cauemello/Housing.ipynb Secret

## Housing.ipynb
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   "source": [
    "# Machine-Learning"
   ]
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   "source": [
    "## Objetivo\n",
    "\n",
    "O objetivo deste trabalho é avaliar a base de dados *\"Boston House Prices\"* utilizando o algoritmo de seleção de variáveis LASSO e comparar o resultado com o modelo tradicional de regressão linear."
   ]
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    "## Carga inicial\n",
    "\n",
    "Será utilizada a biblioteca [scikit-learn](http://scikit-learn.org/) para o trabalho.\n",
    "\n",
    "A partir da biblioteca, é possível carregar diretamente os dados que serão utilizados. Esses dados serão carregados em um DataFrame para facilitar a visualização e a manipulação."
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     "text": [
      "Boston House Prices dataset\n",
      "\n",
      "Notes\n",
      "------\n",
      "Data Set Characteristics:  \n",
      "\n",
      "    :Number of Instances: 506 \n",
      "\n",
      "    :Number of Attributes: 13 numeric/categorical predictive\n",
      "    \n",
      "    :Median Value (attribute 14) is usually the target\n",
      "\n",
      "    :Attribute Information (in order):\n",
      "        - CRIM     per capita crime rate by town\n",
      "        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\n",
      "        - INDUS    proportion of non-retail business acres per town\n",
      "        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
      "        - NOX      nitric oxides concentration (parts per 10 million)\n",
      "        - RM       average number of rooms per dwelling\n",
      "        - AGE      proportion of owner-occupied units built prior to 1940\n",
      "        - DIS      weighted distances to five Boston employment centres\n",
      "        - RAD      index of accessibility to radial highways\n",
      "        - TAX      full-value property-tax rate per $10,000\n",
      "        - PTRATIO  pupil-teacher ratio by town\n",
      "        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\n",
      "        - LSTAT    % lower status of the population\n",
      "        - MEDV     Median value of owner-occupied homes in $1000's\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "\n",
      "    :Creator: Harrison, D. and Rubinfeld, D.L.\n",
      "\n",
      "This is a copy of UCI ML housing dataset.\n",
      "http://archive.ics.uci.edu/ml/datasets/Housing\n",
      "\n",
      "\n",
      "This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\n",
      "\n",
      "The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\n",
      "prices and the demand for clean air', J. Environ. Economics & Management,\n",
      "vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\n",
      "...', Wiley, 1980.   N.B. Various transformations are used in the table on\n",
      "pages 244-261 of the latter.\n",
      "\n",
      "The Boston house-price data has been used in many machine learning papers that address regression\n",
      "problems.   \n",
      "     \n",
      "**References**\n",
      "\n",
      "   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\n",
      "   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\n",
      "   - many more! (see http://archive.ics.uci.edu/ml/datasets/Housing)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "\n",
    "boston = load_boston()\n",
    "print(boston.DESCR)"
   ]
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>Price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.58</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.09</td>\n",
       "      <td>1</td>\n",
       "      <td>296</td>\n",
       "      <td>15.3</td>\n",
       "      <td>397</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0273</td>\n",
       "      <td>0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.42</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.97</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>397</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0273</td>\n",
       "      <td>0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.18</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.97</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>393</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0324</td>\n",
       "      <td>0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.06</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>395</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0691</td>\n",
       "      <td>0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.15</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.06</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>397</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     CRIM  ZN  INDUS  CHAS   NOX   RM  AGE  DIS  RAD  TAX  PTRATIO   B  LSTAT  \\\n",
       "0 0.00632  18   2.31     0 0.538 6.58 65.2 4.09    1  296     15.3 397   4.98   \n",
       "1  0.0273   0   7.07     0 0.469 6.42 78.9 4.97    2  242     17.8 397   9.14   \n",
       "2  0.0273   0   7.07     0 0.469 7.18 61.1 4.97    2  242     17.8 393   4.03   \n",
       "3  0.0324   0   2.18     0 0.458    7 45.8 6.06    3  222     18.7 395   2.94   \n",
       "4  0.0691   0   2.18     0 0.458 7.15 54.2 6.06    3  222     18.7 397   5.33   \n",
       "\n",
       "   Price  \n",
       "0     24  \n",
       "1   21.6  \n",
       "2   34.7  \n",
       "3   33.4  \n",
       "4   36.2  "
      ]
     },
     "execution_count": 2,
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     "output_type": "execute_result"
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   ],
   "source": [
    "import pandas as pd\n",
    "boston_df = pd.DataFrame(boston.data)\n",
    "boston_df.columns = boston.feature_names\n",
    "boston_df['Price'] = boston.target\n",
    "\n",
    "pd.options.display.float_format = '{:,.3g}'.format # Just Format!\n",
    "boston_df.head()"
   ]
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   "source": [
    "## Regressão Linear\n",
    "\n",
    "A regressão linear será realizada utilizando o método dos mínimos quadrados.\n",
    "Apresentamos abaixo os coeficientes calculados."
