{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Building Linear Models\n",
    "> Here we look at the parts that go into building a linear model. Using the concept of a Taylor Series, we focus on the parameters slope and intercept, how they define the model, and how to interpret the them in several applied contexts. We apply a variety of python modules to find the model that best fits the data, by computing the optimal values of slope and intercept, using least-squares, numpy, statsmodels, and scikit-learn. This is the Summary of lecture \"Introduction to Linear Modeling in Python\", via datacamp.\n",
    "\n",
    "- toc: true \n",
    "- badges: true\n",
    "- comments: true\n",
    "- author: Chanseok Kang\n",
    "- categories: [Python, Datacamp, Statistics, Modeling]\n",
    "- image: images/rss_hiking.png"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import statsmodels.api as sm\n",
    "\n",
    "plt.rcParams['figure.figsize'] = (10, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What makes a model linear\n",
    "- Taylor Series\n",
    "    - Things to know:\n",
    "        1. approximate any curve\n",
    "        2. polynomial form: $y = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \\dots + a_n x^n$\n",
    "        3. often, first order is enough: $y = a_0 + a_1 x$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model Components\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Previously, you have been given a pre-defined model to work with. In this exercise, you will implement a model function that returns model values for ```y```, computed from input ```x``` data, and any input coefficients for the \"zero-th\" order term a0, the \"first-order\" term ```a1```, and a quadratic term ```a2``` of a model (see below).\n",
    "\n",
    "$$ y = a_0 + a_1 x + a_2 x_2 $$\n",
    "Recall that \"first order\" is linear, so we'll set the defaults for this general linear model with a2=0, but later, we will change this for comparison."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_prediction(x, y):\n",
    "    \"\"\"\n",
    "    Purpose:\n",
    "        Create a plot of y versus x\n",
    "    Args:\n",
    "        x (np.array): array of values for the indepent variable, e.g. times\n",
    "        y (np.array): array of values for the depedent variable, e.g. distances\n",
    "    Returns:\n",
    "        fig (matplotlib.figure): matplotlib figure object\n",
    "    \"\"\"\n",
    "    from matplotlib.ticker import MultipleLocator\n",
    "    font_options = {'family': 'Arial', 'size': 16}\n",
    "    plt.rc('font', **font_options)\n",
    "    fig, axis = plt.subplots()\n",
    "    axis.plot(x, y, color=\"red\", linestyle=\"-\", marker=\"o\")\n",
    "    axis.grid(True, which=\"both\")\n",
    "    axis.axhline(0, color=\"black\")\n",
    "    axis.axvline(0, color=\"black\")\n",
    "    axis.xaxis.set_major_locator(MultipleLocator(5.0))\n",
    "    axis.xaxis.set_minor_locator(MultipleLocator(1.0))\n",
    "    axis.yaxis.set_major_locator(MultipleLocator(5.0))\n",
    "    axis.yaxis.set_minor_locator(MultipleLocator(1.0))\n",
    "    axis.set_ylabel('Y')\n",
    "    axis.set_xlabel('X')\n",
    "    axis.set_title(\"Plot of modeled Y for given X\")\n",
    "    plt.show()\n",
    "    return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the general model as a function\n",
    "def model(x, a0=3, a1=2, a2=0):\n",
    "    return a0 + (a1 * x) + (a2 * x * x)\n",
    "\n",
    "# Generate array x, then predict y values for specific, non-default a0 and a1\n",
    "x = np.linspace(-10, 10, 21)\n",
    "y = model(x)\n",
    "\n",
    "# Plot the results, y versus x\n",
    "fig = plot_prediction(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model Parameters\n",
    "Now that you've built a general model, let's \"optimize\" or \"fit\" it to a new (preloaded) measured data set, ```xd, yd```, by finding the specific values for model parameters ```a0, a1``` for which the model data and the measured data line up on a plot.\n",
    "\n",
    "This is an iterative visualization strategy, where we start with a guess for model parameters, pass them into the ```model()```, over-plot the resulting modeled data on the measured data, and visually check that the line passes through the points. If it doesn't, we change the model parameters and try again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data(x, y):\n",
    "    \"\"\"\n",
    "    Purpose:\n",
    "        Create a plot of y versus x\n",
    "    Args:\n",
    "        x (np.array): array of values for the indepent variable, e.g. times\n",
    "        y (np.array): array of values for the depedent variable, e.g. distances\n",
    "    Returns:\n",
    "        fig (matplotlib.figure): matplotlib figure object\n",
    "    \"\"\"\n",
    "    from matplotlib.ticker import MultipleLocator\n",
    "    font_options = {'family': 'Arial', 'size': 16}\n",
    "    plt.rc('font', **font_options)\n",
    "    fig, axis = plt.subplots(figsize=(8,6))\n",
    "    axis.plot(x, y, color=\"black\", linestyle=\" \", marker=\"o\")\n",
    "    axis.grid(True, which=\"both\")\n",
    "    axis.axhline(0, color=\"black\")\n",
    "    axis.axvline(0, color=\"black\")\n",
    "    axis.set_ylim([-5*50, 15*50])\n",
    "    axis.set_xlim([-5, 15])\n",
    "    axis.xaxis.set_major_locator(MultipleLocator(5.0))\n",
    "    axis.xaxis.set_minor_locator(MultipleLocator(1.0))\n",
    "    axis.yaxis.set_major_locator(MultipleLocator(5.0*50))\n",
    "    axis.yaxis.set_minor_locator(MultipleLocator(1.0*50))\n",
    "    axis.set_ylabel('Altitude (meters)')\n",
    "    axis.set_xlabel('Step Distance (km)')\n",
    "    axis.set_title(\"Hiking  Trip\")\n",
