YVe9jhhzV6OMSDsKa/8BTp+5879J1hfDPi2Dzd3DY5Y27FdauImEIbYOiF726+x8K+xzmXd6Ldl3FcKUXJB2fJgckku3le26z7UewEdrmCJj2wecYOgR83HfWgczcHqL4+0106RBgdP+uhCJWgU+kGdpi6PsImGSMCVhrqwfeTKr6Gl2/Zwuxxg9T/4V57bew/C1wq4Yc7nM49qT7sB17NjqcAV7PU5/RMPpMWPr33fen98QefVOTZgM7Ph9mcC70zoL19XxYOGQqxjZ+/J0BbAPjDmvaBSsafUzAG1f41vX136z+3TvgkKng+//t3XecVOW9x/HP78zsLOzSe5UFVJCmUSyIKBpLjFHs7SZYoiYxJtdEvdFoclOMMebmhjT7NUaNxljRiDEWkCgiNhRQQCkCUkV6m505z/3jzMLsOrM7M1tmd8/3/Xrta9hznjn7zMMzZ37z1Pb5Xdf58OokmH5LEKBV6Tkczv87tOtZWOCXrAwm8sz+K2xdC92HwMizANMyOM1Bj2FBIF71vsyk3+icW82l8XhmYNClPMa4ffZ01MSimsAhUoiWeFebBJwGPGVmtwF9gJuBKc65BUXNWYoXLcG3znD2/bBjA27DUqx9b+jQG5dM4BXwwW9muNNuh16jsDfuClb8j5bCsFNxX/wxVt4jr25JM8MlK0me/xjRB8/4fOB3wPm48T8k6Sz3SmKGDRgbLEKbbdiAF8H6H5JzPgH4bEnQqpdNYifMeQS+8LXcg7TELpj7OLz088+fWzMP7v0KfOet/PIJwczPWXfBCz+uPhnguevhnAeg/6EK/ArhXFC2Vf+/9VlHsm0n2O8UmPdE5vO994e+BxV2bRGRZqzFBX3OuVfM7HTgp8AjwBbgUeCqomasBq+qq7G8G1bebffx+uzGYebBIZfC4Vfgdm2FaCkGQQtfIePQvCheeVf41gwqP5pGybJ/Q7Qt8WFnUNJlAA4jGslz3b+OfbF9TghaODPZbwKurGt+LZ07N+aQZlPQcperaGnQypfNhiXwwdMw9KTcA8lkApZMh+euy5C/jfDg2XDlexCtObQ0D1XBT5h2eEjGYcOy4P9r8bTgtQ85EcZ+F9p2LSD48+CUP8DGj+GTt6uf6lwB5z7YMN37IiLNTIsL+gCcc5OBycXOR1GklmWx0nb1vpRZsCVcIunDgLFs7TUaDMrKyqlMuoK6UMw53Bl3Yw+eDR/PqH5y0HjcqX/Keyyl67o3Fm0TtOhlS9N3NObl8SG9YyOsm197msVTYd8v5f7h73kw4/fZz1duh9fvgCOv2bNzQ64S8WDM4qKXYP1H0KkC9jku6KJsbi2Hvg/4e7pHE7vyf71VEnH4+FV46JzqXfAzbw3Wp7zoWeg6OL8xk54HJWVwyYvw0Uvw/pNBIL33sTBsQpBGAZ+ItEItMuiThhWNeBDxKHpG6kMAABygSURBVCnZ80FX8JgZL4KVlMFFz+JWvIktmAIYbr+TsT4HYL6ff6tktA2MOhvevi/z+W77YgPH5ZnPHKp+JEY+i2hjHiyvY1jp8ln5T+pIxGHVO/DoxbBpxZ7j7XrC6XfCgMMLnyhScweK+gRoELSQrZkHr/0Blr8BsXIYfhoc9q3guvnm04vAk9+sHvBV2bEBJl8Ol07NP59V418HjYeBqZm85inYE5FWTUGfNLzUB6r1OTCYFIHt6dYuYAmMLXFH2Qm/Irp+UdDqk65jP+LnPMzGjVvo0qGcaI7Xd7EyrOIIWPpK9jTDT8cieQZAsXKo3FHL+bKgG9ryWGJm+6dw/+mfX5x76xp48By4/DXoPDD/7l7nw7wnYdYdsOZ9KOsK+58LY69MBWj5LqtTGYytnPzt6l3ta9+H2Q/CJS9A2y6514Gq2eBbVmdP88nbQctn173zy2uVSBTdBkUkLDTnXRqP5wX7mZa0qdfad0vXb+evb66Gi6YQ/+pkOOgiOOB8kqfeQfKKd5izpR1PvbcO38+9Vc75SRLjr8/e4jfwSGzAGOJ5XJNkPGjVqu3vjjwrv7GHiXjQlZltVnRiJ7z6+/y3DnM+TLkGHr8UVrwZdD1vWg7Tfw13HV1rV3pWlTvgH1dmfn0blsA/r83vtfvJYNxdXTauqDuNiIgo6JPmb68uZfz8mfmc+qdXeWbTIFYf/hPWHXUzM9seyTcfeo+z736Tgd3LieTRirg17tjW7QAS5z0CPfbbcyLaBg6cSOK8v/PKh2vJJ+YjEsONuxrSJu5U0/