0.Intro_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What's in a neural net?\n",
    "\n",
    "A neural net is simply a series of linear regressions with a nonlinear layer.\n",
    "\n",
    "## Linear regression refresher\n",
    "\n",
    "We want to draw a line through some data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')\n",
    "plt.rcParams['figure.figsize'] = (30, 20)\n",
    "plt.rcParams['font.size'] = 24\n",
    "plt.rcParams['lines.markersize'] = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_regression\n",
    "seed = 42"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xs, ys, coef = make_regression(n_features=1, noise=20, coef=True, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_scatter(m=None, b=None):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.scatter(Xs, ys)\n",
    "    ax.set_ylabel('Y')\n",
    "    ax.set_xlabel('X')\n",
    "    ax.set_title('Some data')\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f3060022f90>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 2160x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_scatter()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How do we draw a line through this data that \"best fits\"? What does \"best fit\" mean?\n",
    "\n",
    "Let's start by defining a line - a line is defined by $ y = mx + b $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_regression_line(m, b, ax=None):\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots()\n",
    "    ax.plot(Xs, regression_line(m, b))\n",
    "    ax.set_title(f'Regression Line: m = {m} b = {b}')\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regression_line(m, b):\n",
    "    return m*Xs + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now start plugging numbers into $m$ and $b$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2160x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = draw_scatter()\n",
    "draw_regression_line(10, 5, ax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is that a good line or a bad line?\n",
    "\n",
    "Let's try another value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f305ff963d0>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Fk08+ufjBBx80W+MnP/lJo89cS5188sml84YPH97qe/noZ+af//mfV/o7asyYMaW2VVVVxRkzZrS6Dw2fFeX8evzxx1vdtzXp32abbVZ87LHHynJtAIBK0fycKwAA0MEsWbIkL730Ui6//PIMHjw4f//735Msmz7wl7/8Zaqrq5s99+c//3nmzp2bJNlvv/1y0kknrfJ6P/rRj0rbN910U2kUynL3339/Zs2alWTZiJMrr7xypdMennXWWSuMQmuJLl265LLLLltlu7lz5+bGG29MsmxU1fXXX5/OnTuv9JzDDjss++67b5Jl0zw++OCDjY6/8847pe1NNtlkNXte/jot9eCDD+all14q7V999dUrnU5uxIgROeGEE0r7V111VYuuc9VVV630PT7ppJNSKBSSJPPnz8/f/va3FtVdl2288ca55JJLVtrmq1/9amn7qaeearJNW3wm16avfvWrK4ywbej4449vtP/JT34yX//615ttf+CBB5amNK6rq8szzzxTno5WiJ122imPPvporr766nTp0qXZdu+//35pe1WjeRtq+Hx477331qyTzSgUCrnqqqtW+jvqe9/7Xmlka319fa677rqy9mFdNWDAgIwePTr33HNPXnnllSxatCiLFy/OzJkzc9ddd+Wggw4qtf373/+eQw89NFOmTGnHHgMArFuEgAAAdEiPPvpoCoVCo68uXbpk++23zze+8Y3MmTMnSTJo0KA8/vjj2XvvvVda75577ilt//u//3uL+rDVVltl4MCBSZYFbB+dIu7hhx8ube+1117ZbrvtVlqvpqYmo0aNatG1G/rnf/7nRtPHNecPf/hDFi9enGTZ1Khbb711i+qPGDGitP344483OtZwKr0HH3wwf/3rX1tU86PKVaelGq4Bt+uuu2bPPfdc5Tknn3xyafuVV17JK6+8stL2AwcOzJAhQ1baplevXo2+D6uq2REcfvjhqwxXGq7D9ve//730c9lQW3wmlxs/fnyKxWKKxWKbrAeYZJWf5e23375RQNzcGnbLFQqF7LLLLqX9cvys1NTUlN6Hcn5df/31re5bU44++uiccsopOeWUU/LVr341RxxxROnZ8fzzz+czn/lMTjjhhNIaek1puJ5oU9MNN6dhsFiuNUmXGzZsWLbddttVXr/hFKsPPfRQq6970kkntcn3f9iwYa3uW5IceeSRefXVV3PZZZflsMMOy1ZbbZWuXbumc+fO2XzzzXP00UfngQceyE033VSaPve9997Ll770pXb9BwAAAOsSawICAFCx9txzz/zv//5v+vfvv8q2Tz75ZGn7vvvuy6RJk1p0jYajSmbOnJmddtqptL98/agkqwyDlttrr71a1K6hlgRYSeN7nDt3bk499dQWnTdt2rTS9syZMxsdGzp0aLbaaqu8+uqreeedd7LHHntk1KhROfzwwzN8+PAV1m5rTrnqtNSzzz5b2h4+fHiLztljjz3SrVu3LFq0KEnyzDPPrDRI3XXXXVtUt3fv3nn55ZeTNB4R2VG15L579+7daP+dd95ZYfRWW3wm16aGgV1Tqqqq0qNHj9L6nKtqnywLjZerhJ+V1fXNb36zydcfffTRnHrqqZk2bVpuuummTJw4MY8//niTo4objuhbunRpi6/dMKhe2ajhNTF06NAWt7v00kuTJH/+859TX1+/0tHlHV1Ln/vHH3985s6dW1pTd9KkSbn//vvz2c9+ti27BwDQIQgBAQDokPr165cjjjiitF9bW5vZs2dnypQppaDqT3/6Uz71qU/loYceyo477thsrXfffTcLFy4s7f/f//t/16hP8+fPb7S/fDRikmy++eYtqjFgwIDVvm5Lp8+cPXt2afv555/P888/v9rX+ug9durUKbfffns++9nPZv78+fnggw9y44