   ]
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Intercept</th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>OLS</th>\n",
       "      <td>22.5</td>\n",
       "      <td>-0.92</td>\n",
       "      <td>1.08</td>\n",
       "      <td>0.143</td>\n",
       "      <td>0.682</td>\n",
       "      <td>-2.06</td>\n",
       "      <td>2.67</td>\n",
       "      <td>0.0211</td>\n",
       "      <td>-3.1</td>\n",
       "      <td>2.66</td>\n",
       "      <td>-2.08</td>\n",
       "      <td>-2.06</td>\n",
       "      <td>0.857</td>\n",
       "      <td>-3.75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Intercept  CRIM   ZN  INDUS  CHAS   NOX   RM    AGE  DIS  RAD   TAX  \\\n",
       "OLS       22.5 -0.92 1.08  0.143 0.682 -2.06 2.67 0.0211 -3.1 2.66 -2.08   \n",
       "\n",
       "     PTRATIO     B  LSTAT  \n",
       "OLS    -2.06 0.857  -3.75  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "import numpy as np\n",
    "\n",
    "lr = LinearRegression()\n",
    "\n",
    "_x = boston_df.drop('Price', axis=1)\n",
    "y = boston_df['Price']\n",
    "\n",
    "# Normalization\n",
    "mu = np.mean(_x, axis=0)\n",
    "sigma = np.std(_x, axis=0)\n",
    "x = (_x - mu) / sigma\n",
    "\n",
    "lr.fit(x, y)\n",
    "\n",
    "coef_df = pd.DataFrame(index=np.append(['Intercept'], boston.feature_names))\n",
    "coef_df['OLS'] = np.append([lr.intercept_], lr.coef_) \n",
    "coef_df.T"
   ]
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   "source": [
    "Apresentamos abaixo a média do quadrado dos resídudos, o coeficiente de determinação $R^2$ ..."
   ]
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   "cell_type": "code",
   "execution_count": 4,
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    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OLS</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>MSE</th>\n",
       "      <td>21.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R²</th>\n",
       "      <td>0.741</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      OLS\n",
       "MSE  21.9\n",
       "R²  0.741"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "\n",
    "mse_ls = mean_squared_error(y, lr.predict(x))\n",
    "r2_ls = r2_score(y, lr.predict(x))\n",
    "\n",
    "result_df = pd.DataFrame(index=['MSE', 'R\\u00b2'])\n",
    "result_df['OLS'] = [mse_ls, r2_ls]\n",
    "result_df"
   ]
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   "cell_type": "markdown",
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   "source": [
    "... e o gráfico com a diferença entre o preço real e o calculado."
   ]
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   "cell_type": "code",
   "execution_count": 5,
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4pkQiTXLTTTe7wXaSm6l7ZqV6SURpn+5eN/kG5WmSCMATgZPExkok4iW8bbMQ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\nAXfkAMeOHaa9vb10nVIURSkCKhZFREu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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1132efc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "def scatterPlot(actual, predicted):\n",
    "    plt.scatter(actual, predicted)\n",
    "    range = [actual.min(), actual.max()]\n",
    "    plt.plot(range, range, 'black')\n",
    "    plt.xlabel(\"Preco Real\")\n",
    "    plt.ylabel(\"Preco Calculado\")\n",
    "    plt.show()\n",
    "    \n",
    "scatterPlot(y, lr.predict(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "collapsed": true,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "## Validação Cruzada\n",
    "\n",
    "É possível verificar no gráfico acima que, para os preços mais altos, o modelo não representou bem os dados.\n",
    "\n",
    "Faremos uma validação cruzada para verificar esse comportamento. Os dados serão divididos em 5 grupos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Fold 1] R²: 0.64\n",
      "[Fold 2] R²: 0.71\n",
      "[Fold 3] R²: 0.59\n",
      "[Fold 4] R²: 0.08\n",
      "[Fold 5] R²: -0.26\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OLS</th>\n",
       "      <th>OLS - CV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>MSE</th>\n",
       "      <td>21.9</td>\n",
       "      <td>37.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R²</th>\n",
       "      <td>0.741</td>\n",
       "      <td>0.56</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      OLS  OLS - CV\n",
       "MSE  21.9      37.2\n",
       "R²  0.741      0.56"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cross_validation import KFold\n",
    "\n",
    "kf = KFold(len(x), n_folds=5)\n",
    "p = np.zeros_like(y)\n",
    "for k, (train, test) in enumerate(kf):\n",
    "    lr.fit(x.ix[train], y[train])\n",
    "    p[test] = lr.predict(x.ix[test])\n",
    "    print(\"[Fold {0}] R\\u00b2: {1:.2f}\".\n",
    "          format(k+1, lr.score(x.ix[test], y[test])))\n",
    "\n",
    "mse_ls_cv = mean_squared_error(y, p)\n",
    "r2_ls_cv = r2_score(y, p)\n",
    "\n",
    "result_df['OLS - CV'] = [mse_ls_cv, r2_ls_cv]\n",
    "result_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "É possível verificar que o $R^2$ foi baixo para os dois últimos grupos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qI1lbXoNzVPVKLHaaO2+JE62dkr2SGUt/h5s3b5F4vFeSyQXS0ZGUaLRH/RdK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\nD2X3yFMaYT4yAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10acbda20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatterPlot(y, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "## Regressão LASSO\n",
    "\n",
    "Utilizaremos a técnica *Least Absolute Shrinkage and Selection Operator - LASSO* para selecionar as variáveis explicativas utilizando um parâmetro de regularização $\\alpha = 0.13$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OLS</th>\n",
       "      <th>OLS - CV</th>\n",
       "      <th>LASSO</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>MSE</th>\n",
       "      <td>21.9</td>\n",
       "      <td>37.2</td>\n",
       "      <td>22.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R²</th>\n",
       "      <td>0.741</td>\n",
       "      <td>0.56</td>\n",
       "      <td>0.732</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      OLS  OLS - CV  LASSO\n",
       "MSE  21.9      37.2   22.7\n",
       "R²  0.741      0.56  0.732"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "alpha = 0.13\n",
    "\n",
    "las = Lasso(alpha=alpha)\n",
    "las.fit(x, y)\n",
    "\n",
    "mse_lasso = mean_squared_error(y, las.predict(x))\n",
    "r2_lasso = r2_score(y, las.predict(x))\n",
    "\n",
    "result_df['LASSO'] = [mse_lasso, r2_lasso]\n",
