{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework 2\n",
    "\n",
    "**OBJECTIVES**\n",
    "\n",
    "- Define four function types from class (*linear, quadratic, exponential, trigonmetric*)\n",
    "- Represent functions using symbols, tables, words, and graphs\n",
    "- Choose appropriate functions to model real world data\n",
    "\n",
    "\n",
    "### Problem I: Media Consumption\n",
    "\n",
    "This assignment focuses on reviewing and extending our understanding of the idea of a mathematical function.  Prior to completing the problems, I ask that you visit the results of the google search: [\"mathematical functions\"](https://www.google.com/search?q=mathematical+functions&rlz=1C5CHFA_enUS884US884&oq=mathematical+functions&aqs=chrome..69i57j0l7.3363j0j4&sourceid=chrome&ie=UTF-8) and watch a youtube video or read a wikipedia page -- consume some result of this search; maybe 10 - 20 minutes.  Also, watch the video below.  After doing this, write a few sentences about what you found and whether or not you felt the resource was helpful and why."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<center>\n",
       "<h4>A Movie About Functions</h4>\n",
       "<iframe src=\"https://player.vimeo.com/video/101690069?title=0&byline=0&portrait=0\" \n",
       "width=\"700\" height=\"394\" frameborder=\"0\" webkitallowfullscreen mozallowfullscreen \n",
       "allowfullscreen></iframe>\n",
       "</center>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "\n",
    "HTML('''\n",
    "<center>\n",
    "<h4>A Movie About Functions</h4>\n",
    "<iframe src=\"https://player.vimeo.com/video/101690069?title=0&byline=0&portrait=0\" \n",
    "width=\"700\" height=\"394\" frameborder=\"0\" webkitallowfullscreen mozallowfullscreen \n",
    "allowfullscreen></iframe>\n",
    "</center>\n",
    "''')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 2: Functions\n",
    "\n",
    "Given the following symbolic representations of the functions and their domains, present a table and graph of the function.\n",
    "\n",
    "1. $f(x) = x^3 - x^2 + x - 2; \\text{on} ~ -10 \\leq x \\leq 10$\n",
    "2. $f(x) = 100(0.46)^x; \\text{on} ~ 0 \\leq x \\leq 10$\n",
    "3. $f(x) = 2\\sin(x^2); \\text{on} ~ -\\pi \\leq x \\leq 3\\pi$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#answer 1 here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#answer 2 here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#answer 3 here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 3: Data\n",
    "\n",
    "For each of the problems below, you are given a table and graph of a real world dataset.  You are asked to choose what kind of function you believe would be a good model of the data; *linear, quadratic, exponential*, or *trigonometric*.\n",
    "\n",
    "1. The dataset below is on measurements of three different species of *iris* flowers. We have plotted the petal length on the horizontal axis and petal width on the vertical axis.  What kind of function would be a more appropriate model for this data where we input a measure of a petal length, and output a width? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "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>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)\n",
       "0                5.1               3.5                1.4               0.2\n",
       "1                4.9               3.0                1.4               0.2\n",
       "2                4.7               3.2                1.3               0.2\n",
       "3                4.6               3.1                1.5               0.2\n",
       "4                5.0               3.6                1.4               0.2"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_boston, load_diabetes, load_iris\n",
    "iris = load_iris()\n",
    "iris = pd.DataFrame(iris.data, columns = iris.feature_names)\n",