    "    return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "xd = np.array([  0. ,   0.5,   1. ,   1.5,   2. ,   2.5,   3. ,   3.5,   4. ,\n",
    "         4.5,   5. ,   5.5,   6. ,   6.5,   7. ,   7.5,   8. ,   8.5,\n",
    "         9. ,   9.5,  10. ])\n",
    "\n",
    "yd = np.array([ 161.78587909,  132.72560763,  210.81767421,  179.6837026 ,\n",
    "        181.98528167,  234.67907351,  246.48971034,  221.58691239,\n",
    "        250.3924093 ,  206.43287615,  303.75089312,  312.29865056,\n",
    "        323.8331032 ,  261.9686295 ,  316.64806585,  337.55295912,\n",
    "        360.13633529,  369.72729852,  408.0289548 ,  348.82736117,\n",
    "        394.93384188])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Complete the plotting function definition\n",
    "def plot_data_with_model(xd, yd, ym):\n",
    "    fig = plot_data(xd, yd)  # plot measured data\n",
    "    fig.axes[0].plot(xd, ym, color='red')  # over-plot modeled data\n",
    "    plt.show()\n",
    "    return fig\n",
    "\n",
    "# Select new model parameters a0, a1, and generate modeled `ym` from them.\n",
    "a0 = 150\n",
    "a1 = 25\n",
    "ym = model(xd, a0, a1)\n",
    "\n",
    "# Plot the resulting model to see whether it fits the data\n",
    "fig = plot_data_with_model(xd, yd, ym)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpreting Slope and Intercept\n",
    "- Review: Terminology\n",
    "    $$ y = a_0 + a_1 x $$\n",
    "    - $x$ : independent variable, e.g. time\n",
    "    - $y$ : dependent variable, e.g. distance traveled\n",
    "    - $a_0$ : intercept\n",
    "    - $a_1$ : slope"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Proportionality\n",
    "The definition of temperature scales is related to the linear expansion of certain liquids, such as mercury and alcohol. Originally, these scales were literally rulers for measuring length of fluid in the narrow marked or \"graduated\" tube as a proxy for temperature. The alcohol starts in a bulb, and then expands linearly into the tube, in response to increasing temperature of the bulb or whatever surrounds it.\n",
    "\n",
    "In this exercise, we will explore the conversion between the Fahrenheit and Celsius temperature scales as a demonstration of interpreting slope and intercept of a linear relationship within a physical context."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_temperatures(temps_C, temps_F):\n",
    "    font_options = {'family' : 'Arial', 'size'   : 16}\n",
    "    plt.rc('font', **font_options)\n",
    "    fig, axis = plt.subplots(figsize=(16,4))\n",
    "    axis.plot(temps_C, temps_F)\n",
    "    axis.set_xlabel(\"Temperature (Celsius)\")\n",
    "    axis.set_ylabel(\"Temperature (Fahrenheit)\")\n",
    "    axis.grid()\n",
    "    plt.show()\n",
    "    return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Complete the functino to convert C to F\n",
    "def convert_scale(temps_C):\n",
    "    (freeze_C, boil_C) = (0, 100)\n",
    "    (freeze_F, boil_F) = (32, 212)\n",
    "    change_in_C = boil_C - freeze_C\n",
    "    change_in_F = boil_F - freeze_F\n",
    "    slope = change_in_F / change_in_C\n",
    "    intercept = freeze_F - freeze_C\n",
    "    temps_F = intercept + (slope * temps_C)\n",
    "    return temps_F\n",
    "\n",
    "# Use the convert function to compute values of F and plot them\n",
    "temps_C = np.linspace(0, 100, 101)\n",
    "temps_F = convert_scale(temps_C)\n",
    "fig = plot_temperatures(temps_C, temps_F)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Slope and Rates-of-Change\n",
    "In this exercise, you will model the motion of a car driving (roughly) constant velocity by computing the average velocity over the entire trip. The linear relationship modeled is between the time elapsed and the distance traveled.\n",
    "\n",
    "In this case, the model parameter ```a1```, or slope, is approximated or \"estimated\", as the mean velocity, or put another way, the \"rate-of-change\" of the distance (\"rise\") divided by the time (\"run\")."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "times = np.array([ 0.        ,  0.08333333,  0.16666667,  0.25      ,  0.33333333,\n",
    "        0.41666667,  0.5       ,  0.58333333,  0.66666667,  0.75      ,\n",
    "        0.83333333,  0.91666667,  1.        ,  1.08333333,  1.16666667,\n",
    "        1.25      ,  1.33333333,  1.41666667,  1.5       ,  1.58333333,\n",
    "        1.66666667,  1.75      ,  1.83333333,  1.91666667,  2.        ])\n",
    "\n",
    "distances = np.array([   0.13536211,    4.11568697,    8.28931902,   12.41058595,\n",
    "         16.73878397,   20.64153844,   25.14540098,   29.10323276,\n",
    "         33.35991992,   37.47921914,   41.78850899,   45.66165494,\n",
    "         49.9731319 ,   54.13466214,   58.42781412,   62.40834239,\n",
    "         66.65229765,   70.76017847,   75.00351781,   79.2152346 ,\n",
    "         83.24161507,   87.59539364,   91.74179923,   95.87520786,\n",
    "        100.07507133])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_velocity_timeseries(times, velocities):\n",
    "    fig, axis = plt.subplots()\n",
    "    axis.plot(times, velocities, linestyle=\" \", marker=\".\", color='black', label='Velocities')\n",
    "    axis.axhline(np.mean(velocities), color='red', alpha=0.5, lw=4, label='Mean Velocity')\n",
    "    axis.grid(True, which=\"both\")\n",
    "    axis.set_ylabel(\"Instantaneous Velocity (Kilometers / Hours)\")\n",
    "    axis.set_xlabel(\"Time (Hours)\")\n",
    "    axis.set_ylim([0, 100])\n",
    "    fig.tight_layout()\n",
    "    fig.legend(loc='upper center')\n",
    "    plt.show()\n",