    "result_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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S72Xz5i0F/y6m0oBVbUwloS6XWPw7NmP7/wC3AR8Hnim2oXJsKhalI5e5Il1M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\nnPxtVJG6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11aa15dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatterPlot(y, las.predict(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparação dos coeficientes\n",
    "\n",
    "Abaixo podemos verificar que, ao penalizar os estimadores com um $\\alpha > 0$, quase todos os coeficientes ficaram com valores menores em módulo. O coeficiente de *AGE* ficou igual a 0, ou seja, o algoritmo eliminou um parâmetro da regressão."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Intercept</th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>OLS</th>\n",
       "      <td>22.5</td>\n",
       "      <td>-0.92</td>\n",
       "      <td>1.08</td>\n",
       "      <td>0.143</td>\n",
       "      <td>0.682</td>\n",
       "      <td>-2.06</td>\n",
       "      <td>2.67</td>\n",
       "      <td>0.0211</td>\n",
       "      <td>-3.1</td>\n",
       "      <td>2.66</td>\n",
       "      <td>-2.08</td>\n",
       "      <td>-2.06</td>\n",
       "      <td>0.857</td>\n",
       "      <td>-3.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO</th>\n",
       "      <td>22.5</td>\n",
       "      <td>-0.537</td>\n",
       "      <td>0.596</td>\n",
       "      <td>-0.0366</td>\n",
       "      <td>0.65</td>\n",
       "      <td>-1.43</td>\n",
       "      <td>2.87</td>\n",
       "      <td>-0</td>\n",
       "      <td>-2.21</td>\n",
       "      <td>0.755</td>\n",
       "      <td>-0.479</td>\n",
       "      <td>-1.88</td>\n",
       "      <td>0.74</td>\n",
       "      <td>-3.73</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Intercept   CRIM    ZN   INDUS  CHAS   NOX   RM    AGE   DIS   RAD  \\\n",
       "OLS         22.5  -0.92  1.08   0.143 0.682 -2.06 2.67 0.0211  -3.1  2.66   \n",
       "LASSO       22.5 -0.537 0.596 -0.0366  0.65 -1.43 2.87     -0 -2.21 0.755   \n",
       "\n",
       "         TAX  PTRATIO     B  LSTAT  \n",
       "OLS    -2.08    -2.06 0.857  -3.75  \n",
       "LASSO -0.479    -1.88  0.74  -3.73  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coef_df['LASSO'] = np.append([las.intercept_], las.coef_) \n",
    "coef_df.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "## Validação Cruzada - LASSO\n",
    "\n",
    "Faremos também um teste de validação cruzada, dividindo os dados em 5 grupos.\n",
    "\n",
    "É possível verificar que o $R^2$ continua baixo para os dois últimos grupos, porém o $R^2$ geral da validação cruzada foi maior que o da validação cruzada no método de mínimos quadrados ordinários.\n",
    "\n",
    "Concluímos que, apesar de termos um ajuste pior da amostra de treino utilizando LASSO, o modelo se comporta melhor nos dados fora da amostra."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Fold 1] α: 0.13, R²: 0.69\n",
      "[Fold 2] α: 0.13, R²: 0.74\n",
      "[Fold 3] α: 0.13, R²: 0.58\n",
      "[Fold 4] α: 0.13, R²: 0.06\n",
      "[Fold 5] α: 0.13, R²: -0.04\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OLS</th>\n",
       "      <th>OLS - CV</th>\n",
       "      <th>LASSO</th>\n",
       "      <th>LASSO - CV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>MSE</th>\n",
       "      <td>21.9</td>\n",
       "      <td>37.2</td>\n",
       "      <td>22.7</td>\n",
       "      <td>35.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R²</th>\n",
       "      <td>0.741</td>\n",
       "      <td>0.56</td>\n",
       "      <td>0.732</td>\n",
       "      <td>0.58</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      OLS  OLS - CV  LASSO  LASSO - CV\n",
       "MSE  21.9      37.2   22.7        35.5\n",
       "R²  0.741      0.56  0.732        0.58"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kf = KFold(len(x), n_folds=5)\n",
    "p = np.zeros_like(y)\n",
    "for k, (train, test) in enumerate(kf):\n",
    "    las.fit(x.ix[train], y[train])\n",
    "    p[test] = las.predict(x.ix[test])\n",
    "    print(\"[Fold {0}] \\u03b1: {1:.2f}, R\\u00b2: {2:.2f}\".\n",
    "          format(k+1, alpha, las.score(x.ix[test], y[test])))\n",