    "iris.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fac181c3550>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wrn3rrbagEWKsBk8xYWaZiq0fUFgv0OfWjy3ud2VQL3PwD6URYiynmtcRmFnjycp1L2ZNx6Zh96232oJGiLFa3BGYWaasXPdi5s+aOuy+9VZb0AgxVos7AjPLVGz9gKULZ/fbbunC2YNuGNdbnnyWRoixWnyPwMyG5KyhsaEm6aNmNjZMmzxx0Adk68wpQ3YAQ+1bbxohxkrz0JBZE2p7rIsv3fwIbY917Whr7+xmWVsH7Z3dw+5f7nn0i50773nKvV2l9q9XviIwazKnfeNe7mxPOoCLb2tnUes09p++e67aACh/7v25K9Zlnjvvecq9XTFjuebAVwRmTaTtsa4dnUCfO9q7+n0QA1x9z/rMK4OuzT2cs3wtW7b20t2zjS1bezl7+dpRf0Nu7+zOPHfbY125zpM3nlLjLvfrrjfuCMyayMpHn8297cDaACh/7n3WOSCJM8958sZTatxjvebAHYFZE1l8wPTc2w6sDYDy595nnQOSOPOcJ288pcY91msOcnUEkvaUdJCkP5HkzsOsQS3YfxqLWqf1a1vUOi1XbQCUP/e+deaUzHMv2H9arvPkjafUuMd6zUHROgJJf0QyM+ipwC7ARmASMBO4F/haRNxepTh3cB2BWenaHuti5aPPsviA6SzYP+kY8tYGQPlz74udO+95yr1dpfavpVGtRyDpFuBq4PqI2DTgucOAdwHrIuKKMsc7JHcEZmYjN6qCsoh40xDPrQJWlSE2Mxulan07beRvwZZPrjoCSfOAOYXbF1mD2MyqoFo57WM5d952GrYjkHQlMA94kJ1LTgbgjsCsBgpz2rek/yXPXr6WI1unl/Ube7XOY7WX54rgiIiYW/FIzCyXvpz2LexMZ+zLaS/nB3S1zmO1lycV9B5J7gjM6kS1ctrHeu687ZSnI7iKpDN4RNJaSeskra10YGaWrVo57WM9d952GnY9AkntwMeBdey8R0BEPFHZ0LI5fdQs4awhG4lS1yNYHxE/LnNMZlaias2j7/n6x748HcGvJX0HuB7YMdWe00fNzMaGPB3BriQdwJsL2pw+alZj1ZpWoVrHHEvxNJphO4KIeE81AjGz/Kq1GEsp566WeounEQ2bNSTpKklTCx7vmRaZmVkNVGsxllLOXS31Fk+jypM+Oq9w0rmIeB54TeVCMrOhVGsxllLOXS31Fk+jytMRtEjas++BpFfgtY7NaqZai7GUcu5qqbd4GlWejuCLwN2S/kXSecDdwAWVDcvMiqnWYiylnLta6i2eRjVsQRlAOsXEGwABP4uIhyodWDEuKDNLOGuofuOpR6MqKJM0OSI2A6Qf/IM+/Au3MbPqylvoVYmCsHorMqu3eBrNUENDP5L0RUmLJe3e15iuW/xeSTcBbym2s6QrJT0j6VdFnj9K0u8lrUl/zh39yzBrPF2be3igY9OoM1xWrO7gjKvuZ8XqjiGPmfc87Z3dLGvroL2ze9g4S43d6stQK5QdLelY4H3AkelN4q3AI8B/A++OiKeHOPa3gEtIlrss5o6IOG7EUZs1uFJz34/411t4+oWXAbj14Wc4/6e/5pPHzh10zIBc5zl3xTquvnf9jsdLF87mvBMOzowz7zGtceS6RzDqg0tzgBsi4tUZzx0F/NNIOwLfI7BG17W5hyPPv40tW3dmu0ya0MJd57wh1/DGitUdnHXd4AmAxwHbCx5PHC9A9Gwb+jztnd288aKVg4637H1HcNqVv+gXZ95jWv0Z6h5BnqyhSloo6QFJN0o6qNhGks6U1CapbePGjdWMz6zsSs19v2Fd9oV4qP/jcWphXEv/xqzzrOnYRJaVjz47KM68x7TGUsuOYDWwX0QcAnwFWFFsw4i4PCIWRMSCGTNmVC1As0ooNff9uIP3ymzXgIv77dHL9t7+jVnnmT9rKlkWHzB9UJx5j2mNpWYdQUS8UJCV9BNggqTptYrHrFpKzX0/8dBZ7L3HLv3a9t5jFy46ZX6/Y1645BAuXDL8eVpnTmHpwtn92pYunM2C/acNijPvMa2x5K0jGAfMpODmckSsL77Hjv3mUPwewV5AZ0SEpMOBZSRXCEMG5HsENlaUmvu+YnUHN6x7muMO3osTD51V9Jh5z9Pe2c2ajk3MnzWV1plThozTefuNZ6h7BHlWKPsw8Gmgk50rlEVEzBtmv+8CRwHT030/DUxId75U0oeA9wPbgJeAj0fE3cO9GHcEZmYjV+oKZR8FDoyIrpGcNCJOHeb5S0jSS80aVrW+GRf7tp4nnqx9G+UbfaPE2ejydAQdwO8rHYhZo6nWPPjFcvzzxNP2+HOD9j1sv1c0RB2A1xmonqJDQ5I+nv56EHAgSRFZ4VKVX6p4dBk8NGT1oNRagLyK5fjf+rHFg8bxB8YzcXxLv3z/Yu31WAdQrfe3mYy2jmBK+rMeuAXYpaBtcrmDNGsk1ZoHv1iO/8D2rHiKGVBuUJd1AF5noLqGmmLiswCSTo6I/yp8TtLJlQ7MrJ5Vax78Yjn+A9uz4ilm4BhAPdYBeJ2B6srzFeL/5GwzaxrVmge/WI7/wBvGWfFcuGRe5r6NUAfgdQaqa6h7BMcAxwJvB75f8NQewNyIOLzy4Q3mewRWT5w1VFmNEmcjGFUdgaRDSNYm/ixQOEV0N3B7unZx1bkjMDMbuVHVEUTEA8ADkq6NiK0Vi86sxsr9rbPtsS5WPvosiw+YzoL9pwHZ38qLfcvP+w3eFb9WLkOtULaO9L6SNDDPAIarLDZrBOXOVT/tG/dyZ3tSe3nxbe0sap3G/tN3H5TLT5BZG5BVM5CV95+1JoDXCbDRGmpoaL/01w+mf347/fOdwIsRcV6FY8vkoSErl3Lnqrc91sWSy+4ddTxXLD2M9169alD7LuPEy9t3/j+dOL4FCHq2FbZ5nQAb2qjqCCLiiYh4AjgyIs6OiHXpzyeBv65UsGbVUu5c9ZWPPltSPDc/1JnZPvCKfFyLGCevE2Dlkyd9dHdJr+t7IOkvgd2H2N6sIZQ7V33xAaXNov7muTMz2wdetW/vDbaH1wmw8snTEbwX+KqkxyU9DnwN+PuKRmVWBeXOVV+w/zQWtU7r17aodVpmLn9W29Fz98ps//eTDxlUH3DhkoFtXifARi/3msWS9ki3r+kEdL5HYOXmrCFrBqOtIzgtIq4pmHyuH086Z2bWOEY76VzffYApRX7Mml7X5h4e6NhE1+aeIdvy7luObcu5rzWHoQrKLkt/PT8itlQpHrOGkVWDkDeXfyT1C6XUOnhOf8sjz1KV7SRLTd4BrATuquV9Ag8NWT3Inv8/Xy7/SOoXSql18Jz+Vmi0Q0MAREQrcCqwDjiOZNqJNeUN0ayxZNUg5M3lH0n9Qim1Dp7T3/IadqlKSfsCRwKLgEOAB4E7KxyXWV3LqkHYHr0Q/TuCrFz+kdQvlFLr4Dn9La88dQTrgbOAGyNiYUS8NSL+rcJxmdW17Pn/8+Xyj6R+oZRaB8/pb3nluUdwCPA6YDEwG3gU+J+IuKLy4Q3mewRWT0rJ5R9Jzn8p9QGuLTAYZR3BgANMJukMFgGnARERc8oZZF7uCMzMRm5U6xEU7NwGTATuJrk3sDidjM6sbBrhW6sreW2sGrYjAI6JiI0Vj8SaViPkupdSM2BW73LPNVQvPDQ0tjRCrnt2zcDgNQHqLW6zQiXVEZhVUiPkumfWDGSsCVBvcZvllWdoyKxiGiHXPbNmoDdIV3Ldod7iNstrqDWL/3aoHSPiB+UPx5pNX6772QPG2utpeKVYjEBdx22W11DTUH9ziP0iImqyOI3vEYxNjZB946wha2SjSh+NiPdULiSz/qZNnlj3H6RZMTZC3GbDyXWPQNJbgYOASX1tEXHeMPtcSTJJ3TMR8eqM5wV8GTgWeBE4PSJW5w/dzMzKYdisIUmXAn8HfBgQcDKwX45jfwt4yxDPHwMckP6cCfxnjmOaDdLe2c2ytg7aO7vLsh2UfyEYLw5j9SzPFcFfRsQ8SWsj4rOSvggMe6M4IlZKmjPEJicAV0dyk+JeSVMl7R0RT+WK3Aw4d8U6rr53/Y7HSxfO5rwTDh71dlD+hWBceGb1Lk8dQV9i9IuSXglsBfYvw7n3AToKHm9I28xyae/s7vfhDnD1PesHfePPux0k39zPWb6WLVt76e7ZxpatvZy9fG3u5SQH7vvPyx7g7GWjO55ZteTpCG6QNBW4EFgNPA58rwznVkZbZgqTpDMltUlq27jRs11YYk3HplztebeD8i8Ek3exGrNayjM0dEFE9ADLJd1AcsO4HGsYbwBmFTzeF3gya8OIuBy4HJL00TKc28aA+bOm5mrPux2UfyGYvIvVmNVSniuCe/p+iYiedL3ie4bYPq8fA0uVOAL4ve8P2Ei0zpzC0oWz+7UtXTib1plTRrUdlH8hmLyL1ZjV0lAFZXuRjNlfA7yDnUM5ewCXRsSfDXlg6bvAUcB0oBP4NDABICIuTdNHLyHJLHoReE9EDFsp5oIyG6i9s5s1HZuYP2tq5of7SLeD8i8E48Izq7VRLUwj6d3A6cACoPCT9wXgqlpNMeGOwMxs5EZbWXwVcJWkkyJiecWiMzOzmspzj+AuSVdIuhFA0lxJ761wXGZmViV5OoJvAjcBr0wf/wY4q2IRmZlZVeXpCKZHxHVAL0BEbAO2VzQqMzOrmjwdwR8kTSMt9upL9axoVGZmVjV5Cso+TpLz/ypJdwEzgCUVjcrMzKpm2I4gIlZL+ivgQJJagkciYmvFIzMzs6oYtiOQNAn4APA6kuGhOyRdGhHlmGbCzMxqLM/Q0NVAN/CV9PGpwLdJ1iUwM7MGl6cjODAiDil4fLukByoVkJmZVVeerKFfpplCAEh6LXBX5UIyM7NqynNF8FqSWUL7VvaYDTwsaR0QETGvYtGZmVnF5ekIhlp32MzMGlye9NEnqhGImZnVRp57BGZmNoa5IzAza3LuCMzMmpw7AjOzJueOwMysybkjMDNrcu4IzMyanDsCM7Mm547AzKzJuSMwM2ty7giqpGtzDw90bKJrc0+tQzEz6yfPpHNWoh+t+R3nLF/LhJYWtvb2csFJ8zh+/j61DsvMDPAVQcV1be7hnOVr2bK1l+6ebWzZ2svZy9f6ysDM6oY7ggrb8PxLTGjp/zZPaGlhw/Mv1SgiM7P+3BFU2L577srW3t5+bVt7e9l3z11rFJGZWX/uCCps2uSJXHDSPCZNaGHKxPFMmtDCBSfNY9rkibUOzcwM8M3iqjh+/j4c2TqdDc+/xL577upOwMzqijuCKpk2eaI7ADOrSxUdGpL0FkmPSGqX9MmM50+XtFHSmvTnjErGU29cW2Bm9aBiVwSSxgFfBd4EbADul/TjiHhowKbfj4gPVSqOeuXaAjOrF5W8IjgcaI+I30bEy8D3gBMqeL6G4doCM6snlewI9gE6Ch5vSNsGOknSWknLJM3KOpCkMyW1SWrbuHFjJWKtKtcWmFk9qWRHoIy2GPD4emBORMwDbgWuyjpQRFweEQsiYsGMGTPKHGb1ubbAzOpJJTuCDUDhN/x9gScLN4iIrojoGw/5OnBYBeOpG64tMLN6Usn00fuBAyTtD/wOOAV4R+EGkvaOiKfSh8cDD1cwnrri2gIzqxcV6wgiYpukDwE3AeOAKyPiQUnnAW0R8WPgI5KOB7YBzwGnVyqeeuTaAjOrB4oYOGxf3xYsWBBtbW21DsPMrKFIWhURC7Ke81xDOeUt/mp7rIsv3fwIbY91Dbt/3mO68MzMKslTTOSQt/jrtG/cy53tSQdw8W3tLGqdxrfPOCJz/4Bcx3ThmZlVmoeGhtG1uYcjz7+NLVt3pntOmtDCXee8od/4fttjXSy57N5B+1+x9DA++N1f9tt/4vgWIOjZtvO9zzpm3nObmQ3HQ0MlyFv8tfLRZzP3v/mhzkH7j2sR4zT8MV14ZmbV4I5gGHmLvxYfMD1z/zfPnTlo/+29wfYY/pguPDOzanBHMIy8xV8L9p/GotZp/doWtU7j6Ll7Ddr/wiXzuHDJIcMe04VnZlYNvkeQU9fmnlzFX22PdbHy0WdZfMB0Fuw/bcj98x4z73ZmZsUMdY/AHYGZWRPwzeIyaO/sZllbB+2d3TvasmoGRpLz7/oAM6sHriPI4dwV67j63vU7HsqEKdAAAAqbSURBVC9dOJvfbvzDoJqBJQtm5c75d32AmdULDw0No72zmzdetDLXtruMEy9vH7o2AFwfYGbV56GhEqzp2DTqfYvl/Ls+wMzqiTuCYcyfNXXU+xbL+Xd9gJnVE3cEw2idOYWlC2f3a1u6cHZmzcC/nzx8bQC4PsDM6ovvEeTU3tnNmo5NzJ81ldaZU4DsmoGR5Py7PsDMqsV1BGZmTc43i1N58/azagZ+9tDTnLPsAX720NM72i666WGOuvB2Lrpp5wqbl93+KMd8eSWX3f5ov2OuWN3BGVfdz4rVHSOOx/UGZlZJTXNFkDdvP6tm4N7fdvGbzj/saDtw5u789pk/sLXgrZsgGD9OvFQwtfSu48XDnzuWI/71Fp5+4eUd7XvvsQufPHau1yMws6pp+qGhvHn7I6kZyOttr/5jrv/VM4PaxwHbCx57PQIzq6SmHxrKm7dfSs1AMbf9JnudglD/x16PwMxqpSk6grx5+6XUDBTzhj/NXqdAAy7EvB6BmdVKU3QEefP2i9UMHDhz935tB87cnQkDv9EruSdQaNfx4iun/QV777FLv/a999iFi06Z7/UIzKwuNMU9gj558/azagZ+9tDT3PxQJ2+eO5Oj5+4FJFlDP1r7NCfM24uP/fWfA0nW0Iq1T3HivL153+sP2HHMFas7uGHd0xx38F6ceOisEcXjegMzK1XT3yw2M2t2TX+zeCil5Ohn1RtktZmZ1bOmXo+glBz9rHoDgkFt551wcNnjNjMrp6a9Iuja3MM5y9eyZWsv3T3b2LK1l7OXr811ZdDe2d3vAx/g6nvWZ7b5ysDM6l3TdgSl5OiPpN6gErUJZmbl1LQdQSk5+iOpN6hEbYKZWTk1bUdQSo5+sXqDrLa+9FMzs3rV9OmjpeToZ9UbZLWZmdXaUOmjTZ01BMmVwWiLtFpnThn0YZ/VZmZWzyo6NCTpLZIekdQu6ZMZz0+U9P30+fskzalkPGZmNljFOgJJ44CvAscAc4FTJc0dsNl7gecjohW4CDi/UvGYmVm2Sl4RHA60R8RvI+Jl4HvACQO2OQG4Kv19GXC0pAHTuZmZWSVVsiPYB+goeLwhbcvcJiK2Ab8Hpg08kKQzJbVJatu4cWOFwjUza06V7AiyvtkPTFHKsw0RcXlELIiIBTNmzChLcGZmlqhkR7ABmFXweF/gyWLbSBoP/BHwXAVjMjOzASqZPno/cICk/YHfAacA7xiwzY+BdwP3AEuA22KYwoZVq1Y9K+mJEuKaDmSvH9l4xtJrgbH1esbSa4Gx9XrG0muB/K9nv2JPVKwjiIhtkj4E3ESyVvuVEfGgpPOAtoj4MXAF8G1J7SRXAqfkOG5JY0OS2ooVVTSasfRaYGy9nrH0WmBsvZ6x9FqgPK+nogVlEfET4CcD2s4t+H0LcHIlYzAzs6E17VxDZmaWaMaO4PJaB1BGY+m1wNh6PWPptcDYej1j6bVAGV5Pw006Z2Zm5dWMVwRmZlbAHYGZWZNrmo5A0pWSnpH0q1rHUipJsyTdLulhSQ9K+mitYxotSZMk/ULSA+lr+WytYyqVpHGSfinphlrHUipJj0taJ2mNpPItBFIjkqZKWibp1+n/n4W1jmk0JB2Y/p30/bwg6axRH69Z7hFIWgxsBq6OiFfXOp5SSNob2DsiVkuaAqwCToyIh2oc2oilkwzuHhGbJU0A7gQ+GhH31ji0UZP0cWABsEdEHFfreEoh6XFgQUSMiQIsSVcBd0TENyTtAuwWEQ29sHg60/PvgNdGxKiKbZvmiiAiVjJGpq+IiKciYnX6ezfwMIMn9GsIkdicPpyQ/jTstxNJ+wJvBb5R61isP0l7AItJClmJiJcbvRNIHQ3872g7AWiijmCsShfzeQ1wX20jGb10KGUN8AxwS0Q07GsB/gM4G+itdSBlEsDNklZJOrPWwZToT4CNwDfTobtvSNq91kGVwSnAd0s5gDuCBiZpMrAcOCsiXqh1PKMVEdsjYj7JxISHS2rIoTtJxwHPRMSqWsdSRkdGxKEkC0x9MB1ibVTjgUOB/4yI1wB/AAatnNhI0uGt44H/KuU47ggaVDqevhy4NiJ+UOt4yiG9TP858JYahzJaRwLHp+Pq3wPeIOma2oZUmoh4Mv3zGeCHJAtONaoNwIaCK85lJB1DIzsGWB0RnaUcxB1BA0pvsF4BPBwRX6p1PKWQNEPS1PT3XYE3Ar+ubVSjExH/JyL2jYg5JJfrt0XEaTUOa9Qk7Z4mI5AOobwZaNisu4h4GuiQdGDadDTQcAkWA5xKicNCUOFJ5+qJpO8CRwHTJW0APh0RV9Q2qlE7EngXsC4dWwf4VDrJX6PZG7gqzXxoAa6LiIZPuxwjZgI/TFePHQ98JyJ+WtuQSvZh4Np0SOW3wHtqHM+oSdoNeBPwvpKP1Szpo2Zmls1DQ2ZmTc4dgZlZk3NHYGbW5NwRmJk1OXcEZmZNzh2BjTmSTpf0yhzbfUvSkrztZYjrUwW/z8k7E66ksyQtLcP5PySpYdMlrXLcEdhYdDowbEdQA58afpP+JI0H/h74ThnOfyXwkTIcx8YYdwRW19Jvzr+WdJWktelc8rulzx0m6X/SCdFukrR3+k1+AUnR0BpJu0o6V9L9kn4l6fK0Mjvv+QedI23/uaTz07UUfiNpUdq+m6Tr0li/L+k+SQskfQHYNY3p2vTw4yR9PV2H4ea0snqgN5BMIbAtPX6rpFuVrN+wWtKrJB2VxnhdGssXJL0zjW2dpFcBRMSLwOOSGnmaCKsAdwTWCA4ELo+IecALwAfSuZa+AiyJiMNIvu1+PiKWAW3AOyNifkS8BFwSEX+RrkOxK5BrjYBi5yjYZHxEHA6cBXw6bfsA8Hwa678AhwFExCeBl9KY3pluewDw1Yg4CNgEnJQRxpEk6030uTbd5xDgL4Gn0vZDgI8CB5NUnf9pGts3SKpp+7QBi/K8fmseTTPFhDW0joi4K/39GpLhjZ8CrwZuSb/gj2Pnh+JAr5d0NrAb8ArgQeD6HOc9cJhz9E32twqYk/7+OuDLABHxK0lrhzj+YxHRN0VI4TEK7U2y3gTpvD/7RMQP0+NvSdsB7o+Ip9LH/wvcnO6/Dnh9wfGeAf5siJisCbkjsEYwcB6UAAQ8GBFDLjUoaRLwNZJVtjokfQaYlPO8w52jJ/1zOzv/L+UedirYv+8YWUNDL7Ez3qGOXXis3oLHvfT/fz4pPabZDh4askYwWzvXlj2VZDnLR4AZfe2SJkg6KN2mG5iS/t73Ifpsun7DSLKBhjpHMXcCb0+3n0syVNNnazrcNBIPA60A6ZoTGySdmB5/Yt/9khH4Uxp4BlGrDHcE1ggeBt6dDrO8gmRhkZdJPtTPl/QAsIZkzBzgW8Cl6cysPcDXSYZIVgD35z3pMOco5mskncda4BxgLfD79LnLgbUFN4vzuJFkecU+7wI+kh7/bmCvERwLknsOt45wHxvjPPuo1TUlS3HekN7orXvpdNoTImJLmq3zM5Ibty+XcMwfAmdHxKMlxvYa4OMR8a5SjmNjj+8RmJXXbsDt6RCQgPeX0gmkPkly07ikjgCYDvy/Eo9hY5CvCMzMmpzvEZiZNTl3BGZmTc4dgZlZk3NHYGbW5NwRmJk1uf8Ps7mI477JqWAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "iris.plot('petal length (cm)','petal width (cm)', kind = 'scatter', title = 'Petal Length vs. Petal Width')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. The data below is from Motor Trend magazine and contains data on different models of cars from multiple manufacturers.  We have plotted the measurements for horsepower on the horizontal axis and miles per gallon on the vertical axis.  What kind of function do you think would be an appropriate model for this?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "cars = pd.read_csv('https://raw.githubusercontent.com/jfkoehler/calc_spring_2020/master/notebooks/data/mtcars.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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>Car</th>\n",
       "      <th>mpg</th>\n",
       "      <th>cyl</th>\n",
       "      <th>disp</th>\n",
       "      <th>hp</th>\n",
       "      <th>drat</th>\n",
       "      <th>wt</th>\n",
       "      <th>qsec</th>\n",
       "      <th>vs</th>\n",
       "      <th>am</th>\n",
       "      <th>gear</th>\n",
       "      <th>carb</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Mazda RX4</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.620</td>\n",
       "      <td>16.46</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>Mazda RX4 Wag</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.875</td>\n",
       "      <td>17.02</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>Datsun 710</td>\n",
       "      <td>22.8</td>\n",
       "      <td>4</td>\n",
       "      <td>108.0</td>\n",
       "      <td>93</td>\n",
       "      <td>3.85</td>\n",
       "      <td>2.320</td>\n",
       "      <td>18.61</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>Hornet 4 Drive</td>\n",
       "      <td>21.4</td>\n",
       "      <td>6</td>\n",
       "      <td>258.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.08</td>\n",
       "      <td>3.215</td>\n",