fAYMxYPi1o0VgweaE2i6fmd03nB7Oh37g78/lPF8LLt+S373JiV7BETaZu2CrvT4ZkLedr8iLQdZ+603UZmPs1RURCTP0a0uy1b1PC8cN7MmXOamYv//xM3j4d23D00B7Bml45alMS5eTbX+OW00aw/+Uz2bl6AezcRKTHECq9Um6duhTPM0ZXdM35mvGEz4ZEGZ0veoHY89fBwueCACtWDiPPJnHcjXy6eSfd2pflt7BsXeMP892NJFkJb91be5rZD8DxGZazycb5sHFZHX83Hix6HCvP7ZpmMOgo6LRX9msPGBucl2ahMulTkla344kksWg9d8sRkQajoE9ahF+ePooP12zlw7XVuzk7tI1yx8TRJPKcbWwGo/p3YsLtbzCsdweO3LcbpdFOrJi1hClzVrMrkWTGtV+kTUnuH1ixqMf597zN5UcN5JQz78fFt+Jv20C0Yy92JI07py9jybptTDrvgJyvSWIXDPkyrHwne5qhX8lvAoZFah8nB0FwVrU0TK7XrKvFLdomeytoNskEnHUv3DchWPA6XfvecNrt1dfvk6LxneOfc1fzlxlLWbRuK93alXLW6H5ccHgFUc/yaokXkcahoE+avYhnlMciTPnPcUyevZIpc1YRT/iMGdyVrx42gLYlEWLR/D5Qop5x3Yn7MXPxet5ftZn3V1XfOu6aE4bQvX3+s1hXbNjBVY/O5cYpCxg/pAftSqOs3fIB0xasZVcqz7lONgkyWgqHfgPe/L/MgVpZl2ALunxm3LoEdNsXFkzJnqbLoPx2pIjGYP/z4fkfZ5/IMuL0/He5iMag58hgoeyZt8GiqUHL5tCT4OBLg/GiCviKzneOG56Yy4Oz9rTIbtheyU1T5jNlzmoevuwwtGuaSPGZy7ZzQgiY2XBg7ty5cxk+fHixsyM5qEz4eJ5hFnQlldaj66gy6bMjnuSO6YuZPPsTtuxMMKpfRy45YiBH7NOdiJf/sjWn/unVjF3QVS4eW8G1J+6XX5CajMOWVfDk5dVnG/c7GE69NVizL9+1+jZ9Ar8bmX0rsuN/ESwEnk8wmYzD/GfgsUs+P7Gk277w9eehTcfCF5VOb82s79Iy0mB83/HO8o2ccduMrGmuPn4Ilx05UF29IvU0b948RowYATDCOZdlD9XsFPQp6Au9eMLfHYT5vsN3hW3mHk/4TJmziisfnp3xfMQzpl09nv5dyvK6ru878CsxL0rlZ8tgw1Jcx36U9tibZGWwaHPeXWfJSnj3YXj6O5+fUTvky8GWcfmOFay67oYlMOOPsOKNYImaEWcEM669qFrlWqHKpM8PHnuPx9/+JGuavbqUMf2/jm7CXIm0TvUN+tS9K6GX3urmeYaX3yZx1a5zygF9ePPjDTwws/pSIxHP+NUZI+nVsU3e13U4vvrnt1m2fjsnjepNl/L+bPqokmfmTKVreYyHvzEm/66zSAnsf06wsPPrtwVr6ZV1gwO/BoOPgQLLgEhJMOP2pN+k7ZOrVrnWrCTisXpT7Uv81HVeRJqGgj6RBuSZ8bMJwznvkP489Poy1m3dxeDu7Zg4poKu7WLVZjbmojLp8/S7K3lt0XoA7py+uNr5ZZ9t529vLOPcg/fKe1xjEKANCrpyo7GgS9ZRrzUVgaD7Nr1FTwFfqxZP+AzqVs6MVB3NZGC3HGdsi0ijUtAn0sA8M/br3YEfnTwMzwzfd5TmMQs4XUnE45G3al98+JE3VzBxTEVB1wf2jAfMd5KFCFASMS44vIIHXs++ZM9XxwyoNoxCRIpD70CRRuCZURqNUBLxCg74qqzfWvuCxp9ty2MRZZEGZmYM7F7OtScOzXj+hOG9+I9DCmiJFpEGp6/2Is1YwvcZ0rM9C9dk2YYN2Ldne3zf4RUw21ikIUQ9j0vHDWLcPt2499WlfLh2K93bl3Lewf0ZP7RHoSNERaSBKegTacY8jIuPGMjT763KmubiIyrwnSt4AopIQ4h4wbCGm04fSUnEw3cu+DJS6BI9ItLg1N4u0ox5njGqX0f+60tDMp6/fPxgDh/craAlZkQamme2e7KSZ6Z6KdLMqKVPpJmLeB6XHTmIE0f05r7XlrLss+307tiWiWMGMLh7u4IWkQZI+sEanZt3VrJo7Va6lMcY1L2dBtyLiLRSCvpEWoCo5zGwWzBYPuIZvh/MmrQCu86Svs/2eJJrH5vDc/NWk0gFgMP7dODnE0Ywom9HBX4iIq2M7uoiLUhpNELU84hFvYIDvoBx7p0zeWbOqt0BH8C8lZs5766ZLP10W7ATiIiItBoK+kRCpjLp89y81cxbuTnj+V0Jn0kvLsRHQZ+ISGuioE8khJ6dk302MMDz768hmu9+viIi0qzpri4SQvFk7a14Cd+pe7eViyf8Gr8ni5QTEWkqmsghEjLOOcbu3ZXn5q3OmuawgV2pz7J/6TOANRu4efF9R9I57nttKQ/NWs4nG7ezV5cyzjtkLyaOqcAz6jleVESaKwV9IiETi0Y466D+/OGlj1i3JfMWb98aP5ik7/Ai+X34VyZ8Vm3eyf+9soS3P95AeWmEk0f14czR/Yho3bZmwccx8Z5ZvLZo/e5jC9ds5adPv8/LC9dxzwUHo5hPpHXSHVgkhCKe8fBlhzGoW3m14+1Ko9x8+kgOH9x19yK7uYonfKYuWMsXfzONv8xYypxPNjFz8Wdc/+RcJvzxVXZUJnFOXcbFFE/4PPrmimoBX7ppC9bxjzkrqUz6Gc+LSMumlj6REIpFPfp3LuOlq8fz2qJPmbtyM93KY5w4sjcRr7AWuYTvc+XDs6nMMF5w/uot/PwfH/CL00ZQkmfroTScWNTj728urzXN32Yt55T9+zZRjkSkKamlTySkSlLj7A4d1JULxlRwygF9aFMSybuFD4IWpMfeWsH2ePbJAE+9+8nuXUCkeNZm6dLP9byItFwK+kRCzjMjFvWI1GOJFt85lq7fXmuanZU+67fGC/4bUn++cwzu3q7WNHv3aKfgXKSVUtAnIvXmGfTq2KbWNCURo1NZSRPlSDLxfceFh1fUmuaiwytAC3OLtEoK+kSk3mLRCGeP7k+slq7hLw3vRWmJbjnFFI14HDWkOxeNrch4/vLxgxld0aVerb4i0nxpIoeINIiyWISfThjOD5+YQ81Jun07teVHJw/D6rP4H+ye/at15ArnmfGjk4Zxyv59uH/mx6zcuIP+ncuYeHgFw3p3IOKpbEVaKwV9ItIgSiIeZx3Uj6G92nPH9MWpdfqifGVUby4ZN4iyWKSggMI5h+9gw/Y4Ly9cR9Qzjhnag7YlkVCs++e7YHcU38GOyiTt20RJJF29Frz2PGP/fp0YcUZHSiIelUmfiGd4CqZFWjUFfSLSYKIRj1H9OvGn8w/cHeDtSiQpjUYKup5zjkTS8YPH32Py7JW7JxiURj0mjqngui8PbdWBSmXCZ/22OL989gOenbOaeNKne/tS/uPQvbjimL2JmBXc6ul5hpdqeS1kxraItDwK+kSkQdVszSs04ANwDq5+9F0mz15Z7fiuhM9d/15MaYnHd4/Zp1Vu8+acY+OOOCf/8ZVqO6es27KLSS98yHsrNnHPhQcXMYci0tK0vjuliLQaa7fs4ul3V2Y9/5dXl+K30l0+Er5j0gsfZt0q76X5a5mx6FOSvnbPEJHcKOgTkWYp6fu8NH8NtS0Zt2VXgtnLNxZ8/aTvSPqORNLHOdesth8riXifa+Gs6dG3VtCMsiwizZy6d0Wk2cplvFohk00rEz7zV29h0osLmTp/Lb6DQwZ24dtHD2bs4G7NYoKI7zu27krUmmbzjsqCXr+IhFPx72wiIhlEPI/jhvWsdcZvx7YlHNC/c17XjSd83vz4M864bQYvfrB2d0virCWfccE9b/Do2yuoTBTWfFbVUvjp1l0s/2w7Cd8nXuC1PM8Y3qdDrWlG9utEspV2b4tIw1PQJyLNVueyGGce1C/r+cuOHJT3NWNRjxuenEc8S7/oTc98gF/AjhSVSZ/3Vmzk9FtnMPrGFxh3y1QO/cWL3DrtI/wCtjWLJ3y+fsTArOfblHhMPGxAvSbKiEi4KOgTkWYr4hk3nTaSCw6voDRthm770ihXHb8v3xo/OO+Zu/NXbWbRuq1Zz2/emeBf89bkFahVJn3mrNjEeXe+ztvLNuw+vn5bnEkvfMhVj7yb94STWNTj1C/05eIMu2eUxSLc+bXRlJdqhI6I5E53DBFp1iKeccNJ+3HN8UOYtXQ9Uc/j0EFd8KywxYQ/2x6vO822OL5zu9exq0vUM3757AdZWw+feOcTvnPM3gzq3i6vvHpm3HDSMCaOqeBvbyxj/bY4+/Vqz9kH70Us4rXKpWpEpPEo6BORZq8k4lES8ThmaM96X2vfnu2JeLZ7oedMRvbrmNfuIRt3VPLG0g21pnninU/49tF706Ykv+5YzzMqupVz5bH7AmBWv7UPRSS89DVRREKlc1mMY/fLHjwO7dWeA/fqnNdOFzsrk3Wm