01_intro_AI_on_Supercomputer/01_linear_regression_sgd.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Artificial intelligence in a nutshell\n",
    "\n",
    "In this notebook, we will talk about \n",
    "* What is AI training? \n",
    "* How does large language model work? \n",
    "* A simple AI model: linear regression\n",
    "\n",
    "**How to run this notebook on Polaris**\n",
    "* Go to https://jupyter.alcf.anl.gov, and click \"Login Polaris\"\n",
    "* After login, select ```ALCFAITP``` project and ```ALCFAITP``` queue during the lecture (use ```debug``` queue outside of the lecture)\n",
    "* Load the notebook and select \"datascience/conda-2023-01-10\" python kernel\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/jupyter1.png\" width=\"600\" />\n",
    "  <img src=\"figures/jupyter2.png\" width=\"600\" /> \n",
    "</p>\n",
    "\n",
    "**How to run this notebook on Google Colab**\n",
    "\n",
    "* Go to https://colab.research.google.com/, sign in or sign up\n",
    "* \"File\"-> \"open notebook\"\n",
    "* choose ```01_intro_AI_on_Supercomputer/01_linear_regression_sgd.ipynb``` from the list\n",
    "![Google Colab](figures/colab.png)\n",
    "\n",
    "## What is AI training?\n",
    "**Two ways of learning English** \n",
    "* through learning rules;\n",
    "* through hearing a lot of speakings\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/data_driven.png\" width=\"1000\" /> \n",
    "</p>\n",
    "\n",
    "I learned English in my middle school, and memorized a lot of grammar rules in my mind. Every time when I speak, I try to follow the grammar rules as much as I can. But I always break the rules. \n",
    "\n",
    "However, my daugher learned English differently. She learns speaking by hearing a lot of speaking from TV, teachers, classmates, and her older brother. The fact is that, she seldomly breaks grammar rules. This way of learning by observing patterns is very powerful! This is the essence of AI or data driven science. \n",
    "\n",
    "## How does large language model work? \n",
    "\n",
    "Large Language Models, like GPT, function by pre-training on extensive datasets to learn language patterns, utilizing transformer architecture for contextual understanding, and can be fine-tuned for specific tasks, enabling them to generate coherent and contextually relevant text based on provided inputs.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/llm2.png\" width=\"600\" />\n",
    "  <img src=\"figures/chatgpt_response.png\" width=\"160\" /> \n",
    "</p>\n",
    "\n",
    "**More complicated example**\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/chatgpt_poem.png\" width=\"400\" /> \n",
    "  <img src=\"figures/martin.png\" width=\"450\" /> \n",
    "</p>\n",
    "\n",
    "You can do this on https://chat.openai.com\n",
    "\n",
    "## Simplest AI model example: linear regression\n",
    "This example is adopted from Bethany Lusch, ALCF. \n",
    "\n",
    "Linear regression is the simplest example ``learning\" from existing data for future prediction. \n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/excel_linear_regression.jpg\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "We're going to review the math involved in this process to help understand how training an AI works.\n",
    "\n",
    "First we will load some tools that others wrote and we can use to help us work.\n",
    "* [Pandas](https://pandas.pydata.org/docs/): a toolkit for working with row vs. column data, like excel sheets, and CSV (Comma Seperated Values) files.\n",
    "* [Numpy](https://numpy.org/doc/): a toolkit for managing arrays, vectors, matrices, etc, doing math with them, slicing them up, and many other handy things.\n",
    "* [Matplotlib](https://matplotlib.org/stable/index.html): a toolkit for plotting data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import IPython.display as ipydis\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dataset\n",
    "We used a realestate dataset from Kaggle to produce this reduced dataset. This dataset contains the _sale price_ and _above ground square feet_ of many houses. We can use this data for our linear regression.\n",
    "\n",
    "We use Pandas to read the data file which is stored as Comma Separated Values (CSV). and print the column labels. CSV files are similar to excel sheets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['Unnamed: 0', 'SalePrice', 'GrLivArea'], dtype='object')\n"
     ]
    }
   ],
   "source": [
    "! [ -e ./slimmed_realestate_data.csv ] || wget https://raw.githubusercontent.com/argonne-lcf/ai-science-training-series/main/01_intro_AI_on_Supercomputer/slimmed_realestate_data.csv\n",
    "data = pd.read_csv('slimmed_realestate_data.csv')\n",
    "print(data.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now pandas provides some helpful tools for us to inspect our data. It provides a `plot()` function that, behind the scenes, is calling into the _Matplotlib_ library and calling the function [matplotlib.pyplot.plot()](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html). In this case, we simply tell it the names of the columns we want as our _x_ and _y_ values and the `style` (`'.'` tells `matplotlib` to use a small dot to represent each data point)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot: xlabel='GrLivArea'>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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0XAiBBQsWICoqCgEBAUhOTsaPP/5odI7Lly9j/Pjx0Gg0CAkJwcSJE3Ht2jWjNocOHcKQIUPQsmVLxMTEYNGiRWZ9WbVqFRISEtCyZUv06tULGzZsMDpuT1+IiIiIlHAomLpy5QoGDx4MX19fbNy4EceOHcPrr7+O0NBQqc2iRYvw9ttv47333sPu3bsRFBSElJQU3LhxQ2ozfvx4HD16FFu2bMG6deuwY8cOTJkyRTpeXl6Oe++9Fx06dEB+fj7+/ve/44UXXsAHH3wgtcnNzcUjjzyCiRMn4sCBAxg1ahRGjRqFI0eOONQXIiIiIkWEA+bOnSvuuOMOi8fr6upEZGSk+Pvf/y69VlZWJvz9/cVnn30mhBDi2LFjAoDYu3ev1Gbjxo1CpVKJX3/9VQghxJIlS0RoaKioqqoy+uyuXbtKv//hD38QqampRp+flJQk/vSnP9ndF1t0Op0AIHQ6nV3tiYiIyPPc/fx2aGTqq6++woABA/D73/8e4eHh6Nu3Lz788EPpeFFREUpLS5GcnCy9FhwcjKSkJOTl5QEA8vLyEBISggEDBkhtkpOToVarsXv3bqnN0KFD4efnJ7VJSUlBYWEhrly5IrUx/Bx9G/3n2NMXU1VVVSgvLzf6ISIiIrLGoWDqp59+wtKlS3Hrrbdi8+bNmDp1Kp555hksX74cAFBaWgoAiIiIMHpfRESEdKy0tBTh4eFGx1u0aIE2bdoYtZE7h+FnWGpjeNxWX0xlZmYiODhY+omJibH1lRAREVEz51AwVVdXh379+uHVV19F3759MWXKFEyePBnvvfeeq/rnVhkZGdDpdNLPmTNnPN0lIiIiauQcCqaioqLQvXt3o9e6deuG4uJiAEBkZCQA4Ny5c0Ztzp07Jx2LjIzE+fPnjY7fvHkTly9fNmojdw7Dz7DUxvC4rb6Y8vf3h0ajMfohIiIissahYGrw4MEoLCw0eu2HH35Ahw4dAADx8fGIjIzE1q1bpePl5eXYvXs3tFotAECr1aKsrAz5+flSm5ycHNTV1SEpKUlqs2PHDtTU1EhttmzZgq5du0orB7VardHn6NvoP8eevhAREREp5ki2+p49e0SLFi3EK6+8In788UfxySefiMDAQPGf//xHapOVlSVCQkLEl19+KQ4dOiQeeughER8fLyorK6U2I0aMEH379hW7d+8WO3fuFLfeeqt45JFHpONlZWUiIiJCPProo+LIkSNixYoVIjAwULz//vtSm127dokWLVqIf/zjH+L48eNi4cKFwtfXVxw+fNihvljD1XxERETex93Pb4eCKSGE+Prrr0XPnj2Fv7+/SEhIEB988IHR8bq6OjF//nwREREh/P39xfDhw0VhYaFRm0uXLolHHnlEtGrVSmg0GvHEE0+Iq1evGrU5ePCguOOOO4S/v7+45ZZbRFZWlllfPv/8c9GlSxfh5+cnevToIdavX+9wX6xhMEVEROR93P38VgkhhGfHxhqv8vJyBAcHQ6fTMX+KiIjIS7j7+c29+YiIiIgUYDBFREREpACDKSIiIiIFGEwRERERKcBgioiIiEgBBlNERERECjCYIiIiIlKAwRQRERGRAgymiIiIiBRgMEVERESkAIMpIiIiIgUYTBEREREpwGCKiIiISAEGU0REREQKMJgiIiIiUoDBFBEREZECDKaIiIiIFGAwRURERKQAgykiIiIiBRhMERERESnAYIqIiIhIAQZTRERERAowmCIiIiJSgMEUERERkQIMpoiIiIgUYDBFREREpACDKSIiIiIFGEwRERERKcBgioiIiEgBBlNERERECjCYIiIiIlKAwRQRERGRAgymiIiIiBRgMEVERESkAIMpIiIiIgUYTBEREREp4FAw9cILL0ClUhn9JCQkSMdv3LiB9PR0tG3bFq1atcKYMWNw7tw5o3MUFxcjNTUVgYGBCA8Px+zZs3Hz5k2jNtu2bUO/fv3g7++Pzp07Izs726wvixcvRlxcHFq2bImkpCTs2bPH6Lg9fSEiIiJSyuGRqR49eqCkpET62blzp3Ts2Wefxddff41Vq1Zh+/btOHv2LEaPHi0dr62tRWpqKqqrq5Gbm4vly5cjOzsbCxYskNoUFRUhNTUVw4YNQ0FBAWbOnIlJkyZh8+bNUpuVK1di1qxZWLhwIfbv34/ExESkpKTg/PnzdveFiIiIyCmEAxYuXCgSExNlj5WVlQlfX1+xatUq6bXjx48LACIvL08IIcSGDRuEWq0WpaWlUpulS5cKjUYjqqqqhBBCzJkzR/To0cPo3GlpaSIlJUX6fdCgQSI9PV36vba2VkRHR4vMzEy7+yLnxo0bQqfTST9nzpwRAIROp7P11RAREVEjodPp3Pr8dnhk6scff0R0dDQ6duyI8ePHo7i4GACQn5+PmpoaJCcnS20TEhIQGxuLvLw8AEBeXh569eqFiIgIqU1KSgrKy8tx9OhRqY3hOfRt9Oeorq5Gfn6+URu1Wo3k5GSpjT19kZOZmYng4GDpJyYmxtGvh4iIiJoZh4KppKQkZGdnY9OmTVi6dCmKioowZMgQXL16FaWlpfDz80NISIjReyIiIlBaWgoAKC0tNQqk9Mf1x6y1KS8vR2VlJS5evIja2lrZNobnsNUXORkZGdDpdNLPmTNn7PtiiIiIqNlq4UjjkSNHSv/cu3dvJCUloUOHDvj8888REBDg9M65m7+/P/z9/T3dDSIiIvIiikojhISEoEuXLjh58iQiIyNRXV2NsrIyozbnzp1DZGQkACAyMtJsRZ3+d1ttNBoNAgICEBYWBh8fH9k2huew1RciIiIiZ1AUTF27dg2nTp1CVFQU+vfvD19fX2zdulU6XlhYiOLiYmi1WgCAVqvF4cOHjVbdbdmyBRqNBt27d5faGJ5D30Z/Dj8/P/Tv39+oTV1dHbZu3Sq1sacvRERERE7hSLb6c889J7Zt2yaKiorErl27RHJysggLCxPnz58XQgjx1FNPidjYWJGTkyP27dsntFqt0Gq10vtv3rwpevbsKe69915RUFAgNm3aJNq1aycyMjKkNj/99JMIDAwUs2fPFsePHxeLFy8WPj4+YtOmTVKbFStWCH9/f5GdnS2OHTsmpkyZIkJCQoxWCdrqiz3cvRqAiIiIlHP389uhYCotLU1ERUUJPz8/ccstt4i0tDRx8uRJ6XhlZaWYNm2aCA0NFYGBgeLhhx8WJSUlRuc4ffq0GDlypAgICBBhYWHiueeeEzU1NUZtvv32W9GnTx/h5+cnOnbsKD7++GOzvrzzzjsiNjZW+Pn5iUGDBonvv//e6Lg9fbGFwRQREZH3cffzWyWEEJ4dG2u8ysvLERwcDJ1OB41G4+nuEBERkR3c/fzm3nxERERECjCYIiIislOJrhK5py6iRFfp6a5QI+JQnSkiIqLmauXeYmSsPow6AahVQOboXkgbGOvpblEjwJEpIiIiG0p0lVIgBQB1Anh+9RGOUBEABlNEREQ2FV2skAIpvVohcPridc90iBoVBlNEREQ2xIcFQa0yfs1HpUJcWKBnOkSNCoMpIiIiG6KCA5A5uhd8VPURlY9KhVdH90RUsPfvS0vKMQGdiIjIDmkDYzG0SzucvngdcWGBDKRIwmCKiIjITlHBAQyiyAyn+YiIiIgUYDBFREREpACDKSIiIiIFGEwRERERKcBgioiIiEgBBlNERERECjCYIiIiIlKAwRQRERGRAgymiIiIiBRgMEVERESkAIMpIiIiIgUYTBEREREpwGCKiIiISAEGU0REREQKMJgiIiIiUoDBFBEREZECDKaIiIiIFGAwRURERKQAgykiIiIiBRhMERERESnAYIqIiIhIAQZTRERERAowmCIiIiJSgMEUERERkQIMpoiIiIgUYDBFREREpACDKSIiACW6SuSeuogSXaWnu0JEXkZRMJWVlQWVSoWZM2dKr924cQPp6elo27YtWrVqhTFjxuDcuXNG7ysuLkZqaioCAwMRHh6O2bNn4+bNm0Zttm3bhn79+sHf3x+dO3dGdna22ecvXrwYcXFxaNmyJZKSkrBnzx6j4/b0hYho5d5iDM7KwbgPd2NwVg5W7i32dJeIyIs0OJjau3cv3n//ffTu3dvo9WeffRZff/01Vq1ahe3bt+Ps2bMYPXq0dLy2thapqamorq5Gbm4uli9fjuzsbCxYsEBqU1RUhNTUVAwbNgwFBQWYOXMmJk2ahM2bN0ttVq5ciVmzZmHhwoXYv38/EhMTkZKSgvPnz9vdFyKiEl0lMlYfRp2o/71OAM+vPsIRKiKyn2iAq1eviltvvVVs2bJF3HnnnWLGjBlCCCHKysqEr6+vWLVqldT2+PHjAoDIy8sTQgixYcMGoVarRWlpqdRm6dKlQqPRiKqqKiGEEHPmzBE9evQw+sy0tDSRkpIi/T5o0CCRnp4u/V5bWyuio6NFZmam3X0xdePGDaHT6aSfM2fOCABCp9M15GsiIi+w6+QF0WHuOrOf3JMXPd01ImognU7n1ud3g0am0tPTkZqaiuTkZKPX8/PzUVNTY/R6QkICYmNjkZeXBwDIy8tDr169EBERIbVJSUlBeXk5jh49KrUxPXdKSop0jurqauTn5xu1UavVSE5OltrY0xdTmZmZCA4Oln5iYmIc/m6IyLvEhwVBrTJ+zUelQlxYoGc6RERex+FgasWKFdi/fz8yMzPNjpWWlsLPzw8hISFGr0dERKC0tFRqYxhI6Y/rj1lrU15ejsrKSly8eBG1tbWybQzPYasvpjIyMqDT6aSfM2fOWPkmqLlgYnLTFhUcgMzRveCjqo+ofFQqvDq6J6KCAzzcMyLyFi0caXzmzBnMmDEDW7ZsQcuWLV3VJ4/x9/eHv7+/p7tBjcjKvcVSPo1aBWSO7oW0gbGe7hY5WdrAWAzt0g6nL15HXFggAykicohDI1P5+fk4f/48+vXrhxYtWqBFixbYvn073n77bbRo0QIRERGorq5GWVmZ0fvOnTuHyMhIAEBkZKTZijr977baaDQaBAQEICwsDD4+PrJtDM9hqy9E1jAxuXmJCg6AtlNbBlJE5DCHgqnhw4fj8OHDKCgokH4GDBiA8ePHS//s6+uLrVu3Su8pLCxEcXExtFotAECr1eLw4cNGq+62bNkCjUaD7t27S20Mz6Fvoz+Hn58f+vfvb9Smrq4OW7duldr079/fZl+IrCm6WCEFUnq1QuD0xeue6RARETVKDk3ztW7dGj179jR6LSgoCG3btpVenzhxImbNmoU2bdpAo9Hg6aefhlarxW233QYAuPfee9G9e3c8+uijWLRoEUpLS/HXv/4V6enp0hTbU089hXfffRdz5szBk08+iZycHHz++edYv3699LmzZs3ChAkTMGDAAAwaNAhvvvkmKioq8MQTTwAAgoODbfaFyBp9YrJhQMXEZCIiMuVQMGWPN954A2q1GmPGjEFVVRVSUlKwZMkS6biPjw/WrVuHqVOnQqvVIigoCBMmTMBLL70ktYmPj8f69evx7LPP4q233kL79u2xbNkypKSkSG3S0tJw4cIFLFiwAKWlpejTpw82bdpklJRuqy9E1ugTk59ffQS1QjAxmchLlegqUXSxAvFhQfz/L7mESgghbDdrnsrLyxEcHAydTgeNRuPp7pCHlOgqmZhM5KW4iKR5cvfzm3vzEdnAxGQi78RFJOQuDKaIiKhJ4iISchcGU0RE1CSxuj25C4MpIiJqkljdntzF6av5iIiIGgtWtyd3YDBFRERNWlRwAIMocilO8xEREREpwGCKiIiISAEGU0RE5BYlukrknrrIOk/U5DBnioiIXI6VyKkp48gUERG5FCuRU1PHYIqIiFyKlcipqWMwRURELsVK5NTUMZgiIrdg8nHzxUrk1NQxAZ2IXI7Jx8RK5NSUcWSKiFyKycfWNacRu6jgAGg7tWUgRU0OR6aIyKWsJR8394cqR+yImgaOTBGRSzH5WB5H7IiaDgZTRORSTD6Wx3IBRE0Hp/mIyOWYfGxOP2JnGFBxxI7IO3FkiojckgTN5GNjHLEjajo4MkXUzDEJ2nM4YkfUNHBkiqgZYxK053HEjsj7MZgiasaYBE1EpByDKaJmjGULvENzKuxJ5I0YTBE1Y0yCbvxW7i3G4KwcjPtwNwZn5WDl3mJPd4mITKiEEMJ2s+apvLwcwcHB0Ol00Gg0nu4OkcuU6CqZBN0IlegqMTgrx6x8ws55w3ifiKxw9/Obq/mICFHBAXw4N0LciofIO3Caj4jcivk/9mNOG5F3YDBFRG7D/B/rTANN5rQReQfmTFnBnCki52H+j3XWiqcyp43IMe5+fnNkiogscuaUnLfXtHLl9KSt4qks7EnUuDEBnYhkOXubGW/e2NfVW+4w0ZzIu3FkiojMuGKbGW/N/3HHljtMNCfybhyZIiIzrhop8caNfd0xaqQPNJ9ffQS1QnhNoElE9RwamVq6dCl69+4NjUYDjUYDrVaLjRs3Ssdv3LiB9PR0tG3bFq1atcKYMWNw7tw5o3MUFxcjNTUVgYGBCA8Px+zZs3Hz5k2jNtu2bUO/fv3g7++Pzp07Izs726wvixcvRlxcHFq2bImkpCTs2bPH6Lg9fSEiea4cKfG2/B93jRqlDYzFznnD8Nnk27Bz3jCnTiMSkWs5FEy1b98eWVlZyM/Px759+3D33XfjoYcewtGjRwEAzz77LL7++musWrUK27dvx9mzZzF69Gjp/bW1tUhNTUV1dTVyc3OxfPlyZGdnY8GCBVKboqIipKamYtiwYSgoKMDMmTMxadIkbN68WWqzcuVKzJo1CwsXLsT+/fuRmJiIlJQUnD9/Xmpjqy9EZJm3Tsm5gru+ixJdJYouVnjNiB0RGRAKhYaGimXLlomysjLh6+srVq1aJR07fvy4ACDy8vKEEEJs2LBBqNVqUVpaKrVZunSp0Gg0oqqqSgghxJw5c0SPHj2MPiMtLU2kpKRIvw8aNEikp6dLv9fW1oro6GiRmZkphBB29cUeOp1OABA6nc7u9xA1JWfLrovckxfF2bLrnu6Kx7nyu1ix52cRP2+d6DB3nYift06s2POz0z+DqDlx9/O7wQnotbW1WLFiBSoqKqDVapGfn4+amhokJydLbRISEhAbG4u8vDwAQF5eHnr16oWIiAipTUpKCsrLy6XRrby8PKNz6Nvoz1FdXY38/HyjNmq1GsnJyVIbe/oip6qqCuXl5UY/RM2Zt03JuZKrvgt3JLiTOVbiJ2dyOAH98OHD0Gq1uHHjBlq1aoU1a9age/fuKCgogJ+fH0JCQozaR0REoLS0FABQWlpqFEjpj+uPWWtTXl6OyspKXLlyBbW1tbJtTpw4IZ3DVl/kZGZm4sUXX7TviyAip9FPccWHBTW7wI1lEdzP1aUuqPlxeGSqa9euKCgowO7duzF16lRMmDABx44dc0Xf3C4jIwM6nU76OXPmjKe7RNTkNfctZlgWwb04Ekiu4HAw5efnh86dO6N///7IzMxEYmIi3nrrLURGRqK6uhplZWVG7c+dO4fIyEgAQGRkpNmKOv3vttpoNBoEBAQgLCwMPj4+sm0Mz2GrL3L8/f2llYr6HyJv5C1TGA19sHnL9dmDyf7u5e2V+KlxUly0s66uDlVVVejfvz98fX2xdetW6VhhYSGKi4uh1WoBAFqtFocPHzZadbdlyxZoNBp0795damN4Dn0b/Tn8/PzQv39/ozZ1dXXYunWr1MaevhA1Vd400tOQB5s3XZ+9XFUWoSkFnc7CkUByBYdypjIyMjBy5EjExsbi6tWr+PTTT7Ft2zZs3rwZwcHBmDhxImbNmoU2bdpAo9Hg6aefhlarxW233QYAuPfee9G9e3c8+uijWLRoEUpLS/HXv/4V6enp8Pf3BwA89dRTePfddzFnzhw8+eSTyMnJweeff47169dL/Zg1axYmTJiAAQMGYNCgQXjzzTdRUVGBJ554AgDs6gtRU2RppGdol3aNcqTD0S1mvO36HBEVHODUa2BekDwWSCVXcCiYOn/+PB577DGUlJQgODgYvXv3xubNm3HPPfcAAN544w2o1WqMGTMGVVVVSElJwZIlS6T3+/j4YN26dZg6dSq0Wi2CgoIwYcIEvPTSS1Kb+Ph4rF+/Hs8++yzeeusttG/fHsuWLUNKSorUJi0tDRcuXMCCBQtQWlqKPn36YNOmTUZJ6bb6QtQUeVsys6MPNm+7Pk9pykGnM3hjJX5q3FRCCGG7WfNUXl6O4OBg6HQ65k+RVyjRVWJwVo7ZSM/OecMa9QOjRFdp14PNW6/P3XJPXcS4D3ebvf7Z5Nug7dTWAz0ici93P7+50TFRE+Ktycz21nDy1utzN+YFEbkXR6as4MgUeSt7R3o8SUltKW+4Pk9bubfYbPqUOVPUXLj7+c1gygoGU0TKyQVNtpKjm3MRT2di0EnNlbuf3w5XQCcispdc0DS0SzurydHv7ziFrI0nILgKrUFMA1EGUUSux2CKiFzC0oqyN8cmWlyR91XBWWRuPCG9zlVojmE5BCLPYAI6EbmEpTIGapVKNjk60E+NLINAyvA9rE5tG7dJIfIcBlNE5BKWVpT16xAquyKvoroWlhI4D/1S5tBnN7bK3+7oD7dJIfIcTvMRkUtYK8gpVzSxRFdpVg1db9GmQjzYJ9quqb7GNtXlrv44Wk2eiJyHI1NE5DLW9pyLCg5AXFggii5WoERXKQVfpqNZgP0jLI1tqsud/WENLiLP4cgUkZNxWb8xSyvKLI3YJES2xqjFuUZTfvaOsOT/fEV2qmv/z1eQ2tv998Ld299wmxQiz+DIFJETrdxbjMFZORj34W4MzsrByr3Fnu6SpDHlEVkbsUmMCUXWGMdHWFbuLcbTnx6QPTb90wMeuReeqERubzV5InIejkwROYkzN5d19uhWY8sjsjVi4+gIi/67t5TALuCZEguObuRsC0c9iRonBlNETuKsKR1nBz7ODPKcxZ5kaUcKTsp996ZcOb1mjbOm3hpbQExEv+E0H5GTOGNKxxUJy41xybyzk6XlvntTnlzZpnTqrbEl1hORMQZTRE7ijADBUuCz/lBJgx+ccoGGGnBJYOFIXpa1lX6Okvvux/S7pVGtbFOSs9YYA2Ii+g03OraCGx1TQyjZXLZEV4nBWTmyU1ZKpnZW7i3GvC9+yylSAcga49xposYwDWX63TeWjX6Vfjdyfxc+KhV2zhvG3CkiGe5+fnNkisjJlEzpmI6wGFIytTO0SzsYnlKfkO2saSJXTUM5Oppj+t1buhfuXNnojO+GNaSIGjcmoBM1MvqE5fWHSvC39ceNjjU0idrV9Y4snT//9BXcn2j5/NZWp7lqpMvdI2jO+u5dWUOKqwSJlGEwRYTG9zCJCg5Aau8ovLrhuFO2B3H1ViNy5weAZ1YcQEX1TdlgxVpQ46wViKb31Z0rG/WfHeTn47Tv3pEVjvZqDNOzRN6O03zU7DXWQpuOTO3YmrZy9TSRtBWMyeumU1r6fh48c8Xq1JczEq7f334Kt2ca31d3JXIb/k2NWpKLET0jG+UUHVcJEjkHR6aoWWuMNZgM2TO1Y2tkQT9CMrRLO+ycN8xlCdlpA2MR5N8C002qkOuDlR0/XJD6qVIBpktfDKe+lI6kvb/jFDI3npB+19/X1dO0Lt8M2PRvSghgw+FSpN/VCXfc2s7jyfCG3L3dDVFTxZEpanIcSS72hiXn1hLabY0smI667fjhgku3GunfIdS8DIMKCPRTmwUYpgyDGmsjabbub4muElkGgZRerRC4Xl3n8kRuSwVEl2471agCKcAz290QNUUcmaImxdH8D1fnErmarWDQ3aNu+iBo3urDUsAkBPCPb36QL/cAoA7yQY3cqJw997foYoVssKavraXt1NalmwHHhwXJjrzVAY1uxMfZ290QNVcMpqjJaMiUnbfvnSYXDKpRPxK07/Rlj0zhDO3SDoab5AkA3/140aydWgWsmXY7rlfXWQxqDBOu7b2/lpLh545MMCqZ4MqAct7IBGRuMB4da6xBuitXCRI1FwymqMloaP5HY9w7TS4ok3stKjgAc0ck4LWNJ1D3v/fWARi1OFf2vEof6PYEi0UXKyxuOGxo0h0dkRgTavdn23t/TQNktao+kPrT0E52f5ZSfxraCRCQ7ktjH/FxZXBJ1BwwmKImQ8mUndKHiTMT2eWCMgCygdrKvcV4bdNvgZSeXDCjBhQ90E37NXdEAnq1DzYLrCyNDJn25Yk74hwayXPk/jaG0ZY/3dkJD/aJ5ogPUTPA7WSs4HYy3mfl3mKzKTt31MzJPXUR4z7cbfb6Z5Nvg7ZTWwC2R3VKdJXI//kKnv70gFEwpP5f/o3haz4qFVZP0+LhJblWgxZDi8f1RWrvaAeuyrhvjmxzY3ofRvWNxtoDZ43uCyAfIFrjqftLRN7F3c9vjkxRk+KpEQlboya2pgANj5uSe61WCOw9fcXuQMpHpUK/DvZPqZmytEJN3z/TUTi5+/DnlK7S7wCMgjN7R/Iaw4gTEZEplkagJkfJ3nhKPtPaUn5r5QtMj9vDR6VCfFggzHfwq6cCpL34nJGvI7eE3pBcOQlr++QpKUnhiftLRGQNR6aI7GRrms7SqImtxGlroz5y9NNmk/8v32zqb87Iruh9S4g0+uOsERyp5MEXh2XzsRxNbPf2khRERIYYTBHZwd6VenKJ7LLlC1TAxWs3UKKrtCthW29+ajcMiAs1y5VSq4DV07Rmq+OcOXoztEs72fpJthLbLQWhk+6Ix7LvirxitRsRkTUMpohsULpSz3Spvj4gefqzAikwmytTl8iUj0qF+3pHyY5k1QngerXpmj7nsjSC9o6VxHZ7ViZOuaMjnrgjjoEUEXkt5kwR2eCMLWfSBsZi57xhWDyuL2CwMk8fmAX6+si+T5+mZDhy46ktQCx9rlxie4muEusOncW8L4yD0IzVh81e+2hnkUv7TUTkagymiGxwVvASFRyA0CA/s5yjWiEw/8ujsu8RAGYM74zV07TStKK1ZHdXsvdz9fsBTjcp8QDUB09y19+Y9kIkInIU60xZwTpTpOes+kYlukrcnpljV4VwQ3J5WiW6SocTzJ2x3Y21z7VWj0p/HXI1s3bOG8ZpPiJyGtaZImqEGlrfyFl79cnlaTlatb2h290YXgMAq9djbWWiYbFObqxLRE2JQ9N8mZmZGDhwIFq3bo3w8HCMGjUKhYWFRm1u3LiB9PR0tG3bFq1atcKYMWNw7tw5ozbFxcVITU1FYGAgwsPDMXv2bNy8edOozbZt29CvXz/4+/ujc+fOyM7ONuvP4sWLERcXh5YtWyIpKQl79uxxuC9E9nK0vpF+umvch7sxOCsHK/cW271vnZyGTIeV6CqRe+oiDp65YrXWlT3XcHtmDm7PNL4eU3JTomoV8O4jfbFz3jCkDYyV8sc+m3yb9BoRkTdzKJjavn070tPT8f3332PLli2oqanBvffei4qKCqnNs88+i6+//hqrVq3C9u3bcfbsWYwePVo6Xltbi9TUVFRXVyM3NxfLly9HdnY2FixYILUpKipCamoqhg0bhoKCAsycOROTJk3C5s2bpTYrV67ErFmzsHDhQuzfvx+JiYlISUnB+fPn7e4LkatYWgEY5OdjsdCmLY7kaZXoKvHK+mNSIDRqsfm2M7aCM9NrEDBPnDcNxkzzqtQqYOId8egfF2q2GTELb3o3faBuKyB3l8bWH2peFOVMXbhwAeHh4di+fTuGDh0KnU6Hdu3a4dNPP8Xvfvc7AMCJEyfQrVs35OXl4bbbbsPGjRtx//334+zZs4iIiAAAvPfee5g7dy4uXLgAPz8/zJ07F+vXr8eRI0ekzxo7dizKysqwadMmAEBSUhIGDhyId999FwBQV1eHmJgYPP3005g3b55dfbGFOVPNj7Om5azt1fftiXP44Dv5FWz6yuWmgY/htJytPq7cW2yxuKbpOddMu92sNhXw22q8V9ZbL9dguPeg6fs/3lWED3cUQcCxaUVq/Bo6Zdxc+kOe5+7nt6LVfDqdDgDQpk0bAEB+fj5qamqQnJwstUlISEBsbCzy8vIAAHl5eejVq5cUSAFASkoKysvLcfToUamN4Tn0bfTnqK6uRn5+vlEbtVqN5ORkqY09fTFVVVWF8vJyox9qPuSm5RrK2grAJ+6It7g1iwAw6Y6Ov43sAJgyNB675t2NtIGxNvuoH02yFEgZfm6dAB5ekmt2Dv1n2Aqk9NdjaURg2XdFNkeyyPvY2h6pufeHmqcGB1N1dXWYOXMmBg8ejJ4965NKS0tL4efnh5CQEKO2ERERKC0tldoYBlL64/pj1tqUl5ejsrISFy9eRG1trWwbw3PY6oupzMxMBAcHSz8xMTF2fhvk7ezZP8+RKQRrZQT0x+T+z+ejUuGJO+KknKJdGXfj+fu6W9zjL2P1YRw8c0V6v60E8A8f6280zejIPoEqlXndqx0/XJAN7uypzcVpGe/kjLprTbk/1Dw1eDVfeno6jhw5gp07dzqzPx6VkZGBWbNmSb+Xl5czoGomrP0LeccPFxo0hWBtBaD+2Mc7T2PZzp9QJ8zrNplO4VmqfD5qcS6yxtT3ydLWNGpV/ZYvAX4tLNZ5srZP4PzUbrivdxSA3/b7A2BUBsFwxaGtvfeayrSMs6aFvUlj21exsfWHmqcGjUxNnz4d69atw7fffov27dtLr0dGRqK6uhplZWVG7c+dO4fIyEipjemKOv3vttpoNBoEBAQgLCwMPj4+sm0Mz2GrL6b8/f2h0WiMfqh5sDQtF+inVjSFYC3ROio4AM+ndsOueXcbrWyzNGIj10egfmpQ3yezBHD8Nk04tEs7XLpWJbvaLtBPbfV7GBAXiqKL9QtN9NdjawNnSyNzTWVaxtKUa1MfcfNU0Vhv6Q81Tw6NTAkh8PTTT2PNmjXYtm0b4uPjjY73798fvr6+2Lp1K8aMGQMAKCwsRHFxMbRaLQBAq9XilVdewfnz5xEeHg4A2LJlCzQaDbp37y612bBhg9G5t2zZIp3Dz88P/fv3x9atWzFq1CgA9dOOW7duxfTp0+3uC5Ge6f55+n8hV1TXWg0YnPXZ+nNZG7HR91FuGs6wT3IjYobnBeqn6wzzmR5ekit9lun3MKpvtLSxsmGfbI0IpA2MRUJka+w9fQUD40KlRHdbQZg3sBQQll2vwWubTnj9iJstDa271lz6Q82PQ6v5pk2bhk8//RRffvklunbtKr0eHByMgID6P96pU6diw4YNyM7OhkajwdNPPw0AyM3NBVBfGqFPnz6Ijo7GokWLUFpaikcffRSTJk3Cq6++CqC+NELPnj2Rnp6OJ598Ejk5OXjmmWewfv16pKSkAKgvjTBhwgS8//77GDRoEN588018/vnnOHHihJRLZasvtnA1X/NjWt374JkreGix+d/Ll+m3I1zTEvtOX0ZZZQ1CA/3Qv0Ooon+Jy1UPVwNYk2684u7gmSsYtTjXririJbpK5P98BU/LbO1iyvAc+u8h0E8tBVJy7axVhrcUGMpdp7dVQbe0WtMwSAW877qImopGXQF96dKlAIC77rrL6PWPP/4Yjz/+OADgjTfegFqtxpgxY1BVVYWUlBQsWbJEauvj44N169Zh6tSp0Gq1CAoKwoQJE/DSSy9JbeLj47F+/Xo8++yzeOutt9C+fXssW7ZMCqQAIC0tDRcuXMCCBQtQWlqKPn36YNOmTUZJ6bb6QmTKtKp4RXWtbLvXv/kB3/140ejBqQKk3KWGkM2JAjBqSS6yDEY4EmNCkTXGfBRNbo88S8nkcgxHh/Q/uacuOjwKBlgeudFXcJcbBfSmgENuVE4uV83bRtyIqGG4N58VHJlqHBqS5HvwzBXsOX0Zg+LaGI3qOHouSyNTlqhVwK55dxsFFfZ+nrV97UxHjYouViDIzwfXq+satEeebN8B7Mq42+hcDR1FslZnS1+XqiF7CzYmpqNyc0Z2xWsbT3j1iBtRU9GoR6aIHOGMlU4NWfX13OcF+GL/r9LvY/rdgtf/0Mfhc+nbO6JOQBqJMP28uSMS0Kt9sNXvY+Id8Ub1mfSsrSyUK5pprUSCJZOGxpv1q6GjSPassLK0t6C3rJCTG5ULCfD16hE3ImoYjkxZwZGphnPG0veDZ65g1JJcCAf+S3/r8VJMXJ5v9vpHE/pj8v/ly44aAOab9zZkZAeon+rLzbgbACy+X+77sJYgrn/Pmmm3W81fMlSiq8TtmTl27wOoP39Fda1sENOQUSRr+VTW3uPtJRO8fcSNqCngyBR5PVv5MvZ4f/spZG40r8BdKwT2/3wFqb3lt1GZ+4X8SNK3hRdk81kM6zwZPrwbMrKjt+OHC4hpE2jx/abfh6VCmYYBlRDAukMlsteQf/oK+scZB4RRwQGYPCTe4rY1pkb0iJRdsadnaRTJGkdXWDnj76YxaMh3RUTeTdF2MkRylFYkfn+HfCClN/3TAxa3UbEksX2weX0lQAqkAON6R