       "      <td>19.44</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>Hornet Sportabout</td>\n",
       "      <td>18.7</td>\n",
       "      <td>8</td>\n",
       "      <td>360.0</td>\n",
       "      <td>175</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.440</td>\n",
       "      <td>17.02</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Car   mpg  cyl   disp   hp  drat     wt   qsec  vs  am  gear  \\\n",
       "0          Mazda RX4  21.0    6  160.0  110  3.90  2.620  16.46   0   1     4   \n",
       "1      Mazda RX4 Wag  21.0    6  160.0  110  3.90  2.875  17.02   0   1     4   \n",
       "2         Datsun 710  22.8    4  108.0   93  3.85  2.320  18.61   1   1     4   \n",
       "3     Hornet 4 Drive  21.4    6  258.0  110  3.08  3.215  19.44   1   0     3   \n",
       "4  Hornet Sportabout  18.7    8  360.0  175  3.15  3.440  17.02   0   0     3   \n",
       "\n",
       "   carb  \n",
       "0     4  \n",
       "1     4  \n",
       "2     1  \n",
       "3     1  \n",
       "4     2  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fac4597ac50>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cars.plot('hp', 'mpg', kind = 'scatter', title = 'Horsepower vs. Miles Per Gallon')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. The data below comes from the gapminder organization and contains data on countries GDP, Life Expectancy, and Population.  We have plotted the data from life expectancy in 2007 on the horizontal axis and GDP on the vertical axis.  What kind of relationship would be an appropriate model for this relationship?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "gapminder = pd.read_csv('https://raw.githubusercontent.com/jfkoehler/calc_spring_2020/master/notebooks/data/gapminder_all.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "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>continent</th>\n",
       "      <th>country</th>\n",
       "      <th>gdpPercap_1952</th>\n",
       "      <th>gdpPercap_1957</th>\n",
       "      <th>gdpPercap_1962</th>\n",
       "      <th>gdpPercap_1967</th>\n",
       "      <th>gdpPercap_1972</th>\n",
       "      <th>gdpPercap_1977</th>\n",
       "      <th>gdpPercap_1982</th>\n",
       "      <th>gdpPercap_1987</th>\n",
       "      <th>...</th>\n",
       "      <th>pop_1962</th>\n",
       "      <th>pop_1967</th>\n",
       "      <th>pop_1972</th>\n",
       "      <th>pop_1977</th>\n",
       "      <th>pop_1982</th>\n",
       "      <th>pop_1987</th>\n",
       "      <th>pop_1992</th>\n",
       "      <th>pop_1997</th>\n",
       "      <th>pop_2002</th>\n",
       "      <th>pop_2007</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Africa</td>\n",
       "      <td>Algeria</td>\n",
       "      <td>2449.008185</td>\n",
       "      <td>3013.976023</td>\n",
       "      <td>2550.816880</td>\n",
       "      <td>3246.991771</td>\n",
       "      <td>4182.663766</td>\n",
       "      <td>4910.416756</td>\n",
       "      <td>5745.160213</td>\n",
       "      <td>5681.358539</td>\n",
       "      <td>...</td>\n",
       "      <td>11000948.0</td>\n",
       "      <td>12760499.0</td>\n",
       "      <td>14760787.0</td>\n",
       "      <td>17152804.0</td>\n",
       "      <td>20033753.0</td>\n",
       "      <td>23254956.0</td>\n",
       "      <td>26298373.0</td>\n",
       "      <td>29072015.0</td>\n",
       "      <td>31287142</td>\n",
       "      <td>33333216</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>Africa</td>\n",
       "      <td>Angola</td>\n",
       "      <td>3520.610273</td>\n",
       "      <td>3827.940465</td>\n",
       "      <td>4269.276742</td>\n",
       "      <td>5522.776375</td>\n",
       "      <td>5473.288005</td>\n",
       "      <td>3008.647355</td>\n",
       "      <td>2756.953672</td>\n",
       "      <td>2430.208311</td>\n",
       "      <td>...</td>\n",
       "      <td>4826015.0</td>\n",