    "\n",
    "mse_lasso_cv = mean_squared_error(y, p)\n",
    "r2_lasso_cv = r2_score(y, p)\n",
    "\n",
    "result_df['LASSO - CV'] = [mse_lasso_cv, r2_lasso_cv]\n",
    "result_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PD7vlsieIzcEUE+gR67D2ZhdL3AxgphvFD7ufs1NmM/b7Ze46HWLzOH1UbB6n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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ab30080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatterPlot(y, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "## Caminho LASSO\n",
    "\n",
    "Com a visualização do *LASSO Path*, podemos ver o comportamento de cada coeficiente da regressão de acordo com a variação do parâmetro de regularização $\\alpha$.\n",
    "\n",
    "Quando $\\alpha$ é muito grande, a penalização é significativa e todos os coeficientes ficam muito próximos de 0. A medida que o $\\alpha$ tende a 0, os coeficientes se estabilizam e tendem aos valores calculados pelo método dos mínimos quadrados ordinários."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tO3acS1bWwyQlXa23OX5H9ao0bWqibnkd9SvqsefbiTo5iqhTNWEImxaGXah8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\nIYTISkJCCCFEVhISQgghsvr/q3nxj96MpeYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11aa77588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "las = Lasso()\n",
    "alphas = np.logspace(-3, 1.5, 1000)\n",
    "alphas, coefs, _ = las.path(x, y, alphas=alphas)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(alphas, coefs.T)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(alphas.max(), alphas.min())\n",
    "plt.vlines(alpha, coefs.min(), coefs.max())\n",
    "plt.xlabel(\"Alpha\")\n",
    "plt.ylabel(\"Coeficientes\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "## LASSO com seleção automática do $\\alpha$\n",
    "\n",
    "Faremos uma implementação de validação cruzada para encontrar o melhor parâmetro de regularização $\\alpha$ de acordo com os dados da amostra."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Fold 1] α: 0.76, R²: 0.73\n",
      "[Fold 2] α: 0.66, R²: 0.70\n",
      "[Fold 3] α: 0.67, R²: 0.40\n",
      "[Fold 4] α: 0.02, R²: 0.08\n",
      "[Fold 5] α: 0.16, R²: -0.03\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OLS</th>\n",
       "      <th>OLS - CV</th>\n",
       "      <th>LASSO</th>\n",
       "      <th>LASSO - CV</th>\n",
       "      <th>LASSO - CV (α selection)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>MSE</th>\n",
       "      <td>21.9</td>\n",
       "      <td>37.2</td>\n",
       "      <td>22.7</td>\n",
       "      <td>35.5</td>\n",
       "      <td>38.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R²</th>\n",
       "      <td>0.741</td>\n",
       "      <td>0.56</td>\n",
       "      <td>0.732</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.542</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      OLS  OLS - CV  LASSO  LASSO - CV  LASSO - CV (α selection)\n",
       "MSE  21.9      37.2   22.7        35.5                      38.6\n",
       "R²  0.741      0.56  0.732        0.58                     0.542"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LassoCV\n",
    "\n",
    "las = LassoCV()\n",
    "kf = KFold(len(x), n_folds=5)\n",
    "p = np.zeros_like(y)\n",
    "\n",
    "for k, (train, test) in enumerate(kf):\n",
    "    las.fit(x.ix[train], y[train])\n",
    "    p[test] = las.predict(x.ix[test])\n",
    "    print(\"[Fold {0}] \\u03b1: {1:.2f}, R\\u00b2: {2:.2f}\".\n",
    "          format(k+1, las.alpha_, las.score(x.ix[test], y[test])))\n",
    "\n",
    "mse_lasso_cv_2 = mean_squared_error(y, p)\n",
    "r2_lasso_cv_2 = r2_score(y, p)\n",
    "\n",
    "result_df['LASSO - CV (\\u03b1 selection)'] = [mse_lasso_cv_2, r2_lasso_cv_2]\n",
    "result_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MJhmLncbs/INI0afewtnU2SUtslety2Q3O4yPj9t1p51EukUeT/sJ5q81PchM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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ad2f048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatterPlot(y, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regressão com termos de segunda ordem\n",
