{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression in Python\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Numerical arrays\n",
    "import numpy as np\n",
    "\n",
    "# Plotting.\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plots styles.\n",
    "plt.style.use('ggplot')\n",
    "\n",
    "# Plot size.\n",
    "plt.rcParams['figure.figsize'] = (12, 8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 4., 16.]), array([ 6., 12.]))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create two points.\n",
    "x = np.array([4.0, 16.0])\n",
    "y = np.array([6.0, 12.0])\n",
    "x, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the points.\n",
    "plt.plot(x, y, 'ro')\n",
    "\n",
    "# Give ourselves some space.\n",
    "plt.xlim([-5.0, 25.0])\n",
    "plt.ylim([-5.0, 25.0]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot a straight line.\n",
    "l = np.linspace(-5.0, 25.0, 100)\n",
    "plt.plot(l, 0.5 * l + 4.0, 'g--')\n",
    "\n",
    "# Plot a straight line segment.\n",
    "l = np.linspace(4.0, 16.0, 10)\n",
    "plt.plot(l, 0.5 * l + 4.0, 'b-')\n",
    "\n",
    "# Plot the points.\n",
    "plt.plot(x, y, 'ro')\n",
    "\n",
    "# Give ourselves some space.\n",
    "plt.xlim([-5.0, 25.0])\n",
    "plt.ylim([-5.0, 25.0]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WW2AYBnvttdeq68i6rZx1/v57J//6l8vqOCIiIiJrFYvNxTSjnW4bupVavFRjberr6yktLQWgtLSUUCgEQCAQYPPNN191ubKyMgKBAHa7nfLy8lWfLy8vJxAIrPP2Z82axaxZswAYN24cFRUVbYmb1049FSZPNrnzzhJOOSWFLU9Wpzscji79c5Pf03iQ5jQeZHUaE/lvwYKPMQwHm2xyKA5HUZtuKxfHQ5uK87qYptmqz6/L0KFDGTp06KqPa2pq2pQr3114oZvzzivlkUfCHHJIfqx1rqio6PI/N/kfjQdpTuNBVqcxkf9qav6NyzWQuroE0LafpVXjoWfPnuv8WpvmLYuLiwkGgwAEg0GKipp+sygvL6e2tnbV5QKBAGVlZWt8vra2lrKysrZE6FIOPTTGZpslmThRa51FREQkt6RS1TQ2ft1pl2lAG4vzwIEDeffdpi1H3n33XQYNGrTq83PmzCGZTFJdXc3SpUvZbLPNKC0txe1288MPP2CaJrNnz2bgwIFtfxRdhN0OI0eG+e47rXUWERGR3LJyG7rOuH/zSobZwvUTkyZN4ptvvqGhoYHi4mKOPfZYBg0axMSJE6mpqaGiooJRo0atOoDw+eef5+2338Zms3Hqqaey4447AvDzzz8zdepUEokEO+ywA6eddlqLj7pcsmTJRj7MziOdhqFDKwGYNWsFdrvFgTZAb7tJcxoP0pzGg6xOYyK/LVlyDrHYRwwY8CmG0faDsXJxqUaLi3MuUHFu8tJLLs45p4wpU4IMGxazOs566UlQmtN4kOY0HmR1GhP5yzRT/Pzztvh8f6Gq6o6s3GYuFuc82ZtBmjv44DhbbZVkwgQ/qZTVaURERKSri8U+JZMJ4fUOsTpKu1JxzkM2G4wa1cC8eQ5mzHBbHUdERES6uEjkTcCBx7On1VHalYpznjrwwDh//GPTDhuadRYRERErRSJv4XYPwm5v297NuU7FOU/ZbHDppSHmz3fw3HOadRYRERFrJJOLSSS+xesduuEL5zkV5zy2//6NbLddgkmT/CSTVqcRERGRrigSeQsAr3c/i5O0PxXnPGYYcOmlDSxc6OCZZzxWxxEREZEuKBJ5C4ejNwUFm1sdpd2pOOe5/fZrZMcdE0ya5CORsDqNiIiIdCWZTJxo9D283v1afF6OfKbinOcMAy67rIHFix08+aRmnUVERKTjxGIfYZqxLrFMA1ScO4W99mpk4MAEkyf7icetTiMiIiJdRSTyJobhwuPZ3eooHULFuRNomnUOsWyZncce81odR0RERLqISORN3O7B2GxdY4cvFedOYo89Euy+eyN33eUjGu38a4xERETEWonEPJLJ+fh8nftsgc2pOHcil18eoqbGzj/+oVlnERERaV8rt6HzePa1OEnHUXHuRAYOTDJkSJx77vFRX69ZZxEREWk/kcibFBRsRkFBX6ujdBgV507m8stD1NXZuP9+n9VRREREpJPKZCLEYh/i9XadZRqg4tzpbLNNioMPjnHffV4CAf14RUREJPui0fcxzUSX2YZuJTWrTujSSxuIRg2mTtWss4iIiGRfJPImNpsPt/tPVkfpUCrOndAWW6Q48sgY06d7WL5cP2IRERHJHtM0iUTewuPZC8MosDpOh1Kr6qRGjWogmTS46y7NOouIiEj2JBLfkkot7XLLNEDFudPq1y/NX/8a5bHHvCxaZLc6joiIiHQSkcibAHi9XWcbupVUnDuxiy5qwDBg0iTNOouIiEh2hMNvUFi4HQ5HldVROpyKcyfWq1eGk06K8PTTHn76SbPOIiIi0japVA3x+Gf4fAdYHcUSKs6d3AUXhCksNLn99iKro4iIiEiea1qmYeL17m91FEuoOHdylZUZzjwzwksvufnqK6fVcURERCSPhcOv43D0pLDwj1ZHsYSKcxdwzjlhSkoyjBvntzqKiIiI5KlMJkY0+i5e7/4YhmF1HEuoOHcBRUUm55/fwDvvuPi//+ta+y2KiIhIdkSjH2CasS67vhlUnLuMU0+NUFWVZuzYIkzT6jQiIiKSbyKRNzAML273blZHsYyKcxfhdsPIkQ18+mkBb7xRaHUcERERySOmmSEcnoXXuw82W9ftESrOXchxx0Xp1y/FrbcWkU5bnUZERETyRWPjV6TTy/D5uuZuGiupOHchTidcfnmI775zMmOG2+o4IiIikifC4dcBG17vEKujWErFuYs59NA4f/xjkttv95NIWJ1GRERE8kEk8jpu9yDs9jKro1hKxbmLsdlg9OgQCxc6eOIJj9VxREREJMclk4tpbPymy570pDkV5y5o330b2XXXRiZN8hONds19GEVERKRlIpE3ALr8+mZQce6SDKNp1nnFCjv33++1Oo6IiIjksHD4dZzOARQUbGZ1FMupOHdRgwYl+fOfY0yd6iMQ0DAQERGRNaXTDUSjc7r0SU+aU2Pqwq68soFo1GDSJJ/VUURERCQHRaPvAkmtb/6NinMXtvnmKf761yiPPOJl4UK71XFEREQkx4TDr2OzleB2D7Q6Sk5Qce7iRo1qwG43GT/eb3UUERERySGmmSISeROvdwiG4bA6Tk5Qce7ievTIcMYZEZ5/3sN//6v/FCIiItIkFvuETKZO65ubUXEWRowIU1KS4e9/L7I6ioiIiOSIpm3onHg8e1sdJWeoOAvFxSYXXtjAu++6mD27wOo4IiIiYjHTNAmHX8Xj2R27Xcs5V1JxFgBOOSVCr14pxo4tIpOxOo2IiIhYKZH4lmRyPj7fX6yOklNUnAUAlwsuv7yB//yngJdeclkdR0RERCwUDr8KGPh8f7Y6Sk5RcZZVjjgixlZbJbn11iISCavTiIiIiFXC4X/jcg3E4ai0OkpOUXGWVex2uOqqEAsWOHjsMZ2KW0REpCtKJBbQ2PgNfr+WaaxOxVl+Z999G9l990buuMNHKGRYHUdEREQ6WDj8bwCtb14LFWf5HcOAa68NEQzamTJFp+IWERHpasLhVyks3Bqns4/VUXKOirOsYdttkxx1VJT77/exeLFOxS0iItJVpFLVxOOf4PMdZHWUnKTiLGt1xRUNANx6q/ZuFBER6SrC4dcAE5/vQKuj5KQ2n2N5yZIlTJw4cdXH1dXVHHvssUQiEd58802KiprORnf88cez0047AfDCCy/w1ltvYbPZGD58ODvssENbY0iW9eqV5owzwkyd6uPMMyNsu23S6kgiIiLSzsLhV3E6+1FQsKXVUXJSm4tzz549GT9+PACZTIazzz6bP/3pT7z99tscfPDBHHbYYb+7/KJFi5gzZw533HEHwWCQMWPGMHnyZGw2TX7nmvPPD/PEEx7GjCniqadqMXSsoIiISKeVTtcTjX5AaekZGHrRX6usttWvvvqKqqoqKivXveff3LlzGTx4ME6nk27dulFVVcVPP/2UzRiSJUVFJqNGhfngg0LeeqvQ6jgiIiLSjiKRN4GklmmsR5tnnJv74IMP2H333Vd9/NprrzF79mwGDBjAySefjM/nIxAIsPnmm6+6TFlZGYFAYK23N2vWLGbNmgXAuHHjqKioyGZcaYGLL4aHHjIZN66Uo45K4WjliHE4HPq5ySoaD9KcxoOsTmPCWjU1b+F09mCTTQ7AMKxfCZCL4yFrxTmVSvHpp59ywgknAHDAAQdw9NFHA/DUU0/xyCOPMGLECEzTbPFtDh06lKFDh676uKamJltxpRWuuMLFWWeVMXVqlBNOiLbquhUVFfq5ySoaD9KcxoOsTmPCOplMjGDwVYqKjqG2du0Tmh3NqvHQs2fPdX4ta79OfP755/Tv35+SkhIASkpKsNls2Gw2hgwZws8//wxAeXk5tbW1q64XCAQoKyvLVgxpBwcdFGfgwATjx/uJRLTmSUREpLOJRt/DNGM66ckGZK04r75MIxgMrvr3xx9/TO/evQEYOHAgc+bMIZlMUl1dzdKlS9lss82yFUPaQdNJUeqprrYzbZpOiiIiItLZhMOvYLMV4/HsZnWUnJaVpRqNjY385z//4ayzzlr1uccee4z58+djGAaVlZWrvta7d2922203Ro0ahc1m4/TTT9eOGnlg4MAkhx4a4557vJxwQoQePTJWRxIREZEsMM0U4fAbeL1DMQyn1XFymmG2ZtGxxZYsWWJ1hC5t4UI7e+/djcMOizF5cl2LrqP1atKcxoM0p/Egq9OYsEY0+j6LFh1Hjx4P4PfnzlKNTr3GWTq/Pn3SnHlmmGef9fDll/qNVEREpDNoaPg3huHC693H6ig5T8VZWuWCC8KUl6e58cYi8ue9ChEREVkb08wQDr+K17svNpvb6jg5T8VZWsXvN7nssgY++qiQf//bZXUcERERaYN4/BPS6WX4fIdYHSUvqDhLqx1/fJQ//CHJzTcX0dhodRoRERHZWA0NL2MYhfh8Qzd8YVFxltZzOOD660MsWOBg+nSv1XFERERkI5hmhoaGf+Hx7IvNpu1mW0LFWTbK3ns3st9+cSZP9lNbq2EkIiKSb1Yu0/D7D7U6St5Q45GNdu21ISIRgwkT/FZHERERkVbSMo3WU3GWjbbFFilOPDHKY495+OGHrJxLR0RERDqAlmlsHBVnaZNLLmnA6zW56aYiq6OIiIhIC8Xjn/62TEO7abSGirO0SXl5hosvbuDtt128+Wah1XFERESkBRoaXvptmcb+VkfJKyrO0mbDh0cYMCDFDTcUk0hYnUZERETW53/LNPbRMo1WUnGWNisogOuvr2fePG1PJyIikuv+t0xDu2m0loqzZMWQIY3su2+ciRP91NRoWImIiOQqLdPYeGo4khWG0XRSlFjM4LbbtD2diIhILjLNDOGwlmlsLBVnyZrNN09x6qkRnnjCw3//q+3pREREck08/implHbT2FgqzpJVI0c2UFqa4frrizFNq9OIiIhIcytPeuL15vYyjdGji5k+Pfdqau4lkrxWUmJy+eUNfPhhIS+/7LI6joiIiPymaZnGy3g8+2C35+6yyg8+KODRR70sWWJ1kjWpOEvWnXBClK22SnLzzUXEYlanEREREciPZRqpFFx3XTG9e6cYNSpjdZw1qDhL1tntcNNN9Sxa5GDiRA0xERGRXJAPyzQefdTDd985uf76EG631WnWpFYj7WLw4AQHHRTjttvsLF5stzqOiIhIl/a/3TT2ztllGoGAjfHji9hzz0YOPDBudZy1UnGWdnP99SEAbrqpyOIkIiIiXVss9jGp1FL8/sOtjrJO48b5iUQMbrqpHsOwOs3aqThLu9lkkzSXXZbm5ZfdvP9+gdVxREREuqyGhhkYhhuf7wCro6zVV185eeIJD8OHR9hii5TVcdZJxVna1ahRGXr3TnHddcUkk1anERER6XpMM0lDw8v4fAdgs3msjrMG04RrrimmvDzDqFENVsdZLxVnaVduN9x4Y4jvv3fy0ENeq+OIiIh0OZHIbDKZIH7/MKujrNULL7j55JMCrrwyRFFRbp8EQsVZ2t0BB8TZZ584Eyb4WbFCQ05ERKQjNTTMwGYrwevdx+ooawiHDW6+uYgddkhw7LG5v4etWoy0O8OAG2+sJx43GDtWBwqKiIh0lEwmRjj8Gj7fQRhG7h1vdOedPpYvtzNmTD22PGileRBROoPNNktz5plhnnrKw6efOq2OIyIi0iVEIm9gmhGKioZZHWUNP/9s5777fBxzTJSddsqPA6FUnKXDXHRRmO7d01x7bTGZ3DsZkIiISKcTCs3Ebu+O272r1VF+xzTh2muLcblMrr46ZHWcFlNxlg7j85lcc02IL78s4Mknc++oXhERkc4kna4nGn0Lv/8wDCO3Tkb2yisu3n3XxeWXN1BZmT+zaSrO0qGOOCLGn/7UyNixfoLBHN3dXEREpBMIh/+NaSZybplGNGpw/fXFbL11kpNPjlgdp1VUnKVDGQbccks99fU2br1VBwqKiIi0l4aGGTid/Sgs3N7qKL8zebKPpUvt/P3v9TgcVqdpHRVn6XBbb53i1FMjPPaYhy++0IGCIiIi2ZZKVRONfoDfPwwjh85f/dNPdu69t+mAwEGDElbHaTUVZ7HEpZc2rWm66qpi0mmr04iIiHQuDQ0vAZmcOunJygMC3e78OiCwORVnsURRkcl11zUdKPj44zpQUEREJJsaGmZQWLg1hYWbWx1llX/9y8Xs2S4uvzyUVwcENqfiLJYZNizG4MGN3HprEbW1GooiIiLZkEgsIB7/DL//CKujrBKJGNxwQzF//GOSk06KWh1no6mtiGVWHigYDhvccosOFBQREcmGhoaZAPj9h1uc5H9WHhB4yy11eXdAYHMqzmKpLbZIcdZZTWcUnDs3904FKiIikm8aGmbicg3C6exldRQAfvzRwX33+TjuuCiDBuXHGQLXRcVZLHfxxWF69Ehz5ZXFpFJWpxEREclfjY3fkEh8lzN7N5smXHllMV6vyVVX5ecBgc2pOIvlvF6TG2+s59tvnTz0kNfqOCIiInkrFHoWcOL3H2Z1FACefdbN//1fIVdeGaKiIj8PCGxOxVlywkEHxdlnnzjjx/tZtkzDUkREpLVMM0Uo9AJe7xDs9jKr4xAMGowZU8ROOyU44YT8PSCwOTUUyQmGATffXE8y2XTUrYiIiLRONPoe6XQ1RUVHWx0FgLFji6irszFuXB22TtI4O8nDkM6gf/80F1zQwEsvuXn77UKr44iIiOSVUOg5bLYSvN79rI7CJ584efxxL6efHuGPf+w8BzCpOEtOGTEizKabJrnqqmJisdw5RaiIiEguS6cbCIf/jd9/ODabtZNPqRSMHl1Cjx5pLrmkwdIs2abiLDmlsBDGjq1n4UIHkyf7rI4jIiKSF8LhVzDNeE4s03jwQS/ffuvkppvq8flMq+NklYqz5Jzdd09w9NFRpk3z8cMPebxLuoiISAcJhZ7B6eyPy7WjpTkWL7Zx++1+hgyJ85e/xC3N0h5UnCUnXXddCK/XZPToYjL5v3uNiIhIu0kmFxGL/R9FRUdjGNYuc7zhhqbX7ZtvrsfiKO1CxVlyUnl5hmuuCfHRR4U8/bTb6jgiIiI5KxR6DoCioqMszfHGG4W88oqbiy8O06dP2tIs7SUr74Ofd955uFwubDYbdrudcePGEQ6HmThxIitWrKCyspKRI0fi8zWtWX3hhRd46623sNlsDB8+nB122CEbMaSTOe64KE8/7WbMmGL237+R8nJNPYuIiDRnmiah0LO43bvhdPa2LEckYnD11cVssUWSs88OW5ajvWVtxvn6669n/PjxjBs3DoAZM2aw7bbbcuedd7LtttsyY8YMABYtWsScOXO44447uPrqq3nwwQfJ6L14WQubDcaNqyccbtpAXURERH4vHv+CZHKe5QcFjh/vZ/FiB7fdVkdBgaVR2lW7LdWYO3cue++9NwB77703c+fOXfX5wYMH43Q66datG1VVVfz000/tFUPy3B/+kOKcc8I884yHDz7oxP8TRURENkIo9CyG4cLnO9iyDF9+6eTBB72cdFKEQYOSluXoCFkrzrfccgtXXHEFs2bNAqC+vp7S0lIASktLCYVCAAQCAcrLy1ddr6ysjEAgkK0Y0gldfHGYvn1TXHFFCbGY1WlERERyg2kmaGiYgc/3Z+x2vyUZUim47LISKiszXHllyJIMHSkra5zHjBlDWVkZ9fX13HzzzfTs2XOdlzXNlu/nN2vWrFVFfNy4cVRUVLQ5q3Qsh8ORlZ/bPfeYHHSQk/vv785NN3XOAw66gmyNB+kcNB5kdRoTrVNbO5NMpo5NNjmN0lJrvm8TJ9r4+msH//xnkk03Ld/wFVohF8dDVopzWVkZAMXFxQwaNIiffvqJ4uJigsEgpaWlBINBioqa1qiWl5dTW1u76rqBQGDV9Vc3dOhQhg4duurjmpqabMSVDlRRUZGVn9v228PRR5cwYYKboUNr2XrrznP6zq4kW+NBOgeNB1mdxkTrLFkyHbu9klRqB0u+bwsX2rnxxkr23z/OnnsGyHYEq8bD+iaA27xUIx6PE/vt/fN4PM5//vMf+vTpw8CBA3n33XcBePfddxk0aBAAAwcOZM6cOSSTSaqrq1m6dCmbbbZZW2NIF3D99SGKijJcfnkJaU06i4hIF5ZOBwiHZ1FUdASG0fEnCzNNuOqqYmw2uOWWuk65Z/PatPk7XV9fz+233w5AOp1mjz32YIcddmDTTTdl4sSJvPXWW1RUVDBq1CgAevfuzW677caoUaOw2Wycfvrp2GzaTlo2rKwsw403hrjgglIeftjLaadFrI4kIiJiiVBoBpC0bDeNF1908fbbLm68sZ5evbrO7miG2ZpFxxZbsmSJ1RGklbL9NotpwoknljF3bgFvv13dpf6zdgZ6G1aa03iQ1WlMtIxpmixceADgoG/ff3f4/QeDBvvs041evdK89FINdnv73E+nXKoh0pEMo2lv50wGrrqqhPz5tU9ERCQ7Ghu/orHxG4qLj7Pk/m++uYhg0MZtt9W1W2nOVSrOknd6905z2WUNzJrl4qWXXFbHERER6VD19U9iGC78/iM6/L5nzy7gySe9nHtumG226XoH6qs4S146/fQI222X4Lrriqmr6yJHJIiISJeXycRoaHgBn+8g7PbiDr3vaNTg8stL6N8/xcUXN3TofecKFWfJSw4HjB9fRyBg46abOvaJQ0RExCrh8L/JZEIUF/+1w+/7ttv8/Pqrg9tvr8Pt7vC7zwkqzpK3ttkmxbnnhnnqKQ/vvltodRwREZF2V1//JE5nH9zu3Tr0fj/91MkDD3g5+eQIu+6a6ND7ziUqzpLXRo5sYNNNk1x+eTGRiJZsiIhI55VILCAW+4CiouMwjI6rcI2NcOmlJVRVZbjqqs5/Wu31UXGWvOZywYQJ9SxebGfsWL/VcURERNpNKPQUYFBUdGyH3u/dd/v54Qcn48bV4fd37e2sVJwl7w0alGD48AjTp/v4+OMCq+OIiIhknWmmCYWexuPZB6dz3fsMZ9t33zm46y4fRx4ZZejQxg6731yl4iydwujRDfTuneKSS0r47QzwIiIinUY0OptUammHHhSYTjct0fD7m87cKyrO0kl4vSa33VbPvHkOJk7Ukg0REelc6uv/id1ehs93QIfd5wMPePn88wLGjAlRVqYz9YKKs3Qie+3VyPHHR5g2zcd//uO0Oo6IiEhWpFK1hMOv4/cfhWF0zJLEefPs3HZbEUOHxjn8cL2Vu5KKs3Qq114borIyw6hRJSS67m45IiLSiTQ0PA8kO2yZRjoNo0aVUFhocuutdRjatGoVFWfpVIqLTcaOrePbb51MmeKzOo6IiEibmKZJff2TuFw7Uli4ZYfc5/TpXubOLeTGG+upqtISjeZUnKXTOeCARoYNizJpkp///tdhdRwREZGNFo9/QSLxHUVFHTPb/MsvTdu7DhkS5+ijtURjdSrO0imNGVNPaWmGkSNLtWRDRETyVn394xiGG7//8Ha/r0wGLrmkhIICtERjHVScpVMqKzO59dZ6vvnGyV13aZcNERHJP+l0PQ0NMygqOhK7vf1fy6ZP9/LRR4XccEM9PXpoicbaqDhLp/XnP8c58sgod97p05INERHJO6HQ85hmjOLiE9v9vn75xc7f/+5nv/3iHHuslmisi4qzdGo33VRPeXmGiy/Wkg0REckfTQcFPkph4Q64XNu1631lMk0nOikogNtu0xKN9VFxlk6ttLRpK51vv3UyaZKWbIiISH6Ix+eSSHxPSclJ7X5fDz3k5cMPtUSjJVScpdPbf/9Gjjkmyt1368QoIiKSH+rqHsVmK8LvP6xd72fePDu33OJn3321RKMlVJylS7jxxnoqKzNcfHEJjY1WpxEREVm3dDpAOPwyRUVHY7N52vF+4OKLSykshPHjtUSjJVScpUsoLja57bY6vv/eyR13aMmGiIjkrvr6pzHNRLsfFDhtmo9PPy3gllu0RKOlVJylyxgypJG//jXC1Kk+PvlESzZERCT3mGaG+vpHcbt3obDwD+12P99+6+D22/0cfHCMYcO0RKOlVJylS7nhhhC9eqW56KJSolG9JyUiIrklGn2fZHI+xcXtd1BgIgEXXlhKUVGGsWPrtUSjFVScpUvx+00mTqxjwQI7Y8YUWR1HRETkd+rrH8VuL8PnO6jd7mPiRD/ffONk/Pg6ysu1RKM1VJyly9lttwRnnRXhkUe8vPNOodVxREREAEillhEOv0ZR0XHYbO3z+vTZZ07uvtvHscdGOeAAHS3fWirO0iVdfnmILbZIcsklJQSDeo9KRESsV1//JJCmuPhv7XL7sRhcfHEJPXqkufHG+na5j85OxVm6JJcL7ryzjpoaG1dfXWx1HBER6eJMM019/eN4PHtRUNC/Xe5j7Ngifv7ZyR131FFUZLbLfXR2Ks7SZW27bZKRIxuYOdPDzJkuq+OIiEgXFom8SSq1pN0OCpw9u4AHH/Rx2mlh9tgj0S730RWoOEuXdv75YXbcMcFVV5WwbJn+O4iIiDXq6h7Gbq/C59s/67cdDBqMHFnK5psnueqqhqzffleipiBdmsMBkycHicfhkktKMPXOlYiIdLBE4iei0XcoKTkJw8jueQZME0aPLqG21sZdd9XhduuFri1UnKXL23TTNNdeG+Kdd1xMn+61Oo6IiHQxweB0DKOgXc4U+Nxzbl5+2c2llzaw7bbJrN9+V6PiLAKcckqUIUPi3HxzEd9/77A6joiIdBHpdIhQ6Bn8/sNwOCqyetu//mrn6quL2WWXRs49N5zV2+6qVJxFAMOACRPq8PkynHdeKY3a2lJERDpAKPQ0phmhpOT0rN5uOg0XXVSCYcDkyXXY7Vm9+S5LxVnkN5WVGe64o45vv3UybpzOKigiIu3LNDPU1U3H5RqIy7VdVm/7nnt8fPRRITffXE/v3ums3nZXpuIs0szQoY2cckqE++7zMXt2gdVxRESkE4tE3iKZnE9JyWlZvd2vvnIyfryfQw+NcdRRsazedlen4iyymmuvDbHZZklGjiwlENBZBUVEpH3U1U3Hbq/C7z8oa7cZixmcf34JFRUZxo6tw9DLWFapOIusxu02mTIlSG2tjSuu0BZ1IiKSfe21Bd311xfx888OJk0KUlqqF7BsU3EWWYtttklxxRUhXnnFzVNPua2OIyIinUx7bEH3yisuHn/cy7nnhtlzT50dsD2oOIusw9lnRxg8uJFrry3m5591OLKIiGRH0xZ0T2d1C7rFi21cdlkJ22+f4LLLdHbA9qLiLLIONlvTWQULCmDECG1RJyIi2REKPYVpRrO2BV06DRdeWEoyCVOmNL1uSftQcRZZj549m7ao++9/Cxg7VlvUiYhI2zRtQfdQVregu/NOHx9+WMgtt9TTv7+2nmtPKs4iG/DnP8cZPjzM/ff7ePPNQqvjiIhIHsv2FnRz5zqZONHPEUdEOfpobT3X3lScRVrgmmtCbLVVkpEjS1i+XP9tRERk49TVPYDd3j0rW9DV1xucf34pvXqlGTu2XlvPdQA1AJEWcLngnnuCRCIGF15YSiZjdSIREck3jY1fE42+R2npaW3egs40YfToEpYutXP33UH8fm091xFUnEVaaPPNU4wZE+L99wuZOtVndRwREckzgcC9GIYnK1vQPfmkhxdfdHPppQ3svHMyC+mkJVScRVrh+OOjHHpojNtu8/Ppp9nbsF5ERDq3ZHIJDQ0zKS4+Hru9pE239d13Dq65pog99mjkvPPC2QkoLaLiLNIKhgG33lpHjx5pzjuvlPp6LSgTEZENq6v7B5ChtPTMNt1ONGpwzjml+P0md90VxK7TDHQoR1tvoKamhilTplBXV4dhGAwdOpSDDjqIp59+mjfffJOioqYtvI4//nh22mknAF544QXeeustbDYbw4cPZ4cddmhrDJEOU1zcdEruo46q4NJLS7jvvqAOyBARkXVKpxuor38Mv/8QnM7ebbqta64p5qefHDzxRC3duumAm47W5uJst9s56aSTGDBgALFYjNGjR7Pddk37Eh588MEcdthhv7v8okWLmDNnDnfccQfBYJAxY8YwefJkbDZNfkv+GDgwyZVXhhgzppjp0xOcdlrE6kgiIpKjQqEnyGQaKC09p0238+yzbp56ysNFFzWw1146pbYV2txWS0tLGTBgAABut5tevXoRCATWefm5c+cyePBgnE4n3bp1o6qqip9++qmtMUQ63FlnRRg6NM5NNxXx5Zda7ywiImsyzSTB4AO43bvhcm2/0bfz008OrryymF13bWTUKJ1S2ypZneatrq7ml19+YbPNNgPgtdde49JLL2Xq1KmEw02L1wOBAOXl5auuU1ZWtt6iLZKrbDaYODFIZWWac87RemcREVlTQ8PLpFJLKC09e6NvIxaDc84pxeUyufvuII42rxeQjZW1b308HmfChAmceuqpeDweDjjgAI4++mgAnnrqKR555BFGjBiBabZ8n8FZs2Yxa9YsAMaNG0dFRUW24koHcTgcnfrnVlEB//ynyZAhDq66qjtPPpnSeuf16OzjQVpH40FW19nGhGmaLF78AG73H+jb9zgMY+PmK887z86339qZOTPJttuWZTll7srF8ZCV4pxKpZgwYQJ77rknu+yyCwAlJSWrvj5kyBBuvfVWAMrLy6mtrV31tUAgQFnZ2gfB0KFDGTp06KqPa2pqshFXOlBFRUWn/7ltthlceaWXMWOKGT8+pvXO69EVxoO0nMaDrK6zjYlo9H0ikS/o3n08tbUb9+76zJkuHnigjBEjGhg4sIFO9O3ZIKvGQ8+ePdf5tTYv1TBNk2nTptGrVy8OOeSQVZ8PBoOr/v3xxx/Tu3fTUaQDBw5kzpw5JJNJqqurWbp06aqlHSL56uyzI+y/f9N65y++0HpnERGBQGAadnslfv+RG3X9H390cOmlJQwcmODyy7WuORe0ecb5+++/Z/bs2fTp04fLLrsMaNp67oMPPmD+/PkYhkFlZSVnnXUWAL1792a33XZj1KhR2Gw2Tj/9dO2oIXnPMJrWO//5z5Wcc04pr766gpISnf5URKSramz8jmj0bcrLL8dmc7X6+tGowVlnleJ2m0ybFsCpOZmcYJitWXRssSVLllgdQVqps73ttiGffOLkqKMq2HffRv7xjwD6nfD3utp4kPXTeJDVdaYxsWzZSBoaXmLAgI+x21u3Ltk04cILS3jhBTdPPFHbZbee65RLNUTkfwYOTHLddSHeeMPF1Kk+q+OIiIgFksnFhELPU1z811aXZoBHH/Xw/PMeLr1U+zXnGhVnkSw77bQIhx0W49Zb/bz/foHVcUREpIMFg/cAUFp6bquv++WXTq6/vpj99otz4YXhbEeTNlJxFskyw4Dbb69j001TjBhRytKl+m8mItJVpFIrqK//J0VFR+N09mrVdYPBpnXNFRVpJk8OarlfDtKPRKQdeL0m998fJBYzOPvsMhJ6p01EpEsIBu/HNBOUlY1o1fUyGbj44lKWL7dz771Bysry5hC0LkXFWaSdbL55igkT6vj00wJuvrnI6jgiItLO0uk66usfxu8/hIKCTVt13bvv9jFrlovrr69np52S7ZRQ2krFWaQdHXZYnDPOCPPggz5mzmz9dkQiIpI/6uqmk8mEKSu7oFXXe+edQm67zc+wYVFOPTXaTukkG1ScRdrZNdeEGDSokUsvLeGHH7J2lnsREckhmUyEYPABvN79KSzcusXXW7jQznnnlbLllinGj6/HMNoxpLSZirNIO3M64Z57gng8JqefXkYopGdFEZHOpq7uUTKZOsrKLmzxdWIxg9NPL8M04YEHAng8Wtec61ScRTpAjx4Z7rsvyMKFdi64oJRMxupEIiKSLZlMnGDwXjyePXC7d2rRdUwTLr+8mG+/dXD33UH69Uu3c0rJBhVnkQ6yyy4JbryxnlmzXEyc6Lc6joiIZEko9CTpdHWrZpv/8Q/vqpOc7LdfYzumk2xScRbpQKecEuXYY6PccYef117TwYIiIvnONJMEAvfgcu2M2z24Rdf58MMCbrqpiAMOiOkkJ3lGxVmkAxkGjB1bx/bbJ7jwwhJ++kkHC4qI5LNQ6AVSqUWUlV2I0YIj+5YutXH22aX06ZNm8uQ6neQkz+jHJdLBXC64//4AhYUmp51WSkODDhYUEclHppkmELibwsI/4vUO2eDl43E488wyolGDBx8MUFSkgwHzjYqziAV69cpw771B5s93cOGFJTpYUEQkDzU0zCCZ/Jmysos2ONtsmnDFFSV8/nkBkyfXscUWqQ5KKdmk4ixikd12S3D99SFef92tgwVFRPKMaaaorb2DwsKt8fn+ssHL33efl2ef9XDJJSEOOijeAQmlPWiBpYiFTjstwldfObnjDj9bbpnk4IP1ZCoikg9CoedIJufTs+d0DGP985DvvFPIzTcXcdBBMS6+WAcD5jPNOItYyDBg3Lg6dt45wUUXlfDf/+p3WRGRXGeaSWprJ1JYuB1e7/7rvey8eXZGjCjlD39IMWmSDgbMd/rxiVjM5Wo6Y1RJicnw4WWsWKH/liIiuay+/ilSqV8pL790vWubQyGD4cPLsNlM/vGPAF6vDgbMd3qFFskB3bpleOihWgIBG2ecUUaj9sIXEclJmUwjgcBkXK6d8Hr3W+fl0mk4//xS5s93cN99Qfr00ZkBOwMVZ5Ecsc02TW/jffJJAVdeWYKpiQkRkZwTCv2TVGoJ5eWXrXe2+bbb/Lz5posbb6xn8OBEByaU9qQFlSI55NBD43z/fQMTJ/r5wx+SnH12xOpIIiLym0wmRm3tXbjdu+Dx7LnOyz39tJu77/bzt79FOOWUaAcmlPam4iySY0aNauD77x3cfHMRm2+eYr/9tG5DRCQX1Nc/Rjq9jPLyu9Y52/zRRwVcfnkJu+/eyC231NOCkwlKHtFSDZEcY7PB5Ml1bLllihEjSvnuO/1+KyJitUwmSiBwN273YDyewWu9zPz5dk4/vZTevdPcd18Ap7ODQ0q7U3EWyUEej8lDD9Xi8Ziccop22hARsVpd3SOk0zVUVFy21q/X1xucckoZpmnw8MO1lJToQJXOSK/GIjmqV68MDz0UoLbWxvDhZcRiVicSEemaMpkwweAUPJ69cbv/tMbXk0k455xSFixw8MADAQYM0A4anZWKs0gO2267JHffXccXXzi5+OJSMhmrE4mIdD2BwDTS6QDl5WvONpsmXHttMbNnu7j11jp22007aHRmKs4iOe7AA+Ncc02Il192c+utfqvjiIh0KalUNcHgvfh8h+B277jG1x980Mujj3oZMaKB447TW4OdnY46EskDZ58dYd48B3ff7WfAgJSenEVEOkht7URMM0FFxRVrfO2111zceGMRBx4Y48orGyxIJx1NxVkkDxgG3HJLPQsXOrj88hI22STN7rvr7UARkfaUSPxMff3jFBefSEHBgN997fPPnYwYUcJ22yW56646bHoPv0vQj1kkTzidcO+9AQYMSHHmmWX88IN+7xURaU81NeMwDBfl5SN/9/kFC+ycemoZ3bo1HcTt8WgHja5CxVkkjxQXmzzySIDCQpMTTyxj2TL9FxYRaQ+x2KeEw69QVnYODkflqs8HAgYnnVRGKmXw6KO1VFbqqO2uRK+6Inmmd+80jzwSIBi0cdJJ5TQ06LRUIiLZZJomNTW3YLdXUlp69qrPx+Nw+ullLFrkYPr0AJttpm3nuhoVZ5E8tO22Se67L8j33zs466xSkkmrE4mIdB6RyCxisY8oLx+JzeYFIJOBiy8u5eOPC5k4Mcif/qTjTLoiFWeRPLXvvo3cdlsds2e7uOyyEkwtsRMRaTPTTFNTMxansz/FxSes+vzYsX5eesnNNdfUc/jhcQsTipV0dJFIHvvrX2MsWWJnwoQievVKc9ll2g5JRKQtQqFnSCS+p0ePezEMJ9C0V/PUqX5OOSXCOedELE4oVlJxFslzI0eGWbzYzqRJfnr2TPO3v0WtjiQikpcymRi1teNxuXbE5zsYgJkzXVx/fRF/+UuMMWPqMXRYSZem4iyS5wwDxo2rZ/lyO6NHF1NRkeHPf9bbiCIirRUM3ksqtYyqqikYhsHs2QVcdFEpf/pTgrvvDmK3W51QrKbiLF2eaZpkMg1kMnVkMjFMM/7b3zEymTiQAJwYhgPDaPq76eNC7PZi7PYybLYiDMO6Qwaa9ngOctxx5Zx7bilPPFHLrrvqwBURkZZKJpcQCNyNz3cwHs+ufPWVkzPOKGOzzVJMnx7A5bI6oeQCFWfp9EwzQyq1mETiRxobfyCVWkwqtZxUqpp0uppUajmm2dYZWht2ewk2Wyl2exlOZy+czt44HL1xOlf+6YVhFGTlMa2N19u0x/MRR5Rz6qllPPdcDX/8Y6rd7k9EpDOpqRkLZKisvJZffrFz4olllJZmeOyxWoqLdfS1NFFxlk4lk4kRj39JPP4pjY3fkUj8SCLxE6YZW3UZm82P3d4Nh6MbLteOOBzdsNu7Y7eXYrO5MQzXqr8Nw/3bwSEpTDOFaSZ/+zuBaTaSydSTTgdIp4PN/tQSj39GQ8NLQPM9Pm04nX0pLNyKgoItKSzcisLCLXE6+2IY2Xn/r6wswxNPBDj88Ar+9rdyZs6soW9f7TMqIrI+sdhcGhqep6zsIoLBvvztb+Wk0/D447VUVekEJ/I/Ks6S11KpZcRic4nFPiEe/5R4/CugaZbV4ehFQcHmFBfvQkHBFhQWbk5BwWbY7WUdks00U6RSy0gmF5JM/koyuZBE4gcaG78lHP430DSDYRguCgu3we3eGZdrZ9zunXE4qjb6fnv1SvPEE7UccUQFJ5xQzgsv1NCtm574RUTWxjQzVFdfj8NRhdN5AcceW0Z1tY2nn67VCU5kDSrOkldMM008/jmRyJtEIrNobPwGaCqfLtcOlJWdg8s1ELd75w4ryOtiGA6czk1wOjdZ42uZTOy3Ev0djY1fE49/SV3dQ5jmvUBT6Xe7d8bt3gWPZw+czk0xWnEo9xZbpHjkkVqOO66cv/2tnOeeq6GoSG81ioisLhR6hsbGLykru5vTTtuE775zMn16gJ120pmlZE0qzpLzMpkYkcis3/68RTodAOy43YOoqLgaj2cwhYVbt+v64Wyz2dy4XNvjcm2/6nOZTONvJfpTYrFPf3vr8EUAHI6eeDx7/vZnDxyOyg3ex847J3nggSCnnFLG8OFlPPZYLW53uz0kEZG8k043UFMzlsLCnRk58jQ++qiAKVOC7Ldfo9XRJEepOEtOMs0MsdhHhELPEg6/TCYTxmYrwevdD693CF7v3tjtpVbHzCqbrRC3eyfc7p0oLT0T0zRJJhcQjb5HNDqbcPg1QqGnACgs/CNe7wH4fH+msHCbdc5G77NPI5Mn13H++SWcfXYZDzwQoCB/fr8QEWlXgcBdpNMreOSR53jrLTe33lqnswLKeqk4S05JJH4mFHqOUOg5UqlFGIYXv/8QioqOxO3e9bet4LoGwzAoKOhHQUE/SkpOwjTTNDb+l2h0NpHIWwQCkwkEJuJw9FhVoj2e3daYeR82LEZDg8Ho0SVceGEpU6ZoL1IRkUTiF+rq7uf770/kgQf25Npr6znxRJ1AStav67QQyVmmmSESeYu6uvuJRt8HbHg8e1FRMRqf70BsNq0vADAM+6rlHWVlF5BK1RKJzCIcfp1Q6Gnq6x/GZivC5zsQv/9wPJ49Vv2icdJJUSIRgzFjinG7TSZMqMNm3bbTIiKWW7FiDIlEAVdddRsXXtigU2lLi6g4i2UymSih0DMEgw+STP6Mw1FFRcVoioqOadOuEl2Fw1FOcfFxFBcfRyYTIxp9n3D4FcLhfxMKPY3dXobPdwh+/zDc7kGcc06ESMTGHXf48XozjBkT0qljRaRLcT//PP5x47AvWUxZN7i//3EMG+bn8stDVkeTPKHiLB0ulaqmru5B6uoeI5Opo7Bwe6qq7sbvP+S3PZOltWw2Nz7f/vh8+5PJjCUafYeGhpm/zUQ/gsPRg6Kiozn//OMIh7fnvvt8eL0mV17ZYHV0EZEO4X7+eYovvxxbrGlff9dyOLPmRSInPESjcaTF6bo20zQxMf/3NyYZM0MynXs7mximaVqyR9UXX3zB9OnTyWQyDBkyhGHDhm3wOkuWLGn/YJJVFRUV1NTUAJBOBwgE7qGu7h+YZgKf70BKS8/E5RrUqq3WpOUymQjh8Bs0NDxHJPIOkMHl2oXXXhvOvJudTPLcQEnDItI9e9IwejSxI9v3xaP5eBDpqPGwthfl1T+3tstlzMx6L5Mhs87bWXXdtdzXypfdtWXKkAFz7V9rnmltl8mYmd99vL7baZ539eutLe86v7ae+2n+PVj9Muv63rq9bsLh8Hp/Rqt/31d9L1dedh15/37OE1TUrLkco6bCy8i7j1jnOFhflrU9luaPd42vrWe8rf79Wd9l1jdOVo2RVj6WtY7Z3x7L+sbzhsbQGmN9tTG7Pqdudyq37HJLS/+rZ03Pnj3X+TVLZpwzmQwPPvgg11xzDeXl5Vx55ZUMHDiQTTZZc79byX/pdAN1dfcTDN5HJhPG7z+C8vJRFBT0tzpa1mzohXLlZTbmSa75E9L6bmfdT2RbYrqvwiw4E6PxDWLx1zkmeQ5/sIP9t3cnHYsX47/sUubV/8Kig/Zq0QvuyifU1Z/s1/W4M2YGf42f+lD92rO28D5Wv1y7vICspRA1z7K+vOt74d6on/Nqj6W13/cWFaKNLE0bM2abf29tNhvpdHqtX2vNY1nrGFrtNqTzMTAwDAMDY9XHNsP2+8/99m+bYWPaWkozQFlNhFcXvNp0e81v02CNz/3u3+v6u5WXWf1+bNjWfr1mj2X1r63t8W/wsbQk78pMhm2N7/nqeVp6Hysvt8bjaPZYVn5t1/67tvcwajVLivNPP/1EVVUV3bt3B2Dw4MHMnTs354rznCVz+LHux3Z7MVzf7MCGXrg39sVwjd9i1/Li25L7WP3xri2v00ize1k1u5f8itee5quGEl6t3oplifmYXJD9x7L693YjHsvaChE0+7mspRzno8VTwb7aNqWOeCMV4+9gYOoOa0LloHW9gBirvSiv7QVtjetv4MVsY14MN+ZF+Xf3t5YX5bW9cLfmsbTkxXDl19wuN42NjW17LC148W7tz6Wthchm2DaYda1jbAPf+1WPoxXf97Z831Z9vRXft7aO2cqKSmpra9d7mebfv9YI374LRcFFa3w+06sXX5748UbdprSvXHyX0pLiHAgEKC8vX/VxeXk5P/74oxVR1uvZH5/lqR+earfb35gn5A29mDV/0l39ibC1T8itecH83W0D2/rrOKTbAkqcCX6IlDCrti9LG/0YhoHPmYXHslrebD2WjX0xXJm1pfex8nItmR3YmBmEDc0O9Ljx9LWOyT4heGm/A4k69ydj65m1GYSVH5eVllFXV7fGz7K137e1FaK1XWZjxkLzoiDtKxdfFMVaHqeHqCP7W8LNmOGmvtchXB6d9rtJg4zbTcPo0Vm/P+m8LCnOK2fxmlvbC9WsWbOYNWsWAOPGjaOioqLdszV318F3cdufb2v9b87G71+A13WZzigW+55580ZSXz8Xj2dbNttsMoN9u3Oq1cHk93rfCAsXrvHpWIUHf+ZNfPFXKSnZn549L6K4eGjWxqvD4SDVLZWV25L853A4Ovx5XXJbe4yJ5583uOqqBh577Hl++WwAmz6YhF8XQe/eZG66Ce/xx+PN6j1KtuTic4Qlxbm8vJza2tpVH9fW1lJauuZZ4IYOHcrQoUNXfWzFzIRjtW/RqiUT8juZTITa2skEg/dhs7morBxDScnJ+HxVmlHKQe7LLvvd0eUAcZuHM1bcx58+H8iQIQ9QV/cI33xzCAUFf6C09Az8/iOx2Vxtul/NMEpzGg+yumyPiVdfdXH22aXcdNNofL4abCc+ytIztvn9hTQGc5ZVzxHrOzjQklMgbLrppixdupTq6mpSqRRz5sxh4MCBVkSRLGhoeIX58/cmGJxCUdEw+vV7j9LS0+hKZ/nLN7Ejj6T+tttI9eqFaRikevWi/vZbWbbvUYwatQWzZl1F//4fUlU1CcOws3z5Zfzyy5+oqbmdVEovMiKS+155pak0H3LI++y22wOUlJyOy7XNhq8osh6WbUf32Wef8fDDD5PJZNh33305sgXbYGk7utySTgeprr6GhoYZFBb+kW7dbsHtHvS7y2hGKb/E43DaaWXMnl3IhAl1HHdcDNM0icXmEAzeRyQyC8NwUVR0HGVl5+B09mnV7Ws8SHMaD7K6bI2Jl15ycd55pey8c4wJEwYBQfr1ewebzdf2kNJhcnHG2bIpwZ122omddtrJqruXNgqH32T58stIp2spL7+MsrLzNcPcCbhc8OCDAU47rYxRo0pJJg1OPDGKx7M7Hs/uJBI/EQhMo77+CerrH8PvP5yyshEUFm5ldXQREaDpQMALLyxh550T3HPPOEKhb+jR4wGVZskKS5ZqSP5KpxtYtuwyliw5Gbu9lD59/kV5+cUqzZ2I2w3TpwfYb784V1xRwvTpnlVfKyjYjKqq2+nf//8oLT2dcPhVFiwYyuLFpxCLzbUwtYgIPPecmwsuKOFPf0owffpcGhrG4/UegM93oNXRpJNQcZYWi0bnsGDBUEKhJyktPY8+fV7RerFOyuWCBx4IcOCBMa65poRp035/zLnT2YPKyusZMOBjyssvJRb7lF9/HcaiRccRjX5kUWoR6cqeftrNRReVsNtuCR5+eAWh0CgMo5Du3cd12p2spOOpOMsGmWaG2tqJLFp0LIbhoHfv56msvAqbrdDqaNKOCgth2rQghx4aY8yYYu68c823Oe32UsrLRzJgwMdUVFxLY+N3LFp0JL/+ejTR6BwLUotIV/TPf3oYNaqEPfds5OGHAyQS/yAen0u3bjfhcHS3Op50Inp/XdYrnQ6wdOkFRKPv4PcfSffu47DZtONlV+F0wt13B3E6TW69tYhEwuCSSxpYffLGZvNQVnYOJSWnUF//GIHAVBYtOga3e1fKy0fi8exhzQMQkU7v/vu93HBDMfvuG+f++wPY7b9QUzMWr3cIfv9RVseTTkbFWdYpFvuMpUvPJp2uoVu3sRQXn6S3u7oghwMmTarD6YSJE/3E4wZXXx1aozwD2GxuSkvPpLj4ROrr/0kgMIVFi47D7R5MRcXlwF86PL+IdE6mCZMm+bj99iIOOijG3XcHKSjIsGjRJRhGAd263arXLMk6FWdZg2ma1NU9xIoVN+JwdKd37xm4XNtbHUssZLfD7bfXUVhocs89PkIhg7Fj67Hb1375pgJ9GsXFJ1Bf/ziBwF38+uswGhr+TFHRxbhc23XsAxCRTsU04eabi5g2zccxx0S5/fY6HA4IBh8iFvuI7t3vwOnsYXVM6YRUnOV3MpkYy5dfQkPDTLzeIVRVTcZuX/OsjtL12Gzw97/XU1yc4a67/IRCNu68M0hBwfqu46K09HSKi4+nru4h6uruoa7uL/h8f6G8/FIKC7fsuAcgIp1COg1XXlnM4497GT48zE03hbDZIJGYT03N3/F49qOo6FirY0onpYMDZZVUqppffz2ahoYXKS+/gp49H1Jplt8xDBg9uoFrr63npZfcnHZaGbHYht8KbVoDPYKddvqe8vJLiUbfZ8GCoSxdeiHJ5K8dkFxEOoNkEi68sITHH/dywQUNjBnTVJpNM8Py5ZdiGA7toiHtSsVZAGhs/JaFCw8hkfienj3/QXn5hRiGhoes3TnnRBg/vo533y3k+OPLqK9v2YuUw1FEefnI3/aBPpdw+F/Mn78X1dXXkUrVtnNqEclnsZjBmWeWMWOGh6uuCjF69P8OVK6vf4RY7P+orLwep7OXtUGlU1MzEiKRt/n112GYZprevV/A5zvA6kiSB044Ico99wT54osCjjmmghUrWv50YreXUll5Nf36vYfffzR1ddOZP38wtbUTyWQi7ZhaRPJRMGhw/PFlzJpVyN//Xsd554VXfa2x8UdWrBiDx7MPRUV/tTCldAUqzl1cXd3DLF58Ck5nH/r0eQmXa1urI0keOeSQOA89FODnn+0MG1bB/PnrOFpwHZzOnlRVjadfv7fxePaitvZ2fvllMHV1D2GayXZKLSL5ZMkSG0ceWcGXXxYwbVqQU06JrvpaJtPIsmXnYRhuqqru0BINaXcqzl2UaaZZseJGqquvwuvdh969Z+B09rQ6luShffZp5Kmnaqmrs3H44RX85z/OVt9GQcFm9Ox5P717v0xBweZUV1/N/PlDCIdfxTTNdkgtIvngxx8dHH54BUuW2HnssVoOOST+u6/X1t5KY+PXVFXdoROdSIdQce6CTDPJsmUXEQzeR0nJ6fTsOV0nNZE2GTgwycyZNbhcJkcdVc4772zcWSXd7h3ZZJNn6NlzOoZhsGTJ6SxadBSx2GdZTiwiue6TT5wMG1ZBMmnw3HM17L574ndfj0RmEwzeS3HxSVpiKB1GxbmLyWTiLFlyFg0NL1BRcRXdut2EYbTu7XWRtdlssxQzZ9bQr1+aU04p45ln3Bt1O4Zh4PMdQN++b9Kt2zgSiXn8+uuhLFlyDsnkwiynFpFcNGtWIccdV05JSYaZM2vYZpvU776eTgdYtuxiCgo2o7LyeotSSlek4tyFZDIRliw5hUjkdbp1u4WysvOsjiSdTFVVhuefr2HXXRNcfHEpd93lY2NXWhiGg5KSk+jf/33KykYRicxi/vy9WbHiZtLpUHaDi0jOePRRD6edVsbmm6eYMaOGvn3Tv/u6aZosW3Yp6XSAqqop2Gwb90u6yMZQce4i0ul6Fi06nmh0DlVVkygpOdXqSNJJ+f0mjz5ayxFHRBk3roirry4mldrw9dbFZvNRUXEJ/fu/j99/BMHgNObP3526uocxzTbcsIjklEwGrrrKzujRJey9dyPPPltLZWVmjcvV1z9OJPIaFRWjcbm2sSCpdGUqzl1AKlXDokXHEI//hx497qWo6BirI0knV1AAd95Zx7nnhnn4YS/Dh5cRDrftaHeHo4qqqjvo0+dVCgr+QHX1VSxYsD+RyFtZSi0iVonF4NxzS5kwwc5JJ0WYPj2Az7fm21WJxE+sWHE9Hs9elJaeZUFS6epUnDu5ZHIpixYdRSLxM716PYTff5DVkaSLsNngmmtCjB3bdKKUYcMq+DULJwl0ubb57QDCf2CaCRYvPolFi/5GY+OPbb9xEelwtbU2jjuugn/9y8W4cSnGjq3H4VjzcplMnKVLR/y29dxEnaRLLKFR14mlUitYtOg4Uqll9Or1BF7vPlZHki7o5JOjPPpogEWL7Oyxh5Mvv2z9dnWrazqA8M/06/c2lZU3EI9/xoIFQ6iuvpZ0OpiF1CLSEX76yc6hh1bw9ddO7r03yMiRGda1FXN19bW/bT03EYejqmODivxGxbmTSqcDLFp0PKnUEnr1ehSPZxerI0kXtvfejcyYUUNhIRx5ZDmvvurKyu0aRgGlpWfSv/8HFBf/jbq6h/jllz0IBqdr/bNIjvvggwIOP7yScNjg6adrOPjg+DovW1//FKHQE5SVnY/Pt38HphT5PRXnTqjpQMC/kUzOo1ev6bjdf7I6kghbbpnivfeSbLVVijPOKOWee7wbvePG6uz2Mrp3H0vfvq/jcm3DihXX/Lb+eXZ27kBEsurhhz2ccEI5lZVpXnqphp13XveZQhsbv6a6+irc7t0pL7+sA1OKrEnFuZPJZCIsXnwSjY3f0qPH/Xg8e1odSWSV7t3hmWeaZpZuvrmYiy8uIb7uSaZWKyzcil69nmy2/vl4Fi8eTiIxP3t3IiIbLZmEK68s5qqrmnbOeOmlNbebay6drmfJkrOw2Uro0WMqhrGWxc8iHUjFuRPJZGIsXnwK8fgX9OgxBZ9viNWRRNbgdsM99wS59NIQzz7r4eijK1i6NHtPRSvXP/ft+xYVFVcRjX7AggX7smLFWDKZcNbuR0RaJxAwOOGEch55xMuIEQ1Mnx7A71/3205N+zWPIplcRM+e03A4KjowrcjaqTh3EplMI0uWnEks9iFVVZPw+w+2OpLIOtlsMHJkmAcfDPDDDw4OPriSTz9t+0GDv7+PQsrKzqN///fw+w8jGLybX37Zi1DoGUxzzb1hRaT9fP+9g0MOqeSTTwqYPDnI1Vc3YN/ASWuDwWlEIq9SWXkNbvegjgkqsgEqzp2AaWZYtuxCotG36d59PEVFR1odSaRFDjwwzosv1uBymRx9dAVPPZX9M4A5HN2pqppM794v4XT2ZNmyi/n118OIx7/I+n2JyJpee83FYYdVEIsZPPtsDUcfHdvgdaLRD6mpGYvPdwglJWd0QEqRllFx7gRWrLiJcPhlKiqupbj4eKvjiLTKllum+Ne/VrDLLglGjSrluuuKSK77OKGN5nbvRO/eL9K9+0SSyUUsXHgwy5ZdQiq1Ivt3JiKk0zB2rJ/TTitj002b/p+v7yDAlZLJJSxdei5OZz+6d78dY13704lYQMU5zwWDD1BXdz8lJadTWnq21XFENkppqcljj9Vy5plhHnzQx3HHlbN8efafngzDRnHxsfTr9x6lpecQCj3L/Pl7Egzeh2m2Q1sX6aICARsnnljG3Xf7OeGECM8/X0PPnhteIpVOR1iyZDimGaNnzwew2/0dkFak5VSc81hDw79YseIGfL6/UFl5vX4rl7zmcMANN4S4++4g//mPkz//uZIPPyxol/uy2/1UVl5Lv35v4nLtzIoVN2r7OpEs+c9/nPzlLxV8+GEh48fXMX58Pa4WbN1umhl+/PE0Ghu/oUePqRQWbtH+YUVaScU5T8Vic1m27EJcrp2oqroLw9jAURYieeKII2K8/HINfr/JsceWM21a9vZ7Xl1BwWb06vUYPXtOxzSTLF58PEuWnEEyubB97lCkk3vySTfDhlWQycALL9RwwgnRFl+3tnY8gcAMKiuvx+vdrx1Timw8Fec8lEj8zOLFw3E4etCr10PYbNk/oErESltumeKVV1bw5z/HGTOmmLPOKiUUap93VJq2rzvgt+3rRhOJvMP8+ftSU3M7mcyGD2ISEYjFDC69tJhLLill0KAEr75aww47tHz5Uyj0PIHAnXTvfjolJae3Y1KRtlFxzjOpVA2LF5+EYdjo1esx7PYyqyOJtAu/3+S++4Jcd109r73m4qCDKvn66/Y7+UHT9nUX0K/fbHy+AwkEJjJ//t40NLyM2V5T3iKdQNOWkhU8+aSHCy5o4PHHaykvb/mWj7HYJyxffilu92707z9Zyw4lp6k455GmvZqHk0otp2fPhyko6Gd1JJF2ZRhw9tkRnnmmlmjU4NBDK3noIU+7Ld0AcDp70qPHFDbZ5DlstiKWLj2bRYuOo7Hx+/a7U5E89dRTbg46qIKaGhuPPx5g9OgGHK34/TaZXMSSJafjcPSgZ8/7sNmyu5+7SLapOOcJ0zSprr6SePwzqqruwu3e0epIIh1ml10SvPHGCnbfvZGrry7hjDNKCQbbd1bK49mVvn1fpVu3W2hs/JoFC/anuvo60un6dr1fkXwQiRhcdFEJo0aVssMOSV5/fQV7793YqttIpxtYvPhUTDNBr14P6x1UyQsqznmirm46odBTlJWNxO8/yOo4Ih2uvDzDww8HuO66et5808UBB1Ty8cfts+vGSobhoKTkVPr3f4/i4hOoq/sH8+fvQX39E5hmul3vWyRXffutg4MOquC559yMGtXAU0/VUlXVurNxNr2DejqJxI/06DGNgoLN2imtSHapOOeBaPQDVqy4Aa/3z5SXj7I6johlbLampRszZ9ZQUABHHVXOxIk+0u3cYe32Mrp3H0efPq9SULAZy5dfxsKFhxCLfdK+dyySQzIZuO8+LwcdVEl9vY0nn6zlkks2fOrs1ZlmmmXLLiAW+4Cqqjvwevdun8Ai7UDFOcclk7+yZMnZFBQMoKpqMoahH5nI9tsnefXVFRx+eIzbby/imGPK+fXX9t+S0eXahk02eZ6qqimkUtX8+uvhLFt2EanU8na/bxErLV1q44QTyrnxxmL23ruRWbNWsMceiVbfTtOyw2sIh/9FZeV1FBUd1Q5pRdqPWlgOy2SiLFlyGpChZ89/6AxKIs34/SZ33VXHpElBvv7aydChlTz1lLtdDxyEpu3rioqG0b//bMrKzqeh4UV++WVPAoEpZDKtW+Mpkg/+9S8XQ4d245NPnNx6ax3TpweoqGjd0oyVAoGJ1Nc/QmnpCJ3tVvKSinOOMk2TZctG0dj4HT16TKGgYIDVkURyjmHAMcfEmDVrBdtsk2TUqFJOP72Umpr2f2qz2bxUVFxJ375v4/HsTk3N31mwYD/C4Te0fZ10CuGwwciRJZx1Vhn9+qV47bUVnHhilI3dLa6u7mFqaydQVHQsFRVXZTesSAdRcc5RweAUwuGXqKi4Eq93X6vjiOS03r3TPPNMLddeW8/bb7sYMqSS118v7JD7LijoR69e0+nV63EMw8GSJaeyePFJJBI/dcj9i7SH998vYOjQSp591s1FFzUwY0YNm2668QcTNDS8RHX11Xi9Q+nefbz2apa8peKcg6LROdTU3IrffzilpedaHUckL9hscM45EV55ZQXdumUYPrycSy4ppr6+Y16gvd596Nt3FpWV1xOPf8L8+UOorr5B29dJXgmHDa68spjjjqvA4YDnn6/l8ssbcLZhe+VI5F2WLbsQl2sgPXpMwzDa70RGIu1NxTnHpFI1LF16Pk5nf/1WLrIRttoqxcsvr+D88xt45hkP++3XrcNmnw3DSWnpWfTr9z7FxcdRV/cA8+fvQV3do9q+TnLee+8VMGRIJY8+6uGss8K88cYKBg1q/QGAzUUi77JkyXAKCjajV6+HsNncWUorYg0V5xximhmWLbuATKaenj2nYbN5rY4kkpcKC+HKKxt4+eUaSkubZp/PO6+E2tqOecpzOCro3v2237av25zq6tEsXHgg0eicDrl/kdYIhw1Gjy7mr3+toKAAXnihhuuvD+F2t22tflNpPo2Cgk3ZZJOnsNtLshNYxEIqzjkkELiLaHQ2lZU3Uli4tdVxRPLedtsleeWVFVx6aYh//cvNPvtUMnOmq9133lipafu65+jR4x7S6XoWLTqGJUvOJJFY0DEBRDbgjTcK2W+/Sh57zMPZZ4d5/fVqBg1Ktvl2I5HZv5XmAb+VZp0VUDoHFeccEY1+SG3t7fj9wygu/pvVcUQ6jYICGDkyzKuvrqBv3zQjRpQxfHgZixa1/77P0LR9nd9/GP36vUt5+aVEIm+zYME+rFhxC+l0Q4dkEFnd0qU2zjyzlFNPLcfnM3nhhRquuy6EOwsrKZpK83Cczv4qzdLpqDjngFSqlqVLz8Pp7Ev37rdqXbNIO9hyyxQzZ9Zw7bX1vP9+AfvsU8mUKT6SbZ9caxGbzU15+Uj69XsPv/9wgsGpzJ+/O3V1j2n9s3SYdBqmT/ewzz7deOstF6NHh3j11RVZmWWG35fm3r2fVmmWTkfF2WJN65ovIpMJ0qPHNGw2n9WRRDotu71p5413313B3ns38ve/F3HAAZV8+GFBh2VwOntQVTWJPn1eoaBgU6qrr2DBgj8TiczusAzSNf33vw4OP7yCa64pYeedE7z5ZjUXXBCmIEvDPxJ5R6VZOj0VZ4sFg1OJRt+msvIGXK5trI4j0iX06pXmwQeDPPRQLdGowVFHVXDxxR138CCAy7U9m2zyPD163EsmE2bx4uNZtOgkGhu/77AM0jUEgwZXX13MX/5Sya+/2pkyJcjjjwfo1y9773SEQi+wePEpFBQMUGmWTk3F2ULx+BfU1NyGz3coxcUnWR1HpMvZf/9G3nmnaeu6GTPc7LlnNx54wNthyzea1j8fQr9+71BRcS3x+CcsWDCU5csvJ5Va0TEhpNNKp+GRRzzssUd3HnnEwymnRHj33WqGDYtt9Nn/1iYYfIBly87H7R7EJps8p9IsnZphtuHcsI8++iiffvopDoeD7t27M2LECLxeL9XV1YwcOZKePXsCsPnmm3PWWWcBMG/ePKZMmUIikWDHHXdk+PDhLV7Tu2TJko2NmnMymRgLFhyAacbo2/dN7PZiqyO1i4qKCmpqaqyOITkil8fDjz86uP76It5918Wmmya5/voQQ4Y0dmiGdDpAbe0k6uoexjAKKSsbQWnp2Z1279tcHg/57sMPC7j22mK++cbJbrs1ctNN9Wy9dSqr92GaJrW14wgE7sbn+wtVVXdjs7nadJsaE9KcVeNhZX9dmzbNOG+33XZMmDCB22+/nR49evDCCy+s+lpVVRXjx49n/Pjxq0ozwP3338/ZZ5/NnXfeybJly/jiiy/aEiFv1dTcQjI5j6qqSZ22NIvkk803T/H44wEeeqiWTMbg5JPLOfHEMn78sePOcma3l9Gt20306/c2Xu9e1NaO55df9qC+/glMM7ulRzqnX3+1M2JECUcdVUF9vcG99wZ45pnadijNKZYvv5RA4G6Ki/9Gjx73trk0i+SDNhXn7bffHru9aUunLbbYgkAgsN7LB4NBYrEYW2yxBYZhsNdeezF37ty2RMhLkci71NVNp6TkDDyePayOIyK/MYym5RtvvVXNddfV8+mnTWdSu/baog5d/1xQMICePR9gk02ex+nsyfLll7Fgwf6Ew6/ThjcJpRMLBg1uuqmIvfbqxmuvuRk1qoF3313BIYfEs7osA5reMV2y5ExCoScpK7uYbt1uxTA6ZntHEatl7ZXgrbfeYocddlj1cXV1NZdffjnXX3893377LQCBQIDy8vJVlykvL99g2e5s0ukgy5aNoqBgcyoqRlsdR0TWoqAAzj47wvvvV3PCCVEeesjL4MHdmDjRRzjccdtFejy70Lv3i/TocT+mmWLJkuEsWnQksVjXm3CQtYvH4Z57vOy+e3fuu8/LkUdGee+95VxySUObz/y3NqnUchYtOoZI5A0qK2+mouIybaEqXcoG34McM2YMdXV1a3z+r3/9K4MGDQLg+eefx263s+eeewJQWlrK1KlT8fv9zJs3j/HjxzNhwoRWz5TMmjWLWbNmATBu3DgqKipadf1c9MMPI8lkavjjH2fg8/W2Ok67czgcneLnJtmRb+OhogIeeAAuuSTJDTc4uP32Ih5+2M+VV6Y588xM1rbx2pDKypPp2/d4qqsf4tdfb+bXX4dRVnYYffrciMeTv2cZzbfxkEvSaXjySRs33GBn4UKDAw/McMstKbbZxgm0z8F5DQ2fMH/+MaRSdfzhD/+kvPyIrN+HxoQ0l4vjoU0HBwK88847vPHGG1x33XUUFhau9TI33HADJ510EmVlZdx4441MmjQJgPfff59vvvnmd2ug1yffDw4MhWawbNl5lJdfTnn5RVbH6RA60EOay/fx8NlnTv7+9yL+7/8K6d07xWWXNTBsWAx7B75LnclECQbvJRhs2sauqOgoyssvwens03EhsiTfx4MVMhl4+WUXd9zh58cfnWy3XYJrrgmx++6Jdr3fUOgFli+/FLu9nF69plNY+Md2uR+NCWmu0x0c+MUXXzBz5kyuuOKK35XmUChEJpMBYPny5SxdupTu3btTWlqK2+3mhx9+wDRNZs+ezcCBA9sSIW8kk0uorr4Kl2tnysrOszqOiGyEnXZK8swztTz+eC1FRSYXXljKfvtV8vzzblIddOyezeahvHwk/fvPobT0HBoaXuaXX/Zi+fKrSKWWd0wI6XCZDPzrXy7237+Sc88twzDgnnsC/OtfNe1amk0zzYoVY1m27Hxcru3p0+eVdivNIvmgTTPOF1xwAalUCp+v6Wx3K7ed+/DDD3n66aex2+3YbDaOOeaYVQX5559/ZurUqSQSCXbYYQdOO+20Tr8dnWlmWLz4b8Rin9C37+sUFPS3OlKH0eyBNNeZxsPKIjNpkp/vvnPSv3+KCy9s4MgjYzg6biMOUqll1NZOpr7+CQzDQUnJcMrKRuTFXrqdaTy0F9OE115zcfvtfr791smmmyYZNSrMoYe2/zsd6XQDy5adRyTyJsXFf6Nbt5sxjPZdn6QxIc3l4oxzm5dqdKR8Lc51dY9RXX0F3bqNo6Ska53oRE+C0lxnHA+ZDLz6qouJE/18842Tvn3/V6A7ag00QCKxgNraCTQ0PI9huCkpOY2ysrNzukB3xvGQLckkvPiim3vu8fHtt02/mI0a1cDhh3fM0qB4/L8sXXouyeQCunW7ieLiUzrkIECNCWkuF4uzzhzYzpLJpdTU3IzbvTvFxSdaHUdEssxmg4MOivP66yuYPr2W4uIMl1xSym67dWfaNC+hUMfsOFBQ0JcePe6kb9+38PmGEgxOYd68XampGUc6HeyQDNJ20ajBgw962X33blx4YSmmCZMnB3nnnWqOPLL9S7NpmgSD/+DXXw8lk4myySZPUlJyqnbOEPmNZpzbkWmaLFlyOtHou/Tt+yYFBf2sjtThNHsgzXWF8WCa8PbbhUyb5uODDwrx+TKccEKUM86I0KtXusNyNDZ+T23tHYTDL2Oz+SgpOZ3S0jNyaga6K4yHlgoEbEyf7mX6dA/BoJ1ddmlkxIgwQ4Y0Zn0f5nVJpwMsW3YJkcjreL1D6N59Ig5H+YavmEUaE9JcLs44d+BKvK4nHH6ZSOQ1Kiqu7ZKlWaQrMgzYb79G9tuvka++cnLvvV4efLDpz2GHxTjzzAjbb59s9xyFhX+gZ897aWz8ltraiQQCkwkG76ek5GRKS8/G4ejW7hlkw776ysk//uFl5kw3jY0GBxwQY8SIMIMGtf8YaS4a/ZBly84nlaqhsvIGSkrO0CyzyFpoxrmdpNNB5s/fB4ejJ336vIRhdM3fUTR7IM111fGweLGdBx7w8vjjHiIRGzvskODkkyMcdlgMt7tjMjQ2fksgcDcNDS9iGE6Kiv5KWdkInM5NOibAWnTV8ZBMwiuvuPjHP3x88kkBHk+Go4+OcdppETbfvGNPrW6aCWpr7yIQmITT2YcePe7B5dquQzM011XHhKxdLs44qzi3k2XLRhIKPU/fvl176x49CUpzXX08NDQYPPecm4cf9vLDD05KSjIce2yUk06KMGBAxyzjSCR+IRCYSij0DGBSVHQkZWXnUVCwWYfcf3NdbTwsWmTnqac8PP64h+XL7fTrl+LUUyMce2yU4uKOfymOx79g2bJLSSS+xe8/ku7dx2Kz+To8R3NdbUzI+qk4t1G+FOdIZDaLFx9PWdkFXf602noSlOY0HpqYJnz4YQEPP+zl3/92kUoZ7LFHI8ceG+Uvf4nj8bT/03IyuZhg8F7q6x/HNON4vftTWnoObvcuHfYWfVcYD/F403Zy//ynl/ffb9pmZZ99Ghk+PMK++zZis+AQ/UwmRm3t7QSD92G3d6N797H4fAd0fJC16ApjQlpOxbmN8qE4ZzJR5s/fD8MooG/f17HZXFZHspSeBKU5jYc1LV9u44knPDz9tIeFCx14vRkOPTTGscfG+NOfEu1+YFgqVUt9/cPU1U0nnQ5QWLgDZWXn4PP9pd2XmHXW8WCa8N//OnnqKTcvvOChrs7GJpukOO64KMceG2OTTTruINHVRaNzWL78MpLJ+RQX/42Kimuw24ssy7O6zjomZOOoOLdRPhTn6urrqat7gE02eR6PZxer41hOT4LSnMbDumUy8PHHBTz9tIeXX3YRidjo2zfFUUfFOPTQGFts0b5rXzOZGKHQMwSD95JMzsfp7ENJyekUFR3bbsWqs42Hn36yM3Omh5kzXfz8s5PCQpMDD4zx179G2WOPhCWzyyul0wFqasZRX/84Tmc/une/DY9nd+sCrUNnGxPSNirObZTrxTke/4KFCw+huPgkuncfa3WcnKAnQWlO46FlolGDV15x8fTTHubMKcA0Df7whySHHBLjkEPi7VqiTTNNJPIGgcA04vG5GIaHoqJjKCkZTmHh5lm9r84wHhYtsvPii25mzHDz9ddODMNk110TDBsW4+CDY5SWWvsSa5oJgsF/EAhMJpOJUFp6BuXll2GzddBRqa3UGcaEZI+KcxvlcnE2zTQLFx5KKrWMfv3exW73Wx0pJ+hJUJrTeGi95cttvPKKi5dfdvPRR/8r0QcfHGfo0Djbbptst5nMePw/1NX9g4aGFzHNRjyePSgpOQ2vdyiG0fYzceTjeFi5DOP111289pqLr792ArDjjgkOP7zp3YGqqozFKZvOIxAOv0pNzc0kk/PxePajsvJaCgu3sDraeuXjmJD2o+LcRrlcnOvqHqG6+kqqqqZQVDTM6jg5Q0+C0pzGQ9usrUR365Zm330bGTo0zl57NeLzZf8pvWkd9OPU1z9CKrUUh6MXxcXHU1R0HE7nul9gNiRfxkMsBh9+WMjrr7t44w0XS5faMQyTQYMS7L9/IwcfHKNvX+vWLa8uHv8vK1bcQCz2fxQUbEFl5fV4vftYHatF8mVMSMdQcW6jXC3OqVQt8+fvRWHhVmyyyTPaNL4ZPQlKcxoP2VNba+Pttwt5800X775bSH29DafT5E9/SrDHHo0MHtzI9tsncTqzd5+mmSIcfo36+seIRmcDNrzefSku/hte75BWH0yYq+MhnW46Mcl77xXy3nuFfPJJAY2NBm53hr33buSAA+IMHdpIebn1M8vNxeP/JRCYTDj8CnZ7GeXll1Jc/Le8Oo9Aro4JsYaKcxvlanFetuxSQqFn6Nv3jZx/G6yj6UlQmtN4aB+pFHzySQFvvlnI22+7+Pbbprbs8WTYZZcEu+2WYPDgRv74xyQFBdm5z2RyIfX1/6S+/inS6eXY7d0pLj4Gv//oFq+FzpXxkEjA1187+fTTAj76qIA5cwqpq2ta/7LVVkn23LORPfdsZLfdGjvshDWtEY9/QW3tJCKRN7DZ/JSUDKe09Bzs9mKro7VarowJyQ0qzm2Ui8U5FvuUX389jNLSc6msvMbqODlHT4LSnMZDx6ittfF//9dUAOfMKeDHH5uKdGGhyTbbJNlxxwQ77ZRghx2S9OmTbtOWd6aZIhJ5i/r6x4lE3gbSFBZuS1HRkfj9h+NwdF/nda0YD6YJy5bZ+M9/Cvjkk6ay/OWXBcTjTd+ETTZJsccejey5Z4Ldd2+ksjK3ZpWbi8XmUls7iWj0HWy2EkpLz6Ck5LS8LMwr6TlCmlNxbqNcK85NBwQeRDpdQ79+71p+xqVcpCdBaU7jwRorVjQV6c8/L+Dzz5189dX/imJ5eZqtt06x5ZbJ3/6k2GKL1EadhCWVWkFDw0xCoedpbPwSsOHx7ElR0RF4vQesUejaezwkEjBvnoOvv3au+vPNNw4CgaYDG53Opl8kBg5MMHBggp13TtCjR+4WZWjaNrCh4UXq6x8lHv8cu72c0tKzKSk5pVO8Buk5QppTcW6jXCvOdXUPUV19NT163IPff5jVcXKSngSlOY2H3JBMwvffO/jsswK++KKAb7918MMPDuLxpuUJhmHSt2+aAQNS9O2bom/fNH37pujTJ03fvmnc7g2/bCQSPxEKPUco9Dyp1CLAicezBz7fX/D5DsThKM/KeIjFDJYutbFwoYNffrEzb56DX35p+vPrr3bS6aZfEAoLTbbcMsnWWyfZeusU22yTZNttEzm59GJtEol51Nc/Sn3902QydRQUbE5x8SkUFx+HzeaxOl7W6DlCmlNxbqNcKs6pVA3z5++Fy7UtvXo9qQMC10FPgtKcxkPuSqdhwQI733/v5LvvHHz7rZP58x0sWGAnHP79fndlZWm6dctQWZmhsnLlv9OUl2fw+018vgw+38q/0zidn5FI/ItY7BVSqYWADbd7F6qqjiaT2RXD6EcyadDYCImEQSJhEAoZ1Nfbmv0xqKuzUV1tZ9kyG8uW2Vm2zE59/e+zeb0ZBgxI0b9/U/HfbLMUf/xjkgEDUjjy5xg5ADKZMOHwG4RCT/92MKYDn+8vlJScjNu9W6d83dFzhDSXi8U5z55GckdNzd/JZKJ063ZLp3zyEpGuxW6HAQPSDBiQ5i9/+d/nTROCQYOFC5tK9Pz5DpYts7NiRVOJnTu3gBUr7KuWfqxdT+AQwGTTTb9kr72eZ6+9niMWuwSAX3/dnI8//gsff3wgX3yxD4nE2qeBbTaTysoMPXqk6d8/xW67JaiqSlNVlaZ376aiXFmZaffTlLenTCZKJPImDQ0vEom8hWnGcTh6UF5+GcXFx693zbiItD/NOG+EWGwuv/46jNLS86isvMrqODlNswfSnMZD52Sa0NBgUFtrIxIxCIdtNDT87+9o1CCdNkilmk4tnkoZpNNQWrqYiooX6d59FuXl72G3x8lkXITDg0kk9sBu3xWvd1tKSpwUFzfNYudzKV6XVKqWaPR9IpFXCYffwDRj2O2V+P2H4PMdits9CMOw8HzdHUjPEdKcZpw7AdPMUF19A3Z7FeXlF1kdR0TEcoYBRUUmRUWtOwlIRcUAampOBE4kk4kRi31EJPIWLte7JBI3/XbbLkxzJxobd8Fu34XCwh3y/sysTY/1Y6LR94hGZ9PY+DUAdnsZRUVH4fcfhtu9a1bOzigi2aXi3EoNDTNobPyCqqpJ2Gxeq+OIiHQKNpsbr3efVWe4S6VqiMU+Jhb7kFjsYwKByQQCTTteOJ39cbm2pbBwWwoLt8Hl2ga7vczC9OtmmhmSyXnE4/8hHv8PjY1fEY9/jmk2Ak7c7oGUl1+Ox7MXLtd2KssiOU7FuRUymRg1NX+nsHA7/P6jrI4jItJpORwV+P0H4fcfBEA63UA8/slv5fO/xGKf09Dw4qrL2+3dKSjoj9M5gIKCAav+7XT2xmZr/60zMpk4qdQiEon5JJMLSCYX0Nj4NY2N/yWTCQNNs+eFhVtTUnIKHs9euN27dKodMUS6AhXnVggG7yWVWkpV1d1dZr2ZiEgusNv9eL374vXuu+pz6XSQxsb/Eo9/RSLxI4nEL0QirxEK1f7uujabH7u9Gw5H05+mf5djGB5sNs9vf7ux2dy/LQ3JAClMMw2kMc0Uppkkk6knnQ7+7k8mEyCZ/JVUahnwv0OGDMNDYeEf8PuPxuXaDpdrWwoKtsir01+LyJr0P7iFUqnlBAJT8PkOwuPZ1eo4IiJdnt1eisezJx7Pnr/7fDpdTzL5C4nEzySTi0mnV5BKLSedXkE8/iWp1HJMM7bR92sYBdhspdjtpb9l2B2ns2+zP/2w28u145JIJ6Ti3EI1NeMxzSQVFdpFQ0Qkl9ntxdjtO+By7bDWr5umiWnGMc0YmUyMTCaKaUZ/+7vxt3XG9t9mh+2/fezAbi/Bbi/FMDwqxSJdlIpzC8Tj/yUUepLS0jMpKOhvdRwREWkDwzAwDDfgxq5j8USkFbRQdwNM02TFipuw2UooK7vY6jgiIiIiYhEV5w2IRN4gFvuA8vJLsNuLrY4jIiIiIhZRcV4P00ywYsUYnM5NKSk50eo4IiIiImIhrXFej7q6R0km59Gz50MYhtPqOCIiIiJiIc04r0cmE8HrHYLXO9TqKCIiIiJiMc04r0d5+YWYpqlth0REREREM84botIsIiIiIqDiLCIiIiLSIirOIiIiIiItoOIsIiIiItICKs4iIiIiIi2g4iwiIiIi0gIqziIiIiIiLaDiLCIiIiLSAirOIiIiIiItoOIsIiIiItICKs4iIiIiIi2g4iwiIiIi0gIqziIiIiIiLaDiLCIiIiLSAirOIiIiIiItoOIsIiIiItICKs4iIiIiIi2g4iwiIiIi0gKGaZqm1SFERERERHKdZpylXY0ePdrqCJJDNB6kOY0HWZ3GhDSXi+NBxVlEREREpAVUnEVEREREWkDFWdrV0KFDrY4gOUTjQZrTeJDVaUxIc7k4HnRwoIiIiIhIC2jGWURERESkBRxWB5DO6YsvvmD69OlkMhmGDBnCsGHDrI4kFjrvvPNwuVzYbDbsdjvjxo2zOpJ0sKlTp/LZZ59RXFzMhAkTAAiHw0ycOJEVK1ZQWVnJyJEj8fl8FieVjrC28fD000/z5ptvUlRUBMDxxx/PTjvtZGVM6SA1NTVMmTKFuro6DMNg6NChHHTQQTn5HKHiLFmXyWR48MEHueaaaygvL+fKK69k4MCBbLLJJlZHEwtdf/31q14QpevZZ599OPDAA5kyZcqqz82YMYNtt92WYcOGMWPGDGbMmMGJJ55oYUrpKGsbDwAHH3wwhx12mEWpxCp2u52TTjqJAQMGEIvFGD16NNtttx3vvPNOzj1HaKmGZN1PP/1EVVUV3bt3x+FwMHjwYObOnWt1LBGx0NZbb73GTNHcuXPZe++9Adh77731PNGFrG08SNdVWlrKgAEDAHC73fTq1YtAIJCTzxGacZasCwQClJeXr/q4vLycH3/80cJEkgtuueUWAPbff/+cPFJaOl59fT2lpaVA0wtnKBSyOJFY7bXXXmP27NkMGDCAk08+WeW6C6quruaXX35hs802y8nnCBVnybq1bdRiGIYFSSRXjBkzhrKyMurr67n55pvp2bMnW2+9tdWxRCSHHHDAARx99NEAPPXUUzzyyCOMGDHC4lTSkeLxOBMmTODUU0/F4/FYHWettFRDsq68vJza2tpVH9fW1q76jVG6prKyMgCKi4sZNGgQP/30k8WJJBcUFxcTDAYBCAaDWgPfxZWUlGCz2bDZbAwZMoSff/7Z6kjSgVKpFBMmTGDPPfdkl112AXLzOULFWbJu0003ZenSpVRXV5NKpZgzZw4DBw60OpZYJB6PE4vFVv37P//5D3369LE4leSCgQMH8u677wLw7rvvMmjQIIsTiZVWFiSAjz/+mN69e1uYRjqSaZpMmzaNXr16ccghh6z6fC4+R+gEKNIuPvvsMx5++GEymQz77rsvRx55pNWRxCLLly/n9ttvByCdTrPHHntoPHRBkyZN4ptvvqGhoYHi4mKOPfZYBg0axMSJE6mpqaGiooJRo0ZpTWsXsbbx8PXXXzN//nwMw6CyspKzzjpL71Z2Ed999x3XXXcdffr0WbW08/jjj2fzzTfPuecIFWcRERERkRbQUg0RERERkRZQcRYRERERaQEVZxERERGRFlBxFhERERFpARVnEREREZEWUHEWEREREWkBFWcRERERkRZQcRYRERERaYH/B/v7Xp42kiNpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot a straight line.\n",
    "l = np.linspace(-3.0, 20.0, 100)\n",
    "plt.plot(l, 0.5 * l + 4.0, 'g-')\n",
    "\n",
    "# Plot a parabola.\n",
    "plt.plot(l, 10.0 * (l**2) - 199.5 * l + 644.0, 'b-')\n",
    "\n",
    "# Plot a cubic.\n",
    "plt.plot(l, (l**3)  - 20.0625 * l**2  + 65.75 * l, 'y-')\n",
    "\n",
    "# Plot the points.\n",
    "plt.plot(x, y, 'ro');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "#### Lines\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.01001001,  0.02002002,  0.03003003,  0.04004004,\n",
       "        0.05005005,  0.06006006,  0.07007007,  0.08008008,  0.09009009,\n",
       "        0.1001001 ,  0.11011011,  0.12012012,  0.13013013,  0.14014014,\n",
       "        0.15015015,  0.16016016,  0.17017017,  0.18018018,  0.19019019,\n",
       "        0.2002002 ,  0.21021021,  0.22022022,  0.23023023,  0.24024024,\n",
       "        0.25025025,  0.26026026,  0.27027027,  0.28028028,  0.29029029,\n",
       "        0.3003003 ,  0.31031031,  0.32032032,  0.33033033,  0.34034034,\n",
       "        0.35035035,  0.36036036,  0.37037037,  0.38038038,  0.39039039,\n",
       "        0.4004004 ,  0.41041041,  0.42042042,  0.43043043,  0.44044044,\n",
       "        0.45045045,  0.46046046,  0.47047047,  0.48048048,  0.49049049,\n",
       "        0.5005005 ,  0.51051051,  0.52052052,  0.53053053,  0.54054054,\n",
       "        0.55055055,  0.56056056,  0.57057057,  0.58058058,  0.59059059,\n",
       "        0.6006006 ,  0.61061061,  0.62062062,  0.63063063,  0.64064064,\n",
       "        0.65065065,  0.66066066,  0.67067067,  0.68068068,  0.69069069,\n",
       "        0.7007007 ,  0.71071071,  0.72072072,  0.73073073,  0.74074074,\n",
       "        0.75075075,  0.76076076,  0.77077077,  0.78078078,  0.79079079,\n",
       "        0.8008008 ,  0.81081081,  0.82082082,  0.83083083,  0.84084084,\n",
       "        0.85085085,  0.86086086,  0.87087087,  0.88088088,  0.89089089,\n",
       "        0.9009009 ,  0.91091091,  0.92092092,  0.93093093,  0.94094094,\n",
       "        0.95095095,  0.96096096,  0.97097097,  0.98098098,  0.99099099,\n",
       "        1.001001  ,  1.01101101,  1.02102102,  1.03103103,  1.04104104,\n",
       "        1.05105105,  1.06106106,  1.07107107,  1.08108108,  1.09109109,\n",
       "        1.1011011 ,  1.11111111,  1.12112112,  1.13113113,  1.14114114,\n",
       "        1.15115115,  1.16116116,  1.17117117,  1.18118118,  1.19119119,\n",
       "        1.2012012 ,  1.21121121,  1.22122122,  1.23123123,  1.24124124,\n",
       "        1.25125125,  1.26126126,  1.27127127,  1.28128128,  1.29129129,\n",
       "        1.3013013 ,  1.31131131,  1.32132132,  1.33133133,  1.34134134,\n",
       "        1.35135135,  1.36136136,  1.37137137,  1.38138138,  1.39139139,\n",
       "        1.4014014 ,  1.41141141,  1.42142142,  1.43143143,  1.44144144,\n",