       "      <td>5247469.0</td>\n",
       "      <td>5894858.0</td>\n",
       "      <td>6162675.0</td>\n",
       "      <td>7016384.0</td>\n",
       "      <td>7874230.0</td>\n",
       "      <td>8735988.0</td>\n",
       "      <td>9875024.0</td>\n",
       "      <td>10866106</td>\n",
       "      <td>12420476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>Africa</td>\n",
       "      <td>Benin</td>\n",
       "      <td>1062.752200</td>\n",
       "      <td>959.601080</td>\n",
       "      <td>949.499064</td>\n",
       "      <td>1035.831411</td>\n",
       "      <td>1085.796879</td>\n",
       "      <td>1029.161251</td>\n",
       "      <td>1277.897616</td>\n",
       "      <td>1225.856010</td>\n",
       "      <td>...</td>\n",
       "      <td>2151895.0</td>\n",
       "      <td>2427334.0</td>\n",
       "      <td>2761407.0</td>\n",
       "      <td>3168267.0</td>\n",
       "      <td>3641603.0</td>\n",
       "      <td>4243788.0</td>\n",
       "      <td>4981671.0</td>\n",
       "      <td>6066080.0</td>\n",
       "      <td>7026113</td>\n",
       "      <td>8078314</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>Africa</td>\n",
       "      <td>Botswana</td>\n",
       "      <td>851.241141</td>\n",
       "      <td>918.232535</td>\n",
       "      <td>983.653976</td>\n",
       "      <td>1214.709294</td>\n",
       "      <td>2263.611114</td>\n",
       "      <td>3214.857818</td>\n",
       "      <td>4551.142150</td>\n",
       "      <td>6205.883850</td>\n",
       "      <td>...</td>\n",
       "      <td>512764.0</td>\n",
       "      <td>553541.0</td>\n",
       "      <td>619351.0</td>\n",
       "      <td>781472.0</td>\n",
       "      <td>970347.0</td>\n",
       "      <td>1151184.0</td>\n",
       "      <td>1342614.0</td>\n",
       "      <td>1536536.0</td>\n",
       "      <td>1630347</td>\n",
       "      <td>1639131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>Africa</td>\n",
       "      <td>Burkina Faso</td>\n",
       "      <td>543.255241</td>\n",
       "      <td>617.183465</td>\n",
       "      <td>722.512021</td>\n",
       "      <td>794.826560</td>\n",
       "      <td>854.735976</td>\n",
       "      <td>743.387037</td>\n",
       "      <td>807.198586</td>\n",
       "      <td>912.063142</td>\n",
       "      <td>...</td>\n",
       "      <td>4919632.0</td>\n",
       "      <td>5127935.0</td>\n",
       "      <td>5433886.0</td>\n",
       "      <td>5889574.0</td>\n",
       "      <td>6634596.0</td>\n",
       "      <td>7586551.0</td>\n",
       "      <td>8878303.0</td>\n",
       "      <td>10352843.0</td>\n",
       "      <td>12251209</td>\n",
       "      <td>14326203</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 38 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "  continent       country  gdpPercap_1952  gdpPercap_1957  gdpPercap_1962  \\\n",
       "0    Africa       Algeria     2449.008185     3013.976023     2550.816880   \n",
       "1    Africa        Angola     3520.610273     3827.940465     4269.276742   \n",
       "2    Africa         Benin     1062.752200      959.601080      949.499064   \n",
       "3    Africa      Botswana      851.241141      918.232535      983.653976   \n",
       "4    Africa  Burkina Faso      543.255241      617.183465      722.512021   \n",
       "\n",
       "   gdpPercap_1967  gdpPercap_1972  gdpPercap_1977  gdpPercap_1982  \\\n",
       "0     3246.991771     4182.663766     4910.416756     5745.160213   \n",
       "1     5522.776375     5473.288005     3008.647355     2756.953672   \n",
       "2     1035.831411     1085.796879     1029.161251     1277.897616   \n",
       "3     1214.709294     2263.611114     3214.857818     4551.142150   \n",
       "4      794.826560      854.735976      743.387037      807.198586   \n",
       "\n",
       "   gdpPercap_1987  ...    pop_1962    pop_1967    pop_1972    pop_1977  \\\n",