0F+Pnb11ZS+5lPuyYtW2xl+H3Lfl+Gmwvrfl31XJLtJ8tOfHcDtmeb1juS2rbG0jc3Go6UuqfvkyIbGrGRNRN6KwRQ5nbV96Wwp0VUic4P1PeEEgHmrDxs97G2NJM394jAe7nvLb8UsVcDIXpEWH96WVvHZo1YILN52ymobNSB9H4d/1Zkdl4t5BICH+kSZHTMMvAwDIblihnNHJsgGlaaT/Z4IYpT83egpKZjZ1IttEpHrMJgip1NSkfhfO+2blhIC2P/zb3vSWaoOrlcngLUHzmL1NC2mDI2HEMD6w+Z7NOof3rbOZ40K5sGJqUlD6wverjt0FlkyweODfaJk3/dlQYnNPCjDQChtYKy0z9/OecPwp6Gd7AqwAODQr2U2Psm5AYjSStZKNqp25ibXRNT8MGeKXKIhFYlLdJVYZmcwBQCXK6qNVn4ZrjqzVPPnlyuVsqvlgPrRqjkju0p9zRzdC/NWH7YZGJmyp7mvj9pqgntc26AGn9vWqjlL98Z0anXRxkI8mBhtscyDK5LFG1rJWkm+VVPJ1SIiz2EwRU5j+rB1NBH3451FsoHL4E5tsevUJbPXj5eWY+FXR40e5jvnDcPpi9dxvboGk5bnm1WjrhPCamL4axtPICTAF2kDY6UH+9bj5/DXtUftvg57LNl2ymqQ9tbWk9J0noD56j5L9Bsa2/reTe9Nr/bBZm0MC06alXkYmWBUU8mZAUhDEriVbFHTFLa3ISLP4jQfOYXSaZISXSU+lFl5plYBc0Z0NcsTUgH4bPcZo4d5xurDOF9+A8WXKzD5/4wDKTXqz3NWd8NqP/TneSfnB6w7dBYA0LFdK4euxdCM4Z3l85/siIwEAJUKePeRvlibfrtd044NLXQil7elH+GSG7kxLU4JeDZZXEm+lTNytYioeWMwRYpZmiZxJI+m6GKF7MjLpDs6IlzTEpOG/LYyTa0CHhkUY9a+TgAPLc7FvC/MywzUoX4ay1Zyu/48r3/zI6Z/Wr9K7vCvOtmAyBY1gLGDYjHvvgTbbVXAM3d3lu3LoV/LkBgTapRPZIl+NaEj332JrhKvyayefOqujogKDpDf5kaYJ8l7MgBRkm+l5L1MWicigNN85ATOmCaRq5gNAGeuXJdyi1QAxg2KQUX1TXy654zFczmzCq0AkLXhhNk50+/qhDtubYdDv5TVj9LIvHfqXZ1QdLEC0cEtZc+tv179w3tol3Z499uTZt/BBzuK8MTgeGna8eNdRfhgh+XcMke/e0srIZd8ewqxbQIxtEs72Wrmc0Z0xaJNhQ5V+3ZldfOG5ls19L1NocAoETkHgylyiNzD0J6tQwzfB0DaW+7MlUoIITAgrg3mjkwwGznaeOS3FXcCsBpENYQ9uUhyxxdvO4XYtoH4052d8GCfaLPinyN6RmLp9lNYvO2U7KiWj0qF1dO0ZnvrjR0YI3uN+aev4P7E+jbLbBTitPbdywUJlgJZ/SjXznnDZLeUSRsYiwf7RNsdgLgj+FBSMNOR9zJpnYgMMZgiu1l6GNrav83wfYZJ1aamDIl327XoKRnFylh9WHp4Pp/aDU/cEfdb8vv/5Uv5S6afof9+EmNCpUAHqH+Y3945TDaY0s/u2VOZfc6IrrLfvaUARn//5Kqw60e5LI3c2BuANLXgg0nrRGSIwRTZ5eCZK0ZlAkwfhkO7tMNbj/QBBBDTJgAV1bVSHonhQ9RaHPDB/yp8O3OazpUMNzUG6gOLHT9cwLwvDlu8hqT4NnhzbB+LpQWGdmln9h2oVEC/DqEALI8iGerdPgSAYwFM2sBYJES2xqjFuWYrIPWjXEpGfZpa8GHPaCwRNR8MpsimlXuLZQME/cNwxw8XZEeeVCpgUFyoQ3vcDe7UFjtlyiC4i0pl/4o4tQpGD8+DZ65YDaQAYHfRZRw7W79yTi7Q2TlvGLLG9DILsgwDNsNRQFOGD3RHA5jEmFBkjbE8wqhEUws+bI3GElHzwmCKrNKPbsgFCD4qFQL91BZHnoQAdhddkXmnZZ4MpADgEQs5S3KEqN/UOG1gbH3AaeF7MjVpeT4mDYmXDXTWHypBau8o7Jp3t8VcJMMpt10nL2DJtlNGieyO5LKZUpLEbY0jwYcrk9SdyVXfFRF5H5UQDa1M0/SVl5cjODgYOp0OGo3G093xiNxTFzHuw92yx8b0uwVj+re3eNzbjOwZiafu7IiHFufa/R41gBdH9cDCL486NAKn/t8ImKVK7Ia5TbaCixJdpcUH+sq9xbKJ446Q+/yGBjzW+qrvL1fIEZFS7n5+c2SKrDr8i3kxR73VB37FY9oObuyNa31z9BxSe8vviWdJHYD5DaiOXieAKUPj8dF3p82m6wxzmwynUK0lkFsKaAxHTwL91FIumyP73Zl+PoAGBzzW+trUktSJqPlgMEUWlegq8domy0UuhQB2nrzoxh7BZvK1ErVC4IfSq+YJ4P/7X2d+rFoF9LolGKunabH39BX8bf1xs758trsY7+SclD5XX509IbI1EmNCbX6G4ehR8eUKhwMgueAm43+LEAz75KyAp6klqRNR88FgiixO46w7dNZm4LKt8IIbeviblB6R6BMTYrYpr7O8nVO/J54+oNJPjQGwmPTtKH2S+9OfFUAFYNqwTrJB4ts5J83eWyeAUYtzkTXGejBkrRyFrQBI//dwuaJatvK5KWcFPE0tSZ2Img8GU82crWkcW/aedizBXKmNR0qR2jsKj2s7IDvvZ5d8hkB9APLE7XEY1TdaGgXST5edvHC1QVN7gPnImgCw+NtTDvcv44vDVoMhW+UoLAVApkGY6SidXK6XswIeb1gh5y3J8UTkXkxAt6KpJaAfPHMFe05fxqC4NlLBSP1WLXrWEqOVcmYNKUdKGCj6HMBsFKhEVwltZo7rP9yGKUM64vnUbmavW1s0oOejUmHnvGFGAYHc34MK9d+14WpBAIqT2q2xlaRu2tZdwQ2T44m8BxPQySWe+7wAX+z/VfpdvxLPnmkcZ3HmqRsaSKlVwPRhnWWn0GQ/B8C8Lw4jrJUfAvxaID4sCOfLbzTsw51s2c6f8MQdcWZBhNx0mVxQZPo+uZwlAeCdsX3RtpW/UXDjypIA9hYHdWdww+R4IrKGwVQzcPDMFaNACgC+2P8r7usVafbQdWWCt6epVcDckQm4JcSxh58AMHF5vnSOkT0j7f68sQNjsWJvsUu+U9MK7HqWpstsBUCWcpb0Fe1NP8OTQYS7gxsmxxORNQymmoE9py/Lvn764nX0iQnB/uIy6bWmGkgBwIOJUXht4wmL1xjXNhCnL123eo46Ybz5sqHbO7bB7qIrZtNf2k5t8PRnBRbPqfrf/KejX721XCVre+lZIheEjeobjYeX5Da6qS13BzdMjiciaxhMNQMdw4JkXy+7Xm0USHmaPg9KBaBDm0Ccvmw9sHHU2oISs9diQgNw5kr9HoK2Aim9OgHEtw1EkUn7vJ8uY2367bheXWcUwAyIayM74qcC8O64vtK+e6cvXsfOHy9g6bZTqIN8SQbTVYa2giNrNZ3kco1M61LpAyn9dTeWqS13BzfekBxPRJ7DYKoZCPCTv83vOLiKzJXUKmDNtPpA5NAvZU4vfWAp+V0fSDlCDZgFUvjf+c9crsT9idFGr+sfxIYbResT21N7Rxu103Zqiz9qO0jBzCiTauwqVX0OU/+4UEQFBzQoAdtWrpE+CMs9dbHRTm3pv9OMLw6jDvX3xNXBDbePISJLGEw1A3L/Fe9OagAP9omSHRnSqxOQRnTGffi9Uz9fBWDefQnI2nDC4ak0udGPtIHtLe7fp1LJviw9iPf/fAVCQAqG5BgGM6b9rRNA21b+iAoOaFACtiO5Rl4xtaWPki18787m6VwxImqcGEw1IZZGKaT/irezdpQzdGoXhOfvS0Cgny/iwgKx7/Rlq8GUWgXEhQWi6GKFcyuNA1iTfjsSY0Jx9nIlln/vWG2quSMS0Lt9CAL91FKwt+/0ZYvBlH7KTk5UcABSe9v/ILYWzDQ0AduRXKPGPLXF1XVE1JgwmGoibI1SpA2MRVgrP2lVmqudulCBicvzMabfLXj9D30wIK6N1TpTQgA7friAY7+WO60PagCZY3ohMSYUK/cW4/92O17kc9GmQrN6TJauJWNkQoMf5HKBsLVgpqFTcI6ONjXWqS2uriOixoTBVBNg73+lW8qdcqUv9tdvhhyuaYlJQ+Kx7LsiaVbG8Fmor+fk1IGz/0396L+fhtSmkntARwUHIGvMb/k6+mnEPw3t5PQcJkvBTEOn4Boy2tQYp7a8YgqSiJoNBlNeztIeenJBgKdypz7cUYQNR0qkLUrGJcWgbZAf3skxToB3drf0QeVbj/Rp8DWrAFyqqEKJrtLiqjd9kOOqHCa5YEbJFFxjHW1yRGOegiSi5ofBlBczfHibkvuvdNMVUO6y/nCJFCgJAJ/uls83sqRbVGsUll5tUEBUKwR+vlTh+BsNTP/0gNVVb0DDc3iUTFcpCYoa42iTo5pCUEhETYPa0x2ghjF9eBuy9V/prhyYCm/tb/R7Unyo4s/71+MD8dbYPg16r0oF/H3zDw3+bH3f9cFRiU6+lIK1oMiSEl0lLl2rgtpkJZoj01X6cgrNNZBo7tdPRI0DR6a8lNzDGwDmp3bDfb2jANRveGuYuyPlDrmgP0M6t8Xjg+MwvFskXvjyCLLz6pO9956+omiD49fG9EJUcIDFwpfW6Ddtbgi5PlsbMXI0h8dwVFG/b56wsm8eERE1XgymvFSQn4/s6wPiQrHjhwuyuTuWAjBn+O7kJew6dQkjekRig8F2K/pgoSEWj+srFbWUCl/amaQ+P7UbwjX+VrdxsWZEz0hsPlpqd3DkSA6P6aiiAKAWv1VDZyBlrCFJ/URE7uTwNN+OHTvwwAMPIDo6GiqVCmvXrjU6LoTAggULEBUVhYCAACQnJ+PHH380anP58mWMHz8eGo0GISEhmDhxIq5du2bU5tChQxgyZAhatmyJmJgYLFq0yKwvq1atQkJCAlq2bIlevXphw4YNDvfFW5luPKv3yxX53J0SXaU0euIqdQJGgZReQ+I3tcq8ZlPawFgs+l0vm+/1UalwX+8oqYRBQ2w6Woq5IxPg878qnPaMGKUNjMXOecPw2eTbsHPeMIvJ53JBbR2ANkH+DBZMrNxbjMFZORj34W4MzsrByr3Fnu4SEZEZh4OpiooKJCYmYvHixbLHFy1ahLfffhvvvfcedu/ejaCgIKSkpODGjRtSm/Hjx+Po0aPYsmUL1q1bhx07dmDKlCnS8fLyctx7773o0KED8vPz8fe//x0vvPACPvjgA6lNbm4uHnnkEUycOBEHDhzAqFGjMGrUKBw5csShvngrucDIR6VCnRBWE5ozR/eyWKXbVdQqx0en9HWnDK3cW4y5Xxy2+d45I7pKCdaTh8TLtrHVHyGA9iEBdgVHhuzJ4bF077is35ilpH5LeWtERJ6iEqKhWSWASqXCmjVrMGrUKAD1I0HR0dF47rnn8Oc//xkAoNPpEBERgezsbIwdOxbHjx9H9+7dsXfvXgwYMAAAsGnTJtx333345ZdfEB0djaVLl+Ivf/kLSktL4efnBwCYN28e1q5dixMn6vdsS0tLQ0VFBdatWyf157bbbkOfPn3w3nvv2dUXW8rLyxEcHAydTgeNRtPQr8llVu4tNptWGtqlHQZn5ZhNTxkWnizRVUrbmvyqq2zQNitAfYmDFXvO2Jw6zLgvASEBvkZ705mSy4fyUamwepoWFdW1CPLzMdp015rPJt8Gbae2AOqvVe77mDOyK7I2nrCaU/XuI33N9tlzFrl7Z0+w1pzknrqIcR/uNnvd8P4SEclx9/PbqTlTRUVFKC0tRXJysvRacHAwkpKSkJeXh7FjxyIvLw8hISFSIAUAycnJUKvV2L17Nx5++GHk5eVh6NChUiAFACkpKXjttddw5coVhIaGIi8vD7NmzTL6/JSUFGna0Z6+mKqqqkJVVZX0e3m586pxu4KlpeG2cnf025qU6CrxTNYBs0DKVsL430b1wPBuEYgKDkBi+xCLqwpVAOaN/K2YpelJ1Srgw8f6I9DPFxev3TDLb6oVAqOW5EKI3xK0zT7D5HXTER5LuUz6wMVSIKlC/f55rsJl/baxMCcReQunBlOlpfX5MhEREUavR0RESMdKS0sRHh5u3IkWLdCmTRujNvHx8Wbn0B8LDQ1FaWmpzc+x1RdTmZmZePHFF+272EZCrl6QvQ9qSwnpfxjQHiv3/SL7ntfGmG9TE+jnI5vo/c7/Rnb0hUXlNu0N9POFtlNblOgqZYM4faAkF0jpR5gWbSy0mvQt932U6Crx2kb5QEq/DY2rA5ymUOvJlViYk4i8BVfzGcjIyDAa7SovL0dMTIwHe2TM1qom0+O2HjqW/ss/0MJKwbQB7WWnouTKFvioVOgfF+pwYVFb1KhP1jYcYXowMdpm4Gj6fdgqLcEHduPAETwi8gZODaYiIyMBAOfOnUNUVJT0+rlz59CnTx+pzfnz543ed/PmTVy+fFl6f2RkJM6dO2fURv+7rTaGx231xZS/vz/8/f1lj3lSia4S/9pZhI92FlncqqQhW5lY+i//hMjW+DjXfFPgz/N/Qb8OoWbntXQeAHYXFi26WGEzb0ufQ3W9us7owdqQER5LgaRhIMUl+Y0DR/CIqLFzagX0+Ph4REZGYuvWrdJr5eXl2L17N7RaLQBAq9WirKwM+fn5UpucnBzU1dUhKSlJarNjxw7U1NRIbbZs2YKuXbsiNDRUamP4Ofo2+s+xpy/e4P0dp6DNzMGH3xVZXNVUoqvEvC8atuppaJd2eHNsIhaP64ud84ZhaJd2qKiuxX29Is3aCivnlSsLYG30x3R1nK2yDfrgKzEm1CkVr/UBoKXSB1yST0RE9nJ4ZOratWs4efKk9HtRUREKCgrQpk0bxMbGYubMmfjb3/6GW2+9FfHx8Zg/fz6io6OlFX/dunXDiBEjMHnyZLz33nuoqanB9OnTMXbsWERH16+cGjduHF588UVMnDgRc+fOxZEjR/DWW2/hjTfekD53xowZuPPOO/H6668jNTUVK1aswL59+6TyCSqVymZfGrv3t59C5sYTsscMyx38a2eRzWrdcqMs728/Vb+iDfWjWQ/3vQVrDvwqjW7d2y0C3xw/Z/G8ctOKhkGOtcKiljbulds3UA1g9TQtEmOcmxBuaQqpofvsERFR8+RwMLVv3z4MGzZM+l2fYzRhwgRkZ2djzpw5qKiowJQpU1BWVoY77rgDmzZtQsuWLaX3fPLJJ5g+fTqGDx8OtVqNMWPG4O2335aOBwcH45tvvkF6ejr69++PsLAwLFiwwKgW1e23345PP/0Uf/3rX/H888/j1ltvxdq1a9GzZ0+pjT19aaxKdJXIshBI6QX6qVGiq8RHO4vMjqkAKR9JbgqwrLLGKFCrE8AX+381+t00kAJ+y3OyZ1rRUmHR69Xy2yynDYxFkH8LTP/0gNHrdVbeo5TcFJKSzYeJiKj5UVRnqqnzZJ0pSzV2DL37SF+0aeUn204FIGtML9m6U2rUr5pz9MbrV7nZU8sKsFzjybSdIXvf48p8pob0m4iIGg93P7+dmjNFzmPP1i8qleV2AvVTU+9s/VF265KGRNDvjOtrMRdKP3JjyFZekhx73uPqfKaG9JuIiJovlkZopExXyMlpHxpgNdeoVgh8uueM3Z85smckvjl6TvbzfFQqaa88S7lQgX7msXlDlrZbe4+78pm4JJ+IiOzFYKoR0z/Q1x8qwd/WHzc7rs8jShsYi4TI1lK1cD25LVrkqFXAXINK5acvXsehX8ssFsN0NBeqIUvbLb3HnflMXJJPRET2YDDVyEUFB2CghW1NDEeCEmNCkWUwkqVWAWMHxeKz3cVWp/RMi1TqAwhtp7YWi2F6cpsPbjFCRESNDXOmvIC9I0H6Wk9ThsZDCODT3fW5RJZSr0yLVJrSB1WWyhh4IqeI+UxERNTYcGTKQxxZjeboaMyy736rO6WvIfXO2L74VVdpcx87e3kyp4j5TERE1JgwmPIAR7d+cWTDV7mcojoBtG3lj/sTo+3ax85epjlFzixXYOtczGciIqLGgsGUmzV0NZq9ozG2RrFcFYQ0ZG9Ad5yLiIjI1Zgz5Wb21miSYymHybSNu3OKLAWI9uwN6MpzERERuQNHptzMHavR3J1T5MxyBdzKhYiIvA1HptzMXSNH9oxiOYtcFfaGBojOPBcREZE7cGTKA5raajRHEuTdeS4iIiJ34EbHVnhyo2NncOVmwJY+z1kBojPPRUREzYu7n98cmWqiPLEizpkrBVn6gIiIvAVzppogrogjIiJyHwZTTZCS8gtERETkGAZTTRBXxBEREbkPg6kmiJsBExERuQ8T0JuoplZ+gYiIqLFiMNWEuXtFnLtLMRARETUGDKbIKbg5MRERNVfMmSLFWIqBiIiaMwZTpBhLMRARUXPGYIoUYykGIiJqzhhMkWIsxUBERM0ZE9DJKViKgYiImisGU+Q03JyYiIiaI07zERERESnAYIqIiIhIAQZTRERERAowmCIiIiJSgMEUERERkQIMpoiIiIgUYDBFREREpACDKSIiIiIFGEwRERERKcBgioiIiEgBBlNERERECnBvPiuEEACA8vJyD/eEiIiI7KV/buuf467GYMqKq1evAgBiYmI83BMiIiJy1KVLlxAcHOzyz1EJd4VtXqiurg5nz55F69atoVKpnHLO8vJyxMTE4MyZM9BoNE45Z2PFa226mtP18lqbruZ0vc3pWgFAp9MhNjYWV65cQUhIiMs/jyNTVqjVarRv394l59ZoNM3iDxrgtTZlzel6ea1NV3O63uZ0rUD9c9wtn+OWTyEiIiJqohhMERERESnAYMrN/P39sXDhQvj7+3u6Ky7Ha226mtP18lqbruZ0vc3pWgH3Xy8T0ImIiIgU4MgUERERkQIMpoiIiIgUYDBFREREpACDKSIiIiIFGEwp9MILL0ClUhn9JCQkSMdv3LiB9PR0tG3bFq1atcKYMWNw7tw5o3MUFxcjNTUVgYGBCA8Px+zZs3Hz5k13X4qsHTt24IEHHkB0dDRUKhXWrl1rdFwIgQULFiAqKgoBAQFITk7Gjz/+aNTm8uXLGD9+PDQaDUJCQjBx4kRcu3bNqM2hQ4cwZMgQtGzZEjExMVi0aJGrL82MrWt9/PHHze71iBEjjNp4y7VmZmZi4MCBaN26NcLDwzFq1CgUFhYatXHW3+62bdvQr18/+Pv7o3PnzsjOznb15Zmx53rvuusus/v71FNPGbXxhutdunQpevfuLRVn1Gq12Lhxo3S8Kd1XW9faVO6pnKysLKhUKsycOVN6rSndW1Ny19uo7q8gRRYuXCh69OghSkpKpJ8LFy5Ix5966ikRExMjtm7dKvbt2yduu+02cfvtt0vHb968KXr27CmSk5PFgQMHxIYNG0RYWJjIyMjwxOWY2bBhg/jLX/4iVq9eLQCINWvWGB3PysoSwcHBYu3ateLgwYPiwQcfFPHx8aKyslJqM2LECJGYmCi+//578d1334nOnTuLRx55RDqu0+lERESEGD9+vDhy5Ij47LPPREBAgHj//ffddZlCCNvXOmHCBDFixAije3358mWjNt5yrSkpKeLjjz8WR44cEQUFBeK+++4TsbGx4tq1a1IbZ/zt/vTTTyIwMFDMmjVLHDt2TLzzzjvCx8dHbNq0qdFd75133ikmT55sdH91Op3XXe9XX30l1q9fL3744QdRWFgonn/+eeHr6yuOHDkihGha99XWtTaVe2pqz549Ii4uTvTu3VvMmDFDer0p3VtDlq63Md1fBlMKLVy4UCQmJsoeKysrE76+vmLVqlXSa8ePHxcARF5enhCi/gGuVqtFaWmp1Gbp0qVCo9GIqqoql/bdUaYBRl1dnYiMjBR///vfpdfKysqEv7+/+Oyzz4QQQhw7dkwAEHv37pXabNy4UahUKvHrr78KIYRYsmSJCA0NNbreuXPniq5du7r4iiyzFEw99NBDFt/jrdcqhBDnz58XAMT27duFEM77250zZ47o0aOH0WelpaWJlJQUV1+SVabXK0T9v5gN/0VtypuvNzQ0VCxbtqzJ31chfrtWIZrmPb169aq49dZbxZYtW4yur6neW0vXK0Tjur+c5nOCH3/8EdHR0ejYsSPGjx+P4uJiAEB+fj5qamqQnJwstU1ISEBsbCzy8vIAAHl5eejVqxciIiKkNikpKSgvL8fRo0fdeyEOKioqQmlpqdH1BQcHIykpyej6QkJCMGDAAKlNcnIy1Go1du/eLbUZOnQo/Pz8pDYpKSkoLCzElStX3HQ19tm2bRvCw8PRtWtXTJ06FZcuXZKOefO16nQ6AECbNm0AOO9vNy8vz+gc+jb6c3iK6fXqffLJJwgLC0PPnj2RkZGB69evS8e88Xpra2uxYsUKVFRUQKvVNun7anqtek3tnqanpyM1NdWsT0313lq6Xr3Gcn+50bFCSUlJyM7ORteuXVFSUoIXX3wRQ4YMwZEjR1BaWgo/Pz+zHasjIiJQWloKACgtLTW60frj+mONmb5/cv03vL7w8HCj4y1atECbNm2M2sTHx5udQ38sNDTUJf131IgRIzB69GjEx8fj1KlTeP755zFy5Ejk5eXBx8fHa6+1rq4OM2fOxODBg9GzZ0+pL87427XUpry8HJWVlQgICHDFJVkld70AMG7cOHTo0AHR0dE4dOgQ5s6di8LCQqxevRqAd13v4cOHodVqcePGDbRq1Qpr1qxB9+7dUVBQ0OTuq6VrBZrWPQWAFStWYP/+/di7d6/Zsab4/1lr1ws0rvvLYEqhkSNHSv/cu3dvJCUloUOHDvj888898qAg1xk7dqz0z7169ULv3r3RqVMnbNu2DcOHD/dgz5RJT0/HkSNHsHPnTk93xS0sXe+UKVOkf+7VqxeioqIwfPhwnDp1Cp06dXJ3NxXp2rUrCgoKoNPp8P/+3//DhAkTsH37dk93yyUsXWv37t2b1D09c+YMZsyYgS1btqBly5ae7o7L2XO9jen+cprPyUJCQtClSxecPHkSkZGRqK6uRllZmVGbc+fOITIyEgAQGRlpttpC/7u+TWOl759c/w2v7/z580bHb968icuXL3v9d9CxY0eEhYXh5MmTALzzWqdPn45169bh22+/Rfv27aXXnfW3a6mNRqPxyH9sWLpeOUlJSQBgdH+95Xr9/PzQuXNn9O/fH5mZmUhMTMRbb73VJO+rpWuV4833ND8/H+fPn0e/fv3QokULtGjRAtu3b8fbb7+NFi1aICIiokndW1vXW1tba/YeT95fBlNOdu3aNZw6dQpRUVHo378/fH19sXXrVul4YWEhiouLpTl9rVaLw4cPGz2Et2zZAo1GIw1VN1bx8fGIjIw0ur7y8nLs3r3b6PrKysqQn58vtcnJyUFdXZ30h6/VarFjxw7U1NRIbbZs2YKuXbs2mik+Ob/88gsuXbqEqKgoAN51rUIITJ8+HWvWrEFOTo7Z1KOz/na1Wq3ROfRtDHNa3MHW9copKCgAAKP76y3Xa6qurg5VVVVN7r7K0V+rHG++p8OHD8fhw4dRUFAg/QwYMADjx4+X/rkp3Vtb1+vj42P2Ho/eX4fS1cnMc889J7Zt2yaKiorErl27RHJysggLCxPnz58XQtQvVY2NjRU5OTli3759QqvVCq1WK71fv3Tz3nvvFQUFBWLTpk2iXbt2jaY0wtWrV8WBAwfEgQMHBADxz3/+Uxw4cED8/PPPQoj60gghISHiyy+/FIcOHRIPPfSQbGmEvn37it27d4udO3eKW2+91ahcQFlZmYiIiBCPPvqoOHLkiFixYoUIDAx0e7kAa9d69epV8ec//1nk5eWJoqIi8d///lf069dP3HrrreLGjRted61Tp04VwcHBYtu2bUbLiq9fvy61ccbfrn7Z8ezZs8Xx48fF4sWLPbLM2tb1njx5Urz00kti3759oqioSHz55ZeiY8eOYujQoV53vfPmzRPbt28XRUVF4tChQ2LevHlCpVKJb775RgjRtO6rtWttSvfUEtPVbE3p3soxvN7Gdn8ZTCmUlpYmoqKihJ+fn7jllltEWlqaOHnypHS8srJSTJs2TYSGhorAwEDx8MMPi5KSEqNznD59WowcOVIEBASIsLAw8dxzz4mamhp3X4qsb7/9VgAw+5kwYYIQor48wvz580VERITw9/cXw4cPF4WFhUbnuHTpknjkkUdEq1athEajEU888YS4evWqUZuDBw+KO+64Q/j7+4tbbrlFZGVluesSJdau9fr16+Lee+8V7dq1E76+vqJDhw5i8uTJRktuhfCea5W7TgDi448/lto462/322+/FX369BF+fn6iY8eORp/hLraut7i4WAwdOlS0adNG+Pv7i86dO4vZs2cb1awRwjuu98knnxQdOnQQfn5+ol27dmL48OFSICVE07qv1q61Kd1TS0yDqaZ0b+UYXm9ju78qIYRwbCyLiIiIiPSYM0VERESkAIMpIiIiIgUYTBEREREpwGCKiIiISAEGU0REREQKMJgiIiIiUoDBFBEREZECDKaIiIiIFGAwRURN0gsvvIA+ffp4uhtE1AwwmCIijyotLcWMGTPQuXNntGzZEhERERg8eDCWLl2K69evW3zf6dOnoVKppM1NTf35z38228DUXgkJCfD390dpaWmD3k9EzQuDKSLymJ9++gl9+/bFN998g1dffRUHDhxAXl4e5syZg3Xr1uG///2v7PtqampsnrtVq1Zo27atw33auXMnKisr8bvf/Q7Lly+32b66utrhzyCipoXBFBF5zLRp09CiRQvs27cPf/jDH9CtWzd07NgRDz30ENavX48HHngAAKBSqbB06VI8+OCDCAoKwiuvvGLz3IbTfN988w1atmyJsrIyozYzZszA3XffbfTaRx99hHHjxuHRRx/Fv/71L7PzxsXF4eWXX8Zjjz0GjUaDKVOmAKgPwoYMGYKAgADExMTgmWeeQUVFhfS+f//73xgwYABat26NyMhIjBs3DufPn3fk6yKiRorBFBF5xKVLl/DNN98gPT0dQUFBsm1UKpX0zy+88AIefvhhHD58GE8++aRDnzV8+HCEhITgiy++kF6rra3FypUrMX78eOm1q1evYtWqVfjjH/+Ie+65BzqdDt99953Z+f7xj38gMTERBw4cwPz583Hq1CmMGDECY8aMwaFDh7By5Urs3LkT06dPl95TU1ODl19+GQcPHsTatWtx+vRpPP744w5dBxE1UoKIyAO+//57AUCsXr3a6PW2bduKoKAgERQUJObMmSOEEAKAmDlzplG7oqIiAUAcOHBA9vwLFy4UiYmJ0u8zZswQd999t/T75s2bhb+/v7hy5Yr02gcffCD69Olj9J4JEyYYnbdDhw5i1KhRRq9NnDhRTJkyxei17777TqjValFZWSnbv7179woA4urVq7LHich7cGSKiBqVPXv2oKCgAD169EBVVZX0+oABAxSdd/z48di2bRvOnj0LAPjkk0+QmpqKkJAQqc2//vUv/PGPf5R+/+Mf/4hVq1bh6tWrRucy7cvBgweRnZ2NVq1aST8pKSmoq6tDUVERACA/Px8PPPAAYmNj0bp1a9x5550AgOLiYkXXRUSex2CKiDyic+fOUKlUKCwsNHq9Y8eO6Ny5MwICAoxetzQVaK+BAweiU6dOWLFiBSorK7FmzRqjKb5jx47h+++/x5w5c9CiRQu0aNECt912G65fv44VK1ZY7cu1a9fwpz/9CQUFBdLPwYMH8eOPP6JTp06oqKhASkoKNBoNPvnkE+zduxdr1qwBwAR2oqaghac7QETNU9u2bXHPPffg3XffxdNPP604WLLH+PHj8cknn6B9+/ZQq9VITU2Vjn300UcYOnQoFi9ebPSejz/+GB999BEmT55s8bz9+vXDsWPH0LlzZ9njhw8fxqVLl5CVlYWYmBgAwL59+5xwRUTUGHBkiog8ZsmSJbh58yYGDBiAlStX4vjx4ygsLMR//vMfnDhxAj4+PjbPUVhYaDQiVFBQYLF0wvjx47F//3688sor+N3vfgd/f38A9cnh//73v/HII4+gZ8+eRj+TJk3C7t27cfToUYt9mDt3LnJzczF9+nQUFBTgxx9/xJdffikloMfGxsLPzw/vvPMOfvrpJ3z11Vd4+eWXG/CNEVFjxJEpIvKYTp064cCBA3j11VeRkZGBX375Bf7+/ujevTv+/Oc/Y9q0aTbPMXbsWLPXzpw5I9u2c+fOGDRoEPbs2YM333xTev2rr77CpUuX8PDDD5u9p1u3bujWrRs++ugj/POf/5Q9b+/evbF9+3b85S9/wZAhQyCEQKdOnZCWlgYAaNeuHbKzs/H888/j7bffRr9+/fCPf/wDDz74oM3rI6LGTyWEEJ7uBBEREZG34jQfERERkQIMpoiIiIgUYDBFREREpACDKSIiIiIFGEwRERERKcBgioiIiEgBBlNERERECjCYIiIiIlKAwRQRERGRAgymiIiIiBRgMEVERESkwP8H/RoZDpxePyQAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot(x='GrLivArea', y='SalePrice',style='.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Theory of linear regression\n",
    "\n",
    "The goal of learning regression is to find a line that is closest to all the points. \n",
    "\n",
    "The slope and intercept of such a line $y = m x + b$ can be found as: \n",
    "\n",
    "$$m = { n (\\Sigma xy) - (\\Sigma x) (\\Sigma y) \\over n (\\Sigma x^2) - (\\Sigma x)^2 } $$\n",
    "\n",
    "$$b = { (\\Sigma y) (\\Sigma x^2) - (\\Sigma x) (\\Sigma xy) \\over n (\\Sigma x^2) - (\\Sigma x)^2 } $$\n",
    "\n",
    "Details derivation of this can be found [here](https://en.wikipedia.org/wiki/Simple_linear_regression). \n",
    "\n",
    "We'll break this calculation into a few steps to help make it easier.\n",
    "\n",
    "First lets define $x$ and $y$. $x$ will be our _above ground square footage_ and $y$ will be _sale price_. In our equations we have a few different values we need, such as $n$ which is just the number of points we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = len(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we need our $x$ and $y$ by selecting only the column we care about for each one. Note about data formats: `data` is a Pandas [DataFrame](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.html#pandas.DataFrame) object which has rows and columns; `data['GrLivArea']` is a Pandas [Series](https://pandas.pydata.org/docs/reference/api/pandas.Series.html) object which only has rows; then we also convert from _Pandas_ data formats (in this case a _Series_) to _Numpy_ data formats using the `to_numpy()` function which is part of the Pandas _Series_ object. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = data['GrLivArea'].to_numpy()\n",
    "y = data['SalePrice'].to_numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will calculate $\\Sigma xy$, $\\Sigma x$, $\\Sigma y$, and $\\Sigma x^2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "sum_xy = np.sum(x*y)\n",
    "sum_x = np.sum(x)\n",
    "sum_y = np.sum(y)\n",
    "sum_x2 = np.sum(x*x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The denominator in the equation for $m$ and $b$ are the same so we can calculate that once:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "denominator = n * sum_x2 - sum_x * sum_x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can calculate our fit values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = 87.688145 * x + 34754.077892\n"
     ]
    }
   ],
   "source": [
    "m = (n * sum_xy - sum_x * sum_y) / denominator\n",
    "b = (sum_y * sum_x2 - sum_x * sum_xy) / denominator\n",
    "print('y = %f * x + %f' % (m,b))\n",
    "\n",
    "# saving these for later comparison\n",
    "m_calc = m\n",
    "b_calc = b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can plot the fit results with our data to see how we did. \n",
    "\n",
    "First we define a plotting function because we're going to do this often and we want to reuse our code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data(x,y,m,b,plt = plt):\n",
    "   # plot our data points with 'bo' = blue circles\n",
    "   plt.plot(x,y,'bo')\n",
    "   # create the line based on our linear fit\n",
    "   # first we need to make x points\n",
    "   # the 'arange' function generates points between two limits (min,max)\n",
    "   linear_x = np.arange(x.min(),x.max())\n",
    "   # now we use our fit parameters to calculate the y points based on our x points\n",
    "   linear_y = linear_x * m + b\n",
    "   # plot the linear points using 'r-' = red line\n",
    "   plt.plot(linear_x,linear_y,'r-',label='fit')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now can use this function to plot our results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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17Mknn8QHH3yAZcuWYdOmTfj222+RmZmpllutVowdOxY1NTX49NNP8a9//QuLFi3Ciy++qNY5fvw4xo4di9tuuw179+7F9OnT8Ytf/ALr1q1T6yxZsgQzZszA7Nmz8dlnn2HQoEHIyMjA2bNnPW4LERERkU+IF2bPni2DBg1yWFZeXi6RkZGybNky9djhw4cFgBQXF4uIyOrVqyUiIkJKS0vVOgsWLBCLxSLV1dUiIvLMM89Iv379NOfOysqSjIwM9efhw4fL1KlT1Z+tVqt07txZ5s6d63FbPFFRUSEApKKiwuP3EBERUXAF+vntdc/UkSNH0LlzZ/To0QOTJ0/GyZMnAQC7d+9GbW0t0tPT1bp9+vRBamoqiouLAQDFxcUYMGAAEhMT1ToZGRmorKzEwYMH1Tr257DVsZ2jpqYGu3fv1tSJiIhAenq6WseTtjhSXV2NyspKzYuIiIjIFa+CqREjRmDRokVYu3YtFixYgOPHj2PkyJG4ePEiSktLYTKZEBsbq3lPYmIiSktLAQClpaWaQMpWbitzVaeyshJVVVX4/vvvYbVaHdaxP4e7tjgyd+5cxMTEqK+UlBTPvhgiIiJqtdp4U3nMmDHqfw8cOBAjRoxA165dsXTpUkRFRfm8cYE2a9YszJgxQ/25srKSARURERG5pCs1QmxsLK699locPXoUSUlJqKmpQXl5uaZOWVkZkpKSAABJSUlNVtTZfnZXx2KxICoqCvHx8TAajQ7r2J/DXVscMZvNsFgsmhcRERGRK7qCqUuXLuGrr75Cp06dMHToUERGRqKgoEAtLykpwcmTJ5GWlgYASEtLw/79+zWr7tavXw+LxYK+ffuqdezPYatjO4fJZMLQoUM1derr61FQUKDW8aQtRERERD7hzWz1p556SoqKiuT48ePyySefSHp6usTHx8vZs2dFROTRRx+V1NRU2bhxo+zatUvS0tIkLS1NfX9dXZ30799fRo8eLXv37pW1a9dKQkKCzJo1S61z7NgxiY6OlpkzZ8rhw4dl/vz5YjQaZe3atWqdvLw8MZvNsmjRIjl06JBMmTJFYmNjNasE3bXFE1zNR0REFH4C/fz2KpjKysqSTp06iclkki5dukhWVpYcPXpULa+qqpLHH39c4uLiJDo6WsaPHy9nzpzRnOPEiRMyZswYiYqKkvj4eHnqqaektrZWU6ewsFAGDx4sJpNJevToIQsXLmzSlnnz5klqaqqYTCYZPny4bNu2TVPuSVvcYTBFREQUfgL9/DaIiAS3byx0VVZWIiYmBhUVFZw/RUREFCYC/fz2ajUfERFRa2W1Alu2AGfOAJ06ASNHAkZjsFtFoYDBFBERkRv5+cC0acA33zQcS04G3noL4E5lpGs1HxERUUuXnw9MnKgNpADg9GnleH5+cNpFoYPBFBERkRNWq9Ij5Wh2se3Y9OlKPWq9GEwRERE5sWVL0x4peyLAqVNKPWq9GEwRERE5ceaMb+tRy8