       "        1.45145145,  1.46146146,  1.47147147,  1.48148148,  1.49149149,\n",
       "        1.5015015 ,  1.51151151,  1.52152152,  1.53153153,  1.54154154,\n",
       "        1.55155155,  1.56156156,  1.57157157,  1.58158158,  1.59159159,\n",
       "        1.6016016 ,  1.61161161,  1.62162162,  1.63163163,  1.64164164,\n",
       "        1.65165165,  1.66166166,  1.67167167,  1.68168168,  1.69169169,\n",
       "        1.7017017 ,  1.71171171,  1.72172172,  1.73173173,  1.74174174,\n",
       "        1.75175175,  1.76176176,  1.77177177,  1.78178178,  1.79179179,\n",
       "        1.8018018 ,  1.81181181,  1.82182182,  1.83183183,  1.84184184,\n",
       "        1.85185185,  1.86186186,  1.87187187,  1.88188188,  1.89189189,\n",
       "        1.9019019 ,  1.91191191,  1.92192192,  1.93193193,  1.94194194,\n",
       "        1.95195195,  1.96196196,  1.97197197,  1.98198198,  1.99199199,\n",
       "        2.002002  ,  2.01201201,  2.02202202,  2.03203203,  2.04204204,\n",
       "        2.05205205,  2.06206206,  2.07207207,  2.08208208,  2.09209209,\n",
       "        2.1021021 ,  2.11211211,  2.12212212,  2.13213213,  2.14214214,\n",
       "        2.15215215,  2.16216216,  2.17217217,  2.18218218,  2.19219219,\n",
       "        2.2022022 ,  2.21221221,  2.22222222,  2.23223223,  2.24224224,\n",
       "        2.25225225,  2.26226226,  2.27227227,  2.28228228,  2.29229229,\n",
       "        2.3023023 ,  2.31231231,  2.32232232,  2.33233233,  2.34234234,\n",
       "        2.35235235,  2.36236236,  2.37237237,  2.38238238,  2.39239239,\n",
       "        2.4024024 ,  2.41241241,  2.42242242,  2.43243243,  2.44244244,\n",
       "        2.45245245,  2.46246246,  2.47247247,  2.48248248,  2.49249249,\n",
       "        2.5025025 ,  2.51251251,  2.52252252,  2.53253253,  2.54254254,\n",
       "        2.55255255,  2.56256256,  2.57257257,  2.58258258,  2.59259259,\n",
       "        2.6026026 ,  2.61261261,  2.62262262,  2.63263263,  2.64264264,\n",
       "        2.65265265,  2.66266266,  2.67267267,  2.68268268,  2.69269269,\n",
       "        2.7027027 ,  2.71271271,  2.72272272,  2.73273273,  2.74274274,\n",
       "        2.75275275,  2.76276276,  2.77277277,  2.78278278,  2.79279279,\n",
       "        2.8028028 ,  2.81281281,  2.82282282,  2.83283283,  2.84284284,\n",
       "        2.85285285,  2.86286286,  2.87287287,  2.88288288,  2.89289289,\n",
       "        2.9029029 ,  2.91291291,  2.92292292,  2.93293293,  2.94294294,\n",
       "        2.95295295,  2.96296296,  2.97297297,  2.98298298,  2.99299299,\n",
       "        3.003003  ,  3.01301301,  3.02302302,  3.03303303,  3.04304304,\n",
       "        3.05305305,  3.06306306,  3.07307307,  3.08308308,  3.09309309,\n",
       "        3.1031031 ,  3.11311311,  3.12312312,  3.13313313,  3.14314314,\n",
       "        3.15315315,  3.16316316,  3.17317317,  3.18318318,  3.19319319,\n",
       "        3.2032032 ,  3.21321321,  3.22322322,  3.23323323,  3.24324324,\n",
       "        3.25325325,  3.26326326,  3.27327327,  3.28328328,  3.29329329,\n",
       "        3.3033033 ,  3.31331331,  3.32332332,  3.33333333,  3.34334334,\n",
       "        3.35335335,  3.36336336,  3.37337337,  3.38338338,  3.39339339,\n",
       "        3.4034034 ,  3.41341341,  3.42342342,  3.43343343,  3.44344344,\n",
       "        3.45345345,  3.46346346,  3.47347347,  3.48348348,  3.49349349,\n",
       "        3.5035035 ,  3.51351351,  3.52352352,  3.53353353,  3.54354354,\n",
       "        3.55355355,  3.56356356,  3.57357357,  3.58358358,  3.59359359,\n",
       "        3.6036036 ,  3.61361361,  3.62362362,  3.63363363,  3.64364364,\n",
       "        3.65365365,  3.66366366,  3.67367367,  3.68368368,  3.69369369,\n",
       "        3.7037037 ,  3.71371371,  3.72372372,  3.73373373,  3.74374374,\n",
       "        3.75375375,  3.76376376,  3.77377377,  3.78378378,  3.79379379,\n",
       "        3.8038038 ,  3.81381381,  3.82382382,  3.83383383,  3.84384384,\n",
       "        3.85385385,  3.86386386,  3.87387387,  3.88388388,  3.89389389,\n",
       "        3.9039039 ,  3.91391391,  3.92392392,  3.93393393,  3.94394394,\n",
       "        3.95395395,  3.96396396,  3.97397397,  3.98398398,  3.99399399,\n",
       "        4.004004  ,  4.01401401,  4.02402402,  4.03403403,  4.04404404,\n",
       "        4.05405405,  4.06406406,  4.07407407,  4.08408408,  4.09409409,\n",
       "        4.1041041 ,  4.11411411,  4.12412412,  4.13413413,  4.14414414,\n",
       "        4.15415415,  4.16416416,  4.17417417,  4.18418418,  4.19419419,\n",
       "        4.2042042 ,  4.21421421,  4.22422422,  4.23423423,  4.24424424,\n",
       "        4.25425425,  4.26426426,  4.27427427,  4.28428428,  4.29429429,\n",
       "        4.3043043 ,  4.31431431,  4.32432432,  4.33433433,  4.34434434,\n",
       "        4.35435435,  4.36436436,  4.37437437,  4.38438438,  4.39439439,\n",
       "        4.4044044 ,  4.41441441,  4.42442442,  4.43443443,  4.44444444,\n",
       "        4.45445445,  4.46446446,  4.47447447,  4.48448448,  4.49449449,\n",
       "        4.5045045 ,  4.51451451,  4.52452452,  4.53453453,  4.54454454,\n",
       "        4.55455455,  4.56456456,  4.57457457,  4.58458458,  4.59459459,\n",
       "        4.6046046 ,  4.61461461,  4.62462462,  4.63463463,  4.64464464,\n",
       "        4.65465465,  4.66466466,  4.67467467,  4.68468468,  4.69469469,\n",
       "        4.7047047 ,  4.71471471,  4.72472472,  4.73473473,  4.74474474,\n",
       "        4.75475475,  4.76476476,  4.77477477,  4.78478478,  4.79479479,\n",
       "        4.8048048 ,  4.81481481,  4.82482482,  4.83483483,  4.84484484,\n",
       "        4.85485485,  4.86486486,  4.87487487,  4.88488488,  4.89489489,\n",
       "        4.9049049 ,  4.91491491,  4.92492492,  4.93493493,  4.94494494,\n",
       "        4.95495495,  4.96496496,  4.97497497,  4.98498498,  4.99499499,\n",
       "        5.00500501,  5.01501502,  5.02502503,  5.03503504,  5.04504505,\n",
       "        5.05505506,  5.06506507,  5.07507508,  5.08508509,  5.0950951 ,\n",
       "        5.10510511,  5.11511512,  5.12512513,  5.13513514,  5.14514515,\n",
       "        5.15515516,  5.16516517,  5.17517518,  5.18518519,  5.1951952 ,\n",
       "        5.20520521,  5.21521522,  5.22522523,  5.23523524,  5.24524525,\n",
       "        5.25525526,  5.26526527,  5.27527528,  5.28528529,  5.2952953 ,\n",
       "        5.30530531,  5.31531532,  5.32532533,  5.33533534,  5.34534535,\n",
       "        5.35535536,  5.36536537,  5.37537538,  5.38538539,  5.3953954 ,\n",
       "        5.40540541,  5.41541542,  5.42542543,  5.43543544,  5.44544545,\n",
       "        5.45545546,  5.46546547,  5.47547548,  5.48548549,  5.4954955 ,\n",
       "        5.50550551,  5.51551552,  5.52552553,  5.53553554,  5.54554555,\n",
       "        5.55555556,  5.56556557,  5.57557558,  5.58558559,  5.5955956 ,\n",
       "        5.60560561,  5.61561562,  5.62562563,  5.63563564,  5.64564565,\n",
       "        5.65565566,  5.66566567,  5.67567568,  5.68568569,  5.6956957 ,\n",
       "        5.70570571,  5.71571572,  5.72572573,  5.73573574,  5.74574575,\n",
       "        5.75575576,  5.76576577,  5.77577578,  5.78578579,  5.7957958 ,\n",
       "        5.80580581,  5.81581582,  5.82582583,  5.83583584,  5.84584585,\n",
       "        5.85585586,  5.86586587,  5.87587588,  5.88588589,  5.8958959 ,\n",
       "        5.90590591,  5.91591592,  5.92592593,  5.93593594,  5.94594595,\n",
       "        5.95595596,  5.96596597,  5.97597598,  5.98598599,  5.995996  ,\n",
       "        6.00600601,  6.01601602,  6.02602603,  6.03603604,  6.04604605,\n",
       "        6.05605606,  6.06606607,  6.07607608,  6.08608609,  6.0960961 ,\n",
       "        6.10610611,  6.11611612,  6.12612613,  6.13613614,  6.14614615,\n",
       "        6.15615616,  6.16616617,  6.17617618,  6.18618619,  6.1961962 ,\n",
       "        6.20620621,  6.21621622,  6.22622623,  6.23623624,  6.24624625,\n",
       "        6.25625626,  6.26626627,  6.27627628,  6.28628629,  6.2962963 ,\n",
       "        6.30630631,  6.31631632,  6.32632633,  6.33633634,  6.34634635,\n",
       "        6.35635636,  6.36636637,  6.37637638,  6.38638639,  6.3963964 ,\n",
       "        6.40640641,  6.41641642,  6.42642643,  6.43643644,  6.44644645,\n",
       "        6.45645646,  6.46646647,  6.47647648,  6.48648649,  6.4964965 ,\n",
       "        6.50650651,  6.51651652,  6.52652653,  6.53653654,  6.54654655,\n",
       "        6.55655656,  6.56656657,  6.57657658,  6.58658659,  6.5965966 ,\n",
       "        6.60660661,  6.61661662,  6.62662663,  6.63663664,  6.64664665,\n",
       "        6.65665666,  6.66666667,  6.67667668,  6.68668669,  6.6966967 ,\n",
       "        6.70670671,  6.71671672,  6.72672673,  6.73673674,  6.74674675,\n",
       "        6.75675676,  6.76676677,  6.77677678,  6.78678679,  6.7967968 ,\n",
       "        6.80680681,  6.81681682,  6.82682683,  6.83683684,  6.84684685,\n",
       "        6.85685686,  6.86686687,  6.87687688,  6.88688689,  6.8968969 ,\n",
       "        6.90690691,  6.91691692,  6.92692693,  6.93693694,  6.94694695,\n",
       "        6.95695696,  6.96696697,  6.97697698,  6.98698699,  6.996997  ,\n",
       "        7.00700701,  7.01701702,  7.02702703,  7.03703704,  7.04704705,\n",
       "        7.05705706,  7.06706707,  7.07707708,  7.08708709,  7.0970971 ,\n",
       "        7.10710711,  7.11711712,  7.12712713,  7.13713714,  7.14714715,\n",
       "        7.15715716,  7.16716717,  7.17717718,  7.18718719,  7.1971972 ,\n",
       "        7.20720721,  7.21721722,  7.22722723,  7.23723724,  7.24724725,\n",
       "        7.25725726,  7.26726727,  7.27727728,  7.28728729,  7.2972973 ,\n",
       "        7.30730731,  7.31731732,  7.32732733,  7.33733734,  7.34734735,\n",
       "        7.35735736,  7.36736737,  7.37737738,  7.38738739,  7.3973974 ,\n",
       "        7.40740741,  7.41741742,  7.42742743,  7.43743744,  7.44744745,\n",
       "        7.45745746,  7.46746747,  7.47747748,  7.48748749,  7.4974975 ,\n",
       "        7.50750751,  7.51751752,  7.52752753,  7.53753754,  7.54754755,\n",
       "        7.55755756,  7.56756757,  7.57757758,  7.58758759,  7.5975976 ,\n",
       "        7.60760761,  7.61761762,  7.62762763,  7.63763764,  7.64764765,\n",
       "        7.65765766,  7.66766767,  7.67767768,  7.68768769,  7.6976977 ,\n",
       "        7.70770771,  7.71771772,  7.72772773,  7.73773774,  7.74774775,\n",
       "        7.75775776,  7.76776777,  7.77777778,  7.78778779,  7.7977978 ,\n",
       "        7.80780781,  7.81781782,  7.82782783,  7.83783784,  7.84784785,\n",
       "        7.85785786,  7.86786787,  7.87787788,  7.88788789,  7.8978979 ,\n",
       "        7.90790791,  7.91791792,  7.92792793,  7.93793794,  7.94794795,\n",
       "        7.95795796,  7.96796797,  7.97797798,  7.98798799,  7.997998  ,\n",
       "        8.00800801,  8.01801802,  8.02802803,  8.03803804,  8.04804805,\n",
       "        8.05805806,  8.06806807,  8.07807808,  8.08808809,  8.0980981 ,\n",
       "        8.10810811,  8.11811812,  8.12812813,  8.13813814,  8.14814815,\n",
       "        8.15815816,  8.16816817,  8.17817818,  8.18818819,  8.1981982 ,\n",
       "        8.20820821,  8.21821822,  8.22822823,  8.23823824,  8.24824825,\n",
       "        8.25825826,  8.26826827,  8.27827828,  8.28828829,  8.2982983 ,\n",
       "        8.30830831,  8.31831832,  8.32832833,  8.33833834,  8.34834835,\n",
       "        8.35835836,  8.36836837,  8.37837838,  8.38838839,  8.3983984 ,\n",
       "        8.40840841,  8.41841842,  8.42842843,  8.43843844,  8.44844845,\n",
       "        8.45845846,  8.46846847,  8.47847848,  8.48848849,  8.4984985 ,\n",
       "        8.50850851,  8.51851852,  8.52852853,  8.53853854,  8.54854855,\n",
       "        8.55855856,  8.56856857,  8.57857858,  8.58858859,  8.5985986 ,\n",
       "        8.60860861,  8.61861862,  8.62862863,  8.63863864,  8.64864865,\n",
       "        8.65865866,  8.66866867,  8.67867868,  8.68868869,  8.6986987 ,\n",
       "        8.70870871,  8.71871872,  8.72872873,  8.73873874,  8.74874875,\n",
       "        8.75875876,  8.76876877,  8.77877878,  8.78878879,  8.7987988 ,\n",
       "        8.80880881,  8.81881882,  8.82882883,  8.83883884,  8.84884885,\n",
       "        8.85885886,  8.86886887,  8.87887888,  8.88888889,  8.8988989 ,\n",
       "        8.90890891,  8.91891892,  8.92892893,  8.93893894,  8.94894895,\n",
       "        8.95895896,  8.96896897,  8.97897898,  8.98898899,  8.998999  ,\n",
       "        9.00900901,  9.01901902,  9.02902903,  9.03903904,  9.04904905,\n",
       "        9.05905906,  9.06906907,  9.07907908,  9.08908909,  9.0990991 ,\n",
       "        9.10910911,  9.11911912,  9.12912913,  9.13913914,  9.14914915,\n",
       "        9.15915916,  9.16916917,  9.17917918,  9.18918919,  9.1991992 ,\n",
       "        9.20920921,  9.21921922,  9.22922923,  9.23923924,  9.24924925,\n",
       "        9.25925926,  9.26926927,  9.27927928,  9.28928929,  9.2992993 ,\n",
       "        9.30930931,  9.31931932,  9.32932933,  9.33933934,  9.34934935,\n",
       "        9.35935936,  9.36936937,  9.37937938,  9.38938939,  9.3993994 ,\n",
       "        9.40940941,  9.41941942,  9.42942943,  9.43943944,  9.44944945,\n",
       "        9.45945946,  9.46946947,  9.47947948,  9.48948949,  9.4994995 ,\n",
       "        9.50950951,  9.51951952,  9.52952953,  9.53953954,  9.54954955,\n",
       "        9.55955956,  9.56956957,  9.57957958,  9.58958959,  9.5995996 ,\n",