       "0     5681.358539  ...  11000948.0  12760499.0  14760787.0  17152804.0   \n",
       "1     2430.208311  ...   4826015.0   5247469.0   5894858.0   6162675.0   \n",
       "2     1225.856010  ...   2151895.0   2427334.0   2761407.0   3168267.0   \n",
       "3     6205.883850  ...    512764.0    553541.0    619351.0    781472.0   \n",
       "4      912.063142  ...   4919632.0   5127935.0   5433886.0   5889574.0   \n",
       "\n",
       "     pop_1982    pop_1987    pop_1992    pop_1997  pop_2002  pop_2007  \n",
       "0  20033753.0  23254956.0  26298373.0  29072015.0  31287142  33333216  \n",
       "1   7016384.0   7874230.0   8735988.0   9875024.0  10866106  12420476  \n",
       "2   3641603.0   4243788.0   4981671.0   6066080.0   7026113   8078314  \n",
       "3    970347.0   1151184.0   1342614.0   1536536.0   1630347   1639131  \n",
       "4   6634596.0   7586551.0   8878303.0  10352843.0  12251209  14326203  \n",
       "\n",
       "[5 rows x 38 columns]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gapminder.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fabd0024410>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gapminder.plot('lifeExp_2007', 'gdpPercap_2007', kind = 'scatter', title = 'Life Expectancy vs. GDP')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4. The data below comes from the Central Park weather station for the maximum temperature on each day since 1870.  We have plotted the most recent five years of the data where the date is on the horizontal axis and temperature on vertical.  What kind of a function would be the right model for this data?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "temps = pd.read_csv('https://raw.githubusercontent.com/jfkoehler/calc_spring_2020/master/notebooks/data/2017018.csv', usecols=['DATE', 'TMAX'], \n",
    "                    parse_dates = ['DATE'], index_col='DATE')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "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>TMAX</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DATE</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1870-01-01</td>\n",
       "      <td>43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1870-01-02</td>\n",
       "      <td>54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1870-01-03</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1870-01-04</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1870-01-05</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            TMAX\n",
       "DATE            \n",
       "1870-01-01    43\n",
       "1870-01-02    54\n",
       "1870-01-03    41\n",
       "1870-01-04    35\n",
       "1870-01-05    34"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temps.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Temperatures in Central Park')"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "temps['2015':].plot()\n",
    "plt.title('Temperatures in Central Park')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Models\n",
    "\n",
    "For each of the questions below, you are given a model that your team of data scientists have developed based on a given dataset.  You are asked three main questions:\n",
    "\n",
    "1. Evaluate model at given value.\n",
    "2. Compare model prediction to actual value.\n",
    "3. Discuss whether the model is a good model for the data and why or why not."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 5: Iris Data\n",
    "\n",
    "- **Model**: petal length = petal width $\\times$ .7 or $f(x) = .7x$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the example observation below to compare the offered model to the real data.  How close was your prediction?  Was this good or bad?  Would you recommend this model for other data?  Explain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sepal length (cm)    4.6\n",
       "sepal width (cm)     3.1\n",
       "petal length (cm)    1.5\n",