035sYbb0yhUMgOO+yQffbZJ/vvv38OO+ywfPzjH2+ybrnqtFTD701LR0RWV1dn8803z4svvrhCjab06NGjRXU7depU2v7www9bdM66rCX33fCekxXvu60+k2tLVVVVi35Gl49eSlb/fauEn5Vy+cxnPpMnnngiw4YNy9SpU/O3v/0tX/3qV/PrX/96hbYf+9jHStvLA/2WaDj6r7XPn4/aYostWtSu4YjpDz/8MAsWLGgUDK/PTjvttPzgBz8oTQN+7733CgEBAGI6UAAAOqjtttsuV111Velr7NixpTWD7rzzzmy00UZJlgVfI0eObDQ66KMWLFhQlj7V1tY22m94zQ033LBFNVrarqGWjkopx31+9B6TZaMXp06dmv/4j/9oFGQUi8W88MILueGGG/L5z38+m266ab7xjW80u55Wueq0RMNzV+c9bxggrOr6y9f6W9+U477b6jO5tqzJe7C+/ryUS/fu3Uuj5JLkN7/5TZNrbDacOnnBggVZsmRJi+ovD5c+WqMc1vT3Q7nXJuzIampqGk1d/dxzz7VjbwAA1h1GAgIAUFGqqqpyzDHHpHfv3jnwwANTX1+fl156Kd/61rcyduzYJs/56B9Wn3/++ZWOHGyphoFRw1FNK9PSdmui4X2OGTMmF198cdlq9+/fPz/96U9z2WWX5amnnsoTTzyRCRMm5Mknn8zcuXOTLBtJc/nll+fBBx/M+PHjmxz5VK46q9JwJM/qvOcNg91yjwbi/2urzySN1dfX5/TTTy973aFDhzZav25t2X///bPBBhuUpvkcP358tt9++0ZtGk4PWywW89prr63QpimvvfZaabvcP4tr+vuhtc+gCRMm5NZbb21VjaaceeaZ2Wabbcped1X69etX2l7++wIAYH0nBAQAoCLtv//+OfXUU3PllVcmSa6//vqceuqp2XnnnVdo26tXr3Tq1Kk0vd4LL7xQlj/y9unTp7T9+uuvt+icWbNmtfq6zdl0001L2y+88EKbXGODDTbI8OHDS+vs1dfX56mnnsqVV16ZO+64I8myERoXXnhho1E7bVWnOQ2/N6+++mqLzqmrq2v0fWxYg/Jqq88kjdXX1+enP/1p2esuXry4XULA6urqbLTRRqWpepsKgnbcccdUV1enrq4uybL1QVcVAi5evLjRyLJPfOITZez1imutNqdhENmpU6c1+gcQDT333HNt8v0fNWpUu4SAazL6HgCg0pkOFACAivW9732v9EfSurq6fOc732myXaFQyF577VXa/93vfleW6w8aNKi0PXHixBad09J2a2Lo0KGl7YcffrjF0+C1RlVVVfbee+/cfvvtOf7440uvN7VW19qos9zgwYNL2+PHj2/ROc8++2yjNcT22GOPNbo2q9ZWn0kq25IlSxqtA9nUtJ1dunTJPvvsU9p/+OGHV1l3/PjxpdGFhUIh+++/fxl6+/89+eSTq91ut912S1WVP+k0NGnSpNJ2//7927EnAADrDv/FCABAxerZs2fOPPPM0v69996bP/3pT022HTlyZGn71ltvzZtvvtnq6zf8Q/FTTz2Vl156aaXta2trc/vtt7f6us055JBD0qlTpyTL1pJqbnrUtnLEEUeUthuur9UedQ444IDS9uTJkxv98bg511xzTWl7m222ydZbb71G16Zl2uIzSWM1NTUpFotl/7r++uvb5X7uu+++RutANjdi78gjjyxt33nnnatcW6/h/QwdOrTRtJPlMH78+EyfPn2lbRYvXtzo90PD9e/W1EknndQm3/9hw4a1um+r689//nOefvrp0n65g1oAgI5KCAgAQEUbPXp0o9Eg559/fpPtvva1r6V3795JkkWLFmXUqFFZvHhxi6/TVBh1yCGHlEYjFIvFnH766amvr2+2xg9+8ING072VW9++fXPiiSeW9s8+++xmQ9GmvPXWWykWi41eW511lxpOebfJJpu0SZ2WOuigg7LddtuV9k855ZSVjox85JFH8otf/KK0f+qpp67RdWm5tvhM0nEsXrx4tdbrfOutt/Ltb3+7tL/FFltkyJAhTbY9/vjj06tXryTL/kHEueee22zdJ554InfffXdp/4wzzmhxn1qqWCzm1FNPXenvhwsuuCCzZ89Osmxk9Fe+8pWy92Nd0nBqz1VZsGBBvvCFL5R+P3Xr1i1HHXVUW3UNAKBDEQICAFDRPv7xj+db3/pWaf/+++/PU0891WS7q6++OoVCIUny2GOPZa+99sof//jHZmvPnTs3N9xwQ/bee+9G11iuuro6F154YWn/97//fT73uc81mq4uWTYC8OKLL84555yTzp07r/Y9ro6LLrqoNIJt0aJF2XfffXPZZZc1+8f22trajBs3Ll/60pey5ZZbltbRWu7yyy/PJz/5yVx55ZUrXdfq/vvvz/e+973S/mGHHdYmdVqqUCg0Wktw4sSJOfTQQ5u89t13352RI0eW/kC/00475Wtf+9oaXZeWa4vP5HLDhg1LoVBIoVBoNCqUdcesWbOy1VZb5bzzzmu0Ht9Hffjhh7n77rszZMiQvPzyy6XXL7300tLPzkf17NmzUfB35ZVX5sILL2w0ijBZFv4fccQRpc/+3nvvnaOPPro1t9WkDTbYIA888EBGjRqVefPmNTr24Ycf5rzzzsvFF19ceu0//uM/2mXNvbVp7NixGTZsWG677ba8++67TbYpFov53e9+l8GDB2fq1Kml17/73e+mb9++a6urAADrtJr27gAAALS10047LT/+8Y8zZ86cJMtGA/7+979fod1RRx2VH//4x/nmN7+Z+vr6TJkyJfvvv38GDBiQPffcM717905dXV3mzZuXv/71r5k+fXrpj8MDBw5s8tonnnhiHnjggdx5551Jlk0999vf/jb77rtv+vfvnwULFuTRRx/NP/7xjxQKhfz4xz/OKaeckiRtst5T7969c++99+bggw/O66+/nkWLFuXMM8/MOeeckyFDhmSLLbZI586d8+677+bVV1/N1KlTVzkaZ+rUqTnjjDNyxhlnZIsttsguu+ySPn36pEuXLnn77bczadKkzJgxo9R+wIABTY7ILFedljrssMNyzjnn5Pv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      "text/plain": [
       "<Figure size 2160x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = draw_scatter()\n",
    "draw_regression_line(30, 5, ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That seems better, no?\n",
    "\n",
    "Intuitively, we can look at a line going through these dots and say it fits better - but computers can't do that. We need some way to quantify how good or bad a line is. \n",
    "\n",
    "# The Loss Function\n",
    "\n",
    "The loss function can be anything you can dream up - the only criteria is that it quantifies how good or bad the guess is (and that it's **differentiable** - we'll get into that in a bit)\n",
    "\n",
    "For a linear regression, we often measure the distance each point is from the line. On average, the further the points are away from the line, the worse the line is. We have a decision to make though - what do we do about negative distances? If we take the mean of positive and negative numbers, we are in effect saying that it's okay that this point is wrong as long as another point is equally wrong in a different direction - that sounds a bit silly, no?\n",
