{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 02.1\n",
    "\n",
    "Create a function that receives two inputs a and b, and returns the product of the a decimal of pi and the b decimal of pi.\n",
    "\n",
    "```\n",
    "i.e, \n",
    "pi = 3.14159\n",
    "if a = 2 and b = 4\n",
    "result = 4 * 5\n",
    "result = 20\n",
    "```\n",
    "\n",
    "Caveats:\n",
    "- a and b are between 1 and 15\n",
    "- decimals positions 1 and 2 are 1 and 4, respectively. (remember that python start indexing in 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from math import pi\n",
    "def mult_dec_pi(a, b):\n",
    "    \n",
    "    # Add the solution here\n",
    "    \n",
    "    result = ''\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mult_dec_pi(a=2, b=4)\n",
    "# 20.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mult_dec_pi(a=5, b=10)\n",
    "# 45.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mult_dec_pi(a=14, b=1)\n",
    "# 9.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mult_dec_pi(a=6, b=8)\n",
    "# 10.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Bonus\n",
    "mult_dec_pi(a=16, b=4)\n",
    "# 'Error'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 02.2\n",
    "\n",
    "Using the given dataset. Estimate a linear regression between Employed and GNP.\n",
    "\n",
    "$$Employed = b_0 + b_1 * GNP $$\n",
    "\n",
    "$$\\hat b = (X^TX)^{-1}X^TY$$\n",
    "$$Y = Employed$$\n",
    "$$X = [1  \\quad GNP]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fa5f2357a20>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5f497ac50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "# Import data\n",
    "raw_data = \"\"\"\n",
    "Year,Employed,GNP\n",
    "1947,60.323,234.289\n",
    "1948,61.122,259.426\n",
    "1949,60.171,258.054\n",
    "1950,61.187,284.599\n",
    "1951,63.221,328.975\n",
    "1952,63.639,346.999\n",
    "1953,64.989,365.385\n",
    "1954,63.761,363.112\n",
    "1955,66.019,397.469\n",
    "1956,67.857,419.18\n",
    "1957,68.169,442.769\n",
    "1958,66.513,444.546\n",
    "1959,68.655,482.704\n",
    "1960,69.564,502.601\n",
    "1961,69.331,518.173\n",
    "1962,70.551,554.894\"\"\"\n",
    "\n",
    "data = []\n",
    "for line in raw_data.splitlines()[2:]:\n",
    "    words = line.split(',')\n",
    "    data.append(words)\n",
    "data = np.array(data, dtype=np.float)\n",
    "n_obs = data.shape[0]\n",
    "plt.plot(data[:, 2], data[:, 1], 'bo')\n",
    "plt.xlabel(\"GNP\")\n",
    "plt.ylabel(\"Employed\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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