2R6vO01t2pREaFMSUcAnIgVT0CciofPrM0dlnBnbp2Mb7po4Ou/1+nq0b0PPDqW1pjmkogtRra8iIkWk7l0RCZWIZ5SXRnjqiiN48YM1TJmzmqTvc+S+3ZlwQF/M8t+LNun7XDCmglueW5DxfP8ubTm2juVnREQam4I+EQmdiBcEdUcP7cH4IT12Hy90YkQsGuGb4wezYsMOHnpjGekTdQd0LeP+rx+K7xyRHCeGiIg0BgV9IhJa+bbo1cYz48bTRnD50YN5/O1P2B5PcHBFF44e2oOk7xr0b4mIFEJBn4hIA/HM6Ne5jG8cOQhHsJSLZ4YXUQufiBSfgj4RkQZWmueyLCIiTUH9DSIiIiIhoKBPREREJAQU9ImIiIiEgII+ERERkRBQ0CciIiISAgr6REREREJAQZ+IiIhICCjoExEREQkBBX0iIiIiIRD2HTliAB999FGx8yEiIiJSq7R4JVbI880513C5aWHM7BRgcrHzISIiIpKHCc65p/J9UtiDvo7AUcByIN6If2owQXA5AVjUiH+npVG5ZKZyyU5lk5nKJTuVTWYql+yac9nEgP7Ay865Tfk+OdTdu6kCyztSzpeZVf1zkXNuXmP/vZZC5ZKZyiU7lU1mKpfsVDaZqVyyawFl806hT9REDhEREZEQUNAnIiIiEgIK+kRERERCQEFf01gH/DT1KHuoXDJTuWSnsslM5ZKdyiYzlUt2rbZsQj17V0RERCQs1NInIiIiEgIK+kRERERCQEGfiIiISAgo6BMREREJAQV9jcjMTjWz2Wa208w+NbN7zaxLsfPVlMzMM7NrzGyhme0ys6Vm9jsz65SW5mwzcxl+ZhYz743NzKZked3fTJ3vb2aPmtlGM9thZq+Z2VHFzndjMrMLs5RJ1c89qXShqTNmtq+Z3WRmyzOcy6mOmNmlZvZB6j240swmmVmbpnkFjaOOchlrZi+a2VYzW29mz5vZwRnSbctSj4Y2zatoHHWUTZ3vHQtcb2ZLzCyeum//2MxadMyQrVzquOf4NdK26DoT6m3YGpOZjQUeA54EfgTsBdyUejymiFlrapOAbwC3AK8Aw4CfAUOBE1Jp+gLbgC/VeO7mJspjsfQFHgV+V+P4R2YWBZ4FOgLfBbYC3wOeM7NRzrmFTZrTpjMFGJfheD/gIYIygRDUGTM7jmDZiDFAghr361zriJmdC9wJ3AVcBeyfum4H4OImeTENKIdyOQx4CZgGfC11+IfAVDM7MK1cOgNlwPXA9Bp/5uPGyn9jqqtsUnJ57/wA+DnwK4KyGQ/8JHXuZw2W4SaSQ7lkuucA3ArsDhBbRZ1xzumnEX6AvwNLAS/t2ETAAaOKnb8mKoPuQBK4scbxq1PlMCD1+2+AD4qd3yKUz3rgB1nOfTlVRsekHWsPbAL+t9h5L0JZ/Q/BTTUSljpD8KH7F+CLBB9YrpA6AswCptd47o+BSqBrsV9nI5TLU8BiIJZ2rCfBh/1/px0bmSq/Q4v9mpqqbFJpan3vAAasBu6rcfwegnXrvIbKb3MqlwzPGZGqH8e1pjrToptqm7nDgOedc+lNw8+nHg8pQn6KoSNB68xjNY6/n3qs6uruS9q3qTBIda11IfvrPgyIA1OrDjjntgAzCU/9AcDMOgCXAn9wziVTh1t9nXHO/cg5d4Fz7kWCD5qa6qwjZhYDvgA8V+O5zxO0dnyhEbLeqHIolwXAJOdcPO05a4DP2HPPgaAOQSuqRzmUDdT93hlIECRnqjPdgEH1zmgTy7FcaroamOecez7tWIuvMwr6Gk8vYG2NY1W/92jivBSFc+4j59xXnXPv1Dh1NLAGmJf6vS8w2MwWmFnCzFaY2Q+aNLNNr+rmcUVqzFGlmc1MdU1BUH8+damvl2nWEpL6k+YyIALcnXYsjHWmplzqSDeC4C409yLn3DXOud+nHzOzEQQ9Dy+lHa56Dz6QGqe13cweM7PeTZXXIqnrvdMr9RiaOlOTmfUBziMYnpSuxdcZBX2Np4Sg+2S3tFaKWNNnp3kws4MIxh/9LO2b+MbUz/XA8QTfMG82s28UJ5dNog2wApgDnElwg+lAMB6rB0EdqczwvCQhqj9mVgL8J/Bn59zGtFNhrDM15VJHqh5rpgvNvSjV2nkn8DrwdNqpSmAV8E/gROAagu6/x5s6j02srvdO6OsMwWfUZuCBGsdbfJ3RRI7iCOXed2bWH5hM8Ia5req4c+7kGklfSqX9IXBH0+Ww6Tjn5gH904+Z2VvAfODbdT29sfLVDJ0L9AGqtdyEsc7kKdc6Eoa6dCcwBDgsfbiNc+4+4L60dNPNbAPwVzM72jk3lVaoAd47rbrOmFk7gsmHf3DO7Uw/1xrqjFr6Gk8l0Db9QOobJ8Cups9OcVmwVM1zwErg/AxdUjVNAfYys/aNnrlmwjm3BPiAYABxnBr1JyVGuOrPVcAzzrkPc0gbtjqTSx2pak2vmS4U9yIz+xVwDnBajnWoanb4iMbLVbOU/t4JdZ0hGD9cRjBzNxctqs4o6Gs869gzNqJKz9TjqibOS1GZWRnwDME3xBOdc9vSzvW2YG22jjWeFmnKPDY1MxtnZidlOBUhKKd1QNdU92a6noSk/qSWWdgf+G2N46GsMxnkUkfWAz4hvBeZ2feA7wNnOedqLq+BmZ2VGm6SruozsVW2ZuX43lmXegxjnYkSDCf5m3NudYbzLb7OKOhrPK8BJ9S4IVetS9fqFpDNJvUmeoTgBnKcc259hmR/JhjXlu5Y4OPUbMTW6Ajgb1Z9ker+BN1QcwnqT4Rg3EjV+Q4E60yFpf5cA7yXpcskjHWmpjrriHNuF/AO8JUazz2BoEWn5iSrVsHMzgd+DVzonPtHlmSX8PmB+semHuc2Vt6agbreO4sIAr+a3cAnEPTULGv0HBbP2cAAPl8vqrT4OqMxfY1nEnAa8JSZ3UYwLulmYIpzbkFRc9a07gaOI2gyH2Rm6dP9Nznn5pjZfcD/mFk5sBCYQLBw6KVNntumcw9wJfCMmf2aYOLPDQSLpv4J2EAwu/luM7uOoMXmewTfJlv9mDUzG0VQby6qec45tyqkdaamf5JbHfkN8KCZPUCwhNIwgoD6budcq1nMuoqZHQ/cS/BaPzazI2okeSMVDN8C/MuCXV7+DlQAvwBedc5Na7IMN6Fc3jvOOd/MfgvcZGaTCIbljAPOJ1hXtEW0aBXoKuDlDCtOVGn5dabYCwW25h+CN9NsgjEQnxIEQB2Lna8mLgNXy8+0VJq2BItnLkqV1ULgO8XOexOUzVCCiS2fEgR7LwAHpp3vR9BKugnYAbwKjC12vpuobO4jWNanNMv5UNUZgt0QXIbjOdURgg/0+QSteysJFruONWaei1UuBAFfbfedirS0JxK0im5NvQ/vA7oX+3U1cp2p871DsEDzDwk2GIinHq8DrNivqxHL5ZhU/Ti1jue36DpjqRchIiIiIq2YxvSJiIiIhICCPhEREZEQUNAnIiIiEgIK+kRERERCQEGfiIiISAgo6BMREREJAQV9IiIiIiGgoE9EREQkBBT0iYjUIrVBvTOzimLnRUSkPhT0iYikMbPxqSBvfCNce5qZTWvo64qI5EJBn4iIiEgIKOgTEUkxs6XA1NSvU1O/VxltZq+Y2Q4zW2xml9V4btTMfmpmy8xsp5nNNLNxqXMXmpkDjgKOSrUkXpg6V2ZmvzSzRWa2y8yWmNmNZlbS2K9XRMJFQZ+IyB5nAt9N/fu7qd+r3A48AJwKvAfcbmYj0s7/Ffg+8FvgDGAN8C8zGwJMAcYBs1M/41LHAO4HLgF+DZwI/C/wPeC/G/i1iUjImXOu2HkQEWk2UmP5pgJHO+empVrk/gyc5px7MpWmJ7Aa+LZz7lYzOwL4N3Cxc+7PqTQxYBEw2Tl3RerYNADn3Pi0v3cIsME592Hq9yhBcDnUOXdAo79gEQkNtfSJiORmdtU/nHNrUv/snnr8EpAEHk9180YBH5gFHFLHdd8FTjWzeWa2HagEzgE6NWTmRUSixc6AiEgLZqnHXkAE2JghzeI6rnEPQXfwzcCrwAaCrt2RDZRHERFAQZ+ISEPYAmwDxmc4tyvbk8ysPXAucJNz7idpx9c3cP5ERBT0iYjU4KceI3k852XgSqDMOTe96qCZdQc21bh2+qxcL/WzOe05EWBYnnkWEamTxvSJiFS3LPX4dTM7KcfnPAVMA54ws++b2bGpJV3eA66tce0vmNk5ZraPc24TwaSRq83sa2Z2CvAccDDQviFejIhIFQV9IiJpnHNLCZZP+QpwS47P8YGTCGb5fp9gOZb/Av4I3JSW9BZgKcE4vjGpY+cTtBT+PvX8D4EbgLVm1qteL0ZEJI2WbBEREREJAbX0iYiIiISAgj4RERGREFDQJyIiIhICCvpEREREQkBBn4iIiEgIKOgTERERCQEFfSIiIiIhoKBPREREJAQU9ImIiIiEgII+ERERkRBQ0CciIiISAgr6REREREJAQZ+IiIhICCjoExEREQmB/wdZX+jQb75UOQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=120)\n",