    "\n",
    "We will choose to **square** the error in this case, as this gives us a dual benefit - we get rid of negative numbers, but we also **penalize** large mistakes more than small mistakes. So now we have decided on our loss function - **mean squared error**\n",
    "\n",
    "$$ \\frac{1}{n} \\sum_{n=1}^{n}(\\hat y_i - y_i)^2 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_squared_error(y_hat, y):\n",
    "    return (np.sum(y_hat - y) ** 2) / len(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19793571.01656026"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error_1 = mean_squared_error(regression_line(30, 5), ys)\n",
    "error_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42587722.92476668"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error_2 = mean_squared_error(regression_line(10, 5), ys)\n",
    "error_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error_1 > error_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have the ability to ask our computer to compare any pairs of m, b and tell us if we have a better line or worse - that's powerful!\n",
    "\n",
    "However, we still have infinite possible combinations of m and b to compare - where do we go from here?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_error_curve():\n",
    "    fig, ax = plt.subplots()\n",
    "    ms = np.arange(-100, 100)\n",
    "    preds = [regression_line(m, 0) for m in ms]\n",
    "    errors = [mean_squared_error(pred, ys) for pred in preds]\n",
    "    ax.plot(ms, errors, linewidth=10)\n",
    "    ax.set_ylabel('Mean Squared Error')\n",
    "    ax.set_xlabel('Value of $M$')\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f30600d4b90>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hWbVqVdatW5ck6ejoyBe/+MWcdNJJm3z/KaeckhdffDEzZ87MT3/60/z85z9PV1dXVq9enSTZY4898ld/9VeVutCeil1HpDj59JR3XF8p37jl5xn0//5tza0AAAAAAIBm0lKjXh3+9E//NHPnzs2LL76YZcuWpbu7O4MHD86ee+6Z8ePH55RTTsnYsWO3eI0LL7wwhx9+eO6555689NJL6enpyZgxY3LsscfmzDPPzNChQ/vpt6FVFaeclfK+acnqVVsPP/14ynlzU4w7uP5iAAAAAABAUyjKLT1Ujh1i4cKFO7pCyxg1alSWLFmyo2v0icYtP095+y+qhQ85MoO+8b16C9HUBtK9D73l/qddufdpV+592pV7n3bl3qddufdpZ+7/je25556bfa2lnqkHA1nxmanJzsOqhX/7XymffbreQgAAAAAAQNMw6kGTKHbeJcUpZ1fON279WRy0BQAAAACA9mDUgyZSfPr0ZJddq4Wfeyb57X/VWwgAAAAAAGgKRj1oIsWQnVN87pzK+cYtTusBAAAAAEA7MOpBkylOmpLsOqJaeP6zydOP11sIAAAAAADY4Yx60GSKnYakmHJu5Xzjlp87rQcAAAAAAAOcUQ+aUHHiqcluI6uFX34hefLhegsBAAAAAAA7lFEPmlDRNTjFlPMr5xs3/yxlY32NjQAAAAAAgB3JqAdNqjjhM8nI3auFf/+7lI/+st5CAAAAAADADmPUgyZVdHWlOP0LlfPlrdekXLeuxkYAAAAAAMCOYtSDJlZ8/ORk9w9VCy9elPKhGfUWAgAAAAAAdgijHjSxorMzxdQLKufL269NubanxkYAAAAAAMCOYNSDJlcc88lkz72rhd9cknL2HfUWAgAAAAAA+p1RD5pc0TEoHWd+uXK+nH59ytWramwEAAAAAAD0N6MetIKjJiX7HFAtu2JZypm31dsHAAAAAADoV0Y9aAFFUaTjrD+qnC/vvill99s1NgIAAAAAAPqTUQ9axaFHJQeOr5Zd2Z3y7pvq7QMAAAAAAPQbox60iHdO632lcr6ceVvK5W/V2AgAAAAAAOgvRj1oIcVHDn3nxF4Va1anvOP6egsBAAAAAAD9wqgHLaZXz9abdX1ItWAAACAASURBVEfKpUtqbAMAAAAAAPQHox60mGLfA5OjJlULr1ubctp/1toHAAAAAACon1EPWlDHmX+UFEWlbPngjJSv/77mRgAAAAAAQJ2MetCCijF7pzj2xGrh9etT3nZNvYUAAAAAAIBaGfWgRRVnXJAMGlQpW/5qdsoFr9TcCAAAAAAAqItRD1pUMfrDKY6fXC1clmnc+rN6CwEAAAAAALUx6kELK077QtLZVS38xMMpX36h3kIAAAAAAEAtjHrQwoqRo1KcdGrlfOPmq2tsAwAAAAAA1MWoBy2uOPXcZKch1cJPP5HyuWfqLQQAAAAAAPQ5ox60uGL4bik+fUblfOPmn6YsyxobAQAAAAAAfc2oBwNAccrZydBh1cLP/3fyzJP1FgIAAAAAAPqUUQ8GgGLYLik+e3blfOPmq53WAwAAAACAFmLUgwGi+PQZya4jqoVffiF58pF6CwEAAAAAAH3GqAcDRDFkaIop51bON275WcrG+hobAQAAAAAAfcWoBwNIceKpyQdGVQsvfCXlo/fXWwgAAAAAAOgTRj0YQIquwSlOP79yvrz15ynXrauxEQAAAAAA0BeMejDAFMdNTnb/ULXw4kUpH5pRbyEAAAAAAGC7GfVggCk6O1NMvaByvrztFyl71tTYCAAAAAAA2F5GPRiAimM+mXx4r2rht5amvG9avYUAAAAAAIDtYtSDAajoGJSOs75cOV9Ovz7lyrdrbAQAAAAAAGwPox4MVEd9PNnngGrZlW+nvOvmevsAAAAAAADbzKgHA1RRFOn4/Fcq58sZt6Rc9maNjQAAAAAAgG1l1IOB7JAJycFHVMv2rEk57dp6+wAAAAAAANvEqAcDWFEU6Ti7F6f1fnlXysWLamwEAAAAAABsC6MeDHDF/gclEyZVC69fl/LWa+otBAAAAAAA9JpRD9pAx1l/lBTV/u9e/mpWyldfqrcQAAAAAADQK0Y9aAPFmL1TTDqpWrgs07j56lr7AAAAAAAAvWPUgzZRTL0g6eysFv6vR1POm1tvIQAAAAAAoDKjHrSJYtQeKU48tXK+ceP/SVmWNTYCAAAAAACqMupBGymmnJfsNKRa+Lmnk2eerLcQAAAAAABQiVEP2kgxfLcUnzmzcr5x0/9J2WjU2AgAAAAAAKjCqAdtpvjMWckuu1YLvzI/5eMP1VsIAAAAAADYKqMetJli52EpTj23cr68+eqU69bV2AgAAAAAANgaox60oeKkKcluH6wWfn1hyodm1lsIAAAAAADYIqMetKFi8E4ppl5QOV/edk3KnjU1NgIAAAAAALbEqAdtqjju08keY6qF31qa8r7p9RYCAAAAAAA2y6gHbaoYNCgdZ325cr684/qUK7trbAQAAAAAAGyOUQ/a2dHHJXuPq5btXpHy7pvq7QMAAAAAAGySUQ/aWNHRkY7P/3HlfDnj1pTL36yxEQAAAAAAsClGPWh34yckBx1eLbtmdcpp19XbBwAAAAAAeB+jHrS5oijScfZXKufL2XemXPJajY0AAAAAAIA/ZNQDUow7OJlwbLXw+nUpb/15vYUAAAAAAICNGPWAJEnHWX+UFEWlbPnIrJQLXq65EQAAAAAA8C6jHpAkKcbsk2LSSdXCZZnGzVfX2gcAAAAAAPi/jHrABsXULyWDOquFn/pVynlz6y0EAAAAAAAkMeoB71GM2iPFiZ+rnG/ceFXKsqyxEQAAAAAAkBj1gD9QnHZestOQauHnnkmefrzeQgAAAAAAgFEP2Fgx/AMpJk+tnG/ccFXKxvoaGwEAAAAAAEY94H2KU85Ohu1aLbzg5ZSPzK63EAAAAAAAtDmjHvA+xc7DUpx6buV8ecvPUq7tqbERAAAAAAC0N6MesEnFyaclI0dVCy9dnHLWHfUWAgAAAACANmbUAzap6BqcYuqXK+fLademXNldYyMAAAAAAGhfRj1gs4qPn5TsuXe1cPeKlHfdWGsfAAAAAABoV0Y9YLOKjkHp+PwfV86XM25J+dYbNTYCAAAAAID2ZNQDtuyIjyUHjK+W7elJedsv6u0DAAAAAABtyKgHbFFRFOk456uV8+UD96T8/as1NgIAAAAAgPZj1AO2qjjgkGTCpGrhRiONm39abyEAAAAAAGgzRj2gko7PfyUpKv4n44mHU86bW28hAAAAAABoI0Y9oJLiw3ulOGFy5XzjxqtSlmWNjQAAAAAAoH0Y9YDKijMuSLoGVws/90zy9OP1FgIAAAAAgDZh1AMqKz7wwRSTz6icb9xwVcrG+hobAQAAAABAezDqAb1SfO6cZOddqoUXvJzykdn1FgIAAAAAgDZg1AN6pdh5lxRTzqucL2/5Wcq1PTU2AgAAAACAgc+oB/RacfJpychR1cJLF6e8b3q9hQAAAAAAYIAz6gG9VnQNTjH1y5Xz5fTrUq7srrERAAAAAAAMbEY9YJsUHz8p2XPvauHuFSnvurHWPgAAAAAAMJAZ9YBtUnQMSsfnv1o5X864JeVbb9TYCAAAAAAABi6jHrDtjpiYHDi+WranJ+Vtv6i3DwAAAAAADFBGPWCbFUWRjnO+VjlfPnBPyt+/Wl8hAAAAAAAYoIx6wHYpxh2cHDWpWrjRSOPmn9ZbCAAAAAAABiCjHrDdOs7+SlJU/M/JEw+nnDe33kIAAAAAADDAGPWA7VZ8eK8UJ0yunG/c8JOUZVljIwAAAAAAGFiMekCfKM64IOkaXC38/H8nc35dbyEAAAAAABhAjHpAnyg+8MEUk8+onG/ccFXKxvoaGwEAAAAAwMBh1AP6TPG5c5Kdd6kWXvhKyofurbcQAAAAAAAMEEY9oM8UO++S4rTzKufLW36Wcs2aGhsBAAAAAMDAYNQD+lTxqdOSkaOqhd9amnLGLfUWAgAAAACAAcCoB/SpomtwijO/XDlf3nlDyuVv1dgIAAAAAABan1EP6HPFpJOSMftUC69elfL2/6y1DwAAAAAAtDqjHtDnio5B6Tj3a5Xz5S/vTLloQX2FAAAAAACgxRn1gHocenRyyJHVsuvXp3HTT+vtAwAAAAAALcyoB9SiKIpendbLEw+lfOG3tfUBAAAAAIBWZtQDalPsPe6d5+tV1Lj+P1KWZX2FAAAAAACgRRn1gFoVZ/1R0tlVLTxvbvLkI/UWAgAAAACAFmTUA2pVfHB0ik+fXjnfuOGqlOvW1dgIAAAAAABaj1EPqF0x5bxk2K7Vwq8vTHn/3fUWAgAAAACAFmPUA2pX7LxLitPOr5wvb7sm5aqVNTYCAAAAAIDWYtQD+kVx0pRk1B7VwiuWpbzrxnoLAQAAAABACzHqAf2i6OpKcfZXKufLe25O+dYbNTYCAAAAAIDWYdQD+k0x8YRknwOqhXt6Ut7y83oLAQAAAABAizDqAf2m6OhIx3n/q3K+fHBmygUv19gIAAAAAABag1EP6FfFQYcnR3ysWrhspHHDVfUWAgAAAACAFmDUA/pdxzlfTYqK//mZ8+uUc39TbyEAAAAAAGhyRj2g3xV77p3ihMmV843rf5Ky0aixEQAAAAAANDejHrBDFFMvSAbvVC388gspH7u/3kIAAAAAANDEjHrADlHs9sEUp5xVOV/e9NOUa9fW2AgAAAAAAJqXUQ/YYYrPnp3sOqJa+I3XU943rd5CAAAAAADQpIx6wA5TDNn5nY/hrKicdm3K7rdrbAQAAAAAAM3JqAfsUMUJpyR7jKkWXvl2yunX1VsIAAAAAACakFEP2KGKzs50nPPVyvny3ttSLnmtxkYAAAAAANB8jHrAjjfh2OSAQ6pl161LedPV9fYBAAAAAIAmY9QDdriiKNJx7v+qnC8fnZ3ypedrbAQAAAAAAM3FqAc0hWLcwclHj6ucb1z37ynLssZGAAAAAADQPIx6QNPoOPuPk0GDqoWfeyZ56lf1FgIAAAAAgCZh1AOaRrHHnilOPLVyvnH9T1KuW1tjIwAAAAAAaA5GPaCpFKd/IRkytFr49YUpZ99ZbyEAAAAAAGgCRj2gqRS7jkgx5bzK+fK2X6TsfrvGRgAAAAAAsOMZ9YCmU0yemozcvVq4e0XK6dfWWwgAAAAAAHYwox7QdIquwSk+/8eV8+W9t6dcvKjGRgAAAAAAsGMZ9YCmVHzsE8m+B1YLr1uX8oar6i0EAAAAAAA7UOeOLlDVqlWr8swzz+SFF17I/PnzM2/evKxYsSJJcvnll2fMmDHbdN3ly5fnV7/6VebMmZMXX3wxS5cuTUdHR0aNGpXDDjssp512Wj70oQ9t9v3nn3/+Vn/GN77xjUyaNGmb+kG7Kjo60nH+/07jH75TKV8+/mDKF36b4oBDam4GAAAAAAD9r2VGvTlz5uSyyy7r8+teeOGFWb9+/YavhwwZknXr1mXBggVZsGBB7r333vzZn/1ZTjjhhC1eZ9ddd01Hx6YPPnZ1dfVpZ2gXxYHjk6M/njzxcKV847p/T8d3/iFFUdTcDAAAAAAA+lfLjHpJMmLEiOy///4ZN25cRo4cmSuvvHK7r7l+/foccsghOfnkk3PkkUdmt912S6PRyHPPPZd///d/z0svvZQf//jH2WuvvbLPPvts9jrf//73M3r06O3uA2ys45yvpvFfjyXr1209PP/ZlL9+4J2P7gQAAAAAgAGkZUa9iRMn5phjjtnw9euvv94n1/27v/u7jB8/fqPvdXR05OCDD853v/vdfPOb38yyZcsybdq0XHTRRX3yM4HqitF7pvjUlJQzbq2UL2+4KuWEY1N0Da65GQAAAAAA9J9Nf15kE9rcR1turz8c9N5r+PDhOeqoo5Ik8+fPr+XnA1tXnP6FZOddqoXfeD3lvbfXWwgAAAAAAPpZy4x6O8ouu7wzJDQajR3cBNpXMWzXd4a9ispp16VcsbzGRgAAAAAA0L9a5uM3d5Tf/va3SZK99tpri7nLL788ixYtypo1azJ8+PAccMABOfnkk3P00Uf3R00Y8IpPTUl537Rk8aKth1d1p7ztmhRfurD+YgAAAAAA0A+c1NuCxx57LPPmzUuSfOpTn9pidt68eWk0Ghk0aFCWLl2aRx99NJdeeml++MMfZt26df1RFwa0orMrHed8rXK+/OWdKRe9Wl8hAAAAAADoR07qbcbSpUtz5ZVXJkkmTpyYCRMmbDJ34okn5vjjj8+BBx6YYcOGJUkWLFiQW265JbNmzcojjzySYcOG5cILN39iaMaMGZkxY0aS5NJLL82oUaP6+LcZuDo7O/292