       "petal width (cm)     0.2\n",
       "Name: 3, dtype: float64"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.iloc[3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 6: Cars\n",
    "\n",
    "- **Model**: mpg = hp/10 or $f(x) = \\frac{1}{10} x$ . \n",
    "\n",
    "Same questions above using the test point below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Car     Dodge Challenger\n",
       "mpg                 15.5\n",
       "cyl                    8\n",
       "disp                 318\n",
       "hp                   150\n",
       "drat                2.76\n",
       "wt                  3.52\n",
       "qsec               16.87\n",
       "vs                     0\n",
       "am                     0\n",
       "gear                   3\n",
       "carb                   2\n",
       "Name: 21, dtype: object"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars.iloc[21]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 7: Textbook Problems\n",
    "\n",
    "The questions below come from the [OpenStax](https://openstax.org/books/calculus-volume-1/pages/1-chapter-review-exercises) Calculus text.  Feel free to review the chapters for additional examples of functions.  Answer the questions below:\n",
    "\n",
    "------\n",
    "\n",
    "For the following problems, consider a restaurant owner who wants to sell T-shirts advertising his brand. He recalls that there is a fixed cost and variable cost, although he does not remember the values. He does know that the T-shirt printing company charges $\\$440$ for 20 shirts and $1000 for 100 shirts.\n",
    "\n",
    "a. Find the equation  $C = f(x)$  that describes the total cost as a function of number of shirts and b. determine how many shirts he must sell to break even if he sells the shirts for $10 each.\n",
    "\n",
    "\n",
    "b. Determine how many shirts the owner can buy if he has $8000 to spend.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------\n",
    "\n",
    "For the following problems, consider the population of Ocean City, New Jersey, which is cyclical by season.\n",
    "\n",
    "a. The population can be modeled by  \n",
    "\n",
    "$$𝑃(𝑡)=82.5−67.5cos[(𝜋/6)𝑡]$$\n",
    "\n",
    ",  where  𝑡  is time in months  (𝑡=0  represents January 1) and  𝑃  is population (in thousands). During a year, in what intervals is the population less than 20,000? During what intervals is the population more than 140,000?\n",
    "\n",
    "b. In reality, the overall population is most likely increasing or decreasing throughout each year. Let’s reformulate the model as  \n",
    "\n",
    "$$𝑃(𝑡)=82.5−67.5cos[(𝜋/6)𝑡]+𝑡$$\n",
    "\n",
    ",  where  𝑡  is time in months ( 𝑡=0  represents January 1) and  𝑃  is population (in thousands). When is the first time the population reaches 200,000?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 8: Twitter\n",
    "\n",
    "Look over the following twitter post from Grant Sanderson (creator of the [3blue1brown](https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw) youtube channel): \n",
    "\n",
    "https://twitter.com/3blue1brown/status/1002248647172472832?lang=en .  \n",
    "\n",
    "What do you think the probability of getting between 490,000 and 510,000 heads is?\n",
    "\n",
    "Read some of the responses to the post.  Anything of interest?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 9: The Triangle\n",
    "\n",
    "<center>\n",
    "    <img src = https://wikimedia.org/api/rest_v1/media/math/render/svg/23050fcb53d6083d9e42043bebf2863fa9746043 />\n",
    "    </center>"
   ]
  },
  {
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    "1. Can you find a pattern that is a linear pattern in the triangle?\n",
    "2. Can you find a quadratic pattern in the triangle?\n",
    "3. Add the values in the rows shown above.  Is there a pattern here?  "
   ]
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