    "sns.scatterplot(x=\"theta\", y=\"energy\", hue=\"label\", data=vector_sim_df, ax=ax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### So now what?\n",
    "\n",
    "*   We should fit the model (in machine learning terminology, we would \"train\" the model) to the data to obtain the interaction parameters.\n",
    "\n",
    "*   This should be easy, I just need an input formula.\n",
    "\n",
    "    \\begin{equation}\n",
    "    E(\\theta{})=2J_{1}\\cos\\left(\\theta{}\\right)+2J_{2}\\cos\\left(2\\theta{}\\right)+2J_{3}\\cos\\left(3\\theta{}\\right)+\\dots{}\n",
    "    \\end{equation}\n",
    "\n",
    "*   Wait a second...\n",
    "\n",
    "*   What is the problem here? Why can't I just go ahead and try fitting this now?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**We'll return to this later. But for now, let's talk about some simpler cases.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basics of fitting in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The *Filip* dataset\n",
    "\n",
    "Source: <https://www.itl.nist.gov/div898/strd/lls/data/Filip.shtml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model that generated this dataset was a polynomial summation, $y=\\beta_{0}+\\beta_{1}x+\\beta_{2}x^{2}+\\beta_{3}x^{3}+\\dots{}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "filip_csv_path = Path(\"../../data/nist/filip.csv\")\n",
    "filip_df = pd.read_csv(filip_csv_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=120)\n",
    "sns.scatterplot(x=\"x\", y=\"y\", data=filip_df, ax=ax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the `statsmodels` package and its linear regression methods to perform a fit of the data. For this example, we will fit $y=\\beta_{0}+\\beta_{1}x+\\beta_{2}x^2+\\beta_{3}x^3$ to the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "smf_filip_fit = smf.ols(data=filip_df, formula=\"y ~ x + I(x**2) + I(x**3)\").fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fitting coefficients (the parameters $\\beta_{0}$, $\\beta_{1}$, $\\beta_{2}$, and $\\beta_{3}$) are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>0.390271</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x</th>\n",