    "    return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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9/gK3W939OOB5guXBojAX2AL0y20ws7pAN2BmrGkmkAiclO+YNsD++Y4REdkpLVq0wMy46qqrCu1fvHgxZoaZsWpV+e6S/M4772BmPPHEE0Ue079/f9q0Cb88uplxzz33RBEeAKNGjSIlJSXv/ssvv8xf/vKXyM4vIhJWFMUUU8mXnJaGu28EHgRGm9lVZtYXeANYDzweO+Y74EXgMTO70MxOA6YDnwMvRRGHiOyazIx//rPw1QunTp1axtEUrUuXLrRq1Yrnn3++0P5169Yxffp0Bg0aVMaR/e6CCy5g9uzZeffHjh3LsmXFXZ8sIhIfUSS73YCtEZwn17UE6+leBTxHUIfby93z1+OeRzCjfCdBEvwZcIK7Z0cYh4jsYo488kh++OEHPv300x36XnzxRQ466KByiGpHZsY555zDrFmzWLly5Q79U6dOJTMzk4EDB5ZDdIGmTZty2GGHldvzi4jkCpXsmtkrhdxeM7NPCLb3faYkT+7uo9w9pUBblrsPd/c93D3F3Y91968LHPObu1/k7vXcfTd3P83dl5ckBhGRXAcffDCtW7dm2rRp27X/+OOPfPjhh5x22mk7POatt97i8MMPJzk5maZNmzJy5Eiys3//3r1t2zZuvPFG2rZtS40aNahbty79+/dnyZIlece0aNGCu+66i7/+9a/Uq1ePtLQ0Bg0axIYNha2yGBg4cCA5OTk7xAowadIkevTowV577ZXXNnnyZA488EBq1qxJ69atefDBB4sdi0WLFnHGGWfQqFEjUlNTOfnkk1m4cOF2x3z++eccf/zxpKWl0ahRIwYPHsyaNWuA7csY0tPTmTNnDq+//jpmxscff0yNGjV2KJuYO3cuZsZ///vfYmMTEdkZYWd20whWQMh/qwX8CFwC/D0u0YmIlLH+/fvvUMowdepUDj/8cPIvWwgwc+ZMjj/+eFq2bMm//vUvrr76asaMGcNll12Wd8zQoUN58MEHGT58OG+++Sa33norM2fO5IorrtjuXLfddhtr165lypQpjB49msmTJzN69Ogi42zVqhVdunTZoZRh2bJlzJkzZ7sShokTJ3L22WfTrVs3XnnlFQYNGsTQoUO5++67Cz330qVL6dSpEwsXLuThhx/mH//4Bz/88ANdunRh+fJgXmHx4sV06dKFdevW8fTTT/PAAw/w5ptvcvbZZ+9wvocffpgOHTpw1FFH8f7773PAAQdwwgknMHny5O2OmzRpEgcffDAHHnhgka9bRGRnhd1UIj3OcYhIZTdqVIkeVn3rVqhRI9pYoMTxnHbaadx99918/fXXtGvXDghKGM4444wdjr3++us54ogjmDJlCgC9e/emXr16nHvuuVx99dW0aNGClStXcs899zB48GAAunXrxjfffMOkSZO2O1fTpk2ZPHkyZsaxxx5LRkYG06dP58477ywy1oEDB3LxxRezYsUKGjduDAQzuLVr1+bUU08FgrUur732WgYMGMC4ceMAOPbYYzEzbrnlFi655BJq16693XnHjh3L5s2beeutt2jQoAEQzM62atWKMWPGMGbMGO677z4SExN54403SEsL9vxJTk7mqquuYvXq1dudb7/99iMtLY2UlBSOOOIIAAYNGsQpp5zCN998wz777ENWVhYvvPACI0aM+KM/IhGRnbJTNbtm1sfM7jKzR8zsVjM73rSOjIhUIZ06dWKvvfbKKw9YunQp8+bN26GEYdOmTcybN48TTzyRrKysvFvv3r3JycnJuzjr+eefZ/DgwSxfvpxZs2bx0EMP8e6777J169Ydnjf/X6dNmzblt98K7oq+vTPOOIMaNWrw4osv5rVNmjSJ008/nVq1agGwYMECli9fTp8+fbaL8/jjj2fDhg3Mmzdvh/P++9//pnv37nmJLkCDBg3o2bMnc+bMAYKSg27duuUlugB9+/ZlwYIF1K9fv9i4Afr06UP9+vXzZnffeOMN1q5dy1lnnfWHjxUR2Rlha3Zrm9ls4FXgfIKL0i4BXgf+bWa1i3u8iEhlkr+UYerUqXTq1GmHEoa1a9eSk5PDiBEjqFatWt5t9913B2DFihVAkBS2b9+ePffck/79+zN16lSSk5Nx337p8tzkNFdCQgI5OYVuCpknLS2Nfv365ZUyfPXVV8yfP3+7EobcWdazzz57uzhzLx7LjbPga2vUqNEO7Y0aNWL9+vUArFmzJu+1lkS1atU466yz8pLdSZMm0atXr7wZahGRqITdVOIO4ECgt7u/mdtoZscBzwK3AlcU8VgRkUrl1FNP5b777mPRokVMnTq10BKG3BnN66+/npNPPnmH/iZNmrBu3TpOPPFEunTpwrRp09h7770B+Pvf/878+fMjiXXgwIGccMIJLFmyhOeee45WrVpx9NFH5/XXqVMHCLZ37tSp0w6Pb9my5Q5t9erV4+eff96h/aeffsqbta1Tp84OK0Fs3bqVWbNm0blz59Cxjxs3jo8++ojXXnuNRx55JNTjRER2Rthk93Tg2vyJLoC7zzCz64AbUbIrsmsrYY1s5oYN1KhgW+AeeeSRNG7cmEcffZT//Oc/O1xIBZCamkr79u357rvv6NixY177559/zrBhw/IuLlu7di1XXHFFXqKbk5PDW2+9tcPMbkkdc8wxNG7cmJdeeolp06YxaNCg7coh2rVrR/369Vm6dCmXXHJJXvuMGTO47777eOihh3YoO+jSpQuPPfYYq1atyitlWLVqFTNnzuTiiy/OG6Nnn32WjRs35q26MGvWLE444YRCt/NNTNxxR/nDDjuMfffdlyuvvBKAfv0iWbJdRGQ7YZPdZKDQ/YZj7fWiCUdEpPwlJCRwyimnMGbMGA477LAdShhy3XzzzfTr1486depwyimnsGrVKq6//noSEhI48MAD2bZtG6mpqdxyyy1kZ2ezefNmHnroIT777DPMLJLtcxMTExkwYAAPPvgg33777Q5r6yYlJTFq1Ki8hLJnz5788MMPjBgxgjZt2hQ6szt06FCeeuopjjnmGG644QbcndGjR1O9evW8VSSGDh3KxIkT6dOnD1dddRUbN27kmmuuoX///rRt23aHc+62227Mnz+fjIyMvKXaIJjdHTFiBAMHDtzhQjkRkSiEvUBtPlDUVjznAV9EE46ISMVw6qmnsm3bNk4//fQij+nbty8vv/wyH330EX379uWKK66gc+fOzJ49m1q1alGnTh2mTZvG2rVr6du3L3/7299o0KABL774Ijk5OXzwwQeRxDpo0CAWLlxIt27daNGixQ79Q4YM4ZFHHuGVV17hhBNOYOTIkZx++ul5694W1KxZM9555x2aNGnCwIEDOf/882nevDnvv/8+TZs2BYLyhzlz5lC9enXOPPNMhg0bRr9+/Zg4cWKhMV555ZVs3bqV3r17b7dpx/HHHw/AOeecE8FIiIjsyML8V5qZdQVmAf8h2B74Z6ARQXnD4UA/d38tjnFGpmPHjv7RRx/l3c/IyCA9Pb38AqpENFbh7Qpj9dVXX7HvvvuW+jwbNmwgtYKVMVRUVXGs7rrrLsaNG8eiRYtISPjj+Zew77td4TMYFY1VeBqr8MpjrMzsY3fvWLA97Dq7/zazk4DRwBjAACeY8a00ia6IiFQM06ZNY968eYwbN46bbropVKIrIlISYWt2cff/A/4vtszYbsCv7l78IpAiIiKFWLhwIQ8++CAnn3wyl19+eXmHIyJVWJHJrpkVd9HZZqCGmeVte+Tua6IMTEREqq7hw4czfPjw8g5DRHYBxc3sriIoVQhrx3VlRERERETKUXHJ7mC2T3YTgceBm4BFcYxJRERERCQSRSa77v5U/vtmlpvsvurun8Q5LhERERGRUtPlryJSYlHtAiYSht5vIlISSnZFpESqVavG5s2byzsM2YVs3ryZatWqlXcYIlLJKNkVkRLZfffdWbZsGZs2bdKMm8SVu7Np0yaWLVvG7rvvXt7hiEglE3qdXRGR/NLS0gBYvnw527ZtK/F5tmzZQs2aNaMKq0rblceqWrVqNGrUKO99JyISVnHr7D5QsCn282ozW1mgz91dq4KL7GLS0tJKnXxkZGTQoUOHiCKq2jRWIiI7r7iZ3ZMKaVsMHFFIuwNKdkVERESkQilu6bGWZRmIiIiIiEjUdIGaiIiIiFRZSnZFREREpMpSsisiIiIiVZaSXRERERGpsopMds3soLIMREREREQkasUtPTbLzDKBN2O3t9y94Pq6IiIiIiIVVnFlDA2BfsB3wCXAUjP7yMxuM7NuZqbd10RERESkQitunV0H5sVut5hZGtALOA54CqhvZhnADOBNd18Y92hFRERERHZC6AvU3H29u//T3S+ObThxGPA2cALwSbwCFBEREREpqRKXIrj7N8A3wANmVj26kEREREREohHJ0mPunhnFeUREREREoqR1dkVERESkylKyKyIiIiJVlpJdEREREamyQie7ZraPme0f+z3FzB4ys1fN7Ny4RSciIiIiUgqhkl0zOwX4Ajg31vQPYDBQG5hgZkPiEp2IiIiISCmEndm9HpgCjDCzxsApwM3u3gMYCSjZFREREZEKJ2yyuy/whLtnAScCBkyN9b0PNI9DbCIiIiIipRI22f0VqBf7/UTgh3zbA7cDfok6MBERERGR0gqb7E4H7jKz8QTJ7jMAZnY5cBvwryiDMrNEM/u7mX1rZhvN7AMz65Gv38zsOjP70cw2mdlbZtYuyhhEREREpPILm+xeBrwFHA08AdwRa7+AINEdEXFcVxMk0U8C/YDvgDfMrEOsfyRBHfE9wJ+AOsBMM6sTcRwiIiIiUoklhTyuNzDS3VcWaG/v7jkRxwQwCHjO3W8DMLPZQBfgfDMbAVwFjHL3B2L97wCLgfOBe+MQj4iIiIhUQmFndh8FuhZsjFOiC1ADWJ/vebKBdQR1w0cAKcAr+frXAnMIknIRERERESB8svsz0CCegRTwEHCOmfU0szqx2uD9CZY/axs75rsCj/k+X5+IiIiISOgyhknA/WZ2AvAVO66+4O4+NsK4xgM9gLfztV3v7q/Eyhi2untmgcdsANIijEFEREREKjlz9z8+yOyPyhXc3RMjCcjMgH8D+xFchPYV0Av4OzCU4GK0G9w9ucDjbgUudvcdZqDN7CLgIoBGjRodOmXKlLy+jRs3kpKSEkXoVZ7GKjyNVXgaq/A0VuFprMLTWIWnsQqvPMaqe/fuH7t7x4LtoWZ23T1suUMUjiK4GO0Md38x1pZhZknAXcC1QA0zq+bu2/I9LoWgrncH7j4BmADQsWNHT09Pz+vLyMgg/30pmsYqPI1VeBqr8DRW4WmswtNYhaexCq8ijdVOJbFmlmxm3czsT2ZW18xaxCGmZrGf/ynQ/i5QC3CCHdxaFuhvBXwTh3hEREREpJIKneya2TBgBTCboIa3JfCwmb0T8fq2C2I/jyrQfjiQBfwT2EKw/m5ubHWBbsDMCOMQERERkUouVBmDmQ0h2EjiJuANYF6s636C3dRGA5dGEZC7f2xmrxMk0vUIanbTgWuA+919qZk9CIyO1RIvAK4jWKrs8ShiEBEREZGqIexqDFcAN7n7aDPLuxDN3WeY2bXAKCJKdmNOJ0igryNYW3chwS5uj8b6rwVyCDaXSAHmAoPcvdCaXRERERHZNYVNdvdkxxraXN8D9aMJJ+Dum4FhsVth/VnA8NhNRERERKRQYWt2FwInFdHXM9YvIiIiIlKhhJ3ZvR2YZGa7AdMJVkQ4zMz6E8y+/iVO8YmIiIiIlFjYdXYnm1l14FbgnFjzeGA1MMzdn4pPeCIiIiIiJRd2Zhd3n2hmTwNtCWp01wFfu3t2vIITERERESmNUDW7ZjbLzNp54Bt3n+vu/3P3bDM7yMzmxztQEREREZGdVeTMrpn1zdefDvQ1s/0KObQX0Dr60ERERERESqe4MoYeBGvbQnBB2h3FHFtcn4iIiIhIuSgu2f07MBYwgrV0+wOfFjgmG1jn7hviE56IiIiISMkVmey6eyawGMDMWgLL3X1bWQUmIiIiIlJaoS5Qc/fFQFMze9zMfjCzzWZ2iJnda2YXxDlGEREREZESCbsaw8EEJQxdgFeB6rldwKNmdk5RjxURERERKS9htwseC7wP7AdcSZDk4i60io8AACAASURBVO5DCTaXGBaX6ERERERESiFssns48KC75xCszJDfVKBNpFGJiIiIiEQgbLK7HtijiL69Yv0iIiIiIhVK2GT3ReB2M+tOrIQBcDNrC9wIvBSP4ERERERESiNssnsN8AUwE1gba5sOfAmsjPWLiIiIiFQoxW0qkcfdNwE9zew4oDtQD1gHvAu8GqvlFRERERGpUEIlu7ncfQYwI06xiIiIiIhEKlSya2Y1gcsJVmXYrZBD3N17RhmYiIiIiEhphZ3ZfQw4G3gPWB2/cEREREREohM22T0JGOHud8UzGBERERGRKIVdjWEdwWoMIiIiIiKVRthk9zbgBjNrGs9gRERERESiFLaM4WXgSmCxma0ENhXod3dvHWlkIiIiIiKlFDbZfQZoAjwP/By/cEREREREohM22T0KON/dJ8czGBERERGRKIWt2V0G/BbPQEREREREohY22b0ZuNXMOpqZxTMgEREREZGohC1juAxoDnwAuJkVdoFanUgjExEREREppbDJ7muxm4iIiIhIpREq2XX3m+IdiIiIiIhI1MLO7GJmewDDgG5AGrAaeBe4392Xxyc8EREREZGSC3WBmpntDcwHLgKWArOBX4C/Ap/F+kVEREREKpSwM7v3EGwm0cPdV+c2mlkD4E3gTuDU6MMTERERESm5sEuP9QBuyp/oArj7KuBWoHvUgYmIiIiIlFbYZHcTkFNEXw47UfsrIiIiIlJWwia7/wZuMLO6+RvNrB5wAzAn6sBEREREREor7Izs1cCHwCIzm01Qv9uIoHxhGzAgPuGJiIiIiJRcqJldd18MdAAeB5oQ1PA2jt0/2N2/iluEIiIiIiIlFLrW1t2XEayzKyIiIiJSKRSZ7JrZlTtxHnf3sRHEk//5ewK3AQcRrOn7FHCzu2ebmQHXAhcDDYD3gEvd/esoYxARERGRyq24md17duI8DkSW7JrZUcD/Ac8BI4BDgVsIVn64CRgJDAeuARYB1wMzzWw/d18XVRwiIiIiUrkVmey6e9iVGuLhDuBNdz83dn+WmdUHupvZvcBVwCh3fwDAzN4BFgPnA/eWQ7wiIiIiUgGVZ0JbKDNrCBwFTMjf7u7D3T0dOAJIAV7J17eWYPmz3mUXqYiIiIhUdEUmu2a23swOjf2+IXa/yFuEMR0IGPCbmb1qZlvM7BczG2VmCUDb2HHfFXjc9/n6RERERESKrdkdA6zI97vHPxwAGsZ+Pk1Qs3sv0I2gLnczQYK+1d0zCzxuA5BWRjGKiIiISCVg7oXnsGZWy903hTqJWQd3/zSSgMz+DDwD/MPdB+drHwcMIqjnvd7dkws87lbgYndvUMg5LwIuAmjUqNGhU6ZMyevbuHEjKSkpUYRe5WmswtNYhaexCk9jFZ7GKjyNVXgaq/DKY6y6d+/+sbt3LNhe3MzuDDM77o8SXjMbAdwI1CxljLk2xn6+UaD9LeBvwK9ADTOr5u7b8vWnAIWuxODuE4jVAHfs2NHT09Pz+jIyMsh/X4qmsQpPYxWexio8jVV4GqvwNFbhaazCq0hjVdwFaocCb5pZoWm5me1lZnOAW4HPIozp29jP6gXaq8V+biOo6W1ZoL8V8E2EcYiIiIhIJVdcsns8wYYOb5pZav6OWKnBZ8DhwHVA5whj+hJYBpxeoL0PsByYAmwB+uWLpy5BXe/MCOMQERERkUquuHV255jZMQSbO7xlZscSJMePAGcAnwCD3P1/UQbk7jlmdi0w0czGA1OBXgT1un919/Vm9iAw2sxygAUECfd64PEoYxERERGRyq24ml3c/QMz6wHMAP4N1AMaEexgdru7Z8cjKHd/2sy2EWwJfB6wBPhLrPaWWHsOweYSKcBcgsRbu6eJiIiISJ5ik10Ad59vZunA2wSJbk93nxPvwNx9MjC5iL4sgu2Ch8c7DhERERGpvELtoObuXwFdCGZY7zWzenGNSkREREQkAkXO7JrZA4U0zwdOBt4xs/wXg7m7Xx51cCIiIiIipVFcGcNJRbQvBmoV6HdAya6IiIiIVCjFrcZQcB1bEREREZFKpciaXTNrXZITmtneJQ9HRERERCQ6xV2gNt3M7jezPcOcyMxam9nDwPRoQhMRERERKZ3ikt0OBNvyfm9mc8zscjM72sxamNnuZtbGzLqb2bVmlkGw85kRbDMsIiIiIlLuiqvZ3QRcZmZjgSuAEcDuBBej5TKCLXxfAga7+/dxjFWkUnj//feZNGkSNWrUoHPnKHfSFhERkZ0VZlOJHwhWWrjczPYDWgB1gNXAktgavCJCkOj27NmTrVu3MmnSJGbOnKmEV0REpBz9YbKbn7t/SVCuICKFyMjIIDMzk5ycHDIzM8nIyFCyKyIiUo5C7aAmIuGkp6dTvXp1EhISqF69Ounp6eUdkoiIyC5Nya5IhDp37szMmTMZPHiwShhEREQqgJ0qYxCJp/fff5+MjAzS09MrdZLYuXNntm7dWqlfg4iIbE8XH1deSnalQsi9sCszM5Pq1atrVlQiU1W+ROkfWpHyo4uPK7dQZQxmNs/MhphZw3gHJLum3Au7srOz8y7sEimt3H+gbrjhBnr27Mn7779f3iGVSO7rePLJJyv164Dgtdx+++2V+jXIrqewi4+l8ghbszsfuAlYamavmtnpZlYjjnHJLib3wq7ExERd2FVBVIWkpKp8iaoq/9BWlS8fUDU+H/D7/xhU9tcRb7r4uHILVcbg7heZ2d+APsAAYCKQaWZTgWfcfU4cY5RdQO6FXVXhv5urgqpSVpL7D1Tu66is/0Dlvo6tW7dW6tdR2JePyvi+qiqfj7L6r/mqUEqU+2/Uk08+yeDBgyvt69hVha7ZdfdtBDulvWRmqcCJwF+AWWa2FHgKmODuy+IRqBStKvxFAsFfJpU5/qqkqiQlVeVLVFX5h7aqfPmoKp+PslgXvKp8MQBdfLwzKto1Bubuf3xU/geYNQf+BJwGHAp8DbwBHAu0BM539ykRxxmZjk2a+EcXXZR3f9GiRbRo0aL8AiqlJUuW8PTTT5OdnU1iYiIDBw6kWbNmcXmuyj5WZamyj5XeVxVTvMdqyZIlec8Rrz/vsngOiO9YleXnI55yX0dWVhZJSUlxeR3vvPMOs2fPJsedBDO6d+/O0UcfHelzlKWq8BmMt7J4XxXFbrrpY3fvWLA91Mxu7MK0M4CzgSOAtcAU4G/uPi/fcS8D98f6pAwsWrSI7OxsctwhO5tFixbF5U21ZMkSPv/8cxITEyvtB1DCa9asGQMHDiyTxEfvq4qhrBK4Zs2aVfo/67L8fMTzOXJfx6effkqHDh3i8hwtWrQgMTERYu8rfbEtWll9BuP9vsrNSxzIjmNesjPCljEsB3KA6QQzuq/FyhoK+gRoFVFsEkJZ/EWS/1vaf//730o7iyE7J95Jid5XFUtZfXGuKsrq81EWXz6ys7Pj9lrK6otBVVAWn8GyeF/l5iWelVVhvuCETXaHApPdfXVxB7n7TQSrNkgZKYu/SCritzSp/PS+qlg0A1exVKUvH1VhNr8slMVnsCzeV2XxPwY7zd3/8AbMAtoV0XcQMD/MeSrC7dBDD/X8Zs+e7VK8uXPnenJysickJHhycrLPnTu3vEOq8PS++mN6X+28eL+v5s6d67fddluV+LOo7J/B3M9HYmJi3D8flX2s3MvuvVvZP4NV/X0FfOSF5H5FzuyaWV9+n/lNB/qa2X6FHNoLaB1h/i0VTFW5ElwqFr2vKh6tiFJxVJWVRMpCVVvxIZ6x76rvq+LKGHoAl8V+d+COYo4trm+XVpWWBdOSKxWH3lciRatoyx6VlL58hFNVloIrK7vi+6q4ZPfvwFjAgO+B/sCnBY7JBta5+4b4hFe5VaVvm1Jx6H0lUrSy2ihBKo6qsn6zxE+R2wW7e6a7L3b3RQTr574eu5//tlSJbtGqylalVUlV2OJT7yuRolWVrZUlvNz/mr/lllv05UYKVVzN7gPAPe7+IzAs1lbU4e7ul0cfXuWmb5sVS1WZEdX7quKpKmUlVUFV2VpZds6u+F/zEl5xZQwnAU8APwJ9Cep2i+KAkt0CdtVC8IqqqtR16X1VsVSVL1FVhS58FJGCikx23b1lvt9blEk0VZC+bVYcVWlGVO+riqOqfImqSnTho4jkV2TNbkFmdqaZPZjvfmcze9fMToxPaCLRUl2XxEPul6jExMRK/yVKRKQqCrWDmpldAEwAJuVrXgUsA14yszPdfVoc4hOJlGZEJWoqKxERqdjCbhc8DLjF3W/MbXD3hcCZZnYzMBJQsisiuyR9iRIRqbjCljE0B+YU0TcHaBNNOCIiIiIi0Qmb7H4P9C6iryewJJpwRERERESiE7aM4QFgvJntBrwG/AI0BE4EBgOXxic8EREREZGSC5XsuvsEM0sBRgAX5OtaA1zj7o/EIzgRERERkdIIO7OLu99rZmOBfYB6wDrga3fPjldwIiIiIiKlETrZjdkf6AqkAauBHOCrqIMSEREREYlC2HV2k4AngQGAAVuAmoCb2QvAnzXDKyIiIiIVTdjVGEYCpwF/Beq4ey2gLnAJcBJwfTyCM7MaZvaVmT2Vr83M7Doz+9HMNpnZW2bWLh7PLyIiIiKVW9hk91xgpLtPcPcNAO6+zt0fBUYBg+ITHjcCBRPZkQTJ9T3An4A6wEwzqxOnGERERESkkgqb7NYD5hfR9xnQOJpwfmdmHYDLCLYlzm1LBa4CRrn7A+7+CnAckAqcH3UMIiIiIlK5hU12vwROLqLvZOC7aMIJ5KsRvhtYlq/rCCAFeCW3wd3XEuziVtSmFyIiIiKyiwq7GsPtwDQzqwtMBX4GGgGnE5QSRD2reg1QPfa8p+Rrbxv7WTC5/p6ik3ERERER2UWF3VTiX2b2F+AW4GzACVZlWAVc5u5PRRVQ7GKz64Ce7p5pZvm704Ct7p5Z4GEbYn0iIiIiInnM3cMfHGSe+xKsxLAG+MbdcyILxiwBeAf4xN0vjbXNB+a7+7lmdi1wg7snF3jcrcDF7t6giPNeBFwE0KhRo0OnTJmS17dx40ZSUlKieglVmsYqPI1VeBqr8DRW4WmswtNYhaexCq88xqp79+4fu3vHgu1FzuyaWb0iun6K3QB2y515dfc1pQ0SuBRoDpwYq9vNF44lEezaVsPMqrn7tnz9KbG+Qrn7BGACQMeOHT09PT2vLyMjg/z3pWgaq/A0VuFprMLTWIWnsQpPYxWexiq8ijRWxZUxrCIoVwgrsZSxQFCfuyfBrHF+7YGBwMUE5RMtgQX5+lsB30Tw/CIiIiJShRSX7A5m55LdKFxMsIxYfpMIEtubYj/vB/oBdwHELprrFusXEREREclTZLIb5UVnYbn7DrOzZrYZWO3uH8XuPwiMNrMcguT3OmA98HhZxioiIiIiFV/Ypccws5bEVkkA9gCOAv4MfOnuZZloXgvkEGwukQLMBQa5e5E1uyIiIiKyawqV7JrZwUAGwYVprwJ/y+0CHjWzre7+TDwCdPeDC9zPAobHbiIiIiIiRQq7g9pY4H1gP+BKgiQXdx8KjAeGxSU6EREREZFSCJvsHg48GFtTt+BFa1OBNpFGJSIiIiISgbDJ7nqCOt3C7BXrFxERERGpUMImuy8Ct5tZd2IlDICbWVvgRuCleAQnIiIiIlIaYZPda4AvgJnA2ljbdOBLYGWsX0RERESkQgm1GoO7bwJ6mtlxQDpQn2B73neBV2O1vCIiIiIiFUqRya6ZjQCedvdluW3uPgOYURaBiYiIiIiUVnFlDKOAxWb2ppmdZWY1yygmEREREZFIFJfsNgaGADWBZ4GfzGyCmR1ZJpGJiIiIiJRSkcmuu69x90fcvSvQErgTOAJ418wWmtl1ZrZXWQUqIiIiIrKzQq3G4O4/uvvt7n4Q0AH4J3AR8L2ZzTSzP8czSBERERGRkgi79Fged//M3a9x9+ZAH6ApMDHyyERERERESinU0mP5mVldoD9wJtANWAWMiTguEREREZFSC5Xsmlkq0I8gwe0F5AAvAycDb2qdXRERERGpiIpbZ7cW0Jcgwe0N1ADeI1ih4QV3X18mEYqIiIiIlFBxM7srCZYdW0SwEsPT7v59WQQlIiIiIhKF4pLdycBEd3+nrIIREREREYlSkcmuu19QloGIiIiIiERtp5ceExERERGpLJTsioiIiEiVpWRXRERERKosJbsiIiIiUmWFSnYtcKGZ9Yndb2dm/zOzDWb2VGxNXhERERGRCiXszO51wHhgn9j9yUBt4G7gOOD26EMTERERESmdsMnuucB17n6vme0PtAducvebgWuA0+MUn4iIiIhIiYVNdvcE5sZ+PxHIAV6N3f8RqBNxXCIiIiIipRY22V0K7Bf7/TTgI3dfFbt/DMGWwiIiIiIiFUrYZHcCcJ+ZfQkcCjwEYGYvAsNz74uIiIiIVCRFbhecn7vfbWY/AkcDo939uVjXr8Agd382XgGKiIiIiJRUqGQXwN2fB54v0HZh5BGJiIiIiEQkVLJrZiP/6JjYygwiIiIiIhVG2JndoYW01Y49/lfgW0DJroiIiIhUKGFrdusW1m5mnYGJwK1RBiUiIiIiEoWwqzEUyt3fB25EO6iJiIiISAVUqmQ3Zh3QMoLziIiIiIhEKuwFaocU0pwANAFuAT6PMigRERERkSiEvUDtI8ALaTdgGXB6ZBGJiIiIiEQkbLLbvZA2B9YDn7t7TnQhiYiIiIhEI+xqDHNyfzez2kAqsMbdM+MVmIiIiIhIaYW+QM3MjjGzDwlmc5cBm81snpn1jlt0IiIiIiKlECrZNbNjgOnANoINJs4GhgHZwGuxfhERERGRCiXszO5o4F/ufqS7P+Duz7v7fe7eGZhGsNZuZMws0cyuNLOvzOw3M/vSzIaYmcX6zcyuM7MfzWyTmb1lZu2ijEFEREREKr+wye6BwBNF9D0JHBxNOHluAG4DngX6Ai8A9wFXx/pHAtcD9wB/AuoAM82sTsRxiIiIiEglFnY1hp+AZkX07QX8Fk04YGYJwJXA3e6euw3xTDNrCFxlZuOBq4BR7v5A7DHvAIuB84F7o4pFRERERCq3sDO704DbzKxX/sZYre5o4J8RxlQHeLqQc34DNAR6ACnAK7kd7r4WmAPoYjkRERERyRN2ZncU0Bl408zWAz8DjQiWIJsHXBNVQLHEdUghXScBS4GmsfvfFej/Hjg5qjhEREREpPILu87ub2Z2NHAicDRQF1gDvAu8Hu9NJczsAqAXcBmQBmwtZI3fDbE+EREREREAzL2wXYCLeYBZc6Ax8AWAu2+MQ1z5n28AMBH4F3AGMAK4wd2TCxx3K3Cxuzco5BwXARcBNGrU6NApU6bk9W3cuJGUlJT4vYAqRGMVnsYqPI1VeBqr8DRW4WmswtNYhVceY9W9e/eP3b1jwfawZQyY2anAHUArgq2COwE3mtkG4Dx33xZVsPmecygwhqA+d4C7u5mtA2qYWbUCz5kCrCvsPO4+AZgA0LFjR09PT8/ry8jIIP99KZrGKjyNVXgaq/A0VuFprMLTWIWnsQqvIo1V2E0lziBY/msOcGa+x/0LOIVgKbBImdltBCsrPAOclq9sYSFgQMsCD2lFcBGbiIiIiAgQfjWGkcD97n4BQYILgLs/RbDe7YAogzKzywnKFe4HznX3rHzdc4EtQL98x9cFugEzo4xDRERERCq3sGUMewNXFNH3KUENbyTMrDFwJ/BfYApweGzjtFwfAQ8Co80sB1gAXAesBx6PKg4RERERqfzCJrs/Al2Atwvp6wQsiSwiOA6oQbBr2/uF9DcErgVyCDaXSCGY7R3k7oXW7IqIiIjIrilssjsOuMeCKdbpBBeo7WlmhxDMqt4SVUCx0oinQhw6PHYTERERESlU2HV2H4jVxV5DUKNrwMvANuABd78nfiGKiIiIiJRM6KXH3P0mM7uPYCe1egTLfH3g7qviFZyIiIiISGmETnYBYjWxb8QpFhERERGRSIVKds2sNkH5wglAbXZcsszdvXXEsYmIiIiIlErYmd2HgLOA14ClBCshiIiIiIhUaGGT3VOAYe4+Lp7BiIiIiIhEKewOalnA1/EMREREREQkamGT3eeBwfEMREREREQkamHLGH4ArjWzz4F5wKYC/e7ul0camYiIiIhIKYVNdi8BfgVSgZ6F9DugZFdEREREKpSwO6i1jHcgIiIiIiJRC1uzWywz6xTFeUREREREohR2U4mmwFigG1ADsNwuoCZB0pwYjwBFREREREoq7Mzu/cAxwHPAQuAzYDzwLUHCe1pcohMRERERKYWwyW53YLi7XwE8CWS6+zXAocDbBJtOiIiIiIhUKGGT3VrA/2K/fwV0AHD3HOBhgvIGEREREZEKJWyyuxhoFfv9a2A3M8tdoWET0CDqwERERERESitssjsFGGNmg9x9BfBf4F4zSweuBb6JU3wiIiIiIiUWdlOJW4D6QG9gIvBX4FXgZGADcGpcohMRERERKYWwm0pkAUPy3Z8bK2NoB3zt7uvjFJ+IiIiISImFKmMws1lm1i5/m7uvd/d5QAszmx+X6ERERERESqHImV0z65uvPx3oa2b7FXJoL6B19KGJiIiIiJROcWUMPYDLYr87cEcxxxbXJyIiIiJSLopLdv9OsEWwAd8D/YFPCxyTDaxz9w3xCU9EREREpOSKTHbdPZNgfV1iF6Mtd/dtZRWYiIiIiEhphV2NYbGZtTOz44Ha7Hhhm7v7LZFHJyIiIiJSCqGSXTM7H5gQu7sRyClwiBOsxSsiIiIiUmGE3VTiWuBfwPnuvi6O8YiIiIiIRCZsstsEJboiIiIiUsmE2lQC+BhoH89ARERERESiFnZmdzjwnJklAR8Amwoe4O6fRBmYiIiIiEhphU12/x37eTfBxWj5WawtMaqgRERERESiEDbZ7R7XKERERERE4iDsOrtz4h2IiIiIiEjUws7sYmZ9gG5ADYLSBWI/awFHuPv+0YcnIiIiIlJyYTeVuB64GfgVqAZsi90aEmww8US8AhQRERERKamwS4+dDzwJ1AfuBaa7eyOgI/AL8FV8whMRERERKbmwyW4TYLK7O/AJcCTkLTd2M0EyLCIiIiJSoYRNdtfxe8nDAqC5maXG7n8JtIg4LhERERGRUgub7M4BrjazesBCYD3wp1hfN4JkWERERESkQgmb7F4P7Af8y92zCDaXeMTMFgGjgGfiEt0fMLMLzWyhmW02s/fNrHN5xCEiIiIiFVPYdXa/MbM2wD6x+7eZ2VLgCOBDd/9HHGMslJkNBB4hqBn+ELgUmGFm7d39h7KOR0REREQqnlAzu7HEsmbsgjQA3P1pd78E+D8zuypeARYRjxEkuRPc/SZ3nw70BVYBQ8syFhERERGpuMKWMfwDaFVEXydgdDThhLY30Bx4JbfB3bcBrwO9yzgWEREREamgiixjMLOZwGG5d4HZZpZTyKG1gI/jEFtx2sZ+flug/XugtZklunt2GcckIiIiIhVMcTW7lwKnEyS6I4HJwNICx2QT7Ko2JS7RFS0t9nNDgfYNBLPVtQlWjBARERGRXViRya67fwncBGBmDjzu7svKKrA/YLGfXkT7djPQZnYR/H97dx8sSVXecfz740WDvAiKiIjCLgYhZVYJGBYIRCMC4UU28qYh6mKUSiKCiEAJBlZXDVQQAQEtizIIRlEIRgILli7IAoElC7pbopCFCAuoy8u67LsL4ckf50zo2ztzb0/fl5k7/ftUTc2d06d7Tj/33Oee6ek+zYn55SpJDxUWb0s619dG5lhV51hV51hV51hV51hV51hV51hV14tY7dSusOpsDJ+VtLWk10fEk5I2IV0I9kbg+oi4bQwbWkVrXt8tgaWF8i1IA93VxcoR8XXg6+02JGlBROw1Ho0cNI5VdY5VdY5VdY5VdY5VdY5VdY5Vdf0Uq6qzMRwALAFOzkVfAc4DDgN+LOnY8WleR4vzc/miuanAQ/m2xmZmZmbWcFVnY/g88J/AhZK2AT4MXBARU4ELgbPGqX2dLAYeB2a0CiRtShp8z53gtpiZmZlZn6p0GgOwJ/CeiFgq6fi83r/mZTcCJ41H4zqJiJB0HnCppN8Bd+U2bAt8ucvNtT29wdpyrKpzrKpzrKpzrKpzrKpzrKpzrKrrm1ipyjf+kp4GPhQRcyR9GzggInbMy/4GOD8iXj++TW3brtOAU0iD3J8Bp0XE3RPdDjMzMzPrT1UHu98jnQ97LTAbuDQiPilpBnAxcGtEnDCuLTUzMzMz61LVc3Y/DjwN/CPwE9KteiENdBcDp495y2qQ9FFJiyWtlXS3pH1GqP8WSXMlrZK0RNKZ+VbExTr7S5ovaU3e9ofHdy8mRo1Y7SvpNknLJf1a0lWSXluq83NJUXpM+ilaasTqxjZxCElbFOo0vl9JerRDnELSuYV6A9mvWiS9R1J5zvB29Rqbr1q6iFVj81VLF7FqbL5qqRKrJucrSRtL+qSkX0paLekXkk4q55/SOv2VryKi9gN49WjWH8sH8EHSTS7OBQ4FbibdWGJKh/rbAb8FfpzrfwZ4AfhUoc7upGnMriHdhvhC0ty+R/d6fyc4VrsDa0m3Z/5L4K+BR0injmya67wMWA+cCUwvPPbs9f5OZKzyOkuAi0pxmA5s5H41pP4ebWL0PdLNYXYb5H5ViMG+OUarRqjX2HxVI1aNzVfdxirXbWS+qtGvGpuvgFnAOuBs4F359QvAGR3q912+6naHtwF2JM2vO+TR41+EgEeBrxbKNiXdPviSDut8ljTZ8SsKZbOBZwsJ8ZvAA+TTPXLZ1cCiXne+CY7VZXn5poWyt+eOeWh+/bb8erde72OPY7V1jsMhw2zX/ar9NvYCngdOKJQNXL/K+/Vy4Azg98AyRv5H28h8VTNWjcxXNWPVyHxVJ1Zt1m9EviKdAbACmF0qvwx4qsM6fZevqs6zu5uku3PjHwN+VXg8mp976U2kix6akQAACkZJREFUu2bc0CqIiOeBm0ifGNo5EJgbEWsKZf8OvIqUGFt1boz8WyjU+WNJO4xR2ydanVg9AHwp12tp3YVuSn6eRvrkt5jBUSdW0/LzomG2637V3iXAfwFXFsoGsV9BOuL4adIpYF+pUL+p+Qq6j1VT8xV0H6um5ivoPlZlTclXrwSuAq4vlT8EvEbS5m3W6bt8VfWc3ctJR3Q/ARwNvLfw+Kv83Eu75ueHS+X/A+wiaeMO67SrD7Br/gXuMFydmm3tta5jFRGXR8RlpeIj8vOD+Xka6VPbdyWtkPScpCskbTlWDe+BOv1qGulIweclPZvPRbpW0vYA7lftSToS2Ic0o0ox+Q1iv4L0T3