       "        9.60960961,  9.61961962,  9.62962963,  9.63963964,  9.64964965,\n",
       "        9.65965966,  9.66966967,  9.67967968,  9.68968969,  9.6996997 ,\n",
       "        9.70970971,  9.71971972,  9.72972973,  9.73973974,  9.74974975,\n",
       "        9.75975976,  9.76976977,  9.77977978,  9.78978979,  9.7997998 ,\n",
       "        9.80980981,  9.81981982,  9.82982983,  9.83983984,  9.84984985,\n",
       "        9.85985986,  9.86986987,  9.87987988,  9.88988989,  9.8998999 ,\n",
       "        9.90990991,  9.91991992,  9.92992993,  9.93993994,  9.94994995,\n",
       "        9.95995996,  9.96996997,  9.97997998,  9.98998999, 10.        ])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Set up some x values.\n",
    "x = np.linspace(0.0, 10.0, 1000)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "$$ y = 5 x + 2 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create y - note numpy's element-wise operations.\n",
    "y = 5.0 * x + 2.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.        ,  2.05005005,  2.1001001 ,  2.15015015,  2.2002002 ,\n",
       "        2.25025025,  2.3003003 ,  2.35035035,  2.4004004 ,  2.45045045,\n",
       "        2.5005005 ,  2.55055055,  2.6006006 ,  2.65065065,  2.7007007 ,\n",
       "        2.75075075,  2.8008008 ,  2.85085085,  2.9009009 ,  2.95095095,\n",
       "        3.001001  ,  3.05105105,  3.1011011 ,  3.15115115,  3.2012012 ,\n",
       "        3.25125125,  3.3013013 ,  3.35135135,  3.4014014 ,  3.45145145,\n",
       "        3.5015015 ,  3.55155155,  3.6016016 ,  3.65165165,  3.7017017 ,\n",
       "        3.75175175,  3.8018018 ,  3.85185185,  3.9019019 ,  3.95195195,\n",
       "        4.002002  ,  4.05205205,  4.1021021 ,  4.15215215,  4.2022022 ,\n",
       "        4.25225225,  4.3023023 ,  4.35235235,  4.4024024 ,  4.45245245,\n",
       "        4.5025025 ,  4.55255255,  4.6026026 ,  4.65265265,  4.7027027 ,\n",
       "        4.75275275,  4.8028028 ,  4.85285285,  4.9029029 ,  4.95295295,\n",
       "        5.003003  ,  5.05305305,  5.1031031 ,  5.15315315,  5.2032032 ,\n",
       "        5.25325325,  5.3033033 ,  5.35335335,  5.4034034 ,  5.45345345,\n",
       "        5.5035035 ,  5.55355355,  5.6036036 ,  5.65365365,  5.7037037 ,\n",
       "        5.75375375,  5.8038038 ,  5.85385385,  5.9039039 ,  5.95395395,\n",
       "        6.004004  ,  6.05405405,  6.1041041 ,  6.15415415,  6.2042042 ,\n",
       "        6.25425425,  6.3043043 ,  6.35435435,  6.4044044 ,  6.45445445,\n",
       "        6.5045045 ,  6.55455455,  6.6046046 ,  6.65465465,  6.7047047 ,\n",
       "        6.75475475,  6.8048048 ,  6.85485485,  6.9049049 ,  6.95495495,\n",
       "        7.00500501,  7.05505506,  7.10510511,  7.15515516,  7.20520521,\n",
       "        7.25525526,  7.30530531,  7.35535536,  7.40540541,  7.45545546,\n",
       "        7.50550551,  7.55555556,  7.60560561,  7.65565566,  7.70570571,\n",
       "        7.75575576,  7.80580581,  7.85585586,  7.90590591,  7.95595596,\n",
       "        8.00600601,  8.05605606,  8.10610611,  8.15615616,  8.20620621,\n",
       "        8.25625626,  8.30630631,  8.35635636,  8.40640641,  8.45645646,\n",
       "        8.50650651,  8.55655656,  8.60660661,  8.65665666,  8.70670671,\n",
       "        8.75675676,  8.80680681,  8.85685686,  8.90690691,  8.95695696,\n",
       "        9.00700701,  9.05705706,  9.10710711,  9.15715716,  9.20720721,\n",
       "        9.25725726,  9.30730731,  9.35735736,  9.40740741,  9.45745746,\n",
       "        9.50750751,  9.55755756,  9.60760761,  9.65765766,  9.70770771,\n",
       "        9.75775776,  9.80780781,  9.85785786,  9.90790791,  9.95795796,\n",
       "       10.00800801, 10.05805806, 10.10810811, 10.15815816, 10.20820821,\n",
       "       10.25825826, 10.30830831, 10.35835836, 10.40840841, 10.45845846,\n",
       "       10.50850851, 10.55855856, 10.60860861, 10.65865866, 10.70870871,\n",
       "       10.75875876, 10.80880881, 10.85885886, 10.90890891, 10.95895896,\n",
       "       11.00900901, 11.05905906, 11.10910911, 11.15915916, 11.20920921,\n",
       "       11.25925926, 11.30930931, 11.35935936, 11.40940941, 11.45945946,\n",
       "       11.50950951, 11.55955956, 11.60960961, 11.65965966, 11.70970971,\n",
       "       11.75975976, 11.80980981, 11.85985986, 11.90990991, 11.95995996,\n",
       "       12.01001001, 12.06006006, 12.11011011, 12.16016016, 12.21021021,\n",
       "       12.26026026, 12.31031031, 12.36036036, 12.41041041, 12.46046046,\n",
       "       12.51051051, 12.56056056, 12.61061061, 12.66066066, 12.71071071,\n",
       "       12.76076076, 12.81081081, 12.86086086, 12.91091091, 12.96096096,\n",
       "       13.01101101, 13.06106106, 13.11111111, 13.16116116, 13.21121121,\n",
       "       13.26126126, 13.31131131, 13.36136136, 13.41141141, 13.46146146,\n",
       "       13.51151151, 13.56156156, 13.61161161, 13.66166166, 13.71171171,\n",
       "       13.76176176, 13.81181181, 13.86186186, 13.91191191, 13.96196196,\n",
       "       14.01201201, 14.06206206, 14.11211211, 14.16216216, 14.21221221,\n",
       "       14.26226226, 14.31231231, 14.36236236, 14.41241241, 14.46246246,\n",
       "       14.51251251, 14.56256256, 14.61261261, 14.66266266, 14.71271271,\n",
       "       14.76276276, 14.81281281, 14.86286286, 14.91291291, 14.96296296,\n",
       "       15.01301301, 15.06306306, 15.11311311, 15.16316316, 15.21321321,\n",
       "       15.26326326, 15.31331331, 15.36336336, 15.41341341, 15.46346346,\n",
       "       15.51351351, 15.56356356, 15.61361361, 15.66366366, 15.71371371,\n",
       "       15.76376376, 15.81381381, 15.86386386, 15.91391391, 15.96396396,\n",
       "       16.01401401, 16.06406406, 16.11411411, 16.16416416, 16.21421421,\n",
       "       16.26426426, 16.31431431, 16.36436436, 16.41441441, 16.46446446,\n",
       "       16.51451451, 16.56456456, 16.61461461, 16.66466466, 16.71471471,\n",
       "       16.76476476, 16.81481481, 16.86486486, 16.91491491, 16.96496496,\n",
       "       17.01501502, 17.06506507, 17.11511512, 17.16516517, 17.21521522,\n",
       "       17.26526527, 17.31531532, 17.36536537, 17.41541542, 17.46546547,\n",
       "       17.51551552, 17.56556557, 17.61561562, 17.66566567, 17.71571572,\n",
       "       17.76576577, 17.81581582, 17.86586587, 17.91591592, 17.96596597,\n",
       "       18.01601602, 18.06606607, 18.11611612, 18.16616617, 18.21621622,\n",
       "       18.26626627, 18.31631632, 18.36636637, 18.41641642, 18.46646647,\n",
       "       18.51651652, 18.56656657, 18.61661662, 18.66666667, 18.71671672,\n",
       "       18.76676677, 18.81681682, 18.86686687, 18.91691692, 18.96696697,\n",
       "       19.01701702, 19.06706707, 19.11711712, 19.16716717, 19.21721722,\n",
       "       19.26726727, 19.31731732, 19.36736737, 19.41741742, 19.46746747,\n",
       "       19.51751752, 19.56756757, 19.61761762, 19.66766767, 19.71771772,\n",
       "       19.76776777, 19.81781782, 19.86786787, 19.91791792, 19.96796797,\n",
       "       20.01801802, 20.06806807, 20.11811812, 20.16816817, 20.21821822,\n",
       "       20.26826827, 20.31831832, 20.36836837, 20.41841842, 20.46846847,\n",
       "       20.51851852, 20.56856857, 20.61861862, 20.66866867, 20.71871872,\n",
       "       20.76876877, 20.81881882, 20.86886887, 20.91891892, 20.96896897,\n",
       "       21.01901902, 21.06906907, 21.11911912, 21.16916917, 21.21921922,\n",
       "       21.26926927, 21.31931932, 21.36936937, 21.41941942, 21.46946947,\n",
       "       21.51951952, 21.56956957, 21.61961962, 21.66966967, 21.71971972,\n",
       "       21.76976977, 21.81981982, 21.86986987, 21.91991992, 21.96996997,\n",
       "       22.02002002, 22.07007007, 22.12012012, 22.17017017, 22.22022022,\n",
       "       22.27027027, 22.32032032, 22.37037037, 22.42042042, 22.47047047,\n",
       "       22.52052052, 22.57057057, 22.62062062, 22.67067067, 22.72072072,\n",
       "       22.77077077, 22.82082082, 22.87087087, 22.92092092, 22.97097097,\n",
       "       23.02102102, 23.07107107, 23.12112112, 23.17117117, 23.22122122,\n",
       "       23.27127127, 23.32132132, 23.37137137, 23.42142142, 23.47147147,\n",
       "       23.52152152, 23.57157157, 23.62162162, 23.67167167, 23.72172172,\n",
       "       23.77177177, 23.82182182, 23.87187187, 23.92192192, 23.97197197,\n",
       "       24.02202202, 24.07207207, 24.12212212, 24.17217217, 24.22222222,\n",
       "       24.27227227, 24.32232232, 24.37237237, 24.42242242, 24.47247247,\n",
       "       24.52252252, 24.57257257, 24.62262262, 24.67267267, 24.72272272,\n",
       "       24.77277277, 24.82282282, 24.87287287, 24.92292292, 24.97297297,\n",
       "       25.02302302, 25.07307307, 25.12312312, 25.17317317, 25.22322322,\n",
       "       25.27327327, 25.32332332, 25.37337337, 25.42342342, 25.47347347,\n",
       "       25.52352352, 25.57357357, 25.62362362, 25.67367367, 25.72372372,\n",
       "       25.77377377, 25.82382382, 25.87387387, 25.92392392, 25.97397397,\n",
       "       26.02402402, 26.07407407, 26.12412412, 26.17417417, 26.22422422,\n",
       "       26.27427427, 26.32432432, 26.37437437, 26.42442442, 26.47447447,\n",
       "       26.52452452, 26.57457457, 26.62462462, 26.67467467, 26.72472472,\n",
       "       26.77477477, 26.82482482, 26.87487487, 26.92492492, 26.97497497,\n",
       "       27.02502503, 27.07507508, 27.12512513, 27.17517518, 27.22522523,\n",
       "       27.27527528, 27.32532533, 27.37537538, 27.42542543, 27.47547548,\n",
       "       27.52552553, 27.57557558, 27.62562563, 27.67567568, 27.72572573,\n",
       "       27.77577578, 27.82582583, 27.87587588, 27.92592593, 27.97597598,\n",
       "       28.02602603, 28.07607608, 28.12612613, 28.17617618, 28.22622623,\n",
       "       28.27627628, 28.32632633, 28.37637638, 28.42642643, 28.47647648,\n",
       "       28.52652653, 28.57657658, 28.62662663, 28.67667668, 28.72672673,\n",
       "       28.77677678, 28.82682683, 28.87687688, 28.92692693, 28.97697698,\n",
       "       29.02702703, 29.07707708, 29.12712713, 29.17717718, 29.22722723,\n",
       "       29.27727728, 29.32732733, 29.37737738, 29.42742743, 29.47747748,\n",
       "       29.52752753, 29.57757758, 29.62762763, 29.67767768, 29.72772773,\n",
       "       29.77777778, 29.82782783, 29.87787788, 29.92792793, 29.97797798,\n",
       "       30.02802803, 30.07807808, 30.12812813, 30.17817818, 30.22822823,\n",
       "       30.27827828, 30.32832833, 30.37837838, 30.42842843, 30.47847848,\n",
       "       30.52852853, 30.57857858, 30.62862863, 30.67867868, 30.72872873,\n",
       "       30.77877878, 30.82882883, 30.87887888, 30.92892893, 30.97897898,\n",
       "       31.02902903, 31.07907908, 31.12912913, 31.17917918, 31.22922923,\n",
       "       31.27927928, 31.32932933, 31.37937938, 31.42942943, 31.47947948,\n",
       "       31.52952953, 31.57957958, 31.62962963, 31.67967968, 31.72972973,\n",
       "       31.77977978, 31.82982983, 31.87987988, 31.92992993, 31.97997998,\n",
       "       32.03003003, 32.08008008, 32.13013013, 32.18018018, 32.23023023,\n",
       "       32.28028028, 32.33033033, 32.38038038, 32.43043043, 32.48048048,\n",
       "       32.53053053, 32.58058058, 32.63063063, 32.68068068, 32.73073073,\n",
       "       32.78078078, 32.83083083, 32.88088088, 32.93093093, 32.98098098,\n",
       "       33.03103103, 33.08108108, 33.13113113, 33.18118118, 33.23123123,\n",
       "       33.28128128, 33.33133133, 33.38138138, 33.43143143, 33.48148148,\n",
       "       33.53153153, 33.58158158, 33.63163163, 33.68168168, 33.73173173,\n",
       "       33.78178178, 33.83183183, 33.88188188, 33.93193193, 33.98198198,\n",
       "       34.03203203, 34.08208208, 34.13213213, 34.18218218, 34.23223223,\n",
       "       34.28228228, 34.33233233, 34.38238238, 34.43243243, 34.48248248,\n",
       "       34.53253253, 34.58258258, 34.63263263, 34.68268268, 34.73273273,\n",
       "       34.78278278, 34.83283283, 34.88288288, 34.93293293, 34.98298298,\n",
       "       35.03303303, 35.08308308, 35.13313313, 35.18318318, 35.23323323,\n",
       "       35.28328328, 35.33333333, 35.38338338, 35.43343343, 35.48348348,\n",
       "       35.53353353, 35.58358358, 35.63363363, 35.68368368, 35.73373373,\n",
       "       35.78378378, 35.83383383, 35.88388388, 35.93393393, 35.98398398,\n",
       "       36.03403403, 36.08408408, 36.13413413, 36.18418418, 36.23423423,\n",
       "       36.28428428, 36.33433433, 36.38438438, 36.43443443, 36.48448448,\n",
       "       36.53453453, 36.58458458, 36.63463463, 36.68468468, 36.73473473,\n",
       "       36.78478478, 36.83483483, 36.88488488, 36.93493493, 36.98498498,\n",
       "       37.03503504, 37.08508509, 37.13513514, 37.18518519, 37.23523524,\n",
       "       37.28528529, 37.33533534, 37.38538539, 37.43543544, 37.48548549,\n",
       "       37.53553554, 37.58558559, 37.63563564, 37.68568569, 37.73573574,\n",
       "       37.78578579, 37.83583584, 37.88588589, 37.93593594, 37.98598599,\n",
       "       38.03603604, 38.08608609, 38.13613614, 38.18618619, 38.23623624,\n",
       "       38.28628629, 38.33633634, 38.38638639, 38.43643644, 38.48648649,\n",
       "       38.53653654, 38.58658659, 38.63663664, 38.68668669, 38.73673674,\n",
       "       38.78678679, 38.83683684, 38.88688689, 38.93693694, 38.98698699,\n",
       "       39.03703704, 39.08708709, 39.13713714, 39.18718719, 39.23723724,\n",
       "       39.28728729, 39.33733734, 39.38738739, 39.43743744, 39.48748749,\n",
       "       39.53753754, 39.58758759, 39.63763764, 39.68768769, 39.73773774,\n",
       "       39.78778779, 39.83783784, 39.88788789, 39.93793794, 39.98798799,\n",