RgioiIyIlOnXxbj1omBlNEREROjByprNozGByXGwxASopSj1ovBlNEREROGI1K+gOgaUBl+/nNN5lvqrVjMEVERORCZiawfDnQpYv2eHKycpx5pohJO4mIiNzIzATGjWMGdHKMwRQREZEHjEbg1luD3QoKRRzmIyIiItKBwRQRERGRDgymiIiIiHRgMEVERESkA4MpIiIiIh0YTBERERHpwGCKiIiISAcGU0REREQ6MJgiIiIi0oHBFBEREZEODKaIiIiIdGAwRURERKQDgykiIiIiHRhMEREREenAYIqIiIhIBwZTRERERDowmCIiIiLSgcEUERERkQ4MpoiIiIh0YDBFREREpAODKSIiIgq88nJg0SLg44+D3RLd2gS7AURERNRKXL4MfPABkJcHrF4N1NQAP/kJMHp0sFumC4MpImr1rFZgyxbgzBmgUydg5EjAaAx2q4haiJoaYN06IDcXeP994IcfGsr69gV+/GNABDAYgtdGnRhMEVGrlp8PTJsGfPNNw7HkZOCtt4DMzOC1iyisWa1AYaHSA7VihTKkZ9O9O5CTA2RnAwMGBK2JvqRrztQrr7wCg8GA6dOnq8euXLmCqVOnokOHDmjXrh0mTJiAsrIyzftOnjyJsWPHIjo6Gh07dsTMmTNRV1enqVNUVIQhQ4bAbDajV69eWLRoUZPPnz9/Prp164a2bdtixIgR2LFjh6bck7YQUeuVnw9MnKgNpADg9GnleH5+cNpFFJbq64FPPwX++7+BLl2U4bt//lMJpDp1AqZPB7ZvB776Cnj55RYTSAEApJl27Ngh3bp1k4EDB8q0adPU448++qikpKRIQUGB7Nq1S66//nq54YYb1PK6ujrp37+/pKeny549e2T16tUSHx8vs2bNUuscO3ZMoqOjZcaMGXLo0CGZN2+eGI1GWbt2rVonLy9PTCaTvPPOO3Lw4EF55JFHJDY2VsrKyjxuizsVFRUCQCoqKpr5LRFRqKqrE0lOFlHGF5q+DAaRlBSlHhE5UV8v8tlnIs88I5Kaqv2fqEMHkV/+UqSwMOD/IwX6+d2sYOrixYtyzTXXyPr16+WWW25Rg6ny8nKJjIyUZcuWqXUPHz4sAKS4uFhERFavXi0RERFSWlqq1lmwYIFYLBaprq4WEZFnnnlG+vXrp/nMrKwsycjIUH8ePny4TJ06Vf3ZarVK586dZe7cuR63xR0GU0QtV2Gh80DK/lVYGOyWEoWgL74Qeeklkd69tf/DtGsncv/9IqtXi9TUBK15gX5+N2uYb+rUqRg7dizS09M1x3fv3o3a2lrN8T59+iA1NRXFxcUAgOLiYgwYMACJiYlqnYyMDFRWVuLgwYNqncbnzsjIUM9RU1OD3bt3a+pEREQgPT1dreNJWxqrrq5GZWWl5kWtm9UKFBUp8yaLipSfqWU4c8a39YhavJMngVdfBYYMAfr0AV56CSgpAcxmYMIEYPly4OxZ4P/+DxgzBoiMDHaLA8brCeh5eXn47LPPsHPnziZlpaWlMJlMiI2N1RxPTExEaWmpWsc+kLKV28pc1amsrERVVRUuXLgAq9XqsM4XX3zhcVsamzt3LubMmePi6qk14cTklq1TJ9/WI2qRysqAZcuUf1F++mnD8TZtlHQG2dnAuHGAxRK8NoYAr4KpU6dOYdq0aVi/fj3atm3rrzYFzaxZszBjxgz158rKSqSkpASxRRQstonJItrjtonJy5czoAp3I0cqwfHp003vM6Cs0k5OVuoRtSoXLgArVyoB1MaNysRyQPmf4pZblABqwgQgPj647QwhXgVTu3fvxtmzZzFkyBD1mNVqxebNm/HnP/8Z69atQ01NDcrLyzU9QmVlZUhKSgIAJCUlNVl1Z1thZ1+n8aq7srIyWCwWREVFwWg0wmg0Oqxjfw53bWnMbDbDbDZ78Y1QS2S1Kj1Sjh6wtlQo06cr/xhjLqLwZTQqvYwTJyr31P5+29LdvPkm7zG1Ej/8oOSAyssD1qwBamsbyoYPV1IZ3HuvskqPmvBqztSoUaOwf/9+7N27V30NGzYMkydPVv87MjISBQUF6ntKSkpw8uRJpKWlAQDS0tKwf/9+nD17Vq2zfv16WCwW9O3bV61jfw5bHds5TCYThg4dqqlTX1+PgoICtc7QoUPdtoXIkS1bmi6VtycCnDql1KPwlpmp9DI2fj4kJ7P3kVqB6mpg1Sqlp6ljR+C++5SAqrZWSVvw8stKGoPt25V/QTKQck7vDHb71XwiSjqC1NRU2bhxo+zatUvS0tIkLS1NLbelRhg9erTs3btX1q5dKwkJCQ5TI8ycOVMOHz4s8+fPd5gawWw2y6JFi+TQoUMyZcoUiY2N1awSdNcWd7iar3VavNizVV6LFwe7peQrdXXKqr3Fi4Oyipv8iPe2kdpakXXrRB58UCQmRvuXWs+eIs8/L3LgQLBbqVtYpEaw1ziYqqqqkscff1zi4uIkOjpaxo8fL2fOnNG858SJEzJmzBiJioqS+Ph4eeqpp6S2tlZTp7CwUAYPHiwmk0l69OghCxcubPLZ8+bNk9TUVDGZTDJ8+HDZtm2bptyTtrjCYKp14pJ5opZhxYqmucSSk5XjrYrVKrJli8jUqSIdO2q/kC5dRGbMENm5U8kZ1UIE+vltEHE0M4QAZQJ6TEwMKioqYGnlKxVaE6sV6NbN/cTk48c5n4YoVDlbRGKbD9fih3FFgD17lEnkS5YocxNsOnRQ5j/l5AA33QRE6NoMJSQF+vnNvfmIGuHEZKLw1qoXkRw+rEwiz8sDvvyy4bjFAowfr8yPGjWqVeWACgQGU0QO2CYmO8oz9eabLfxftERhzptFJLfeGrBm+c+JE0rvU24u8PnnDcfbtgXuukvpgRozRvmZ/ILBFJETmZnKv1y3bFGyYHfqpOQcanH/kiVqYVpFdvvSUmDpUqUHyn5XjzZtgIwMJYC6+27g6quD18ZWhMEUkQtGYwv5lytRK9Jis9ufP69MBrPtb2WfTPO22xqSabZvH9RmtkYMpoiIqEVpUdntL11SckHl5QHr1mmTaV5/fUMyzbCLDFsWBlNERNSihP0ikitXlCzkubnAhx8CVVUNZYMGKT1QWVlA9+7BayNpMJgiIqIWJ+wWkdTWKvvg5eYq++JVVjaU9eql9EBlZwP/2SmEQguDKSIi8jurNfCLOUJ+EUl9PbB1qzKEt2wZ8P33DWXJyUrwlJ0NDBnS0KVGIYnBFBER+VV+vuMeorfe8n8PUcgtIhEBdu9uSKZ5+nRDWUJCQzLNG25okck0WyoGU0RE5DfOMpGfPq0cb/GZyG0OHVICqLw84OjRhuMWi/IF5OQAP/6xktqAwg63k3GB28kQETWfbWsmZwk0W/zWTMeONSTT3L+/4XhUlJIDKjsbuP12JtP0A24nQ0QtTjDmy1DwtbpM5ADw7bcNyTS3b284HhmpBE45OUpW8nbtgtdG8jkGU0TkV8GcL0PB1SoykQPAuXPAihVKD9SmTQ1jmhERytBddrbyyx4XF9x2kt8wmCIiv+F8mdatxWYiB4CLF5Vkmrm5wMcfA3V1DWU33KD0QE2cCCQlBa+NFDCcM+UC50wRNV+rny/jgZY+/Gn7HXCXiTxsfgeqqoDVq5UhvA8/VJJr2gwerARQWVlA165BayIpOGeKiFqEVjlfxgutYfgz7DORA0oyzQ0blB6o995TeqRsrr22IZlmnz5BayIFH4MpIvKLVjNfphla0/Bn2GUiB5Rkmlu2KAHU8uXKnCib1NSGZJqDBzOZJgFgMEVEftKi58voYLUqgYWjYS8R5dk8fbqSuTuke2y8EPKZyAHly9+5UxnCW7JEWZVn07EjMGmSEkClpTGZJjXBYIqolfPXvJ2RI5XeB3fzZUaO1P9Z4aS1Dn+GXCZymwMHGpJpHjvWcDwmBpgwQRnGu/VWJtMkl/jbQdSK+XPeTouYL+MHHP4MAV99pQRPubnAwYMNx6OjlWSaOTlARgZgNgevjRRWGEwRtVKBmLcTlvNl/IzDn0Fy+rQyfJeXpwzn2ZhMwJgxSgB1553AVVcFr40UtpgawQWmRqCWKtBpC1p6CgBvtLh0AaHs+++VaD4vD9i8WZtMc9QoJYAaPx6IjQ1qM8n3mBqBiPwu0PN2Qna+TBBw+NPPKiuVFAa5ucD69Ur0anPTTcok8nvvVSaVE/kIgymiVojzdoLLm+FP9up5oKoK+OgjJYD66COgurqhbMgQpQdq0iQlrQGRHzCYImqFOG8n+DxJF9AaEns2W02N0vOUl6f0RF261FDWp09DMs1rrw1aE6n14JwpFzhniloqztsJfc4WCNiGAltSYk+PWa3K3KfcXGVj4fPnG8q6dlWCp5wcYOBAJtNs5Thnioj8jvN2QltrTOzplAiwfbvSA7V0qXbsOTFR2QsvOxu4/noGUBQ0DKaIWqlgpC3g/B/PtNbEnioRYP/+hmSaJ040lMXFNSTTvOUW/gJRSGAwRdSKBXKbD87/cc0+0Dx0yLP3tLgFAkeONCTTPHy44fhVVwH33KP0QI0ereSGIgohDKaIWjlnaQt82YvUmjb2bQ5HgaYnWsQCgVOnlOG73Fxg9+6G42YzcMcdSgB1551KdnKiEMUJ6C5wAjq1Vr7sRQp0glB/8OfwpLNA05Vw+M5c+u47YNkypRdqy5aG40YjkJ6uDOHdc4+yPx5RM3ACOhEFla97kcJ9/o8/hyddTTR3JmwXCJSXNyTTLCjQJtMcOVIJoCZOBBISgtVComZjMEVEKn+sIgvnBKH+Hp50F2g6Elb7Gl6+DHzwgdIDtXq1khvKZtgwZQgvK0u5KKIwxmCKiFT+6EUK1wShgUhP4GkA+fzzQN++YbICsqYGWLdOCaBWrQJ++KGhrG9fpQcqKwu45prgtZHIxxhMEZHKH71II0cqHQ/uEoSOHOn5OQMhEMOTngaQo0aF5hCoymoFiooakmmWlzeUde/ekEyzf3/mgqIWKcKbygsWLMDAgQNhsVhgsViQlpaGNWvWqOVXrlzB1KlT0aFDB7Rr1w4TJkxAWVmZ5hwnT57E2LFjER0djY4dO2LmzJmoq6vT1CkqKsKQIUNgNpvRq1cvLFq0qElb5s+fj27duqFt27YYMWIEduzYoSn3pC1EpOWPXiRbglCg6XM0lOf/BGJ40hZoOmMwACkpoRdoAlCiyU8/BX71K6BLF2Xi+D//qQRSnTop3XbbtgFffQX8/vfAgAEMpKjlEi+8//778tFHH8mXX34pJSUl8utf/1oiIyPlwIEDIiLy6KOPSkpKihQUFMiuXbvk+uuvlxtuuEF9f11dnfTv31/S09Nlz549snr1aomPj5dZs2apdY4dOybR0dEyY8YMOXTokMybN0+MRqOsXbtWrZOXlycmk0neeecdOXjwoDzyyCMSGxsrZWVlah13bfFERUWFAJCKigqv3kcUrurqRJKTRQwGEeVpqX0ZDCIpKUo9b61YoZzb/nwpKcrxUFRY6Pg7aPwqLNT3OTNnOj+3wRBi3099vciePSLPPivStau2se3bi0yZonwhzfkFIfKhQD+/vQqmHImLi5N//OMfUl5eLpGRkbJs2TK17PDhwwJAiouLRURk9erVEhERIaWlpWqdBQsWiMVikerqahEReeaZZ6Rfv36az8jKypKMjAz15+HDh8vUqVPVn61Wq3Tu3Fnmzp0rIuJRWzzBYIpaoxUrlId444DKdkzPw72uTnnWLl7c8Mx1dCwU+DOwtLF9186CqZkzfXc9upSUiLz0kkifPtoGtmsn8tOfinz0kch//g4PB6H6O0e+EzbBVF1dneTm5orJZJKDBw9KQUGBAJALFy5o6qWmpsrrr78uIiIvvPCCDBo0SFN+7NgxASCfffaZiIiMHDlSpk2bpqnzzjvviMViERGR6upqMRqNsnLlSk2dn/3sZ3L33XeLiHjUFk8wmKLWKlC9SI4+Jzk5dHpj/B1YNr52Xwdrunz9tcirr4pcd522YWazyIQJIsuWiVy+HKTGNV+o/86RbwT6+e31BPT9+/cjLS0NV65cQbt27bBy5Ur07dsXe/fuhclkQmxsrKZ+YmIiSktLAQClpaVITExsUm4rc1WnsrISVVVVuHDhAqxWq8M6X3zxhXoOd21xpLq6GtXV1erPlZWVbr4NopYpENvMNDftQCD39/Pn/oUhmX+rrKwhmeYnnzQcNxqVbVyys5VkmmGaxJiZ+MlfvA6mevfujb1796KiogLLly/HAw88gE2bNvmjbQE3d+5czJkzJ9jNINLFV8GGs21mfKG5aQeCsb+fvwLLkMm/VV6ufLG5ucDGjUB9vXLcYABuvllZhTdhAhAf7+eG+FcgUl1Q6+V1MGUymdCrVy8AwNChQ7Fz50689dZbyMrKQk1NDcrLyzU9QmVlZUhKSgIAJCUlNVl1Z1thZ1+n8aq7srIyWCwWREVFwWg0wmg0Oqxjfw53bXFk1qxZmDFjhvpzZWUlUlJSPPlaiEJCuGwm3JxemWD2KvgjsPR3/i2XQfUPPyjJNHNzgbVrtck0hw9XeqAmTVJW6bUQIdkTSC2GV6kRHKmvr0d1dTWGDh2KyMhIFBQUqGUlJSU4efIk0tLSAABpaWnYv38/zp49q9ZZv349LBYL+vbtq9axP4etju0cJpMJQ4cO1dSpr69HQUGBWseTtjhiNpvVtA+2F1G4sAUbjR8YtmAjPz847XLE214Zd70KgNKrYL9DSaizpUVwli1AT1qE/HxlP8TbbgPuu0/589qu1Sh+bpXS09Sxo/Ln++8rgVT//sDLLwNHjwLbtwNPPtmiAikghHoCqWXyZoLVc889J5s2bZLjx4/Lvn375LnnnhODwSAff/yxiCjpCFJTU2Xjxo2ya9cuSUtLk7S0NPX9ttQIo0ePlr1798ratWslISHBYWqEmTNnyuHDh2X+/PkOUyOYzWZZtGiRHDp0SKZMmSKxsbGaVYLu2uIJTkCncBHyk5kb8TbtQKDSFASaPya4268QNKJW0vGx/AMPyXnEaj+kRw+R3/xGZP9+319YCGqpv0PkWEiv5nvooYeka9euYjKZJCEhQUaNGqUGUiIiVVVV8vjjj0tcXJxER0fL+PHj5cyZM5pznDhxQsaMGSNRUVESHx8vTz31lNTW1mrqFBYWyuDBg8VkMkmPHj1k4cKFTdoyb948SU1NFZPJJMOHD5dt27Zpyj1pizsMpihchNuDwtu0A4sXe3Z9ixcH97qaw5crJ+vqRFK6WOUGbJV5mCql6Kg58TfoLH9r96TUFe9Qcka1IoFIdUGhI9DPb4OIo45zApQ5UzExMaioqOCQH4W03FxlOMedxYuV0Z1gs1qVUaXZs5uW2Ya97OdAFRUpQ1XuFBaG53wX3YsGRIA9e3Dy1TzIkiXoipNq0ffogGW4F3nIxhaMhCAibL8nvWxD4YB2yNjR7xyFt0A/v7k3H1ELEE6bCTuaJG+vSxfgkUeA6moliBo5Mnz39/NUsye4f/GFEknn5QFffonU/xyuxNVYifHIRQ4KMAp1iNS8rbXOC/Jnqgtq3dgz5QJ7pihcWK3KhGN3wcbx44Fd9t24x+W774CsLMdtBJSyTz5xvBoRYK8CAODECWDJEiWI+vzzhuNt2+LsiDvx6KYcrMEYXEGU01O01p4pm0DmKqPgCPTzm8GUCwymKJyE2hCGox4oo9H7FXf27QeanjMlpRX0KpSWKsk0c3OB4uKG423aABkZSiqDceNQY74ayclK0OpIsIJqokBjMBVCGExRuHEUwAQj2HCWE6q57IMAoJX0Kly4AKxYoQzhFRZqk2neeqsy+S0zE+jQAYD74dNW14NHrRqDqRDCYIrCUbCHMGxDjq4SJDaXJ8NTwb5+XS5dUnI/5eYC69YBtbUNZddfr/RA3Xsv0Lmz5m2eBK+togeP6D84AZ2IdPHnNjCecJdpWg93E6dDMQO82+DuyhUlC3lurpKVvKqqoWzgQCWAys4Gund3en5nCU1tEhKUfJwmk2+uiYi0GEwRkU/5c6XYkSPOy0JxE1tnwd2fXq/DeEuBMoSXnw/Yb6req5cyhJedDfxnZwhXPAlev/sO+PTT1j3pnMifGEwR+VBYDzH5iD/TL/z978BvftP0O/Vku5lp0wK7iW3j4M6AetyIT3DfN7m4cdJyAHazxJOTlaWMOTnAkCHO95hxgNukEAUfgykiHwnFIaZgcJcTSo9vvnG8Ea0nvTPffKMkCn3xRd+2yZGG4E4wFLuRjTxkYQlS0NDIcxHxiJtyLyLuywFuvBGIaN5WqeGUY4yopWIwReQDvhxi8kfvViB7zIxGJYCcOFHpYGmcpkFvgOWoh2XVKs/eO3u2sqevv4Pb3f/vEKZ8k4ts5OEaHFWPV8CCfGQiD9koqB+FDVltcKuHiUad3cOWntCUKCwEZNOaMMW9+cgTvtxk2NE+bcnJzdunzZ/nbO7nJiR4tseeN/sLrljh3fv9tv/asWMiv/+9yMCBmg/8AVGSh0kyDivFjKpm7SXo7h76Y8NkonAW0hsdtzYMpsgTvtpk2PZAdBSMNfeB6I9zeqOuTrnuxYuVP999t/lBlKOg1F0g29x74bFvvxV5802RESM0H2BtEymrcJfk4N9yFS7qaoen99CXGyYThTtudBxCmGeKPOGLTYbd5WZqTuZqf5zT3ee5G0r0dMNiR20Fmg6XNvd8ujZ8PndOGdfNzVUaYPsrNCJCaUxODqx3j0e3Ie1dzhtLSXH/3Xt7D7kAgkjBPFNEYcYXE4DdTaAWAU6dUp7do0Z59nmentPRhG5veTr53pP5Pe3bA23bKnXsz+Uo4WRzV6h5PRn74kVlYlZenpJMs66uoSwtTYnM7r0XSEoCABjRMG/Mmexs94GOt/cw2DnGiFqr5i0fISKVLUBwtprdYFB6IVxNAPY0KJg0SQlcPBGoJfO2yfeNH/q2yff27bVNTgeafl+2n//2N+Drr5Vs54sXK38eP+540ri3QZEn90JVVaU0/t57gY4dgfvvBz76SAmkBg8GXnlFadinnwL//d9qIGWTmQk8/bTz0//hD+7vJdMeEIUHBlNEOnkSILz5puteCE+DgvPnmwYoes/pKhGmO57kd5o+Xbu5cWamMlzXpYu2fpcuDcN4tlVqnTopgcKWLY43SHYXyNqz1fnjH5Xz2UbpNOetrQXWrAEeeABITAQmTFAadeUKcO21ynLAQ4eAPXuAZ59VxuBcfDe5ua7b1Pi7aYxpD4jCREBmZoUpTkBvHRpPkm7uSi89E4BtE6kdTTT2ZCK2s3N26eL+fMnJzb/m5k6+X7Giadu6dHE9mdrZCkRnK9kcreKbOdPBPepilU2/LRL55S9FOnRw/Kbdu0Xq6wPy3dhz93vhzUpRV5/hi99/olDC1XwhhMFUy+frtAF6HkzOVm25ewi7+sw5c/y7um3xYs/OP326++u0BUQzZ3q/AtHRfYyPF7n5ZpF77hH54x9FliyxP2+9DMMO+SOelG/QWfvGjh1Fpk4V2bpVxGpt1vdSVyfy61979t24S4/gz7QHwUqbQeRvDKZCCIOpli3YaQOctal9e88fwu4ehp6mIvA031Fjnva+ACJLl4ps2OD6+gwGEaPRdbmznhhbUDl9uojF0vS9EREi/bBf/ge/kSPoqSm8gBjJu+pBqVvzsUhtbXNvn4go333jDi69gaw/0h6E4u8/ka8wNUIIYWqE8OPp0vBApw3wRkEBkJ7uvt6cOcBLLymPQHu2uUFPPw0sXAh8/737cxUWNm8VmLvv0V5EBFBf7/1nOPL888qqxsb3Nz9fmeZkrwe+QjbykI08DMAB9fgPiMb7uBu5yME6ZKAG5mZ/D64+3xlvf8d8mfYglH//iXwh4M/vgIRsYYo9U+HFmyELXyXa9AdP5skkJ3s2H8rdyxdzbrzNQO7Ll/39tU/g2RnfyHS8LtswXPOGakTKe7hbspAr0bjksx66xp/vyfcezN6fUP79J/KFQD+/