JKRFzChrc9b6ep+Qq6jFWD8xV036+amq+g+1j9vyblq4j4XUScFBE/LS06AngiIla3Wa3v8lXVeXanA8dHxPfHugFjZKv8XD7BfCVpQL856TB8eZ129VvLhttm8T0nmzqxGkLSG4ALgAXArbl4GrA9sJB04eLbSBcyTiGd4zMZ1YnVNNLXYytJHwSnkm7KcqukPUbYZvE9J5vR9qtTgTtjw6kDB7FfERFPdrlKU/NVnVgN0aB8VSdWTc1Xo+1XjcpXZZI+Qjoye3KHKn2Xr6oOdp8inVzcr1pX+JU/nbXKX+ywTqdPcy/W3OZkMKr9yv845pIGMO8rfKo9E3h5RNyTX98h6SngGkn7R8Qdo2/6hKsTqwuB70TEbfn1PEm/BO4BjuWlO/y5X7UqSG8G/hw4ps3iQexXdTQ1X41Kw/JVHU3NV7U1PV8p3Vjsa8B1wKWdqtFn+arqaQwXAudK2m6sGzBGnsvP5a8KtiAFrd1h9ufa1N+ysGxFqay4zeJ7TjZ1YgWkqURIt43eCnh3RDzSWhYRPy38gbfckp/fOqoW907XsYqIBwv/OFpl84HlpDi4X23oSGAV6W6MQwxov6qjqfmqtgbmq641OF+NRmPzlaRTSReR3Uj6tr/TgLbv8lXVwe7+wC7Ak5IelrSo9Fg41g3rUutk8Kml8qnAQx1+IYs71Cevswr4zTB1/rtmW3utTqyQtDcwjzS11P4RsaiwbBNJM/PXXkWb5efJOsdg17GS9D5JB5TKRPqq8Bn3q7YOAW6OiHXFwgHuV3U0NV/V0tB81bUG56vRaGS+kvRF0oHPq0nTg60fpnrf5auqg91VpKvkvgXcAdxXetw/1g3r0mLgcWBGq0DSpsBhvPQ1TNlc4MDSlYQzSCeX/6xQ54jSxTUzgJ9HxNIxavtE6zpWknYmzZm6FNg3IoZcaRoRL5CmGplVWvUo0tQsk/UWznX61d8DF0sq/m0dSkp48/Jr96uX6og0hU/5aMgg96s6mpqvutbgfFVHU/NVLU3NV5JOIc1ccTEwM+/rcPovX43HfGa9eAD/QPq69AukP9Y5pEPlU/PyXYDphfqvI31VcztwOGmy5PKkx28lTRB9PWmaki+RzjE5ptf7O8Gx+kGOzfvZcFLt1+U6J+bYXEw6cf3TpIndL+j1/k5wrA7O9b8NvBv4GGkOx+vcr4bGKpftnPf9sA7bHMh+VdrHWZTm+HS+GlWsGpuvasSqsfmq21jlssblq5x71pGmpyv/PU0nXfvV9/mq54Ec41/KaaS7wawhnau1T2HZlUCU6u8F3JV/kY8BZ7bZ5sGkTyLrSIfWZ/Z6PycyVqQbAzyfO2G7R7Hzzsx/EGtJcy+fRb4Lz2R+1OhXhwP3ks5T/TXpSvDN3K/axupPcz/ab5htDmS/KuzfLDb8R+t8VSNWzle1+lVj81WNWDUuX+X96fT3FMC2kyFfKb/hBpTuEz3ceXZDRMSknYLEzMzMzAbTcFOPtQ4pm5mZmZlNSh2P7JqZmZmZTXZVZ2MwMzMzM5t0PNg1MzMzs4Hlwa6ZmZmZDSwPds3MzMxsYHmwa2Y2AklXSooRHrMk7Zx/PrqHbb1A0rn555m5Pdt2qPuopEsntoVt2yFJ8yW9o9dtMbPBM9zUY2ZmlswGvlZ4fRXpFsmzC2VPAE8D+zAO93avQtLbSXcO27UX719XRISkM4ArJE2LiLW9bpOZDQ4Pds3MRhARjwCPtF5LWgM8HRH3tKnermyinA9cHhGre9iGWiLidknLgL8Dvtzr9pjZ4PBpDGZmY6R8GkM+/eE6SZ+S9ISk1ZKulbSVpHMkLZX0jKRLJG1U2M52kq6StEzSKkk3SJoywnvvAbwTuGYU7d9C0j9L+pWktZLulXRQYfk78v7tVVpvuaRZ+eeZeZ9Oz88PSXqFpL0lzZO0Mu/XtZJ2KjXhu8ApknwgxszGjAe7Zmbj6yDgvcBHgdPzzwuA6cCHgG8CHweOA5C0GXAb8Ge5/APA9sA8SdsM8z7vBxblo9BlG0vapPwoVsiD7VuAE4DzcjuXAHMkHdzlPm+dt3M8cHYumwM8CRxJisWfsOHA/N+AnUingpiZjQl/ejYzG19bAEdFxG8AJH0A+CNgz4hYCdwi6Vhgb+A7wAeBNwNviYgH8zpzgcdIg9/PdXifdwL3d1j22wrtPAzYDzgkIn6Yy26WdDfwReCHHdfc0MbAOa3t5HOJXwVcEhF357JngL+QtFFEvAgQEY9Jejbvyx1dvJ+ZWUce7JqZja/HWwPdbCmwcR7otjxLOhoKaaC3GHi4cPR1DWnw9y46D3Z3Bm7usOxA4Lk25TcUfj4AWFkY6LZcA1wkacsO2+7kF4WfHwSWAf8h6RrgJuDWiLi9zXpLSPtiZjYmPNg1MxtfK9uUrRmm/quB3YDn2yxbPMx6rxxmuwsj4plyoaT1hZfbkAbiZa2ybge7T7V+iIiVkg4AziGduvExYLmksyLiq6X11pD2xcxsTHiwa2bWX54DFgIfabPs98Os9yyjGyQuA17bpnz7wvLIPxcvphOw+Ugbj4gHgOMkvQzYHzgFuFzS/RExv1B1G4YeFTYzGxVfoGZm1l/uBKYAj0bEgohYANwHnAocPsx6jwM7jvJ9t2xzMdpxwH0RsQ5Ykct2KCyfzggHTiQdIukpSa+JiPURMZd0/jHAGwv1lLe9ZBT7YWY2hI/smpn1l28AJwM/kvRPpCOqJwJHAUcMs95c4JhRvO9NwHzgW5LOJg04TyBdONd630WkGRVmS3oe2Ip0DnG784GL7gUEXC/pfGA98AlgOWnmiZbdSOcu/2gU+2FmNoSP7JqZ9ZGIWEG6WOxB0l3bfkCajuvIiJgzzKrXA7tI2qXm+/4vcEjezhfy8xuAQyPipkKdY4F1efm5wBnAwyNse1ne9jrgauD7wB8AB5bOJT6IdCe6e+vsg5lZO4qIkWuZmVnfk/QT4M6I+Eyv21KHpIXAv0TERb1ui5kNDg92zcwGhKT9SDdm+MPS1GZ9T9KBwBXA7hGxttftMbPB4dMYzMwGRETcRboxxem9bks38oVp5wF/64GumY01H9k1MzMzs4HlI7tmZmZmNrA82DUzMzOzgeXBrpmZmZkNLA92zczMzGxgebBrZmZmZgPLg10zMzMzG1j/B7VMYpqB2k75AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute an array of velocities as the slope between each point\n",
    "diff_distances = np.diff(distances)\n",
    "diff_times = np.diff(times)\n",
    "velocities = diff_distances / diff_times\n",
    "\n",
    "# Characterize the center and spread of the velocities\n",
    "v_avg = np.mean(velocities)\n",
    "v_max = np.max(velocities)\n",
    "v_min = np.min(velocities)\n",
    "v_range = v_max - v_min\n",
    "\n",
    "# Plot the distribution of velocities\n",
    "fig = plot_velocity_timeseries(times[1:], velocities)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Intercept and Starting Points\n",
    "In this exercise, you will see the intercept and slope parameters in the context of modeling measurements taken of the volume of a solution contained in a large glass jug. The solution is composed of water, grains, sugars, and yeast. The total mass of both the solution and the glass container was also recorded, but the empty container mass was not noted.\n",
    "\n",
    "Your job is to use the preloaded pandas DataFrame ```df```, with data columns ```volumes``` and ```masses```, to build a linear model that relates the ```masses``` (y-data) to the ```volumes``` (x-data). The slope will be an estimate of the density (change in mass / change in volume) of the solution, and the intercept will be an estimate of the empty container weight (mass when volume=0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('./dataset/linear_data.csv', index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "container_mass   = 5.4349\n",
      "solution_density = 1.1029\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 masses   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 1.328e+05\n",
      "Date:                Fri, 19 Jun 2020   Prob (F-statistic):          1.19e-156\n",
      "Time:                        17:29:13   Log-Likelihood:                 102.39\n",
      "No. Observations:                 101   AIC:                            -200.8\n",
      "Df Residuals:                      99   BIC:                            -195.5\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      5.4349      0.023    236.805      0.000       5.389       5.480\n",
      "volumes        1.1029      0.003    364.408      0.000       1.097       1.109\n",
      "==============================================================================\n",
      "Omnibus:                        0.319   Durbin-Watson:                   2.072\n",
      "Prob(Omnibus):                  0.852   Jarque-Bera (JB):                0.169\n",