       "       40.03803804, 40.08808809, 40.13813814, 40.18818819, 40.23823824,\n",
       "       40.28828829, 40.33833834, 40.38838839, 40.43843844, 40.48848849,\n",
       "       40.53853854, 40.58858859, 40.63863864, 40.68868869, 40.73873874,\n",
       "       40.78878879, 40.83883884, 40.88888889, 40.93893894, 40.98898899,\n",
       "       41.03903904, 41.08908909, 41.13913914, 41.18918919, 41.23923924,\n",
       "       41.28928929, 41.33933934, 41.38938939, 41.43943944, 41.48948949,\n",
       "       41.53953954, 41.58958959, 41.63963964, 41.68968969, 41.73973974,\n",
       "       41.78978979, 41.83983984, 41.88988989, 41.93993994, 41.98998999,\n",
       "       42.04004004, 42.09009009, 42.14014014, 42.19019019, 42.24024024,\n",
       "       42.29029029, 42.34034034, 42.39039039, 42.44044044, 42.49049049,\n",
       "       42.54054054, 42.59059059, 42.64064064, 42.69069069, 42.74074074,\n",
       "       42.79079079, 42.84084084, 42.89089089, 42.94094094, 42.99099099,\n",
       "       43.04104104, 43.09109109, 43.14114114, 43.19119119, 43.24124124,\n",
       "       43.29129129, 43.34134134, 43.39139139, 43.44144144, 43.49149149,\n",
       "       43.54154154, 43.59159159, 43.64164164, 43.69169169, 43.74174174,\n",
       "       43.79179179, 43.84184184, 43.89189189, 43.94194194, 43.99199199,\n",
       "       44.04204204, 44.09209209, 44.14214214, 44.19219219, 44.24224224,\n",
       "       44.29229229, 44.34234234, 44.39239239, 44.44244244, 44.49249249,\n",
       "       44.54254254, 44.59259259, 44.64264264, 44.69269269, 44.74274274,\n",
       "       44.79279279, 44.84284284, 44.89289289, 44.94294294, 44.99299299,\n",
       "       45.04304304, 45.09309309, 45.14314314, 45.19319319, 45.24324324,\n",
       "       45.29329329, 45.34334334, 45.39339339, 45.44344344, 45.49349349,\n",
       "       45.54354354, 45.59359359, 45.64364364, 45.69369369, 45.74374374,\n",
       "       45.79379379, 45.84384384, 45.89389389, 45.94394394, 45.99399399,\n",
       "       46.04404404, 46.09409409, 46.14414414, 46.19419419, 46.24424424,\n",
       "       46.29429429, 46.34434434, 46.39439439, 46.44444444, 46.49449449,\n",
       "       46.54454454, 46.59459459, 46.64464464, 46.69469469, 46.74474474,\n",
       "       46.79479479, 46.84484484, 46.89489489, 46.94494494, 46.99499499,\n",
       "       47.04504505, 47.0950951 , 47.14514515, 47.1951952 , 47.24524525,\n",
       "       47.2952953 , 47.34534535, 47.3953954 , 47.44544545, 47.4954955 ,\n",
       "       47.54554555, 47.5955956 , 47.64564565, 47.6956957 , 47.74574575,\n",
       "       47.7957958 , 47.84584585, 47.8958959 , 47.94594595, 47.995996  ,\n",
       "       48.04604605, 48.0960961 , 48.14614615, 48.1961962 , 48.24624625,\n",
       "       48.2962963 , 48.34634635, 48.3963964 , 48.44644645, 48.4964965 ,\n",
       "       48.54654655, 48.5965966 , 48.64664665, 48.6966967 , 48.74674675,\n",
       "       48.7967968 , 48.84684685, 48.8968969 , 48.94694695, 48.996997  ,\n",
       "       49.04704705, 49.0970971 , 49.14714715, 49.1971972 , 49.24724725,\n",
       "       49.2972973 , 49.34734735, 49.3973974 , 49.44744745, 49.4974975 ,\n",
       "       49.54754755, 49.5975976 , 49.64764765, 49.6976977 , 49.74774775,\n",
       "       49.7977978 , 49.84784785, 49.8978979 , 49.94794795, 49.997998  ,\n",
       "       50.04804805, 50.0980981 , 50.14814815, 50.1981982 , 50.24824825,\n",
       "       50.2982983 , 50.34834835, 50.3983984 , 50.44844845, 50.4984985 ,\n",
       "       50.54854855, 50.5985986 , 50.64864865, 50.6986987 , 50.74874875,\n",
       "       50.7987988 , 50.84884885, 50.8988989 , 50.94894895, 50.998999  ,\n",
       "       51.04904905, 51.0990991 , 51.14914915, 51.1991992 , 51.24924925,\n",
       "       51.2992993 , 51.34934935, 51.3993994 , 51.44944945, 51.4994995 ,\n",
       "       51.54954955, 51.5995996 , 51.64964965, 51.6996997 , 51.74974975,\n",
       "       51.7997998 , 51.84984985, 51.8998999 , 51.94994995, 52.        ])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Look at y.\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2e3c554b7c0>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot x versus y.\n",
    "plt.plot(x, y, 'k.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5., 2.])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Do regression on the x and y arrays using numpy.\n",
    "np.polyfit(x, y, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "$$ y = 3 x - 1 + \\epsilon $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a y with noise.\n",
    "y = 3.0 * x - 1.0 + np.random.normal(0.0, 1.0, len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.80243008e+00,  4.65032561e-01, -1.04536179e+00, -3.83957536e-01,\n",
       "       -1.43800669e+00, -2.82581286e+00, -1.23403356e+00, -3.27647837e-01,\n",
       "       -2.41505154e+00, -1.02597216e+00, -4.80400105e-01, -1.72770264e+00,\n",
       "        3.48693899e-01,  2.42385683e-01, -3.58794203e-01, -3.38358508e-01,\n",
       "       -2.25615807e+00,  4.67828105e-01, -1.82599992e+00,  1.02836593e+00,\n",
       "       -4.47957911e-01, -1.35349411e+00,  1.22072835e-01, -8.92757468e-02,\n",
       "       -1.79594834e+00, -7.39470118e-01,  1.10338734e+00,  3.36417972e-01,\n",
       "       -1.27642001e-02,  1.90609082e+00,  1.83254074e+00,  4.53296747e-02,\n",
       "       -1.47347249e+00,  4.60243029e-01, -2.58764039e-01,  7.05028377e-01,\n",
       "       -9.14812046e-01, -2.21140535e-01, -9.81144942e-01, -2.96664277e+00,\n",
       "       -1.01576913e-01, -1.03678696e+00,  1.32714281e+00,  7.82415060e-01,\n",
       "       -9.02187331e-01,  1.30082104e+00, -1.14899186e+00,  3.75463123e-01,\n",
       "        1.36017935e+00, -1.36392803e-01,  7.19732590e-01,  1.60584938e+00,\n",
       "       -7.58713024e-01, -3.01503954e-01,  1.13250309e+00,  3.01760455e+00,\n",
       "        7.49500785e-01, -7.39606767e-01,  2.00557180e+00, -1.13017270e+00,\n",
       "       -2.67683649e-01,  1.39773603e+00,  1.78955152e+00,  2.34652926e+00,\n",
       "        2.29140992e+00, -1.13295264e+00,  1.87430773e+00,  1.68834260e+00,\n",
       "        1.97624013e+00, -3.61542654e-01,  6.86463806e-01,  4.25337266e-01,\n",
       "        1.89983621e+00, -6.93769032e-02,  1.55815327e-01,  9.93203804e-01,\n",
       "       -1.20365294e+00,  1.59400293e+00,  3.76497069e+00,  1.64853286e+00,\n",
       "        9.14096719e-01,  5.34896931e-01,  4.43489636e-01,  2.51605192e+00,\n",
       "        1.19469218e+00, -6.04222370e-01,  1.80694356e+00,  2.77749521e+00,\n",
       "        1.01994273e+00,  1.49339969e+00,  1.87959561e+00,  1.57118037e+00,\n",
       "        3.18312646e+00,  3.71023994e+00,  2.16705780e+00,  1.19451525e+00,\n",
       "        1.37327206e+00,  2.27582870e+00,  1.56064245e+00,  1.77623398e+00,\n",
       "        1.36480895e+00,  7.00443648e-01,  2.65047790e+00,  2.54266832e+00,\n",
       "        1.91737795e+00,  3.20864926e+00,  2.15866237e+00,  1.56211127e+00,\n",
       "        1.70971958e+00,  1.93012848e+00,  3.33818080e+00,  3.24007446e+00,\n",
       "        3.88638179e-01,  3.35280736e+00,  2.23007290e+00,  1.83429393e+00,\n",
       "        3.03977773e+00,  2.65236364e+00,  3.44602071e+00,  1.72558347e+00,\n",
       "        1.64650990e+00,  1.14044122e+00,  1.54728616e+00,  2.69844929e+00,\n",
       "        2.41374708e+00,  1.85479918e+00,  1.31877413e+00,  2.23563803e+00,\n",
       "        5.27764790e+00,  3.53044973e+00,  3.98222376e+00,  3.64947373e+00,\n",
       "        3.99296969e+00,  2.61117208e+00,  2.96863046e+00,  3.73037648e+00,\n",
       "        2.57437946e+00,  2.56759565e+00,  1.70768269e+00,  4.13690306e+00,\n",
       "        3.96085444e+00,  1.33327499e+00,  3.13714035e+00,  3.31308457e+00,\n",
       "        3.19152397e+00,  2.39906016e+00,  4.78396726e+00,  2.16324954e+00,\n",
       "        4.96999912e+00,  3.83261215e+00,  3.03697534e+00,  3.21929815e+00,\n",
       "        2.30074017e+00,  5.31322599e+00,  2.07260784e+00,  2.42674938e+00,\n",
       "        2.24729853e+00,  4.33675202e+00,  4.85454548e+00,  1.65807519e+00,\n",
       "        3.46290130e+00,  2.55107736e+00,  4.30265606e+00,  3.45918109e+00,\n",
       "        3.78439896e+00,  5.52572852e+00,  4.10684130e+00,  3.64752652e+00,\n",
       "        3.60276603e+00,  4.95391078e+00,  5.95196148e+00,  4.12378098e+00,\n",
       "        4.22388740e+00,  3.60210071e+00,  4.37706973e+00,  5.88168551e+00,\n",
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       "        2.46558201e+01,  2.49228866e+01,  2.36937041e+01,  2.38203016e+01,\n",
       "        2.35766686e+01,  2.35280408e+01,  2.46833882e+01,  2.77541296e+01,\n",
       "        2.45368935e+01,  2.34844679e+01,  2.38286718e+01,  2.26193506e+01,\n",
       "        2.41090298e+01,  2.45204344e+01,  2.41127460e+01,  2.46623595e+01,\n",
       "        2.52390090e+01,  2.31471077e+01,  2.46049590e+01,  2.51318111e+01,\n",
       "        2.50761259e+01,  2.62006793e+01,  2.36585492e+01,  2.42340070e+01,\n",
       "        2.51436429e+01,  2.70935736e+01,  2.62756425e+01,  2.53292225e+01,\n",
       "        2.52062745e+01,  2.50336159e+01,  2.60811286e+01,  2.43283044e+01,\n",
       "        2.45831373e+01,  2.70707799e+01,  2.53943499e+01,  2.36974910e+01,\n",
       "        2.50484425e+01,  2.63730961e+01,  2.65113730e+01,  2.65221571e+01,\n",
       "        2.63001576e+01,  2.57667863e+01,  2.50677124e+01,  2.43734422e+01,\n",
       "        2.62921566e+01,  2.55820496e+01,  2.54167227e+01,  2.69906321e+01,\n",
       "        2.47252065e+01,  2.57190884e+01,  2.60329711e+01,  2.64962626e+01,\n",
       "        2.71602797e+01,  2.59820398e+01,  2.49904336e+01,  2.68352978e+01,\n",
       "        2.50838466e+01,  2.88791898e+01,  2.66689858e+01,  2.45103792e+01,\n",
       "        2.57458988e+01,  2.53816508e+01,  2.75649851e+01,  2.50026900e+01,\n",
       "        2.70079416e+01,  2.67990265e+01,  2.65537254e+01,  2.54800428e+01,\n",
       "        2.73342058e+01,  2.73877793e+01,  2.64226901e+01,  2.75151127e+01,\n",
       "        2.62079018e+01,  2.59621501e+01,  2.57092507e+01,  2.71658509e+01,\n",
       "        2.56917288e+01,  2.69001009e+01,  2.57171384e+01,  2.69128258e+01,\n",
       "        2.70741280e+01,  2.80610391e+01,  2.82007383e+01,  2.86829492e+01,\n",
       "        2.80477133e+01,  2.62019005e+01,  2.87092106e+01,  2.74672041e+01,\n",
       "        2.77074549e+01,  2.59133954e+01,  2.43833555e+01,  2.81805726e+01,\n",
       "        2.74873447e+01,  2.73480497e+01,  2.80841594e+01,  2.81040461e+01,\n",
       "        2.72037134e+01,  2.61035538e+01,  2.66422010e+01,  2.86358287e+01,\n",
       "        2.74804775e+01,  2.83703257e+01,  2.83412890e+01,  2.74187435e+01,\n",
       "        2.73773179e+01,  2.75309567e+01,  2.52637996e+01,  2.89777383e+01,\n",
       "        2.59658190e+01,  2.81935754e+01,  2.60604713e+01,  2.76220619e+01,\n",
       "        2.77282785e+01,  2.79772852e+01,  2.65438120e+01,  2.72271413e+01,\n",
       "        2.95704191e+01,  2.77082771e+01,  2.84518103e+01,  2.94003386e+01,\n",
       "        2.85312593e+01,  2.67152562e+01,  2.80859087e+01,  2.83600815e+01,\n",
       "        2.68938137e+01,  2.85000650e+01,  2.97938266e+01,  2.91044130e+01,\n",
       "        2.75354688e+01,  2.94146330e+01,  2.68523101e+01,  2.78378031e+01,\n",
       "        2.88784958e+01,  2.85913794e+01,  2.74319937e+01,  2.79880033e+01,\n",
       "        2.82449638e+01,  2.71040195e+01,  2.90126540e+01,  2.86476981e+01,\n",
       "        2.90665809e+01,  3.01011112e+01,  2.86533378e+01,  2.92088685e+01,\n",
       "        2.52766240e+01,  2.88675554e+01,  2.95182727e+01,  2.92938596e+01,\n",
       "        2.82405262e+01,  3.00064739e+01,  2.68181322e+01,  2.90728093e+01,\n",
       "        2.99934403e+01,  2.88235978e+01,  2.95566745e+01,  2.87431494e+01])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Look at y.\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.01209078, -1.06067635])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Do regression on the x and y arrays using numpy.\n",
    "np.polyfit(x, y, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.0120907776499664, -1.060676350019941)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create variables with those values.\n",
    "m, c = np.polyfit(x, y, 1)\n",
    "# Have a look at m and c.\n",
    "m, c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2e3c55dee50>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot x and y and the regression line in red.\n",
    "plt.plot(x, y, 'k.')\n",
    "plt.plot(x, m * x + c, 'r-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we can easily calculate the best m and c ourselves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.0120907776499637, -1.0606763500199374)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate mean x and mean y.\n",
    "x_avg = np.mean(x)\n",
    "y_avg = np.mean(y)\n",
    "\n",
    "# Subtract means from x and y.\n",
    "x_zero = x - x_avg\n",
    "y_zero = y - y_avg\n",
    "\n",
    "# Dot product of mean-adjusted x and y divided by dot product of mean adjusted x with itself.\n",
    "m = np.sum(x_zero * y_zero) / np.sum(x_zero * x_zero)\n",
    "# Subtract m times average x from average y.\n",
    "c = y_avg - m * x_avg\n",
    "\n",
    "# Let's have a look - same values as above.\n",
    "m, c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "$$ y = 2 x^2 + 5x + 1 + \\epsilon $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create y from a polynomial in x.\n",