uZqPWgRvlucD/llybrUqq8McrhLzgierAx95RJuHqTk8XWnoTmamsiotGOzv77YPv8cd37yNQtyKU0jBG5iBEdgBKyLwMX6Ch/BPJKIM92AVliAbl3FVk/PpWRXnyWbLNvHx3u3X6GtMuUDkW0zaSWHP3fJ8g0F52I8b1xA0+HrJuadJKz1lSx/Q+Jzt2wO/+hXQs6f352wsPh746199swHzuHFKUKaXwaAMB3oaiLaTSozHe4idnIe02vW4EQ3JNLfiRuQiB8sxEWeR6PZz9W4G7E3g8cYbwQukAKZcIPK5gPR/hSkO84WH5gxZ+HLJua8n8tqvztuwQWT27KaTtuPj9Q+Rvfuu521yN4Ta3D3yHH1fttV8zu5NW1yWCVgmy5EpVTBrCnfjOnkar0oKvvb6c/UOuXkzGT/Yw2eBSLlAFExczRdCGEyFB0+X5zeeD+OLJefugghvckLZVqL5IlDy5QPdXcqGOXOU9nuahsHZy2hUAinbZ9p/r21QI2PwkfwffiqVaKd542H0lhfxkqx69QuPArqICO3PvtoM2NOAUk9eL1/yZ8oFomBjMBVCGEyFBz2TafUuOff0szdscJ4LylEb/P3ytNfBmwBh+nT97bJ/iNdV18me1zfKjuumyPfQds0dR1eZi2dlEPYIUK/eX08mwy9d6r8klZ58figFKf5IuUAUCpgaIYQwNUJ4sC3zdrV5rqtl3nqWnOfmAvfd575e+/bKVjA2tvlUgDKBOtD/F65Y4dmcnaIi4Lbb/N4clQGCOzvuwHvZuYhYtlQzEakUiViKSchFDrbhegDKDPrG9zc/H5gyBTh3TnvuDh2Uff/8PVcp2J/vLV+mXCAKFYF+fjOYcoHBVPiwreYDtIGJbcWa3pVTzh44zQ02DAalnR06NH3o+tucOcCLL3pW19NgEfB+8ngDQX8cQA5ykY089MDxhqK4OGDCBGzpko3b5tyKeoPRo/trW1lZVKT8fOutyitQQUKwP5+otWMwFUIYTIUXRyvqUlKUVWZ6AilXK/XGjXPdKxZqkpOBEyc8f6jrDRZd6YmjyEYecpCLfjikHr+Eq/D9DePQ7blsICMDMJkA+O/+ElHLw2AqhDCYCj++HrKw9Xg1/r/EvkcEcNwrFkqa20NntQJdu3qX02r6dOVzHOVc6n3VNxj7wxLkIBfDsFs9Xg0TVuMO5CIHH2EsPiq8ymEmcg5JEZEnGEyFEAZTrZs3W26sWtW01yQYQ3jO6OnB+e1vgdmzPa9fWKhsYXPvvcrP8fgOE7EcOcjFzdii1quDEQUYhVzkYCXGoxIx3MaEiHwi0M9vJu0kcsJdRmsR4NQppV5mpjLkZ99rYrV6tseevyQkAJMnK+3S04NzzTWe101JAUaMAPolV+ABrEQ28pCODWiDholUmzESecjGckzEd+jY5Bx6M7ITEQUagykiJ7zdcsNo1G6Sa7UqvSyBnk/lbBPg5g6ReZoFOwqX8fvBH2JjbB4O1axGW1SrZbswFLnIwVJMwjdIcfh+o1GZ8M75T0QUbhhMETnhiy03HnnEuyEyPWxDZC+91DRIau52N1ar8mqc2sEmEjUYjY9xnyEXE9qsgvmDH9SyQ/gRcpGDPGTjKNx3b1mtSm8aEVG4YTBF5MTIka57llzt5+YoePGlxqvlXG1a7GwSvW2TYGeT0p1dQwSsuBVFyEYeJmAF2uMCIABqgePopgZQ+zEAtlxQnuLGukQUjhhMETlhNCo9NxMn+iZ48QWDQekliopq2stkm2BuG847fRooKwNeftlxW0QcbwLt+BoE12MbspGHSViKTihV61ZelYTK27MwYUUOdmA4vA2g7HFj3fDAVZVEjXiTLv33v/+9DBs2TNq1aycJCQkybtw4+eKLLzR1qqqq5PHHH5f27dvLVVddJZmZmVJaWqqp8/XXX8sdd9whUVFRkpCQIE8//bTU1tZq6hQWFsp1110nJpNJevbsKQsXLmzSnj//+c/StWtXMZvNMnz4cNm+fbvXbXGF28mQiHdbbvhiw18929M0d2saR5tAA/UyEHtlLp6V4+iqecM5xMnbeERuxUbpmlwn776rfxsZbqwbHtxteh0M9puD+3qLIApPIb03X0ZGhixcuFAOHDgge/fulTvuuENSU1Pl0qVLap1HH31UUlJSpKCgQHbt2iXXX3+93HDDDWp5XV2d9O/fX9LT02XPnj2yevVqiY+Pl1mzZql1jh07JtHR0TJjxgw5dOiQzJs3T4xGo6xdu1atk5eXJyaTSd555x05ePCgPPLIIxIbGytlZWUet8UdBlOti6u/kD39y9rTvfr0vp54wvEef642JHb1st8E+pNFJfIC5sgh9NFUqkQ7+T/8VO7AhxKJas3733hDXyDFjXXDg7PfsWDew1AM7ij4QjqYauzs2bMCQDZt2iQiIuXl5RIZGSnLli1T6xw+fFgASHFxsYiIrF69WiIiIjQ9RAsWLBCLxSLV1dUiIvLMM89Iv379NJ+VlZUlGRkZ6s/Dhw+XqVOnqj9brVbp3LmzzJ071+O2uMNgqvVw9ReyN//qXbw4MMGU7dW+vcicOSLV1fp6xN548muRV1+V8z2GaAqqYJblyJSJWCpR+MHp+x9/XCQhwbNgrkMH7c/cWDc8uOt1DUbvYigGdxQawiqYOnLkiACQ/fv3i4hIQUGBAJALFy5o6qWmpsrrr78uIiIvvPCCDBo0SFN+7NgxASCfffaZiIiMHDlSpk2bpqnzzjvviMViERGR6upqMRqNsnLlSk2dn/3sZ3L33Xd73BZ3GEy1Dq7+Qnb08Hf1r95A9Uw1flks3r8nAWXyOP4sW3CjpqAWRlmN2+V+/EssKPdpOw0G5fv7+GOR559XXhs2cFgmHHj6u20/ZOxPoRjcUegI9PO72RPQ6+vrMX36dNx4443o378/AKC0tBQmkwmxsbGauomJiSgtLVXrJCYmNim3lbmqU1lZiaqqKly4cAFWq9VhnS+++MLjtjRWXV2N6uqG3DiVlZXuvgYKc1arsmJNpGmZ7VjjLOauVsG5WwHoL57+qsagHOOxEjnIxSgUwIh6AEA9DNiCm5H7n2Sa5xDvl3aKKBPnJ08GvvtOOfa733mWpiHUtLZJ2N7mXfM3b5LqOtqaiMiXmh1MTZ06FQcOHMDWrVt92Z6gmjt3LubMmRPsZlAAufsL2RFbkORoFZy7FYCBDLBsovED7sIHyEYexmANzKhRy3bgv5CLHCzDvTiN5IC1yRZI2bhL0xBqnOXteuMNID6+ZQZYvsi75kuhFtxR69asYOqJJ57Ahx9+iM2bNyM5ueEv4KSkJNTU1KC8vFzTI1RWVoakpCS1zo4dOzTnKysrU8tsf9qO2dexWCyIioqC0WiE0Wh0WMf+HO7a0tisWbMwY8YM9efKykqkpDjO1kwtg56/aE+dAoqKlIel/cMzM1MJChw9bN98E6ivBx5+2PPeJLMZsOsw9YgJ1cjAOmQjD+OwClfhslp2AP3UXFDH0NO7E/uJiPM0DaHGWeqLb75p2I/QJhx73JzRk3fNH0ItuKNWzpsxwfr6epk6dap07txZvvzyyybltknfy5cvV4998cUXAjSdgG6/6u7tt98Wi8UiV65cERFlAnr//v01587JyWkyAf2JJ55Qf7ZardKlS5cmE9BdtcUdzplq+fTOcWrb1vl8KnerA+fMUSaQ+2o+khG1Mgrr5R94SM4jVlN4FD3kd/i19MN+n86B8scrUHNumsPb1BctbSK0bX5h4zmGwbhO271wtuiBc6Zat5CegP7YY49JTEyMFBUVyZkzZ9TX5cuX1TqPPvqopKamysaNG2XXrl2SlpYmaWlparktNcLo0aNl7969snbtWklISHCYGmHmzJly+PBhmT9/vsPUCGazWRYtWiSHDh2SKVOmSGxsrGaVoLu2uMNgKjw5C2IcHXf3F3JzXt48VOrqlAnYzQ2qDLDKDdgqf8ITUoqOmsJv0Fn+iCflv7BdgPqgB0mevuzTNISa5gTfLe2h7k3etUC0JVSCOwotIR1MAXD4sk+oaUuUGRcXJ9HR0TJ+/Hg5c+aM5jwnTpyQMWPGSFRUlMTHx8tTTz3lMGnn4MGDxWQySY8ePRwm7Zw3b56kpqaKyWSS4cOHy7Zt2zTlnrTFFQZTwedtMr4VK0S6dNH+xdqli8jMmc5THzj7C1nPKyVFSVfgn9xU9TIYn8n/YqacQKqm8FxEBzma/ku5GUUSgbqgB0bNeb3xRugmX9ST+iKUe9y8FUpJMkMpuKPQEejnt0FEJBjDi+GgsrISMTExqKiogMViCXZzwoovVjp5uzlvfj4wYYLn57dNCJ8zB7hwAXj3XeD7771royvx8drzxccDP/2pMifI/vvIzQXuu8/9+XrjC2QjD9nIQx+UqMcrcTXewz3IQw4eWpyOJ5+J9NuegP5mNCq/OzahNueoqAi47bbmvXfxYiAnx6fNof9obSsryb2AP78DErKFKfZMNY/ejMR1dSKzZ7v+V75dLlb1Pb6Yf5SQIHLnnf7vfbH/PubMcV4vFSdkJv5XPsNgTcFltJWlmCiZWC5tcVmuvlpk+nR9mcjtX/HxIu3aOS83GJT8W43vc0KCb7+nUBuu0TMs3JJ6pohCXUgP87U2DKa8pzcj8YoVngVFRqPI0qUN73MXfIXiy2BQhh8bH++IUnkCf5KtuEFTUIM28iHukMn4f3I1KvzeNkf/3fheNh7usWVidzUpuEOHpkOxRqPrtoTSnCNvh4VDrf1ErQGH+UIIh/m8Y7UC3bo5z9tkWzp9/LjjLnhvh+kAYMUK5U9v3xcqIiKUVAmxuIBM5CMHubgNhZpkmkW4FXnIRj4y/ZZM0xGDAWjfHmjbVlkOb5OSoqR4cDb0ZksdACjhhP35ACVtxLhxDcMyZWXAk0+6b09hYegkX3Q0BO2I/TWHylAlUWsQ6Oc3gykXGEx5x9P5JI4eilYrkJjYNNu4Ox06NH3Yh4urcAl3431kIw+3Yy1MqFXLtmEE8pCNpZiEM+gcxFYCGzY0zaXlbj6Ko2DDWRDm6Zwxd3OO9Mybac57G7/nu++AGTM8u2Yi8q9AP7+bnQGdqDE9GYlfftn7QApo3nuCyYRqjMEa5CAXd+EDRKNKLduHAchFDpYgC8fRI4it1Dp71nEQ4yoAyczU9j65ClB8kXzR28UKvniv0dj0HwWZmZwITdQaMZgin2nuQ9FqVR5cLZURdfgxNiIHuRiPlYhFhVp2FD3VbOSH0C+IrXTuyBHPemEaByCOgg1H9GbWdpaR3JMtavS81xFPr5mIWhYO87nAYT7PWa3KMN+kScD5847rOJszpWe5eagyoB434hNkIw/3Yhk6omEzum/QBUuQhVzkYDeGAjAEr6Ee8HQoVc/8IE/mWTk6p555enrn+BFR6Ar08zvC759ALV5+vvJQSk93HUgByvyRxg+mVav82bpAEgzBbryGp/E1umILbsZU/AUd8R2+Qzz+gsdwMzYhFSfxNP6I3RgGfwZSHToowYBe5855NifNFgRNn67NFeUJ236GXbpojycnuw7O3G1ULaLsobhli2/fS0Rkj8N8pIuzYZLGbJv8Nn4oWq1Kssxw1geHkYNcZCMP1+KIerwCFqzEeOQiBxvxY9QhMqDteughYO5c98NzvmQfgDhaZOBqPpE386xs9MzT0/NegIkiiagBgynyWOOHxw03KBN3XQVS7dsDeXlKCoCzZ5UhPdtDx2oF5s3zbdbxQOmG48jCEuQgF4OwTz1+GVH4AHchD9lYgzGoRtugtTEvTwmmnE2SPn0amDoVqKhw+HZdGgcgnk7y9nbOkZ7J63req2fCOxG1PJwz5QLnTDVw9PBISFB6OtxpXC8+HujZE/j8c+DKFd+31V+ScAaTsBTZyEMatqnHaxCJdchALnLwAe7CJVwdxFZquUpr4M+5avbpL5z1XvoiB5Nt3pO7yeuu5kx5+15/Xg8R+Qa3kwkhzICucJbVvDW82uN7+QX+JgW4Taxo+BKsMMgG/Fgext8lDueC3k6n7W+UTd5+Gxs9m/Y6ezXO9m3bfsXT+np+P11lavfVewNxPUSkX6Cf35yATi5Zre6H8lqadriI+/BvfIA7UYok/B1T8GMUIgKCT5GGX+EtdMFppKMA/8QvcAHtg91kpxovCLAt+c/P93yYy1OOFhkEYpJ3cyevN+e9nLRORI5wzhS59PLL/pusHErMuII7sBrZyMOd+FCTTHMvBqnJNL9Gt+A10gdElKBn+nTg6FElaPDV/XW0yEDvJG9PNWfyenPeG6jrIaLwwmCKnMrPB2bPDnYr/KcNajEKBWoyTQsuqmVf4ho1meYX+FEQW+l7tt6TTz9VJkx7shrTtoegTUKCsgVMt27Kf3fp4jgA8XaSt54VcnoSZnr6Xl9kayeilocT0F1ozRPQ3SU0DFcG1OMmbEUOcjERy5GAhqWEp5CMPGQjFznYg+sQask0DQbfDrfa9rrLzwemTPFsa5527ZTAqrKy4ZirVWzeTPJetSr0V8jpmfBORIHDpJ0UEtzNDQkvgmHYiT/gKZxEKjbjFjyGvyIB3+MsEjAfj+MmbEFXfI1n8Br2YAhCLZACfD9v7ch/UmJlZgJlZcCcOUoqC1cuXdIGUoB2HlZjRmPDVkGGRl+p/RyrVauUczT+nXN17mDw9HoYSBG1MgGZ5h6mWvNqvunTg78STe+rLw7I/+A3cgQ9NQUXECP/xIPyE6wTI2qD3k5fvmyr0Bqv4nNW19FqtQ0bPHt/43O5WsW2YkXTVXApKcrxcFwh5+p6iCj4Av385jCfC61hmM/RHBWrVckFdfGi+/eHmu44hmzkIQe5GIAD6vHLiML7uBu5yMFa3I4amIPYSv0iIoDbbwd27tTm8EpJAbKzgXfecT9s52hIypZI9cknm9cu+/xSjTmbD+VpvitX5w4GZkAnCl2Bfn5zAnor4egvfkdzVDp0AC5fBqqqnJ8r1HTCt8jCEmQjDyOwQz1eg0iswRjkIRsf4C78gHZBbKVv1dcDq1cDS5cqE8Dtt4vJylL6StwR0W794igxq7dcrWJzNsm7uSvkAh3MOPq8UAruiCh4GEy1Avn5wK9+pd2stn17x5sSezIJORS0xzlMxHJkIw+3YBMioEQPVkRgI36MXORgJcajHHFBbql/PfaYMt/Jtj1Pt26eBVL2zpzxfI9Fd5qziq05K+QCvZ0Lt48hIpcCMpgYplrCnKkVK4I/j8dXr6tRIT/F/8lHGCM1aKMp3IobZCrmSSLOBL2dgX7NmaPc68LC5r1/wwbXc5Y8eemZ12SbM+Usy37jczvLyO9JxvPmCPTnEZF+zIBOPmO1Kkvew1lbVCETK7AME1GGRPw//Ax3YA0iUYfPcB2ewf+iK07gJnyC+XgCZUgKdpMD7k9/Uu61t4kiDQZljhWgb2hP7yo2b1bIucrIbzs2fbpSzxcC/XlEFJ4YTLVgRUXhM2xnrw1qMQar8S/8DGVIxApMxESsQBSu4Av0xmy8hD44jKH4DK/hGZxE12A3OajOnVPm8ngzxGYfpJw9q+/zPdm2xR1Pt3UJ9HYu3D6GiDzBOVMtWFFRsFvguQhYMRJb1GSaHdAwoetrpKrJND/HIIRiDqhgKygAXnhBCT6cJZS0Fx8PTJ6szJ3ztlfFYFDe/8YbzjOfN4cn27oEejsXbh9DRJ5gMNWC2W//EZoEw7ED2chDFpagMxqeSKVIxFJMQh6ysQ3XQ9iJ6tLvfgcsWqRkNP/DH5xnS7/zTmDbNmXV35tvKq/kZGUV5/nz7oMwQKnz3XdKIOXr1WzutnUJ9HYu3D6GiDzBYKoFc5fNOlj6Yz9ykIts5KEHjqvHLyAWKzABechGEW6Flb+eXjl9Wgmknn4ayM3VDk/Z8k/94Q9NAyb7nixvtqwJRm/MyJHuN2dOSVHq+fLz3G0f46vPI6LwxKdVC+EoB05SCM3F7omjyEYespGH/jioHv8B0ViFcchFDj7G6LBPpmkvOVnJ2eUoBUVj0dFKXT1ElId7Xh7w1VfKRsa234cbbgB69nQ+kdpgUILvtm21KTRcCUZvjNGo9L699przOtnZvss3ZZscP3Fi00CT28cQkSogawbDVLikRnC0tUVysrJkPphL9rvglDyJP8oODNMUXIFJVmKcTEKeRONSUNvor9ejj4pUV3uWmsJi8f3nFxZqf0c8TZuwYYP77WSCub2Lu61nAP+0jdvHEIUXpkYgj1mtwG9/C0yY4HiD2JdeUubCBFI8vsOjWIAi3IKTSMXreAr/hV2ogxHrMBoP4h0kogzj8R6WIguXcVVgGxggf/2r0hMEACtWOL4P7f6TkL3xxsG+0HgIztMhubNngVGjgL//Xel5CbXNfD3ZgNsfq+syM4ETJ5QtbRYvVv48fpwJO4lIwWG+MOVu6w+Rpg9Cf7GgAvfgPWQjDz/BerRBw/KwLbgJucjBckzEd+gYmAb5yV13AR984Hn906eV4aHly5Us5UVFDSssR44EHn4YuHTJHy1tOgTn7URqW6oCR1m/33wzeEFEMFfXuZscT0StFzc6diFUNzr2duuPCROU3hFfisJljMVHyEEu7sBqtEW1WrYbQ5CLHCxBFr5Bim8/OIji44ErV7wLgBxtJgx4vrmvt5x9nm2rGXcTqR29L5Q28w3XTZGJKLC40TG55CojszM/+pFvPjsSNRiNj5GNPIzDKlyNhqjiEH6kBlBHcK1vPjDEnDvn3fcOKPXtNxO28XSSd+M9FO1X5dnOb+NqCK65E6lDrTeGq+uIKBQxmAoznswZaezmm5U5O83Jhh4BK27BJuQgFxOwAu1xQS07jm5qMs39GICWnkzTNnTavj1gNgPffuv5e+2HnfLzlS1IPLF0qRLQNO4Zuv5674fgQnXozhtcXUdEoYjDfC6E4jBfbi5w333evadzZ2WSs+fDU4IR2I4c5GISlqITStWSM0jCUkxCLnKwHSPQ0gMoZzZsUB7YBQVKwkx3bMNOng7ROht2s9fcIbhQG7pzxVlbHc0ZTEkJn6CQiPwr0M9vBlMuhGIwVVAApKf748yCgdin5oLqjhNqyXnEYTkmIg/Z2IRbUI8QffIG0OLFSr4jb+YiAUpddz2Lth4WvfvdhTtHAVNystIzlZkZXkEhEQVWoJ/fXqdG2Lx5M+666y507twZBoMB7733nqZcRPDiiy+iU6dOiIqKQnp6Oo4cOaKpc/78eUyePBkWiwWxsbF4+OGHcalRt8m+ffswcuRItG3bFikpKXj11VebtGXZsmXo06cP2rZtiwEDBmD16tVet6W164UjeAG/xUH0w+cYjFl4Bd1xApdwFd7FZNyJD5CEUvwSf0MhfsxA6j9sq95sw06A+zQCng7RxsczkLL14DlK+TFxolJum8+Vk6P8yUCKiILG28RUq1evlt/85jeSn58vAGTlypWa8ldeeUViYmLkvffek88//1zuvvtu6d69u1RVVal1br/9dhk0aJBs27ZNtmzZIr169ZKcnBy1vKKiQhITE2Xy5Mly4MAByc3NlaioKHn77bfVOp988okYjUZ59dVX5dChQ/L8889LZGSk7N+/36u2uBKKSTsXL9af0DEZJ+UpvCa7MERTUAWzrMB4mYilEoUffJ5IsrmvNm2C3wZ3CSs9Sero6b17993A/k6FGneJOYOZNJSIwkOgn99eB1OaNzcKpurr6yUpKUlee+019Vh5ebmYzWbJzc0VEZFDhw4JANm5c6daZ82aNWIwGOT06dMiIvKXv/xF4uLipLq6Wq3z7LPPSu/evdWfJ02aJGPHjtW0Z8SIEfLLX/7S47a4E4rBlKeZrBu/ElAmj2G+bMZNmoJaGGU1bpefYZFYUB70YCWUXwaD8nKW9bquTrk/ixcrfzZ+2Ht67xpnL29t+D0RkV5hnQH9+PHjKC0tRbrdpJ6YmBiMGDECxcXFAIDi4mLExsZi2LBhap309HRERERg+/btap2bb74