       "      <td>-0.303364</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>I(x ** 2)</th>\n",
       "      <td>-0.053719</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>I(x ** 3)</th>\n",
       "      <td>-0.002726</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           coefficients\n",
       "Intercept      0.390271\n",
       "x             -0.303364\n",
       "I(x ** 2)     -0.053719\n",
       "I(x ** 3)     -0.002726"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(smf_filip_fit.params, columns=[\"coefficients\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the `predict` method to generate our model curve that we can compare with the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_df = pd.DataFrame({\"x\": np.arange(-9, -3, 0.01)})\n",
    "model_df[\"y\"] = smf_filip_fit.predict(model_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualizing both on the same plot, we get:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=120)\n",
    "sns.scatterplot(x=\"x\", y=\"y\", data=filip_df, ax=ax)\n",
    "sns.lineplot(x=\"x\", y=\"y\", data=model_df, ax=ax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Obviously this is not that good a fit and we should try something else. But, how do we know when what we have is good enough? And, how do we know when we've gone too far?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Overfitting\n",
    "\n",
    "*   We cannot just keep trying additional terms until the fit \"looks good\"\n",
    "\n",
    "*   This can lead to overfitting, where your model is too complicated and starts to closely fit to the pecularities of the training dataset\n",
    "\n",
    "*   Put another way, you start fitting to statistical noise\n",
    "\n",
    "*   Also means that the model won't generalize, meaning it only works for this very specific dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Where data science comes in\n",
    "\n",
    "How can we select the model that best fits the above data? Can we find the polynomial coefficients and the correct cutoff that generated this data?"
   ]
  }
 ],
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