      "Skew:                           0.100   Prob(JB):                        0.919\n",
      "Kurtosis:                       3.019   Cond. No.                         20.0\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.formula.api import ols\n",
    "\n",
    "# Fit a model to the data\n",
    "model_fit = ols(formula=\"masses ~ volumes\", data=df)\n",
    "model_fit = model_fit.fit()\n",
    "\n",
    "# Extract the model parameter values, and assign them to a0, a1\n",
    "a0 = model_fit.params['Intercept']\n",
    "a1 = model_fit.params['volumes']\n",
    "\n",
    "# Print model parameter values with meaningful names, and compare to summary()\n",
    "print( \"container_mass   = {:0.4f}\".format(a0) )\n",
    "print( \"solution_density = {:0.4f}\".format(a1) )\n",
    "print( model_fit.summary() )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Optimization\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Residual Sum of the Squares\n",
    "In a previous exercise, we saw that the altitude along a hiking trail was roughly fit by a linear model, and we introduced the concept of differences between the model and the data as a measure of model goodness.\n",
    "\n",
    "In this exercise, you'll work with the same measured data, and quantifying how well a model fits it by computing the sum of the square of the \"differences\", also called \"residuals\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_data():\n",
    "    num_pts=21;a0=3.0*50;a1=0.5*50;mu=0;sigma=1;ae=0.5*50;seed=1234;\n",
    "    np.random.seed(seed)\n",
    "    xmin = 0\n",
    "    xmax = 10\n",
    "    x1 = np.linspace(xmin, xmax, num_pts)\n",
    "    e1 = np.array([np.random.normal(mu, sigma) for n in range(num_pts)])\n",
    "    y1 = a0 + (a1*x1) + ae*e1\n",
    "    return x1, y1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(x, a0=150, a1=25):\n",
    "    \"\"\"\n",
    "    Purpose: \n",
    "        For a given measured data x, compute the model prediction for y\n",
    "        The form of the model is y = a0 + a1*x\n",
    "    Args:\n",
    "        x (float, np.ndarray): independent variable, e.g. time\n",
    "        a0 (float): default=150, coefficient for the Zeroth order term in the model, i.e. a0\n",
    "        a1 (float): default=25, coefficient for the 1st order term in the model, i.e. a1*x\n",
    "    Returns:\n",
    "        y (float, np.ndarray): model values predicted for corresponding input x.\n",
    "    \"\"\"\n",
    "    y = a0 + (a1*x)\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RSS = 14444.484117694472\n"
     ]
    }
   ],
   "source": [
    "# Load the data\n",
    "x_data, y_data = load_data()\n",
    "\n",
    "# Model the data with specified values for parameters a0, a1\n",
    "y_model = model(x_data, a0=150, a1=25)\n",
    "\n",
    "# Compute the RSS value for this parameterization of the model\n",
    "rss = np.sum(np.square(y_data - y_model))\n",
    "print(\"RSS = {}\".format(rss))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Minimizing the Residuals\n",
    "In this exercise, you will complete a function to visually compare model and data, and compute and print the RSS. You will call it more than once to see how RSS changes when you change values for a0 and a1. We'll see that the values for the parameters we found earlier are the ones needed to minimize the RSS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data_with_model_and_title(xd, yd, ym, title):\n",
    "    fig = plot_data(xd, yd)\n",
    "    fig.axes[0].plot(xd, ym, color=\"red\")\n",
    "    fig.axes[0].set_title(title)\n",
    "    plt.show()\n",
    "    return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters a0=150, a1=25 yield RSS=14444.48\n"
     ]
    }
   ],
   "source": [
    "# Complete function to load data, build model, compute RSS, and plot\n",
    "def compute_rss_and_plot_fit(a0, a1):\n",
    "    xd, yd = load_data()\n",
    "    ym = model(xd, a0, a1)\n",
    "    residuals = ym - yd\n",
    "    rss = np.sum(np.square(residuals))\n",
    "    summary = \"Parameters a0={}, a1={} yield RSS={:0.2f}\".format(a0, a1, rss)\n",
    "    fig = plot_data_with_model_and_title(xd, yd, ym, summary)\n",
    "    return rss, summary\n",
    "\n",
    "# Chose model parameter values and pass them into RSS function\n",
    "rss, summary = compute_rss_and_plot_fit(a0=150, a1=25)\n",
    "print(summary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing the RSS Minima\n",
    "In this exercise you will compute and visualize how RSS varies for different values of model parameters. Start by holding the intercept constant, but vary the slope: and for each slope value, you'll compute the model values, and the resulting RSS. Once you have an array of RSS values, you will determine minimal RSS value, in code, and from that minimum, determine the slope that resulted in that minimal RSS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_rss(yd, ym):\n",
    "    rss = np.sum(np.square(yd - ym))\n",
    "    return rss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_rss_vs_a1(a1_array, rss_array):\n",
    "    \"\"\"\n",
    "    Purpose:\n",
    "        Plot RSS values (y-axis) versus a1 parameters values (x-axis)\n",
    "        Also plot a point where the minimum RSS value occurs, and the \n",
    "        corresponding a1 value whose model resulted in that minimum RSS.\n",
    "    Args:\n",
    "        a1_array (np.array): an array of trial values for a1 (model slope)\n",
    "        rss_array (np.array): an array of computed RSS values resulting from the a1_array\n",
    "    Returns:\n",
    "        fig (matplotlib.figure): figure object on which the data is plotted\n",
    "    \"\"\"\n",
    "    from matplotlib.ticker import MultipleLocator\n",