    "y =  2.0 * x * x + 5.0 * x + 1.0 + np.random.normal(0.0, 1.0, len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.85539905e+00, 1.46158550e+00, 1.05484267e+00, 1.65755501e+00,\n",
       "       1.04129132e+00, 1.01738921e-01, 2.09238991e+00, 2.20103767e+00,\n",
       "       5.42429101e-01, 3.90055080e+00, 1.27835309e+00, 9.38275968e-01,\n",
       "       2.33649514e+00, 2.52332352e+00, 3.49606562e+00, 2.05259511e+00,\n",
       "       2.07280213e+00, 2.96161957e+00, 6.84454247e-01, 2.22682499e+00,\n",
       "       1.79353984e+00, 2.77178656e+00, 1.40422367e+00, 1.67456205e+00,\n",
       "       1.88905361e+00, 8.66820546e-02, 1.23215152e+00, 1.58169272e-01,\n",
       "       3.20156341e+00, 1.25681971e+00, 1.86241183e+00, 2.52078411e+00,\n",
       "       1.82799904e+00, 3.01592052e+00, 3.48643922e+00, 3.45337491e+00,\n",
       "       6.03264985e+00, 3.18339995e+00, 2.82105467e+00, 2.00695620e+00,\n",
       "       2.44009842e+00, 2.33557272e+00, 2.73990875e+00, 3.08485726e+00,\n",
       "       3.23347874e+00, 3.78366946e+00, 3.12338587e+00, 4.31737409e+00,\n",
       "       3.45581310e+00, 3.21866371e+00, 5.22591493e+00, 4.29986671e+00,\n",
       "       4.29728694e+00, 3.33132656e+00, 4.69477228e+00, 3.98204251e+00,\n",
       "       5.49100341e+00, 3.47259482e+00, 5.43433871e+00, 3.39423771e+00,\n",
       "       4.62094105e+00, 4.84210030e+00, 4.20825371e+00, 3.49995349e+00,\n",
       "       5.09922052e+00, 4.58325015e+00, 7.15675755e+00, 4.37272711e+00,\n",
       "       5.19772304e+00, 4.56731182e+00, 6.56350136e+00, 5.91586361e+00,\n",
       "       4.05676534e+00, 7.09775164e+00, 6.18587747e+00, 6.10756380e+00,\n",
       "       5.70019714e+00, 5.31972068e+00, 4.63961438e+00, 6.28914636e+00,\n",
       "       6.37214902e+00, 5.69017033e+00, 7.36550947e+00, 6.29915360e+00,\n",
       "       6.96672076e+00, 6.38817515e+00, 5.57400550e+00, 7.84852630e+00,\n",
       "       5.95730434e+00, 6.34791071e+00, 7.46373180e+00, 6.30244638e+00,\n",
       "       9.05601225e+00, 7.79158403e+00, 8.44079172e+00, 8.40384737e+00,\n",
       "       8.53320120e+00, 6.16814899e+00, 8.95757548e+00, 8.33739482e+00,\n",
       "       7.51656682e+00, 8.91789575e+00, 7.85939944e+00, 8.66107968e+00,\n",
       "       9.54968676e+00, 8.84341302e+00, 7.56028694e+00, 7.10071091e+00,\n",
       "       9.21561800e+00, 8.40473478e+00, 8.15551321e+00, 8.66178663e+00,\n",
       "       9.52992786e+00, 1.02248472e+01, 9.74995813e+00, 9.70335140e+00,\n",
       "       8.79796469e+00, 1.10575932e+01, 9.37905040e+00, 9.00631454e+00,\n",
       "       1.09733092e+01, 1.04936731e+01, 8.95650467e+00, 1.05409358e+01,\n",
       "       1.02306773e+01, 9.53187094e+00, 1.10365840e+01, 9.97121588e+00,\n",
       "       1.18497272e+01, 1.01811097e+01, 1.02586869e+01, 9.41270216e+00,\n",
       "       9.72971151e+00, 1.20314450e+01, 1.02836623e+01, 1.17741712e+01,\n",
       "       1.10226092e+01, 1.15324403e+01, 1.34575142e+01, 1.26547286e+01,\n",
       "       1.26949982e+01, 1.16819869e+01, 1.30434082e+01, 1.20128345e+01,\n",
       "       1.55093679e+01, 1.37934441e+01, 1.22801141e+01, 1.26003838e+01,\n",
       "       1.33576444e+01, 1.19225365e+01, 1.42834470e+01, 1.33029571e+01,\n",
       "       1.37608079e+01, 1.35721183e+01, 1.54994901e+01, 1.33944847e+01,\n",
       "       1.23760514e+01, 1.56268907e+01, 1.37597761e+01, 1.38500304e+01,\n",
       "       1.58749363e+01, 1.32296096e+01, 1.45291961e+01, 1.36498837e+01,\n",
       "       1.48808322e+01, 1.29669676e+01, 1.45072202e+01, 1.45223465e+01,\n",
       "       1.70585639e+01, 1.51960444e+01, 1.33705581e+01, 1.53288936e+01,\n",
       "       1.39246797e+01, 1.53703992e+01, 1.67297502e+01, 1.62918580e+01,\n",
       "       1.64677830e+01, 1.54090780e+01, 1.68496400e+01, 1.66759609e+01,\n",
       "       1.52267578e+01, 1.60280136e+01, 1.67892541e+01, 1.49119185e+01,\n",
       "       1.85979466e+01, 1.71205838e+01, 1.77588379e+01, 1.72192254e+01,\n",
       "       1.80898195e+01, 1.98775300e+01, 1.58204871e+01, 1.59852793e+01,\n",
       "       1.71073636e+01, 1.84716702e+01, 1.85508766e+01, 1.87145346e+01,\n",
       "       1.77083050e+01, 1.88088644e+01, 1.78682003e+01, 2.06391221e+01,\n",
       "       1.93689846e+01, 1.74680505e+01, 1.98048334e+01, 1.73043976e+01,\n",
       "       1.88864390e+01, 1.91784726e+01, 1.93313519e+01, 2.01063737e+01,\n",
       "       1.97093512e+01, 2.12816733e+01, 2.07192393e+01, 2.23766855e+01,\n",
       "       2.05723528e+01, 1.97254510e+01, 2.28723349e+01, 2.39759161e+01,\n",
       "       2.11722055e+01, 2.05735293e+01, 2.17330039e+01, 2.10262869e+01,\n",
       "       2.12278486e+01, 2.26279109e+01, 2.19250803e+01, 1.96021608e+01,\n",
       "       2.28131805e+01, 2.32364246e+01, 2.31858399e+01, 2.26748850e+01,\n",
       "       2.12811547e+01, 2.32585673e+01, 2.25477288e+01, 2.30897011e+01,\n",
       "       2.42784738e+01, 2.29499842e+01, 2.54220539e+01, 2.42601851e+01,\n",
       "       2.44727435e+01, 2.49121929e+01, 2.42054806e+01, 2.40660209e+01,\n",
       "       2.59669956e+01, 2.40282924e+01, 2.42799567e+01, 2.42746256e+01,\n",
       "       2.44957656e+01, 2.63158703e+01, 2.55341752e+01, 2.53027754e+01,\n",
       "       2.42985943e+01, 2.45603283e+01, 2.60234347e+01, 2.60326051e+01,\n",
       "       2.62839246e+01, 2.70880792e+01, 2.66358671e+01, 2.60455432e+01,\n",
       "       2.65808510e+01, 2.86944292e+01, 2.57562022e+01, 2.74420862e+01,\n",
       "       2.68190654e+01, 2.58743203e+01, 2.79203318e+01, 2.77424469e+01,\n",
       "       2.95374770e+01, 2.92372592e+01, 2.90494493e+01, 2.74398664e+01,\n",
       "       2.77656620e+01, 2.87783416e+01, 2.98336450e+01, 2.90106666e+01,\n",
       "       3.04472396e+01, 2.88084162e+01, 3.24404442e+01, 3.12721835e+01,\n",
       "       3.08835397e+01, 3.01842204e+01, 3.13100047e+01, 3.01203603e+01,\n",
       "       2.99456550e+01, 3.27969255e+01, 3.02441621e+01, 3.02703931e+01,\n",
       "       3.13102073e+01, 3.00857319e+01, 3.17263074e+01, 3.28940990e+01,\n",
       "       3.30269091e+01, 3.13832014e+01, 3.25171289e+01, 3.28667863e+01,\n",
       "       3.14654108e+01, 3.35831763e+01, 3.17452579e+01, 3.39901099e+01,\n",
       "       3.35923142e+01, 3.34797333e+01, 3.32123600e+01, 3.57681806e+01,\n",
       "       3.44545158e+01, 3.47945213e+01, 3.37933812e+01, 3.34747511e+01,\n",
       "       3.57496811e+01, 3.49319117e+01, 3.42095617e+01, 3.43127240e+01,\n",
       "       3.39150633e+01, 3.57539291e+01, 3.70769689e+01, 3.48999514e+01,\n",
       "       3.59333051e+01, 3.64480643e+01, 3.87790076e+01, 3.66286216e+01,\n",
       "       3.62268309e+01, 3.89976777e+01, 3.55876103e+01, 3.58049390e+01,\n",
       "       3.71117612e+01, 3.82473495e+01, 3.85363985e+01, 3.86677812e+01,\n",
       "       3.89560927e+01, 3.99176009e+01, 3.86996676e+01, 3.85008816e+01,\n",
       "       3.92801259e+01, 3.75375885e+01, 3.88522303e+01, 3.88755620e+01,\n",
       "       4.01176222e+01, 3.87599960e+01, 3.95652589e+01, 4.09492808e+01,\n",
       "       4.09454406e+01, 3.99646232e+01, 4.08312076e+01, 4.18216278e+01,\n",
       "       4.09772398e+01, 4.11990957e+01, 4.13389133e+01, 4.15169953e+01,\n",
       "       4.22970206e+01, 4.13422176e+01, 4.15638301e+01, 4.25079181e+01,\n",
       "       4.23738566e+01, 4.32864105e+01, 4.47833042e+01, 4.28076588e+01,\n",
       "       4.44082026e+01, 4.33259271e+01, 4.36624443e+01, 4.42014663e+01,\n",
       "       4.62658536e+01, 4.57210969e+01, 4.30760418e+01, 4.44769478e+01,\n",
       "       4.43900190e+01, 4.53289407e+01, 4.48646809e+01, 4.48851650e+01,\n",
       "       4.65284464e+01, 4.60190304e+01, 4.74042911e+01, 4.51832432e+01,\n",
       "       4.90715748e+01, 4.72221470e+01, 4.73061521e+01, 4.82480008e+01,\n",
       "       4.82964672e+01, 4.64511986e+01, 4.83940765e+01, 4.73496896e+01,\n",
       "       4.92706880e+01, 4.76535311e+01, 4.89517474e+01, 4.99413100e+01,\n",
       "       4.71220820e+01, 4.73221796e+01, 4.90219143e+01, 4.80710550e+01,\n",
       "       5.08795979e+01, 5.02413177e+01, 5.06349662e+01, 5.00554576e+01,\n",
       "       5.23810856e+01, 4.98482423e+01, 4.86219674e+01, 5.08253806e+01,\n",
       "       5.22431560e+01, 5.15591142e+01, 5.26222309e+01, 5.04336527e+01,\n",
       "       5.25976941e+01, 5.24162538e+01, 5.22270855e+01, 5.47638550e+01,\n",
       "       5.31609533e+01, 5.22596299e+01, 5.42990341e+01, 5.42163744e+01,\n",
       "       5.46490966e+01, 5.57414605e+01, 5.42683341e+01, 5.30408585e+01,\n",
       "       5.41100999e+01, 5.54030906e+01, 5.42696588e+01, 5.47415661e+01,\n",
       "       5.66534959e+01, 5.47727186e+01, 5.68464502e+01, 5.55726611e+01,\n",
       "       5.49328379e+01, 5.68194738e+01, 5.72941330e+01, 5.71041759e+01,\n",
       "       5.55939951e+01, 5.80710763e+01, 5.90313997e+01, 5.76769163e+01,\n",
       "       5.88552388e+01, 5.90852307e+01, 6.00284057e+01, 5.62642735e+01,\n",
       "       5.82246198e+01, 5.98642281e+01, 6.04169863e+01, 5.91861357e+01,\n",
       "       5.96384850e+01, 6.04652177e+01, 6.12498288e+01, 6.14990294e+01,\n",
       "       6.03118133e+01, 6.21179095e+01, 6.13312881e+01, 6.11816188e+01,\n",
       "       6.31970961e+01, 6.21570739e+01, 6.12889762e+01, 6.33912429e+01,\n",
       "       6.30251659e+01, 6.33741830e+01, 6.17410215e+01, 6.33375166e+01,\n",
       "       6.50076632e+01, 6.40284032e+01, 6.45329478e+01, 6.50800923e+01,\n",
       "       6.31273380e+01, 6.47502003e+01, 6.47622181e+01, 6.36778266e+01,\n",
       "       6.62670598e+01, 6.61827478e+01, 6.61755194e+01, 6.84644090e+01,\n",
       "       6.64604589e+01, 6.83358686e+01, 6.71352306e+01, 6.76994148e+01,\n",
       "       6.74752379e+01, 6.71807067e+01, 6.73609090e+01, 6.90352558e+01,\n",
       "       6.80671522e+01, 6.86465565e+01, 7.00504053e+01, 6.94794119e+01,\n",
       "       6.98473974e+01, 7.00005773e+01, 7.06655190e+01, 7.16737335e+01,\n",
       "       7.02987958e+01, 7.07650507e+01, 7.00360743e+01, 7.15545354e+01,\n",
       "       7.19671963e+01, 7.15304334e+01, 7.14612843e+01, 7.10515459e+01,\n",
       "       7.35791913e+01, 7.18273843e+01, 7.15526698e+01, 7.13062501e+01,\n",
       "       7.18316453e+01, 7.42449324e+01, 7.31899004e+01, 7.37460209e+01,\n",
       "       7.35137177e+01, 7.48135002e+01, 7.46147958e+01, 7.38998518e+01,\n",
       "       7.66410159e+01, 7.46107847e+01, 7.64628892e+01, 7.68474867e+01,\n",
       "       7.55144268e+01, 7.58649498e+01, 7.62137568e+01, 7.78390776e+01,\n",
       "       7.93785589e+01, 7.72646627e+01, 7.60135023e+01, 7.76762084e+01,\n",
       "       7.99076181e+01, 7.80174713e+01, 7.99002998e+01, 7.81132894e+01,\n",
       "       7.71026712e+01, 8.02686292e+01, 7.91580876e+01, 8.11452450e+01,\n",
       "       7.87698499e+01, 7.96230292e+01, 8.14007199e+01, 8.11653383e+01,\n",
       "       8.06240395e+01, 8.09256412e+01, 8.08499838e+01, 8.21905900e+01,\n",
       "       8.35334114e+01, 8.19197505e+01, 8.19947394e+01, 8.17644814e+01,\n",
       "       8.44126967e+01, 8.24203841e+01, 8.41478136e+01, 8.53965844e+01,\n",
       "       8.47645574e+01, 8.47197845e+01, 8.33080448e+01, 8.57086670e+01,\n",
       "       8.61460838e+01, 8.63683540e+01, 8.52713100e+01, 8.55055051e+01,\n",
       "       8.92594776e+01, 8.71769797e+01, 8.64803560e+01, 8.69488774e+01,\n",
       "       8.91568097e+01, 8.83122159e+01, 8.80633416e+01, 8.87403269e+01,\n",
       "       8.98671208e+01, 8.92444085e+01, 8.78612351e+01, 9.00755413e+01,\n",
       "       8.86358676e+01, 9.20146624e+01, 8.89520638e+01, 9.06580685e+01,\n",
       "       9.03101207e+01, 8.99400826e+01, 9.15518879e+01, 9.06638449e+01,\n",
       "       9.16661384e+01, 9.19087750e+01, 9.05785294e+01, 9.20184530e+01,\n",
       "       9.35464079e+01, 9.19401234e+01, 9.48485076e+01, 9.45710469e+01,\n",
       "       9.36705587e+01, 9.43631025e+01, 9.47188782e+01, 9.33320595e+01,\n",
       "       9.56081706e+01, 9.59978521e+01, 9.50016283e+01, 9.56887977e+01,\n",
       "       9.65046810e+01, 9.58171244e+01, 9.81276203e+01, 9.70543779e+01,\n",
       "       9.72324691e+01, 9.60928548e+01, 9.67542322e+01, 9.92526975e+01,\n",
       "       1.00584044e+02, 9.85389159e+01, 9.94563659e+01, 9.85868968e+01,\n",
       "       1.00850546e+02, 1.01795639e+02, 1.02108041e+02, 1.00402138e+02,\n",
       "       1.00942058e+02, 1.01406086e+02, 1.01206592e+02, 1.01980832e+02,\n",
       "       1.01397943e+02, 1.02688518e+02, 1.02984485e+02, 1.02725385e+02,\n",
       "       1.03369550e+02, 1.02567991e+02, 1.04851946e+02, 1.03115442e+02,\n",
       "       1.05755103e+02, 1.03380832e+02, 1.03515227e+02, 1.05059851e+02,\n",
       "       1.04962433e+02, 1.06203285e+02, 1.07333838e+02, 1.07498410e+02,\n",
       "       1.07571987e+02, 1.07336406e+02, 1.07421154e+02, 1.07709475e+02,\n",
       "       1.07112365e+02, 1.08677997e+02, 1.09414995e+02, 1.08260898e+02,\n",
       "       1.08376012e+02, 1.10207475e+02, 1.11013274e+02, 1.10826794e+02,\n",
       "       1.10775846e+02, 1.11276165e+02, 1.10454124e+02, 1.10157079e+02,\n",
       "       1.12574257e+02, 1.13164558e+02, 1.11749425e+02, 1.13030505e+02,\n",
       "       1.14939020e+02, 1.13364966e+02, 1.12021569e+02, 1.14576184e+02,\n",
       "       1.13713003e+02, 1.15147626e+02, 1.15707948e+02, 1.14598281e+02,\n",
       "       1.14822197e+02, 1.15296341e+02, 1.17181851e+02, 1.17036709e+02,\n",
       "       1.14960510e+02, 1.17241812e+02, 1.16780286e+02, 1.18691487e+02,\n",
       "       1.17821097e+02, 1.16880305e+02, 1.16721715e+02, 1.19082975e+02,\n",
       "       1.18136477e+02, 1.20059551e+02, 1.18463227e+02, 1.17598772e+02,\n",
       "       1.19808032e+02, 1.19678919e+02, 1.20720321e+02, 1.20796941e+02,\n",