ZJpNJrZORkYGSkhJcuHBBrZPeaPJQRkaG+jmetKWx6upqVFZWal6hwmpVcuycPq0MA3kiBuX4ORZiLTLwLTrjL5iKkdiKehiwCTfjUSxAJ5zBHViD/8MDqESMX68h3CUnux5+czfsZFvW7yyZqsHg2016w1UwE3MSETWHT1MjlJYqq74SExM1xxMTE9Wy0tJSdOyozYTdpk0btG/fXlOne/fuTc5hK4uLi0Npaanbz3HXlsbmzp2LOXPmeHaxAeQu27m9aPyAO/EhcpCLMVgDM2rUsj3GYcg352Dh5Uk4jWQ/tjj4OnQAfv5z4I9/1H+uyZOBBx/UPy+Hy/o94222diKiYOPefHZmzZqFiooK9XXq1KlgNwnLlzvee8+eCdW4C+/j37gPZUjEEmTjHqyCGTU4iL54Af+Da3AEx5fuxEuVM/DkH3wTSA0f7pPT+JzBAPztb0piy2XLgIQEfef797+VwGzVKv1ts+V66tJFe9xdr1drwh48Igo3Pg2mkpKSAABlZWWa42VlZWpZUlISzp49qymvq6vD+fPnNXUcncP+M5zVsS9315bGzGYzLBaL5hVMS5YAWVmOyyJgRTo24F+Rv0ApkvA+xuE+5KIdfsAxdMfL+DUGYB/64yD+lfI8/ndFL2RmKr0e06fr3wA5Lk7JrxQXp+88vpaSog1KJk5UhoNsG9Q+/3zzzmu/ikwvbprrmjcrJImIQoFPg6nu3bsjKSkJBQUF6rHKykps374daWlpAIC0tDSUl5dj9+7dap2NGzeivr4eI0aMUOts3rwZtbW1ap3169ejd+/eiPvP0zstLU3zObY6ts/xpC2h7JlnlG1D6usbjhlQjzR8ij/hv3EaXbAeP8HPav+JOJTjW3TCG5iO4diOnvgKz+NlHMAAJCQAJSVK1u7cXGXe1XPPNS8bur0LF4DRo5U/gyUlRckQ7i4osZ/LNGpU8z7LNiQ3fboyf00vLut3jT14RBRWvJ2xfvHiRdmzZ4/s2bNHAMjrr78ue/bska+//lpElHQEsbGxsmrVKtm3b5+MGzfOYWqE6667TrZv3y5bt26Va665RpMaoby8XBITE+X++++XAwcOSF5enkRHRzdJjdCmTRv5wx/+IIcPH5bZs2c7TI3gri2uBGs139Kl9quW6mUwPpNX8IycQKpmOdP3aC9/xRS5BYUSgTqnq57i44O/Es5Zu+bM8f59HTqIbNjQvKXxtmX3BkPz281VZIHjboUkEZEjIZ8aobCwUAA0eT3wwAMioqQkeOGFFyQxMVHMZrOMGjVKSkpKNOc4d+6c5OTkSLt27cRisciDDz4oFy9e1NT5/PPP5aabbhKz2SxdunSRV155pUlbli5dKtdee62YTCbp16+ffPTRR5pyT9riSjCCqbo6Jci4Fl/Ii3hJDqO35kleiXbyL9wvY/CRtEFN0AMiR4HOa695VnfdOvc5hRy9li3T94BdsaIhzUFzrnHxYn/ceSIi8pVAP7+5nYwLAd9O5uuv8dXvl6Dib3kYgj3q4Ssw40PciTxk4yOMxRVE+b8tOjz/vGf71dm2ZMnPVybZeyIrC/jkE+dbjHjK0QrJhATgu+/cv9e2zx4REYWmQD+/fZoagZqhrExZcpabC3z6KXr+53At2uBjjEYesrEK43ARobE3oC/ZlrZnZipzn2x73TnTvr0yKb8x2+Rwb+bSZGYC48Zp93a74QagZ0/3++xxFRkREdljMBUMFRXKkz8vD9i4sWGWucGAC4NuwXN7s7ECE3AOHmbnDDE336wEHd4EJffeqxy/917H9e3/bExEKZs+XQmQPJ3MbZsEbo95oIiIyFvMMxUMn38O/OIXwIYNSiA1fDjwxhvAqVOw7CrE6uRfhm0gBQAREc1b2j5xIrBihRJo2UtOBl56yfUKRBHg1Cmlp0kPriIjIiJvsWcqCKxpN6Fi2Gic6nELqsZl47+yeqiBhRENvSOhNJutcU+NK2fPKkN2y5c3nZeUnKwEUs6CEkfDbyNHKsOAnvDFFiPO2sAeKSIicoQ9UwGWnw906xGBDrvWYfDSXyNtcg9066ZNBmnrHfF0D74IH9zFmBhlPlJhoTJc1jhreHIy4OlOO/ZzoXyVnDLQW4wwDxQREXmKq/lc8PVqgPx8xz1OtqGvxsNI//438NOfuj/vtGkNw2rNkZCg9B7Z7SsNq7VpzwwAdOvmfC4UoEwSX7q0+QGIo1V2ycnKKOiTT7qfh3X8OAMfIqLWLtCr+dgzFSBWqxIkOAoEbMcaZ9duPG/HmXvuUd7rLYNBef31r9pACnDcM+Nqmw+b8+eB9HQ06W3zhC3YbLwP4enTwKRJSlscfTYnhxMRUTAxmAqQLVtcb1bsaAK1Nxu+jhvnfZuaM6na2QTtxrzdy86TYDMvTxmK5ORwIiIKJQymAsTTidH29bzZ8NVd4AUoc7A+/lj//CXbXKgNG5RhPUec9bY542mwmZDATYKJiCi0cDVfgDR3ArWtJ8jdqjhb4OUqR9LbbwM/+UmzL0HDNux3/rzzOva9be4yhnsTbDrKD0VERBQs7JkKEG+G7BrzdFVcoHMkNae3zZlAr9YjIiLyFfZMBYgnPUeuJlB72htjy5FUVKS8AOV9/ujJ8WUAZAs2uZULERGFG/ZMBVCgeo5WrQJ+/nNls+Hf/a75q+vc0dPb1pg388OIiIhCCYOpAPNlIktHXKUX8GZ1nSd8HQBxKxciIgpHTNrpQqCTfulltSo9UM5WxfkrsaWjRJspKa63jXHFUcJQ9kgREZGnAv38ZjDlQrgFU0VFwG23ua9XWOj7OVQMgIiIKFQE+vnNCegtiC9X13mL6QqIiKi1YjDVggQzvQB7poiIqLXiBPQWxJer67yRn6/M1brtNuC++5Q//bF6kIiIKBQxmGpBgpFeIJCrB4mIiEIRg6kWJpDpBTzZnNjTvfmIiIjCFedMtUC2LOj+nsPk6ebEnuzNR0REFK4YTLVQgVhdF8zVg0RERKGCw3zUbNycmIiIiMEU6RCs1YNEREShhMEUNRs3JyYiImIwRTpxc2IiImrtOAGddAvU6kEiIqJQxGCKfIJ78xERUWvFYT4iIiIiHRhMEREREenAYIqIiIhIBwZTRERERDowmCIiIiLSgcEUERERkQ4MpoiIiIh0YDBFREREpAODKSIiIiIdmAHdBREBAFRWVga5JUREROQp23Pb9hz3NwZTLly8eBEAkJKSEuSWEBERkbfOnTuHmJgYv3+OQQIVtoWh+vp6fPvtt7j66qthMBh8cs7KykqkpKTg1KlTsFgsPjlnqOK1tlyt6Xp5rS1Xa7re1nStAFBRUYHU1FRcuHABsbGxfv889ky5EBERgeTkZL+c22KxtIpfaIDX2pK1puvltbZcrel6W9O1AspzPCCfE5BPISIiImqhGEwRERER6cBgKsDMZjNmz54Ns9kc7Kb4Ha+15WpN18trbbla0/W2pmsFAn+9nIBOREREpAN7poiIiIh0YDBFREREpAODKSIiIiIdGEwRERER6cBgSqeXXnoJBoNB8+rTp49afuXKFUydOhUdOnRAu3btMGHCBJSVlWnOcfLkSYwdOxbR0dHo2LEjZs6cibq6ukBfikObN2/GXXfdhc6dO8NgMOC9997TlIsIXnzxRXTq1AlRUVFIT0/HkSNHNHXOnz+PyZMnw2KxIDY2Fg8//DAuXbqkqbNv3z6MHDkSbdu2RUpKCl599VV/X1oT7q715z//eZN7ffvtt2vqhMu1zp07F//1X/+Fq6++Gh07dsQ999yDkpISTR1f/e4WFRVhyJAhMJvN6NWrFxYtWuTvy2vCk+u99dZbm9zfRx99VFMnHK53wYIFGDhwoJqcMS0tDWvWrFHLW9J9dXetLeWeOvLKK6/AYDBg+vTp6rGWdG8bc3S9IXV/hXSZPXu29OvXT86cOaO+vvvuO7X80UcflZSUFCkoKJBdu3bJ9ddfLzfccINaXldXJ/3795f09HTZs2ePrF69WuLj42XWrFnBuJwmVq9eLb/5zW8kPz9fAMjKlSs15a+88orExMTIe++9J59//rncfffd0r17d6mqqlLr3H777TJo0CDZtm2bbNmyRXr16iU5OTlqeUVFhSQmJsrkyZPlwIEDkpubK1FRUfL2228H6jJFxP21PvDAA3L77bdr7vX58+c1dcLlWjMyMmThwoVy4MAB2bt3r9xxxx2Smpoqly5dUuv44nf32LFjEh0dLTNmzJBDhw7JvHnzxGg0ytq1a0Puem+55RZ55JFHNPe3oqIi7K73/fffl48++ki+/PJLKSkpkV//+tcSGRkpBw4cEJGWdV/dXWtLuaeN7dixQ7p16yYDBw6UadOmqcdb0r215+x6Q+n+MpjSafbs2TJo0CCHZeXl5RIZGSnLli1Tjx0+fFgASHFxsYgoD/CIiAgpLS1V6yxYsEAsFotUV1f7te3eahxg1NfXS1JSkrz22mvqsfLycjGbzZKbmysiIocOHRIAsnPnTrXOmjVrxGAwyOnTp0VE5C9/+YvExcVprvfZZ5+V3r17+/mKnHMWTI0bN87pe8L1WkVEzp49KwBk06ZNIuK7391nnnlG+vXrp/msrKwsycjI8PcludT4ekWUv5jt/6JuLJyvNy4uTv7xj3+0+Psq0nCtIi3znl68eFGuueYaWb9+veb6Wuq9dXa9IqF1fznM5wNHjhxB586d0aNHD0yePBknT54EAOzevRu1tbVIT09X6/bp0wepqakoLi4GABQXF2PAgAFITExU62RkZKCyshIHDx4M7IV46fjx4ygtLdVcX0xMDEaMGKG5vtjYWAwbNkytk56ejoiICGzfvl2tc/PNN8NkMql1MjIyUFJSggsXLgToajxTVFSEjh07onfv3njsscdw7tw5tSycr7WiogIA0L59ewC++90tLi7WnMNWx3aOYGl8vTb//ve/ER8fj/79+2PWrFm4fPmyWhaO12u1WpGXl4cffvgBaWlpLfq+Nr5Wm5Z2T6dOnYqxY8c2aVNLvbfOrtcmVO4vNzrWacSIEVi0aBF69+6NM2fOYM6cORg5ciQOHDiA0tJSmEymJjtWJyYmorS0FABQWlqqudG2cltZKLO1z1H77a+vY8eOmvI2bdqgffv2mjrdu3dvcg5bWVxcnF/a763bb78dmZmZ6N69O7766iv8+te/xpgxY1BcXAyj0Ri211pfX4/p06fjxhtvRP/+/dW2+OJ311mdyspKVFVVISoqyh+X5JKj6wWA++67D127dkXnzp2xb98+PPvssygpKUF+fj6A8Lre/fv3Iy0tDVeuXEG7du2wcuVK9O3bF3v37m1x99XZtQIt654CQF5eHj777DPs3LmzSVlL/H/W1fUCoXV/GUzpNGbMGPW/Bw4ciBEjRqBr165YunRpUB4U5D/Z2dnqfw8YMAADBw5Ez549UVRUhFGjRgWxZfpMnToVBw4cwNatW4PdlIBwdr1TpkxR/3vAgAHo1KkTRo0aha+++go9e/YMdDN16d27N/bu3YuKigosX74cDzzwADZt2hTsZvmFs2vt27dvi7qnp06dwrRp07B+/Xq0bds22M3xO0+uN5TuL4f5fCw2NhbXXnstjh49iqSkJNTU1KC8vFxTp6ysDElJSQCApKSkJqstbD/b6oQqW/sctd/++s6ePaspr6urw/nz58P+O+jRowfi4+Nx9OhRAOF5rU888QQ+/PBDFBYWIjk5WT3uq99dZ3UsFktQ/rHh7HodGTFiBABo7m+4XK/JZEKvXr0wdOhQzJ07F4MGDcJbb73VIu+rs2t1JJzv6e7du3H27FkMGTIEbdq0QZs2bbBp0yb86U9/Qps2bZCYmNii7q2767VarU3eE8z7y2DKxy5duoSvvvoKnTp1wtChQxEZGYmCggK1vKSkBCdPnlTH9NPS0rB//37NQ3j9+vWwWCxqV3Wo6t69O5KSkjTXV1lZie3bt2uur7y8HLt371brbNy4EfX19eovflpaGjZv3oza2lq1zvr169G7d++QGeJz5JtvvsG5c+fQqVMnAOF1rSKCJ554AitXrsTGjRubDD366nc3LS1Ncw5bHfs5LYHg7nod2bt3LwBo7m+4XG9j9fX1qK6ubnH31RHbtToSzvd01KhR2L9/P/bu3au+hg0bhsmTJ6v/3ZLurbvrNRqNTd4T1Pvr1XR1auKpp56SoqIiOX78uHzyySeSnp4u8fHxcvbsWRFRlqqmpqbKxo0bZdeuXZKWliZpaWnq+21LN0ePHi179+6VtWvXSkJCQsikRrh48aLs2bNH9uzZIwDk9ddflz179sjXX38tIkpqhNjYWFm1apXs27dPxo0b5zA1wnXXXSfbt2+XrVu3yjXXXKNJF1BeXi6JiYly//33y4EDByQvL0+io6MDni7A1bVevHhRnn76aSkuLpbjx4/Lhg0bZMiQIXLNNdfIlStXwu5aH3vsMYmJiZGioiLNsuLLly+rdXzxu2tbdjxz5kw5fPiwzJ8/PyjLrN1d79GjR+W3v/2t7Nq1S44fPy6rVq2SHj16yM033xx21/vcc8/Jpk2b5Pjx47Jv3z557rnnxGAwyMcffywiLeu+urrWlnRPnWm8mq0l3VtH7K831O4vgymdsrKypFOnTmIymaRLly6SlZUlR48eVcurqqrk8ccfl7i4OImOjpbx48fLmTNnNOc4ceKEjBkzRqKioiQ+Pl6eeuopqa2tDfSlOFRYWCgAmrweeOABEVHSI7zwwguSmJgoZrNZRo0aJSUlJZpznDt3TnJycqRdu3ZisVjkwQcflIsXL2rqfP7553LTTTeJ2WyWLl26yCuvvBKoS1S5utbLly/L6NGjJSEhQSIjI6Vr167yyCOPaJbcioTPtTq6TgCycOFCtY6vfncLCwtl8ODBYjKZpEePHprPCBR313vy5Em5+eabpX379mI2m6VXr14yc+ZMTc4akfC43oceeki6du0qJpNJEhISZNSoUWogJdKy7qura21J99SZxsFUS7q3jthfb6jdX4OIiHd9WURERERkwzlTRERERDowmCIiIiLSgcEUERERkQ4MpoiIiIh0YDBFREREpAODKSIiIiIdGEwRERER6cBgioiIiEgHBlNEREREOjCYIiIiItKBwRQRERGRDgymiIiIiHT4/46HBRfZ/RzfAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(x,y,m,b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training through Stochastic Gradient Descent (SGD)\n",
    "\n",
    "SGD is a common method in AI for training deep neural networks on large datasets. It is an iterative method for optimizing a loss function that we get to define. We will use this simple linear regression to demonstrate how it works.\n",
    "\n",
    "#### The model\n",
    "\n",
    "In AI, neural networks are often referred to as a _model_ because, once fully trained, they should model (AKA predict) the behavior of our system. In our example, the system is how house prices vary based on house size. We know our system is roughly driven by a linear function:\n",
    "\n",
    "$$ \\hat{y_i}(x_i) = m * x_i + b $$\n",
    "\n",
    "We just need to figure out $m$ and $b$. Let's create a function that calculates our model given $x$, $m$, and $b$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(x,m,b):\n",
    "   return m * x + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "\n",
    "#### The Loss Function\n",
    "\n",
    "A _loss function_, or _objective function_, is something we define and is based on what we want to achieve. In the method of SGD, it is our goal to minimize (or make close to zero) the values calculated from the _loss function_. In our example, we ideally want the prediction of our _model_ to be equal to the actual data, though we will settle for \"as close as possible\".\n",
    "\n",
    "So we will select our _loss function_ to be the [Mean Squared Error](https://en.wikipedia.org/wiki/Mean_squared_error) function:\n",
    "\n",
    "$$ L(y_i,\\hat{y_i}) = (y_i - \\hat{y_i}(x_i))^2 $$\n",
    "\n",
    "where $y_i$ is our $i^{th}$ entry in the `data['SalePrice']` vector and $\\hat{y_i}$ is the prediction based on evaluting $m * x_i + b$.\n",
    "\n",
    "This function looks like the figure below when we plot it with $x=y_i - \\hat{y_i}(x_i)$ and we we want to be down near $y_i - \\hat{y_i}(x_i) = 0$ which indicates that our $y_i$ is as close as possible to $\\hat{y_i}$.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/loss_func.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "Here we crate a function that calculates this for us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss(x,y,m,b):\n",
    "   y_predicted = model(x,m,b)\n",
    "   return np.power( y - y_predicted, 2 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Minimizing the Loss Function\n",
    "\n",
    "We want to use the loss function in order to guide how to update $m$ and $b$ to better model our system. In calculus we learn to minimize a function with respect to a variable you calculate the _partial derivative_ with respect to the variable you want to vary.\n",