kh5yhl5c/YdWfv/s3fnUVcV9P743/s8D4gggwpOqGCaZOLYoJImJmqa4a0UtWy8ate06X771r2/LG26v7pZ3korLSvUytmcR7TMKS2URLrOomiKIjMyPJz9/cOgSJB94NlMz+u1Fmtxzvl8zn7j2utxLd7svf8ybvnDCxem21W/Tr///Fb9wVYD5z5dmfOfrsq5T1fl3Kercu7TVTn36aqc+3Rlzv/qlHpLMXfu3Hz729/O9OnTM2DAgPzbv/3bMmdPPPHEV703cODAfOITn0ifPn1y5ZVX5pZbbsmhhx6agQMHLvU7RowYkREjRix+/eKLL678H6KL6N+/v/9eXUz5L8ckVUq9JPPu+X1euOO3KYYMrTnVqufcpytz/tNVOffpqpz7dFXOfboq5z5dlXOfrsz5v6QttthimZ+5/eY/mT9/fv77v/87jz32WPr06ZMvfvGL6dOnzwp91+GHH57u3bunLMuMHTu2k5NC11S8bkiKt+xTeb550Tkpm80aEwEAAAAAQP2Uev+go6Mj3/3udzN+/Pj06tUrJ5988ms2osvTo0ePbLXVVkmS559/vrNiQpdXvPdDSXu3asNPPZbyD7+rNxAAAAAAANRMqfc3CxcuzP/8z/9k7Nix6dGjR/7zP/8zgwcP7rTvL4qi074Lurqi/6Yp9n935fny8vNSzptXYyIAAAAAAKiXUi9Js9nMmWeemXvuuSfdu3fP5z//+Wy//fYr/b1z587N008/nSQZMGDASn8f8HfFIUckG1S8Ne7UF1PefEW9gQAAAAAAoEZdvtQryzJnn312br/99rS3t+dzn/tchg4dWnn3tVx66aWZP39+iqLI7rvv3hlxgb8pevZKMfLoyvPldZemnD61xkQAAAAAAFCftarUmzFjxuJfs2fPXvz+7Nmzl/is2WwusTdq1KiMGjUqF1100au+c/To0bnlllvS1taWz372s9l1110r5zn99NPz61//Oo899lg6OjoWv//ss8/mxz/+ca644pUrg/bdd99sueWWrf5xgeUo9jko2WxgteF5L6e88lf1BgIAAAAAgJq0r+4ArTj22GOX+v7JJ5+8xOszzjgjm2yyyXK/78UXX8y11167+PXZZ5+ds88+e5nzP/nJT5Z4PWPGjNx99925/PLL02g00rNnzyxYsCDz/uHZXXvuuWeOO+645WYBWle0t6dx+EfTPOPrlebL39+U8h2Hphg4qOZkAAAAAADQudaqUq+z/eMVfQsXLsz06dNb2n/Pe96TrbfeOo888kheeumlzJo1K0VRZJNNNsnrX//6DB8+PLvssktnxwb+0c5vSYbslDz0wPJny2aal/w8bZ8+tfZYAAAAAADQmdaqUm9pt89cmb1NNtlkhb8zSXbZZRelHaxmRVGkMepjaX7935PlPOcySTJ+bMrxY1MM9ZxLAAAAAADWHmvVM/UAlqbYetsUe+5Xeb550TkpFy6sMREAAAAAAHQupR6wTije88Gke/dqw399OuVtN9QbCAAAAAAAOpFSD1gnFBtunOLA91SeL6/8ZcrZs2pMBAAAAAAAnUepB6wzioPem/TdsNrwrJkpr7mw3kAAAAAAANBJlHrAOqPosX6Kwz5Qeb685eqUzz1TYyIAAAAAAOgcSj1gnVK8bf9kq22qDS9cmOYlP683EAAAAAAAdAKlHrBOKRptaRx5bPWFcfek/Mu4+gIBAAAAAEAnUOoB65xiyE7JbntWnm9e+NOUzYU1JgIAAAAAgJWj1APWSY3DP5q0tVcbfmZiyttvqjcQAAAAAACsBKUesE4qNtk8xYh3V54vf/PLlHNm15gIAAAAAABWnFIPWGcVh4xKevetNjxzesprL643EAAAAAAArCClHrDOKnr2SnHYByrPl2OuTDn5rzUmAgAAAACAFaPUA9Zpxd4HJAMHVRvu6Ejz0l/UmgcAAAAAAFaEUg9YpxVtbWkceWz1hbF3pXxofH2BAAAAAABgBSj1gHVescMuyS5vrTzfvOinKZsLa0wEAAAAAACtUeoBXULj8I8mbW3Vhp96POWdt9QbCAAAAAAAWqDUA7qEYrOBKfY7tPJ8efl5KefOqTERAAAAAABUp9QDuozi0COTDXpXG54xLeV1l9YbCAAAAAAAKlLqAV1G0WuDFCPfX3m+vPE3KV98vsZEAAAAAABQjVIP6FKKt78z2XyrasMdC1JeOrreQAAAAAAAUIFSD+hSira2NEb9a+X58o+3p3x0Qo2JAAAAAABg+ZR6QJdTDN09GfqmyvPNC36astmsMREAAAAAALw2pR7QJTVGfSxpVPwROPHRlHf/ttY8AAAAAADwWpR6QJdUbL5ViuGHVJ4vLz835by5NSYCAAAAAIBlU+oBXVbx7qOSnhtUG572UsrrL6s3EAAAAAAALINSD+iyig36vFLsVVTecFnKKS/UmAgAAAAAAJZOqQd0acXwQ5LNBlYbXjA/5WWj6w0EAAAAAABLodQDurSivT2Nwz9Web6857aUj0yoMREAAAAAALyaUg9g5zcnb9y18njzgp+kbC6sMRAAAAAAACxJqQd0eUVRpDHqX5Oi4o/Epx5LeceYekMBAAAAAMA/UOoBJCkGDkqx70GV58vLz0s5Z3aNiQAAAAAA4O+UegB/U4x8f9KzV7XhmdNTXnNhvYEAAAAAAOBvlHoAf1P07pvi3UdXni/HXJXyuUk1JgIAAAAAgFco9QD+QTH8kGTzraoNL1yY5kU/qzcQAAAAAABEqQewhKK9PY1R/1p94YE/pnzgj/UFAgAAAACAKPUAXqUYunuyy1srzzcvPCdlx4IaEwEAAAAA0NUp9QCWojHqY0lbe7Xh559JecvV9QYCAAAAAKBLU+oBLEWxyRYpRoysPF9efWHKGVNrTAQAAAAAQFem1ANYhuLQUUnfDasNvzwn5eXn1xsIAAAAAIAuS6kHsAxFj54p3vOhyvPlHTennPhojYkAAAAAAOiqlHoAr6HYa79k8OurDZdlmhf8JGVZ1hsKAAAAAIAuR6kH8BqKRiONo46rvvDoX1Lec1t9gQAAAAAA6JKUegDLUWz7hhR77ld5vrzkFynnza0xEQAAAAAAXY1SD6CC4n0fStbrUW142pSU119abyAAAAAAALoUpR5ABUW/jVMcckTl+fKGy1O++HyNiQAAAAAA6EqUegAVFQcclgzYrNrwgvlpXvzzegMBAAAAANBlKPUAKiq6dU/jiI9VXxh7Z8r//XN9gQAAAAAA6DKUegCt2HWPZIddKo83L/hJyoULawwEAAAAAEBXoNQDaEFRFGkceWzSqPjj85mJKX9/Q72hAAAAAABY5yn1AFpUDByUYt+DK8+Xv/llytkza0wEAAAAAMC6TqkHsAKKw96f9OpdbXj2zJRX/rreQAAAAAAArNOUegAroOjVO8VhH6g8X/722pTPTKwxEQAAAAAA6zKlHsAKKt5+UDJwULXhZjPNC3+asizrDQUAAAAAwDpJqQewgoq2tjSOOq76wl/GJWPvqi8QAAAAAADrLKUewEoo3rBzsvuwyvPNi85JOW9ejYkAAAAAAFgXKfUAVlLj8I8k7d2qDb/0QsrrL601DwAAAAAA6x6lHsBKKgZsluKg91SeL6+/NOULz9WYCAAAAACAdY1SD6ATFAcfnvTbuNpwx4I0Lzqn3kAAAAAAAKxTlHoAnaBYr0eKUR+rvnD/H1KO/1N9gQAAAAAAWKco9QA6SfHmvZMhO1Web/76JykXLKgxEQAAAAAA6wqlHkAnKYoijaOOSxoVf7ROfjblzVfWGwoAAAAAgHWCUg+gExVbDk6x37sqz5fXXJhy6pQaEwEAAAAAsC5Q6gF0smLk0UnvvtWG581Neckvas0DAAAAAMDaT6kH0MmKnhukeO+HKs+X9/wu5cPja0wEAAAAAMDaTqkHUINi2P7JNttXnm/++uyUCxfWmAgAAAAAgLWZUg+gBkWjkcbRH0+KotrCpCdT/u66ekMBAAAAALDWUuoB1KTY5vUp3jai8nx5xS9TzpxeYyIAAAAAANZWSj2AGhXv/VDSs1e14TmzU15+Xr2BAAAAAABYKyn1AGpU9O6bYuQHKs+Xt9+U8slHakwEAAAAAMDaSKkHULNi+MHJwEHVhssyzV+dlbLZrDcUAAAAAABrFaUeQM2KtrY0jv549YUnHk551y31BQIAAAAAYK2j1ANYBYohQ1O8ZZ/K8+Wlo1POmVVjIgAAAAAA1iZKPYBVpDj8o8l6PaoNz5ye8spf1xsIAAAAAIC1hlIPYBUpNuqf4l2jKs+Xt16T8pmJNSYCAAAAAGBtodQDWIWKEYclm2xRbbjZTPPXZ6csy3pDAQAAAACwxlPqAaxCRbduaRx1XPWFhx5I+cc76gsEAAAAAMBaQakHsIoVO70p2eWtlefLi3+Wct7cGhMBAAAAALCmU+oBrAaNUf+atHerNjz1xZTXXlxvIAAAAAAA1mhKPYDVoNhk8xQHvafyfHnj5Smff7bGRAAAAAAArMmUegCrSXHwEclGA6oNd3Sk+euzUpZlvaEAAAAAAFgjKfUAVpNivfXSGPWx6gsP3pfcd1d9gQAAAAAAWGMp9QBWp92HJW/YufJ488Kfppw3t8ZAAAAAAACsiZR6AKtRURRpHH180tZWbeGlF1Nec2G9oQAAAAAAWOMo9QBWs2KLrVO849DK8+WNV6Rj0pP1BQIAAAAAYI2j1ANYAxTvPjrpu1G14YUdmfnT01OWZb2hAAAAAABYYyj1ANYAxfo9Uxzx0crz88fdm/KPd9SYCAAAAACANYlSD2ANUbz17cmQnSrPlxf9NOXcOTUmAgAAAABgTdFyqTdx4sRMnDgxU6ZMqSMPQJdVFEUa7/940tZWbWHaSymvurDeUAAAAAAArBFaLvU+//nP5/Of/3zGjh1bRx6ALq3YYusUIw6rPF+OuTLlM0/VmAgAAAAAgDVBy6Ve9+7dkyTbbLNNp4cBICkOPTLZsH+14YUL0/zVj1OWZb2hAAAAAABYrVou9TbaaKMkSbPZ7PQwACRFj/XTOPJfqy88PD7lPbfVFwgAAAAAgNWu5VJvxx13TJI8+uijnR4GgL/ZfVjyxl0rj5cX/yzly3NqDAQAAAAAwOrUcqn3zne+M+3t7bnqqqsya9asOjIBdHlFUaRx9MeTtvZqC9OnprzyV/WGAgAAAABgtWm51Nt6661z7LHHZtq0aTnllFMyYcKEOnIBdHnFZgNTHPSeyvPlLVennPREjYkAAAAAAFhdKl4C8nc//OEPkyRbbLFFJk2alK985SvZeOONM2jQoPTq1SuNxrJ7wqIocsIJJ6x4WoAupjjkiJR3/zZ56YXlDzebaf7yrDQ+//+nKIraswEAAAAAsOq0XOr97ne/e9V7U6ZMyZQpUyrtK/UAqivW65HGUcel+cP/qrbw6ISUd92aYtg76g0GAAAAAMAq1fLtNwFYxXbdIxn6psrj5SU/TznHM08BAAAAANYlLV+pd+GFF9aRA4BlKIoijaOPT/OUk5KOBctfmDk95W9+meL9H68/HAAAAAAAq4Qr9QDWAsUmm6d45/sqz5e/vS7lU4/VmAgAAAAAgFVJqQewligOfl/Sf9Nqw2UzzV/+OGWzWW8oAAAAAABWCaUewFqi6L5eGkcdX33h8YdS3jmmvkAAAAAAAKwyLT9T75/dd999GTduXCZOnJhZs2YlSTbYYIMMGjQou+66a3bdddeVDgnAK4pdv6QahAAAIABJREFU3pLs8tZk3D2V5stLR6fcbc8UvXrXnAwAAAAAgDqtcKn32GOP5Ywzzsizzz671M8nTJiQ6667LltuuWVOPPHEvO51r1vhkAD8XePIY9P8y/3J/PnLH541I+Xl56U45hP1BwMAAAAAoDYrdPvNBx54IF/+8peXKPTa2trSt2/f9O3bN21tbYvfnzRpUr70pS9l/PjxK58WgBQDNkuvwz9ceb687YaUTzxSYyIAAAAAAOrW8pV6s2fPzumnn56Ojo4kydve9rYcdNBB2XbbbdPe/srXdXR05LHHHsuNN96Y22+/PR0dHTn99NPzgx/8ID179uzcPwFAF9TrsPdn9s1XJ5P/uvzhskzzlz9K4//7dopG2/LnAQAAAABY47R8pd4NN9yQ2bNnpyiKfPrTn86nPvWpDBkyZHGhlyTt7e0ZMmRIPvnJT+Yzn/lMiqLIrFmzcv3113dqeICuqui+XhpHH199YeKjKX97XX2BAAAAAACoVcul3tixY5Mkw4cPz7Bhw5Y7v9dee2X48OFL7AKw8oqhb0p236vyfHn5eSmnTakxEQAAAAAAdWm51PvrX1+51VuVQm+RRbOLdgHoHI1Rxybd16s2PPfllBf9rN5AAAAAAADUouVS7+WXX06S9OnTp/JO7969kyRz585t9XAAvIZi4wEpDj2y8nx57+9TPnhfjYkAAAAAAKhDy6XeBhtskCR5/vnnK+9Mnjx5iV0AOk9xwGHJ5ltVnm/+8kcp58+rMREAAAAAAJ2t5VJv0KBBSZIxY8ZU3rn55puTJFtvvXWrhwNgOYr2bml84ITqCy88l/K6S+sLBAAAAABAp2u51Ntjjz2SJOPGjcv555+fZrO5zNlms5nzzz8/f/7zn5Mke+655wrGBOC1FEOGptjrHZXny+svSfncMzUmAgAAAACgM7W3urDffvvlmmuuybPPPpurrroq9913X/bbb79sv/326devX5Jk2rRpefjhh3PLLbfkmWde+UvjgQMHZr/99uvc9AAsVhzx0ZTj7knmzFr+cEdHmr/6cRqf/WqKoqg/HAAAAAAAK6XlUq+trS1f+MIXcuqpp2bq1KmZNGlSzjvvvNfc2WijjfKFL3whjUbLFwYCUFHRu2+K93045XlnVlv4y7iU99yWYo996w0GAAAAAMBKW6GWbbPNNsu3v/3t7LPPPmlra1vmXHt7e/bdd998+9vfzqabbrrCIQGoptj7gGTbN1SeLy86J2WVK/sAAAAAAFitWr5Sb5HevXvnpJNOyoc+9KGMHz8+Tz31VGbOnLn4s6233jpDhw5Nnz59Oi0sAK+taDTSOOaENL/22eQ1nnm62IxpKS8/P8UH/q3+cAAAAAAArLAVLvUW6dOnT4YNG5Zhw4Z1Rh4AVlKx5TYpRoxMeeNvKs2Xv7su5bD9U2zz+pqTAQAAAACwolq+/eZpp52W0047LbfddlsdeQDoBMW7j0427F9tuCzTPP+HKZsL6w0FAAAAAMAKa7nUu/fee3PvvfemX79+deQBoBMUPdZP46jjqi889VjKW6+rLxAAAAAAACul5VJv0TPyPCsPYA23257Jzm+pPF7+5ryU06bUGAgAAAAAgBXVcqk3cODAJMmLL77Y6WEA6DxFUaRx9PFJ9+7VFua+nPLCc+oNBQAAAADACmm51Bs2bFiS5I477uj0MAB0rqL/pikOParyfPnH21OOH1tjIgAAAAAAVkTLpd6IESPyute9LnfeeWduvPHGOjIB0ImKAw5LNt+q8nzzVz9OOX9ejYkAAAAAAGhV26mnnnpqKwtTpkzJzjvvnEceeSS33nprJkyYkGazmbIss2DBgrz88suZM2fOMn/17Nmzpj/KumPmzJmrO8Jao2fPnpkzZ87qjgGrXCvnftFoSzFwUMo7x1T78jmzkkYjxRt2XomEUB8/++mqnPt0Vc59uirnPl2Vc5+uyrlPV+b8X1Lv3r2X+Vl7q1924oknLvF6woQJmTBhQqXdoihywQUXtHpIAFZSsf3QFMP2r1zslddfmnKPfVNstmXNyQAAAAAAqKLl22+ujLIsV+XhAPgHxeEfSXot+195LKGjI81f/tjPbQAAAACANUTLV+odfvjhdeQAoGZF774p3vfhlOeeUW3hf/+c8p7bUuyxb73BAAAAAABYrpZLvSOOOKKOHACsAsXbRqS84+bksf+tNF9e+NOUQ9+UotcGNScDAAAAAOC1tFzqrS4vv/xyHnzwwTz66KN5/PHH89hjj2XmzJlJktNPPz0DBw5cqe+fM2dOrrzyyvzhD3/ICy+8kO7du2fw4ME58MADs+eeey53/6677sqNN96YiRMnZv78+RkwYED22GOPHHbYYVl//fVXKhtAZykajTSO+USaX/tM0mwuf2Hm9JSXn5vimE/UHw4AAAAAgGVqudT7whe+kCTZf//9c+CBB3Z6oGV54IEHctppp9Xy3VOmTMkpp5ySyZMnJ0l69OiRl19+OePHj8/48eNzwAEH5Ljjjlvm/llnnZUxY8YkSdra2tKtW7c888wzueyyy3LHHXfkK1/5SjbaaKNasgO0qthycIoRh6W88fJK8+VtN6Tc6x0ptn1DzckAAAAAAFiWRqsLTz31VJ588smVvjJuRfTt2ze77bZbDj/88Bx//PGd8p1lWea73/1uJk+enAEDBuRrX/tazj333IwePTrHHHNMiqLITTfdlJtvvnmp+zfeeGPGjBmToihyzDHH5Nxzz825556br33taxkwYECef/75nH766Z2SFaCzFO8+Ktmof7XhskzzvDNTdnTUGwoAAAAAgGVqudTr06dPkqRnz56dHua1vPnNb85PfvKT/Od//mdGjRqVnXfeuVO+9957780jjzySoijyf//v/82QIUOSJN27d8/IkSNz8MEHJ0kuuuiidPzTX2gvWLAgF198cZLkkEMOyciRI9OtW7ckyZAhQ/K5z30uRVHkoYceyh//+MdOyQvQGYoe66dxdAv/OOKZiZWv7AMAAAAAoPO1XOoNGjQoSfL88893epjX0mi0HLWS22+/PUmy8847Z/Dgwa/6fOTIkSmKItOmTcv48eOX+OyBBx7I9OnTUxRF3v3ud79qd5tttslOO+20xHEA1hTFrnsmu7y18nx59YUpJ/+1xkQAAAAAACxLy03Z29/+9iTJrbfe2ulhVocHH3wwSbLLLrss9fONNtooW265ZZK8qtRb9HqrrbZa5jPzFn3vP+8CrAkaRx+fdF+v2vCC+Wme/8OUZVlvKAAAAAAAXqXlUm/vvffObrvtlvvvvz/nn39+ms1mHblWienTp2fmzJlJsri4W5pFn02aNGmJ95955pnKuzNmzMiMGTNWKi9AZys23iTFyPdXX/jLuJR/+G1teQAAAAAAWLr2VhcmTJiQgw8+OC+99FKuuuqq3HvvvRk2bFgGDx6cXr16Lfc2mW984xtXOGxnmzp16uLfL+tKuyTZcMMNXzX/j6+r7CbJtGnTFj+TEGBNUYwY+UpR9/QTlebLC89JOfRNKTbw8wwAAAAAYFVpudT7yle+ssTr5557Lpdddlml3aIocsEFF7R6yNrMmzdv8e+7d+++zLn11nvl1nRz585d6n6V3aXtL3LzzTfn5ptvTpJ885vfTP/+/ZeTnEXa29v996JL6uxzf8Env5iX/uP4pMrV17NmpPtVv07fT36x044PrfCzn67KuU9X5dynq3Lu01U59+mqnPt0Zc7/6lou9VbGmvYcppXN01l/nhEjRmTEiBGLX7/44oud8r1dQf/+/f33okvq9HN/w01S7PeulGOuqjQ+95ZrMn/3YSmG7NR5GaAiP/vpqpz7dFXOfboq5z5dlXOfrsq5T1fm/F/SFltssczPWi71TjjhhJUKsybp0aPH4t/Pnz9/mXOLrsj7x/l/fF1ld2n7AGuS4l8+kHLsXcnUav8DbZ73wzRO+V6Kbsu+WhkAAAAAgM7Rcqk3fPjwGmKsHv/4LLyXXnopW2+99VLnFj077x+fj7fo9ZNPPpmXXnppmcf4x+fw9evXb2XiAtSq6NEzjfcfn+aZ/1Vt4flnUl53SYqR7683GAAAAAAAaazuAKtTnz590rt37yTJpEmTljm36LMtt9xyifcXva6y26dPn/Tp02el8gLUrdh1z2TXPSvPl9ddkvKvy/4ZCAAAAABA5+jSpV6S7LjjjkmSP//5z0v9/KWXXlpczA0dOnSpu08//fQyr9Zb9L3/vAuwpmocfXzSY/1qwx0daZ5/Zspms95QAAAAAABd3Cop9ZrNZl588cU18kGHe++9d5Jk3LhxefLJJ1/1+dVXX52yLLPhhhu+qpjbaaed0rdv35RlmauvvvpVu08++eTiUm+fffbp/PAANSg26p/iXz5YfeHhB1PecXN9gQAAAAAAeO1S78QTT8wnP/nJPPfcc0v9fNasWbn22mtz7bXXvuZBnnnmmZx44ok56aSTVjxpkhkzZiz+NXv27MXvz549e4nPmv90xcioUaMyatSoXHTRRa/6zre85S15/etfn7Isc9ppp+Xhhx9OkixYsCBXXXVVrrnmmiTJEUcckfb2JR9B2K1btxxxxBFJkmuuuSZXXXVVFixYkCR5+OGHc9ppp6UsywwZMiRvetObVurPDrAqFfsdnGyzfeX58pJfpJwxrcZEAAAAAABdW/trfbjoyrqOjo6lfj516tSMHj06RVHkkEMOWe7ByrJcgYh/d+yxxy71/ZNPPnmJ12eccUY22WSTSt9ZFEX+/d//PaecckomT56ck08+OT169MiCBQuycOHCJMkBBxyQESNGLHX/wAMPzBNPPJExY8bkvPPOy69+9at069Ytc+fOTZJsuumm+exnP1v1jwiwRigabWl88MQ0v/7ZpMqtNefMSnnhOSmO+z/1hwMAAAAA6IJes9SramXLutVt4403zn//93/niiuuyD333JPJkyenR48eGTx4cA488MDstdder7n/8Y9/PDvttFNuuummPPnkk5k/f34GDhyYPfbYI4cddljWX7/is6kA1iDFVtukOOCwlDdcXmm+vOd3KffaL8XQ3WtOBgAAAADQ9XRKqbeqLO32mZ2117Nnzxx99NE5+uijV+gYw4YNy7Bhw1ZoF2BNVbz76JR/vCOZMrnSfPOXP0rj1DNSrLdezckAAAAAALqW13ymHgBdW7FejzSOOaH6wovPp7z6gvoCAQAAAAB0UUo9AF5TMfRNKd6yT+X58sbLU056osZEAAAAAABdj1IPgOUqjjo26dmr2nCzmea5Z6ZsLqw3FAAAAABAF6LUA2C5ij4bpnjfR6ovPPFwyt9dX1seAAAAAICuRqkHQCXF3gck272x8nx52bkpp06pMREAAAAAQNeh1AOgkqLRSONDJyZt7dUW5r6c5gVn1xsKAAAAAKCLqPQ3szfccEP69u37qvenT5+++PeXXHLJMvf/cQ6AtVex+VYpDn5fyqsvrLYw9q6UY+9Ksfte9QYDAAAAAFjHVSr1brzxxuXOXHzxxSsdBoA1X3HIESnv+X0y+dlK881fnZXGG3ZK0XODmpMBAAAAAKy73H4TgJYU3bqnccwJ1Remv5Ty0tH1BQIAAAAA6AJe80q9E05o4S9tAegyih12SbHXO1LedUul+fK2G1K+dd8UQ4bWnAwAAAAAYN30mqXe8OHDV1EMANY2xREfS/nAvcmsmZXmm+eekcap30/RrXvNyQAAAAAA1j1uvwnACil690lx5LHVFyY/m/KqC+oLBAAAAACwDlPqAbDCij2GJzvuVnm+vOGylE8/UV8gAAAAAIB1lFIPgBVWFEUaHzwxWa9HtYVmM83RP0i5cGG9wQAAAAAA1jFKPQBWSrHxJin+5ZjqCxMfTTnmyvoCAQAAAACsg5R6AKy04h3vSrbZvvJ8ecUvU77wXI2JAAAAAADWLUo9AFZa0WhL48OfTNraqi3Mn5/meWemLMt6gwEAAAAArCOUegB0imLgoBQHH1594S/jUt55S32BAAAAAADWIUo9ADpNccioZLMtK8+XF52TcsbUGhMBAAAAAKwblHoAdJqiW7c0PnxS9YU5s1Je8NP6AgEAAAAArCOUegB0qmK7N6YYfkjl+fLe36ccd0+NiQAAAAAA1n5KPQA6XfHeDyUb9q883zz/RylfnlNjIgAAAACAtZtSD4BOV6zfM40PnFB9YdqUlJeNri8QAAAAAMBaTqkHQC2KXd6S4i37VJ4vf3tdykcm1JgIAAAAAGDt1b6sD4488shOP1hRFLngggs6/XsBWDMVRx2XcsL9yeyZleab556Rxpf/J0W37jUnAwAAAABYu6zSK/XKslyVhwNgNSv69Esx6mPVF56blPKai+oLBAAAAACwllrmlXr77rvvay5OnDgxTz75ZJKkZ8+eGTx4cPr165eyLDNjxow88cQTmTNnTpJk8ODBGTRoUOelBmCtUez1jpR/+F0y4f5K8+X1l6Z8894pthxcbzAAAAAAgLXIMku9T3ziE8tc+t3vfpc77rgj/fr1ywc/+MHsueeeaW9f8qsWLlyYu+66K+eff34mTZqUd73rXXn729/eeckBWCsURZHGMZ9I89RPJvPnLX9h4cJXbsP5H99K0WirPyAAAAAAwFqg5dtvPvnkkzn77LOz/vrr5xvf+Eb23nvvVxV6SdLW1