{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Correlação"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.preprocessing import normalize\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "capt4.ipynb               inferencia.ipynb            pesos-alturas.csv\r\n",
      "capt9.ipynb               inflacao.csv                Primeiro.ipynb\r\n",
      "dolar.csv                 LinearRegression.ipynb      Segundo.ipynb\r\n",
      "ds-env.yml                mod-preditivo.csv           Untitled.ipynb\r\n",
      "inferencia (cópia).ipynb  mod-preditivo-original.csv\r\n"
     ]
    }
   ],
   "source": [
    "ls"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fonte: IPEA DATA\n",
    "\n",
    "Taxa de desemprego aberto na RMSP\n",
    "Frequência: Mensal de 1984.12 até 2017.08\n",
    "Fonte: Fundação Sistema Estadual de Análise de Dados, Pesquisa de Emprego e Desemprego (Seade/PED)\n",
    "Unidade: (%)\n",
    "Comentário: Quadro: Taxas de desemprego, por tipo - Região Metropolitana de São Paulo, município de São Paulo e demais municípios da Região Metropolitana de São Paulo. In: http://www.seade.gov.br . Obs.: Região Metropolitana de São Paulo (RMSP). Não inclui desemprego oculto (trabalho precário e desemprego por desalento).\n",
    "Atualizado em: 02/10/2017\n",
    "\n",
    "\n",
    "Taxa de câmbio comercial para compra: real (R$) / dólar americano (US$) - média\n",
    "Frequência: Mensal de 1953.01 até 2017.10\n",
    "Fonte: Banco Central do Brasil, Boletim, Seção Balanço de Pagamentos (Bacen / Boletim / BP)\n",
    "Unidade: R$\n",
    "Comentário: Quadro: Taxas de câmbio do real. Obs.: Cotações para contabilidade.\n",
    "Atualizado em: 01/11/2017"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dolar = pd.read_csv('dolar.csv')\n",
    "desemprego = pd.read_csv('desemprego.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Periodo</th>\n",
       "      <th>Dolar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2007.08</td>\n",
       "      <td>1.9652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2007.09</td>\n",
       "      <td>1.8988</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2007.10</td>\n",
       "      <td>1.8002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2007.11</td>\n",
       "      <td>1.7691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2007.12</td>\n",
       "      <td>1.7852</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Periodo   Dolar\n",
       "0  2007.08  1.9652\n",
       "1  2007.09  1.8988\n",
       "2  2007.10  1.8002\n",
       "3  2007.11  1.7691\n",
       "4  2007.12  1.7852"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dolar.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "        text-align: right;\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Periodo</th>\n",
       "      <th>Dolar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>121.000000</td>\n",
       "      <td>121.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2012.189091</td>\n",
       "      <td>96.254918</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.943821</td>\n",
       "      <td>415.140965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2007.080000</td>\n",
       "      <td>1.563100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2010.020000</td>\n",
       "      <td>1.789014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2012.080000</td>\n",
       "      <td>2.188057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2015.020000</td>\n",
       "      <td>3.135572</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2017.080000</td>\n",
       "      <td>2313.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Periodo        Dolar\n",
       "count   121.000000   121.000000\n",
       "mean   2012.189091    96.254918\n",
       "std       2.943821   415.140965\n",
       "min    2007.080000     1.563100\n",
       "25%    2010.020000     1.789014\n",
       "50%    2012.080000     2.188057\n",
       "75%    2015.020000     3.135572\n",
       "max    2017.080000  2313.000000"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dolar.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dolar.loc[dolar.Dolar > 1000, ['Dolar']] = dolar['Dolar'] / 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style>\n",
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       "        text-align: right;\n",
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       "\n",
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       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Periodo</th>\n",
       "      <th>Dolar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>121.000000</td>\n",
       "      <td>121.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2012.189091</td>\n",
       "      <td>2.324150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.943821</td>\n",
       "      <td>0.682049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2007.080000</td>\n",
       "      <td>1.563100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2010.020000</td>\n",
       "      <td>1.779000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2012.080000</td>\n",
       "      <td>2.060100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2015.020000</td>\n",
       "      <td>2.815839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2017.080000</td>\n",
       "      <td>4.051715</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Periodo       Dolar\n",
       "count   121.000000  121.000000\n",
       "mean   2012.189091    2.324150\n",
       "std       2.943821    0.682049\n",
       "min    2007.080000    1.563100\n",
       "25%    2010.020000    1.779000\n",
       "50%    2012.080000    2.060100\n",
       "75%    2015.020000    2.815839\n",
       "max    2017.080000    4.051715"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dolar.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Periodo</th>\n",
       "      <th>Desemprego</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2007.08</td>\n",