       "       1.22148783e+02, 1.23104984e+02, 1.22598763e+02, 1.23079837e+02,\n",
       "       1.24884667e+02, 1.23091375e+02, 1.23342734e+02, 1.22792253e+02,\n",
       "       1.22240845e+02, 1.22873844e+02, 1.23985771e+02, 1.26000579e+02,\n",
       "       1.24495740e+02, 1.23214861e+02, 1.25897165e+02, 1.26241877e+02,\n",
       "       1.26362705e+02, 1.28011429e+02, 1.26288950e+02, 1.26348203e+02,\n",
       "       1.28252648e+02, 1.29475198e+02, 1.28867074e+02, 1.28853196e+02,\n",
       "       1.30398136e+02, 1.28716314e+02, 1.30210405e+02, 1.29565842e+02,\n",
       "       1.33058351e+02, 1.32091545e+02, 1.29797317e+02, 1.30687502e+02,\n",
       "       1.29758924e+02, 1.32349742e+02, 1.30670242e+02, 1.33137260e+02,\n",
       "       1.32436359e+02, 1.33075167e+02, 1.32680590e+02, 1.33393982e+02,\n",
       "       1.34813114e+02, 1.33373549e+02, 1.36144512e+02, 1.34847752e+02,\n",
       "       1.34431251e+02, 1.36739197e+02, 1.37757684e+02, 1.36722673e+02,\n",
       "       1.36715058e+02, 1.37258341e+02, 1.37594849e+02, 1.38462174e+02,\n",
       "       1.38547407e+02, 1.37726171e+02, 1.39782762e+02, 1.38810532e+02,\n",
       "       1.38717546e+02, 1.39620224e+02, 1.40862357e+02, 1.41778308e+02,\n",
       "       1.42284263e+02, 1.41287314e+02, 1.43272505e+02, 1.41848743e+02,\n",
       "       1.42486513e+02, 1.42289805e+02, 1.42350107e+02, 1.42418109e+02,\n",
       "       1.43619573e+02, 1.43534785e+02, 1.45104279e+02, 1.43946482e+02,\n",
       "       1.45496882e+02, 1.45637383e+02, 1.44898884e+02, 1.46188591e+02,\n",
       "       1.46547872e+02, 1.48034955e+02, 1.46475535e+02, 1.47816706e+02,\n",
       "       1.48031886e+02, 1.47897389e+02, 1.48071834e+02, 1.48367309e+02,\n",
       "       1.48982227e+02, 1.50459312e+02, 1.47212848e+02, 1.50679065e+02,\n",
       "       1.50172733e+02, 1.51424655e+02, 1.50389381e+02, 1.51595386e+02,\n",
       "       1.53384466e+02, 1.53112524e+02, 1.53791085e+02, 1.51886542e+02,\n",
       "       1.52181078e+02, 1.54808000e+02, 1.54927852e+02, 1.54045090e+02,\n",
       "       1.53538799e+02, 1.56428977e+02, 1.53716579e+02, 1.56689740e+02,\n",
       "       1.57231911e+02, 1.55482466e+02, 1.55659953e+02, 1.58201978e+02,\n",
       "       1.59257882e+02, 1.56818773e+02, 1.57879873e+02, 1.58685143e+02,\n",
       "       1.58491938e+02, 1.61089222e+02, 1.60594063e+02, 1.61337732e+02,\n",
       "       1.60467891e+02, 1.61693532e+02, 1.60448510e+02, 1.61835028e+02,\n",
       "       1.61339108e+02, 1.63229607e+02, 1.61909217e+02, 1.62752209e+02,\n",
       "       1.61911453e+02, 1.62426092e+02, 1.63355609e+02, 1.65186480e+02,\n",
       "       1.64449204e+02, 1.63625502e+02, 1.65311125e+02, 1.64594894e+02,\n",
       "       1.66943760e+02, 1.66013570e+02, 1.67763504e+02, 1.68857782e+02,\n",
       "       1.69866793e+02, 1.67479962e+02, 1.69840813e+02, 1.69412671e+02,\n",
       "       1.69020572e+02, 1.69022475e+02, 1.70122569e+02, 1.69969922e+02,\n",
       "       1.71397769e+02, 1.71023000e+02, 1.71810380e+02, 1.73006704e+02,\n",
       "       1.73347255e+02, 1.70942914e+02, 1.73590620e+02, 1.71617254e+02,\n",
       "       1.72489796e+02, 1.74192651e+02, 1.75201216e+02, 1.75218476e+02,\n",
       "       1.73221730e+02, 1.74913593e+02, 1.76218320e+02, 1.76833755e+02,\n",
       "       1.77083879e+02, 1.77059982e+02, 1.76161428e+02, 1.77099634e+02,\n",
       "       1.77649893e+02, 1.79444737e+02, 1.78763001e+02, 1.77452039e+02,\n",
       "       1.79473051e+02, 1.82470487e+02, 1.79305613e+02, 1.83359245e+02,\n",
       "       1.81530265e+02, 1.81773256e+02, 1.82858617e+02, 1.83319209e+02,\n",
       "       1.83025767e+02, 1.82629233e+02, 1.82315799e+02, 1.83503374e+02,\n",
       "       1.85115947e+02, 1.83822270e+02, 1.85113281e+02, 1.84095945e+02,\n",
       "       1.88005563e+02, 1.86975755e+02, 1.88203778e+02, 1.86518822e+02,\n",
       "       1.86097725e+02, 1.89087038e+02, 1.88957862e+02, 1.87459595e+02,\n",
       "       1.88277397e+02, 1.89868822e+02, 1.89783046e+02, 1.91146403e+02,\n",
       "       1.89811853e+02, 1.91228985e+02, 1.90448347e+02, 1.90779265e+02,\n",
       "       1.92369601e+02, 1.93686118e+02, 1.94351982e+02, 1.92367597e+02,\n",
       "       1.94744304e+02, 1.94144679e+02, 1.95858345e+02, 1.95413868e+02,\n",
       "       1.95746458e+02, 1.95992687e+02, 1.97031651e+02, 1.97122874e+02,\n",
       "       1.97548262e+02, 1.97678146e+02, 1.96564688e+02, 1.97443823e+02,\n",
       "       1.99092683e+02, 1.97699489e+02, 1.98850818e+02, 2.00461601e+02,\n",
       "       1.99937265e+02, 2.01970856e+02, 2.00639107e+02, 2.00335685e+02,\n",
       "       2.02321840e+02, 2.01245657e+02, 2.01733545e+02, 2.02302475e+02,\n",
       "       2.04143680e+02, 2.03952261e+02, 2.04921817e+02, 2.05134553e+02,\n",
       "       2.04173118e+02, 2.07468611e+02, 2.06046967e+02, 2.05912458e+02,\n",
       "       2.07528152e+02, 2.07822567e+02, 2.07066029e+02, 2.07770612e+02,\n",
       "       2.08469895e+02, 2.08096347e+02, 2.08639746e+02, 2.11267524e+02,\n",
       "       2.10198604e+02, 2.11065522e+02, 2.10245819e+02, 2.11205364e+02,\n",
       "       2.12453154e+02, 2.14030532e+02, 2.11646077e+02, 2.12937216e+02,\n",
       "       2.13536339e+02, 2.15211403e+02, 2.14306150e+02, 2.13818683e+02,\n",
       "       2.16424944e+02, 2.14800041e+02, 2.14312398e+02, 2.17257320e+02,\n",
       "       2.18245295e+02, 2.17702264e+02, 2.16734051e+02, 2.17441865e+02,\n",
       "       2.17710221e+02, 2.17859675e+02, 2.18315644e+02, 2.18295100e+02,\n",
       "       2.20153984e+02, 2.18177066e+02, 2.20638290e+02, 2.19784674e+02,\n",
       "       2.21395755e+02, 2.23753307e+02, 2.23757540e+02, 2.22667230e+02,\n",
       "       2.23862653e+02, 2.25047886e+02, 2.25297279e+02, 2.24873935e+02,\n",
       "       2.25135043e+02, 2.25645984e+02, 2.25316025e+02, 2.26162398e+02,\n",
       "       2.25234149e+02, 2.27816793e+02, 2.26665924e+02, 2.27995687e+02,\n",
       "       2.29230485e+02, 2.28828624e+02, 2.28403380e+02, 2.27984310e+02,\n",
       "       2.29184738e+02, 2.30420313e+02, 2.31319802e+02, 2.33378207e+02,\n",
       "       2.31196720e+02, 2.33330755e+02, 2.32127340e+02, 2.31224849e+02,\n",
       "       2.33865356e+02, 2.34316006e+02, 2.35452319e+02, 2.35769632e+02,\n",
       "       2.34586214e+02, 2.35455218e+02, 2.36413434e+02, 2.35373801e+02,\n",
       "       2.36892980e+02, 2.36534554e+02, 2.38066559e+02, 2.38822467e+02,\n",
       "       2.37301905e+02, 2.41073102e+02, 2.40327071e+02, 2.41322783e+02,\n",
       "       2.41747708e+02, 2.43349740e+02, 2.40758279e+02, 2.43476964e+02,\n",
       "       2.43159914e+02, 2.41430736e+02, 2.43326463e+02, 2.44157708e+02,\n",
       "       2.44717708e+02, 2.43657635e+02, 2.45607360e+02, 2.46422637e+02,\n",
       "       2.44780232e+02, 2.47620975e+02, 2.46532157e+02, 2.47694429e+02,\n",
       "       2.47431699e+02, 2.48740756e+02, 2.47173038e+02, 2.50462420e+02,\n",
       "       2.50957170e+02, 2.52003901e+02, 2.52772123e+02, 2.49865665e+02])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Look at y.\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(25.00301522766029, -32.29058148957602)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Blindly try the regression - we get answers.\n",
    "# Create variables with those values.\n",
    "m, c = np.polyfit(x, y, 1)\n",
    "# Have a look at m and c.\n",
    "m, c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2e3c584c850>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the line and the points.\n",
    "plt.plot(x, y, 'k.')\n",
    "plt.plot(x, m * x + c, 'r-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2e3c586d880>]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create variables with those values.\n",
    "a, b, c = np.polyfit(x, y, 2)\n",
    "\n",
    "# Plot the line and the points.\n",
    "plt.plot(x, y, 'k.')\n",
    "plt.plot(x, a * x * x + b * x + c, 'r-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note how the points below the line are bunched in a specific $x$ range.\n",
    "\n",
    "***\n",
    "\n",
    "## Multiple linear regression\n",
    "\n",
    "Let's try multiple linear regression using sklearn.\n",
    "[https://scikit-learn.org/stable/](https://scikit-learn.org/stable/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import linear_model from sklearn.\n",
    "import sklearn.linear_model as lm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a linear regression model instance.\n",
    "m = lm.LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's use pandas to read a csv file and organise our data.\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read the iris csv from online.\n",
    "df = pd.read_csv('https://datahub.io/machine-learning/iris/r/iris.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepallength</th>\n",
       "      <th>sepalwidth</th>\n",
       "      <th>petallength</th>\n",
       "      <th>petalwidth</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepallength  sepalwidth  petallength  petalwidth           class\n",
       "0            5.1         3.5          1.4         0.2     Iris-setosa\n",
       "1            4.9         3.0          1.4         0.2     Iris-setosa\n",
       "2            4.7         3.2          1.3         0.2     Iris-setosa\n",
       "3            4.6         3.1          1.5         0.2     Iris-setosa\n",
       "4            5.0         3.6          1.4         0.2     Iris-setosa\n",
       "..           ...         ...          ...         ...             ...\n",
       "145          6.7         3.0          5.2         2.3  Iris-virginica\n",
       "146          6.3         2.5          5.0         1.9  Iris-virginica\n",
       "147          6.5         3.0          5.2         2.0  Iris-virginica\n",
       "148          6.2         3.4          5.4         2.3  Iris-virginica\n",
       "149          5.9         3.0          5.1         1.8  Iris-virginica\n",
       "\n",
       "[150 rows x 5 columns]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ petalwidth = t (sepallength) + u (sepalwidth) + v (petallength) + c $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's pretend we want to do linear regression on these variables to predict petal width.\n",
    "x = df[['sepallength', 'sepalwidth', 'petallength']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Here's petal width.\n",
    "y = df['petalwidth']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Ask our model to fit the data.\n",
    "m.fit(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.248723586024453"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Here's our intercept.\n",
    "m.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.21027133,  0.22877721,  0.52608818])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Here's our coefficients, in order.\n",
    "m.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9380481344518986"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# See how good our fit is.\n",
    "m.score(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9380481344518986"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating the score by hand.\n",
    "t, u, v = m.coef_\n",
    "c = m.intercept_\n",
    "\n",
    "y_avg = y.mean()\n",
    "\n",
    "u = ((y - (t * x['sepallength'] + u * x['sepalwidth'] + v * x['petallength'] + c))**2).sum()\n",
    "v = ((y - y.mean())**2).sum()\n",
    "\n",
    "1 - (u/v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "## Using statsmodels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             petalwidth   R-squared:                       0.938\n",
      "Model:                            OLS   Adj. R-squared:                  0.937\n",
      "Method:                 Least Squares   F-statistic:                     736.9\n",
      "Date:                Sun, 17 Oct 2021   Prob (F-statistic):           6.20e-88\n",
      "Time:                        16:44:34   Log-Likelihood:                 36.809\n",
      "No. Observations:                 150   AIC:                            -65.62\n",
      "Df Residuals:                     146   BIC:                            -53.57\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===============================================================================\n",
      "                  coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------\n",
      "const          -0.2487      0.178     -1.396      0.165      -0.601       0.103\n",
      "sepallength    -0.2103      0.048     -4.426      0.000      -0.304      -0.116\n",
      "sepalwidth      0.2288      0.049      4.669      0.000       0.132       0.326\n",
      "petallength     0.5261      0.024     21.536      0.000       0.478       0.574\n",
      "==============================================================================\n",
      "Omnibus:                        5.603   Durbin-Watson:                   1.577\n",
      "Prob(Omnibus):                  0.061   Jarque-Bera (JB):                6.817\n",
      "Skew:                           0.222   Prob(JB):                       0.0331\n",
      "Kurtosis:                       3.945   Cond. No.                         90.0\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Using statsmodels.\n",
    "import statsmodels.api as sm\n",
    "\n",
    "# Tell statmodels to include an intercept.\n",
    "xwithc = sm.add_constant(x)\n",
    "\n",
    "# Create a model.\n",
    "msm = sm.OLS(y, xwithc)\n",
    "# Fit the data.\n",
    "rsm = msm.fit()\n",
    "# Print a summary.\n",
    "print(rsm.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## End"
   ]
  }
 ],
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