pa99947X//617P++uvnrLPOylNPPdUpoQFYuxQDNktx2AeqLzzxcMpbrq4vEAAAAADAWqblUu/aa69NR0dHRo4cmf79+y93vn///hk5cmQ6Ojpy9dX+ghagqyr2f3cyaLvK8+Xl56d84bkaEwEAAAAArD1aLvUefPDBJMkOO+xQeWfR7KJdALqeoq0tjQ9/MmmreEvN+fPSPO/MlGVZbzAAAAAAgLVAy6XetGnTkrzyjKRWTZ8+veUdANYdxVbbpDjovdUX/jIu5e031RcIAAAAAGAt0XKp17NnzyTJQw89VHnn4YcfTpKsv/76rR4OgHVMceiRyaYDK8+XF/8s5Usv1pgIAAAAAGDN13Kpt912rzwP6YorrsjUqVOXOz916tRcccUVS+wC0HUV3bqn8aETqy+8PCfN83/oNpwAAAAAQJfWcql3wAEHJHnlVppf/OIXc88996TZbL5qrizL3HvvvTn55JMX33bzoIMOWsm4AKwLiu2Hpnj7O6svPPDHlH/4bW15AAAAAADWdO2tLuy+++7Zf//9M2bMmEyZMiXf+c530rt377zuda9Lnz59UhRFpk+fnscffzwzZ85cvLf//vtn11137dTwAKy9ivd9OOUDf0ymVru1Zvnrn6TcYdcUfTesORkAAAAAwJqn5VIvSY4//vj06dMnV1xxRZrNZmbOnJlx48YtdbbRaOSwww7LkUceuVJBAVi3FD17pfHBT6T5/a9WW5gzK81fnZW2E/6j3mAAAAAAAGugFSr1kuSoo47K29/+9tx4440ZN25cnn322SU+32KLLbLLLrvkwAMPzBZbbLHSQQFY9xQ7vTnFnvulvPvWagtj70z5pztSvOlt9QYDAAAAAFjDrHCpl7xS3H3kIx9JknR0dGTWrFlJkg022CDt7Sv11QB0EcVRx6accF8yY1ql+eYvf5zGkJ1SbNCn5mQAAAAAAGuORmd9UXt7e/r165d+/fop9ACorOjVO40P/Fv1hZnTU1740/oCAQAAAACsgTqt1AOAFVXsPqylW2qWd/825bh7a0wEAAAAALBmWalL6ubOnZu77747Dz30UKZOnZr58+fnhBNOyIABAxbPzJgxIy+//HK6deuWjTbaaKUDA7BuKt5/fMqH/pzMmllpvnn+mWm8/owUPTeoORkAAAAAwOq3wqXebbfdltGjRy9+jt4i8+bNW+L12LFj86Mf/Sjdu3fPWWedlZ49e67oIQFYhxV9Nkxx1PEpf/qdagvTXkp5yS9SfOikeoMBAAAAAKwBVuj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      "text/plain": [
       "<Figure size 2160x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_error_curve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that as we change m, the error value changes, so we get this bowl shape - we want to get to the bottom!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2160x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = draw_error_curve()\n",
    "error = mean_squared_error(regression_line(-50, 0), ys)\n",
    "ax.annotate('We are here', (-50, error), \n",
    "             xytext=(0, 100), \n",
    "             textcoords='offset points', \n",
    "             arrowprops={'facecolor': 'black'},\n",
    "            fontsize=36)\n",
    "ax.scatter(-50, error, c='black', zorder=3)\n",
    "\n",
    "ax.scatter(23, 0, c='black', zorder=4)\n",
    "ax.annotate('We need to get here!', \n",
    "             (23, 0), \n",
    "             xytext=(0, 100), \n",
    "             textcoords='offset pixels',\n",
    "            arrowprops={'facecolor': 'black'},\n",
    "             ha='center',\n",
    "            fontsize=36);\n",
    "plt.savefig('images/annotated_error_curve.png', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One way we can find our way down the hill is to take one step in a given direction and see if we are any closer to where we want to be - we are *descending* the error curve. How do we know that we are getting closer to the flat bit? \n",
    "\n",
    "Calculus to the rescue! Calculus gives us a tool to find how steep any given point of a curve is - differentiation! We can take the gradient of the curve, so we can figure out which way is down towards the flat bit. If the slope is negative, we want to take a step in the positive direction and vice versa. We want to *descend* the error curve by taking the *gradient* - Gradient Descent!\n",
    "\n",
    "Another way of thinking of it, taking the gradient is the same as asking, if I change the value of $m$ a tiny bit, how does that affect my error? Remember, we want to change $m$ so the error goes down\n",
    "\n",
    "In addition, since we know how steep it is, we can make the assumption that the steeper it is, the further away the flat bit is, so we take a bigger step\n",
    "\n",
    "If we do that over and over again, we eventually get to the bottom, giving us the best value for $m$!"
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    "# It's regressions all the way down!\n",
    "\n",
    "You now have all the knowledge to start understanding how a neural network works! If you can understand how a linear regression works, you can understand how neural nets work.\n",
    "\n",
    "Let's put this into practice and build one from scratch!"
   ]
  }
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