       "      <td>10.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2007.09</td>\n",
       "      <td>10.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2007.10</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2007.11</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2007.12</td>\n",
       "      <td>9.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Periodo  Desemprego\n",
       "0  2007.08        10.4\n",
       "1  2007.09        10.5\n",
       "2  2007.10        10.0\n",
       "3  2007.11        10.0\n",
       "4  2007.12         9.3"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "desemprego.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Periodo</th>\n",
       "      <th>Desemprego</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>121.000000</td>\n",
       "      <td>121.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2012.189091</td>\n",
       "      <td>10.012397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.943821</td>\n",
       "      <td>2.200325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2007.080000</td>\n",
       "      <td>6.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2010.020000</td>\n",
       "      <td>8.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2012.080000</td>\n",
       "      <td>9.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2015.020000</td>\n",
       "      <td>10.700000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2017.080000</td>\n",
       "      <td>15.900000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Periodo  Desemprego\n",
       "count   121.000000  121.000000\n",
       "mean   2012.189091   10.012397\n",
       "std       2.943821    2.200325\n",
       "min    2007.080000    6.900000\n",
       "25%    2010.020000    8.500000\n",
       "50%    2012.080000    9.400000\n",
       "75%    2015.020000   10.700000\n",
       "max    2017.080000   15.900000"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "desemprego.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlação entre dolar e desemprego"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.          0.72697675]\n",
      " [ 0.72697675  1.        ]]\n"
     ]
    }
   ],
   "source": [
    "print(np.corrcoef(dolar['Dolar'],desemprego['Desemprego']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f6bf179ae10>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6bf185f4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(dolar['Dolar'],desemprego['Desemprego'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gráfico do desemprego e do câmbio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6bf1729f98>]"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZJkipqAsgIkeH17fuZUdvjoQZqaSRTBipRPk6sd/9g55LevcT5l+P0Z5eUM09cAp3EaEv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\nMfT/AdJcmzh5EqGgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6bf17523c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(dolar['Periodo'],dolar['Dolar'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6bf16bf5f8>]"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BhvZeTC0rSu8q41d9tWsgiZ+/uA/3vLgXHX1JXDCvEh+5cA72tfYC0F9Dz8bU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\nUUAw0ImIAoKBTkQUEAx0IqKA+P8HffY07IuyYAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6bf18a66d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(desemprego['Periodo'],desemprego['Desemprego'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Correlações não lineares\n",
    "Spearman"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SpearmanrResult(correlation=0.4841515871869444, pvalue=1.8418838317919234e-08)\n"
     ]
    }
   ],
   "source": [
    "print(stats.spearmanr(dolar['Dolar'],desemprego['Desemprego']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vamos criar duas variáveis com correlação 1/log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "independente = np.linspace(1,stop=5,num=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  1.08163265,  1.16326531,  1.24489796,  1.32653061,\n",
       "        1.40816327,  1.48979592,  1.57142857,  1.65306122,  1.73469388,\n",
       "        1.81632653,  1.89795918,  1.97959184,  2.06122449,  2.14285714,\n",
       "        2.2244898 ,  2.30612245,  2.3877551 ,  2.46938776,  2.55102041,\n",
       "        2.63265306,  2.71428571,  2.79591837,  2.87755102,  2.95918367,\n",
       "        3.04081633,  3.12244898,  3.20408163,  3.28571429,  3.36734694,\n",
       "        3.44897959,  3.53061224,  3.6122449 ,  3.69387755,  3.7755102 ,\n",
       "        3.85714286,  3.93877551,  4.02040816,  4.10204082,  4.18367347,\n",
       "        4.26530612,  4.34693878,  4.42857143,  4.51020408,  4.59183673,\n",
       "        4.67346939,  4.75510204,  4.83673469,  4.91836735,  5.        ])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "independente"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(101)\n",
    "dependente = [1 / (np.log(x) + (np.random.rand()*0.7)) for x in independente] \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f6bf031a828>"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wOAkgN0W/6zDP16/bTcjoKgGAyGQJbt7yDgCRIbgBIDIENwBEhuAGgMgQ3AAQGYIbACJT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\nRIbgBoDIENwAEBmCGwAiQ3ADQGT+H5W80VF+Sj7lAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6bf03ae7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(independente,dependente)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r Pearson [[ 1.        -0.6051513]\n",
      " [-0.6051513  1.       ]]\n",
      "r Spearman SpearmanrResult(correlation=-0.89733493397358943, pvalue=1.1314262188109336e-18)\n"
     ]
    }
   ],
   "source": [
    "# Calculando Pearson:\n",
    "pearson_r = np.corrcoef(independente,dependente)\n",
    "# Calculando Spearman\n",
    "spearman_r = stats.spearmanr(independente,dependente)\n",
    "print('r Pearson',pearson_r)\n",
    "print('r Spearman',spearman_r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}