    "    font_options = {'family': 'Arial', 'size': 16}\n",
    "    plt.rc('font', **font_options)\n",
    "    fig, axis = plt.subplots(figsize=(12,4))\n",
    "    min_rss = np.min(rss_array) \n",
    "    best_slope = a1_array[np.where(rss_array==min_rss)]\n",
    "    axis.plot(a1_array, rss_array, marker=\"o\", color='black')\n",
    "    axis.plot(best_slope, min_rss, marker=\"o\", markersize=12, linestyle=\" \", color='red')\n",
    "    axis.xaxis.set_major_locator(MultipleLocator(5.0))\n",
    "    axis.xaxis.set_minor_locator(MultipleLocator(1.0))\n",
    "    axis.grid(True, which=\"major\")\n",
    "    axis.set_ylabel(\"RSS\")\n",
    "    axis.set_xlabel(\"Slope $a_1$\")\n",
    "    axis.set_ylim([0,100000])\n",
    "    axis.set_title(\"Minimum RSS = {:.02f} \\n came from $a_1$={}\".format(min_rss, best_slope[0]))\n",
    "    plt.show()\n",
    "    return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "rss_list = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The minimum RSS = 14411.193019771845, came from a1 = [24.8]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Loop over all trial values in a1_array, computing rss for each\n",
    "a1_array = np.linspace(15, 35, 101)\n",
    "for a1_trial in a1_array:\n",
    "    y_model = model(x_data, a0=150, a1=a1_trial)\n",
    "    rss_value = compute_rss(y_data, y_model)\n",
    "    rss_list.append(rss_value)\n",
    "\n",
    "# Find the minimum RSS and the a1 value from whence it came\n",
    "rss_array = np.array(rss_list)\n",
    "best_rss = np.min(rss_array) \n",
    "best_a1 = a1_array[np.where(rss_array==best_rss)]\n",
    "print('The minimum RSS = {}, came from a1 = {}'.format(best_rss, best_a1))\n",
    "\n",
    "# Plot your rss and a1 values to confirm answer\n",
    "fig = plot_rss_vs_a1(a1_array, rss_array)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Least-Squares Optimization\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Least-Squares with `numpy`\n",
    "The formulae below are the result of working through the calculus discussed in the introduction. In this exercise, we'll trust that the calculus correct, and implement these formulae in code using numpy.\n",
    "\n",
    "$$ a_1 = \\frac{covariance(x, y)}{variance(x)} $$\n",
    "$$ a_0 = mean(y) - a_1 mean(x) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# prepare the means and deviations of the two variables\n",
    "x_mean = np.mean(x_data)\n",
    "y_mean = np.mean(y_data)\n",
    "x_dev = x_data - x_mean\n",
    "y_dev = y_data - y_mean\n",
    "\n",
    "# Complete least-squares formulae to find the optimal a0, a1\n",
    "a1 = np.sum(x_dev * y_dev) / np.sum( np.square(x_dev) )\n",
    "a0 = y_mean - (a1 * x_mean)\n",
    "\n",
    "# Use the those optimal model parameters a0, a1 to build a model\n",
    "y_model = model(x_data, a0, a1)\n",
    "\n",
    "# plot to verify that the resulting y_model best fits the data y\n",
    "fig, rss = compute_rss_and_plot_fit(a0, a1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimization with Scipy\n",
    "It is possible to write a numpy implementation of the analytic solution to find the minimal RSS value. But for more complex models, finding analytic formulae is not possible, and so we turn to other methods.\n",
    "\n",
    "In this exercise you will use ```scipy.optimize``` to employ a more general approach to solve the same optimization problem.\n",
    "\n",
    "In so doing, you will see additional return values from the method that tell answer us \"how good is best\". Here we will use the same measured data and parameters as seen in the last exercise for ease of comparison of the new scipy approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import optimize\n",
    "\n",
    "# Define a model function needed as input to scipy\n",
    "def model_func(x, a0, a1):\n",
    "    return a0 + (a1 * x)\n",
    "\n",
    "# Load the measured data you want to model\n",
    "x_data, y_data = load_data()\n",
    "\n",
    "# call curve_fit, passing in the model function and data; then unpack the results\n",
    "param_opt, param_cov = optimize.curve_fit(model_func, x_data, y_data)\n",
    "a0 = param_opt[0] # a0 is the intercept in y = a0 + a1*x\n",
    "a1 = param_opt[1] # a1 is the slope     in y = a0 + a1*x\n",
    "\n",
    "# test that these parameters result in a model that fits the data\n",
    "fig, rss = compute_rss_and_plot_fit(a0, a1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Least-Squares with `statsmodels`\n",
    "Several python libraries provide convenient abstracted interfaces so that you need not always be so explicit in handling the machinery of optimization of the model.\n",
    "\n",
    "As an example, in this exercise, you will use the statsmodels library in a more high-level, generalized work-flow for building a model using least-squares optimization (minimization of RSS)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.formula.api import ols\n",
    "\n",
    "x_data, y_data = load_data()\n",
    "df = pd.DataFrame(dict(x_column=x_data, y_column=y_data))\n",
    "\n",
    "# Pass data and 'formula' into ols(), use and '.fit()' the model to the data\n",
    "model_fit = ols(formula='y_column ~ x_column', data=df).fit()\n",
    "\n",
    "# Use .predict(df) to get y_model values, then over-plot y_data with y_model\n",
    "y_model = model_fit.predict(df)\n",
    "fig = plot_data_with_model(x_data, y_data, y_model)\n",
    "\n",
    "# Extract the a0, a1 values from model_fit.params\n",
    "a0 = model_fit.params['Intercept']\n",
    "a1 = model_fit.params['x_column']\n",
    "\n",
    "# Visually verify that these parameters a0, a1 give the minimum RSS\n",
    "fig, rss = compute_rss_and_plot_fit(a0, a1)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}