    "\n",
    "$$ { \\partial L \\over \\partial m } = 0 $$\n",
    "\n",
    "The location of the solution to this is the minimum as shown in the figure above. We can write down the partial derivative of the loss function as:\n",
    "\n",
    "$$ { \\partial L \\over \\partial m } = -2 x_i (y_i - \\hat{y_i}(x_i)) $$\n",
    "$$ { \\partial L \\over \\partial b } = -2 (y_i - \\hat{y_i}(x_i)) $$\n",
    "\n",
    "We can use this to calculate an adjustment to $m$ and $b$ that will reduce the loss function, effectively improving our fitting parameters. This is done using this equation:\n",
    "\n",
    "$$ m' = m - \\eta { \\partial L \\over \\partial m }$$\n",
    "$$ b' = b - \\eta { \\partial L \\over \\partial b }$$\n",
    "\n",
    "Here our original $m$ and $b$ are adjusted by the partial derivative multiplied by some small factor, $\\eta$, called the _learning rate_. This learning rate is very important in our process and must be tuned for every problem.\n",
    "\n",
    "In our example, the selection of the learning rate essentially defines how close we can get to the minimum, AKA the best fit solution. This figure shows what happens when we pick a large learning rate. We first select a starting point in our loss function (typically randomly), then every update from $m$/$b$ to $m'$/$b'$ results in a shift to somewhere else on our loss function (following the red arrows). In this example, our learning rate ($\\eta$) has been selected too large such that we bounce back and forth around the minimum, never reaching it.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/parabola_largeLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "If we select a smaller learning we can see better behavior in the next figure.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/parabola_smallLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "Though, keep in mind, too small a learning rate results is so little progress toward the minimum that you may never reach it!\n",
    "\n",
    "A pit fall of SGD that one must be aware of is when your loss function is complex, with many minima. The next figure shows such a case, in which we select a small learning rate and our starting point happens to be near a local minimum that is not the lowest minimum. As shown, we do reach a minimum, but it isn't the lowest minimum in our loss function. It could be that we randomly select a starting point near the minimum we care about, but we should build methods that are more robust against randomly getting the right answer.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/local_min_smallLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "Then, if we increase our learning rate too much, we bounce around again.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/local_min_largeLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "What we want to do in this situation is start with a large learning rate and slowly reduce its size as we progress. That is shown in this next figure.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/local_min_variableLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "As you can see, this process is not perfect and could still land in a local minimum, but it is important to be aware of these behaviors as you utilize SGD in machine learning.\n",
    "\n",
    "So let's continue, we'll build functions we can use to update our fit parameters, $m$ and $b$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def updated_m(x,y,m,b,learning_rate):\n",
    "   dL_dm = - 2 * x * (y - model(x,m,b))\n",
    "   dL_dm = np.mean(dL_dm)\n",
    "   return m - learning_rate * dL_dm\n",
    "\n",
    "def updated_b(x,y,m,b,learning_rate):\n",
    "   dL_db = - 2 * (y - model(x,m,b))\n",
    "   dL_db = np.mean(dL_db)\n",
    "   return b - learning_rate * dL_db"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Putting it together\n",
    "\n",
    "We can now randomly select our initial slope and intercept:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y_i = 5.00 * x + 1000.00\n"
     ]
    }
   ],
   "source": [
    "m = 5.\n",
    "b = 1000.\n",
    "print('y_i = %.2f * x + %.2f' % (m,b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can calculate our Loss function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "first 10 loss values:  [3.03421561e+10 3.55511025e+10 1.24579082e+10 1.91656336e+10\n",
      " 1.60604929e+10 2.04432804e+10 1.72410030e+10 1.76517796e+10\n",
      " 1.52769600e+10 2.18152900e+10]\n"
     ]
    }
   ],
   "source": [
    "l = loss(x,y,m,b)\n",
    "print('first 10 loss values: ',l[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y_i = 5.47 * x + 1000.00     previously calculated: y_i = 87.69 * x + 34754.08\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learning_rate = 1e-9\n",
    "m = updated_m(x,y,m,b,learning_rate)\n",
    "b = updated_b(x,y,m,b,learning_rate)\n",
    "print('y_i = %.2f * x + %.2f     previously calculated: y_i = %.2f * x + %.2f' % (m,b,m_calc,b_calc))\n",
    "plot_data(x,y,m,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[029]  dy_i = 88.89 * x + 32912.24     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478200827.641291\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1440x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set our initial slope and intercept\n",
    "m = 5.\n",
    "b = 1000.\n",
    "# batch_size = 60\n",
    "# set a learning rate for each parameter\n",
    "learning_rate_m = 1e-7\n",
    "learning_rate_b = 1e-1\n",
    "# use these to plot our progress over time\n",
    "loss_history = []\n",
    "# convert panda data to numpy arrays, one for the \"Ground Living Area\" and one for \"Sale Price\"\n",
    "data_x = data['GrLivArea'].to_numpy()\n",
    "data_y = data['SalePrice'].to_numpy()\n",
    "# we run our loop N times\n",
    "loop_N = 30\n",
    "for i in range(loop_N):\n",
    "   # update our slope and intercept based on the current values\n",
    "   m = updated_m(data_x,data_y,m,b,learning_rate_m)\n",
    "   b = updated_b(data_x,data_y,m,b,learning_rate_b)\n",
    "\n",
    "   # calculate the loss value\n",
    "   loss_value = np.mean(loss(data_x,data_y,m,b))\n",
    "\n",
    "   # keep a history of our loss values\n",
    "   loss_history.append(loss_value)\n",
    "\n",
    "   # print our progress\n",
    "   print('[%03d]  dy_i = %.2f * x + %.2f     previously calculated: y_i = %.2f * x + %.2f    loss: %f' % (i,m,b,m_calc,b_calc,loss_value))\n",
    "   \n",
    "   # close/delete previous plots\n",
    "   plt.close('all')\n",
    "   \n",
    "   # create a 1 by 2 plot grid\n",
    "   fig,ax = plt.subplots(1,2,figsize=(18,6),dpi=80)\n",
    "   # lot our usual output\n",
    "   plot_data(data_x,data_y,m,b,ax[0])\n",
    "\n",
    "   # here we also plot the calculated linear fit for comparison\n",
    "   line_x = np.arange(data_x.min(),data_x.max())\n",
    "   line_y = line_x * m_calc + b_calc\n",
    "   ax[0].plot(line_x,line_y,'b-',label='calculated')\n",
    "   # add a legend to the plot and x/y labels\n",
    "   ax[0].legend()\n",
    "   ax[0].set_xlabel('square footage')\n",
    "   ax[0].set_ylabel('sale price')\n",
    "\n",
    "   # plot the loss \n",
    "   loss_x = np.arange(0,len(loss_history))\n",
    "   loss_y = np.asarray(loss_history)\n",
    "   ax[1].plot(loss_x,loss_y, 'o-')\n",
    "   ax[1].set_yscale('log')\n",
    "   ax[1].set_xlabel('loop step')\n",
    "   ax[1].set_ylabel('loss')\n",
    "   plt.show()\n",
    "   # gives us time to see the plot\n",
    "   time.sleep(2.5)\n",
    "   # clears the plot when the next plot is ready to show.\n",
    "   ipydis.clear_output(wait=True)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework\n",
    "## Mini Batch Training\n",
    "In AI, datasets are often very large and cannot be processed all at once as is done in the loop above. The data is instead randomly sampled in smaller _batches_ where each _batch_ contains `batch_size` inputs. How can you change the loop above to sample the dataset in smaller batches? Hint: Our `data` variable is a Pandas `DataFrame` object, search for \"how to sample a DataFrame\".\n",
    "\n",
    "Instead of using the entire dataset like \n",
    "```python\n",
    "data_x = data['GrLivArea'].to_numpy()\n",
    "data_y = data['SalePrice'].to_numpy()\n",
    "```\n",
    "Use \n",
    "```python\n",
    "data_batch = data.sample(batch_size)\n",
    "data_x = data_batch['GrLivArea'].to_numpy()\n",
    "data_y = data_batch['SalePrice'].to_numpy()\n",
    "```\n",
    "\n",
    "You also have to adjust the loop_N accordingly to make sure that it loop over the entire datasets the same number of times.\n",
    "```python\n",
    "loop_N = 30*len(data)//batch_size\n",
    "```\n",
    "\n",
    "Please plot your learning curve for different batch size, such as 32, 64, 128, 256, 512. \n",
    "\n",
    "## Learning rate issue (Bonus)\n",
    "As described above, if the learning rate is too large, it will affect the convergence. Do your training with (batch_size = 64, learning_rate_m = 1e-7, learning_rate_b = 1e-1). Then linearly increase the batch size and learning rate until you see the training does not converge. \n",
    "```\n",
    "(64, 1e-7, 1e-1)*1\n",
    "(64, 1e-7, 1e-1)*2\n",
    "(64, 1e-7, 1e-1)*4\n",
    "(64, 1e-7, 1e-1)*8\n",
    "...\n",
    "```\n",
    "\n",
    "**How to submit your homework**\n",
    "* Fork the github repo to your personal github \n",
    "* Make change to the 01_linear_regression_sgd.ipynb, and then push to your personal github\n",
    "* Provide the link of 01_linear_regression_sgd in the personal github. \n",
    "\n",
    "Follow the below instruction on how to do this: \n",
    "https://github.com/argonne-lcf/ai-science-training-series/blob/main/00_introToAlcf/03_githubHomework.md"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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