    "\n",
    "Repetiremos as regressões adicionando o quadrado das variáveis explicativas ao modelo. Vamos verificar se o modelo de segunda ordem pode predizer melhor o preço dos imóveis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OLS X²</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>18.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>-2.96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>-0.988</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>0.0311</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>0.0536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOX</th>\n",
       "      <td>-2.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>1.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>0.0627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>-3.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>3.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>-2.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>-1.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>-0.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>-5.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CRIM²</th>\n",
       "      <td>0.213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN²</th>\n",
       "      <td>0.397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS²</th>\n",
       "      <td>0.331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS²</th>\n",
       "      <td>0.182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOX²</th>\n",
       "      <td>-0.0441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM²</th>\n",
       "      <td>0.859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE²</th>\n",
       "      <td>0.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS²</th>\n",
       "      <td>0.599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD²</th>\n",
       "      <td>-0.667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX²</th>\n",
       "      <td>0.427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO²</th>\n",
       "      <td>0.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B²</th>\n",
       "      <td>-0.318</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT²</th>\n",
       "      <td>1.15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           OLS X²\n",
       "Intercept    18.7\n",
       "CRIM        -2.96\n",
       "ZN         -0.988\n",
       "INDUS      0.0311\n",
       "CHAS       0.0536\n",
       "NOX         -2.62\n",
       "RM           1.89\n",
       "AGE        0.0627\n",
       "DIS         -3.24\n",
       "RAD          3.83\n",
       "TAX         -2.23\n",
       "PTRATIO     -1.32\n",
       "B           -0.36\n",
       "LSTAT       -5.32\n",
       "CRIM²       0.213\n",
       "ZN²         0.397\n",
       "INDUS²      0.331\n",
       "CHAS²       0.182\n",
       "NOX²      -0.0441\n",
       "RM²         0.859\n",
       "AGE²         0.13\n",
       "DIS²        0.599\n",
       "RAD²       -0.667\n",
       "TAX²        0.427\n",
       "PTRATIO²     0.58\n",
       "B²         -0.318\n",
       "LSTAT²       1.15"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col2 = ['{0}\\u00b2'.format(c) for c in list(x.columns)]\n",
    "df2 = x.copy()**2\n",
    "df2.columns = col2\n",
    "\n",
    "x2 = pd.concat([x, df2], axis=1)\n",
    "\n",
    "lr = LinearRegression()\n",
    "lr.fit(x2, y)\n",
    "\n",
    "coef_df_2 = pd.DataFrame(index=np.append(['Intercept'], x2.columns))\n",
    "coef_df_2['OLS X\\u00b2'] = np.append([lr.intercept_], lr.coef_) \n",
    "coef_df_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OLS</th>\n",
       "      <th>OLS - CV</th>\n",
       "      <th>LASSO</th>\n",
       "      <th>LASSO - CV</th>\n",
       "      <th>LASSO - CV (α selection)</th>\n",
       "      <th>OLS X²</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>MSE</th>\n",
       "      <td>21.9</td>\n",
       "      <td>37.2</td>\n",
       "      <td>22.7</td>\n",
       "      <td>35.5</td>\n",
       "      <td>38.6</td>\n",
       "      <td>14.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R²</th>\n",
       "      <td>0.741</td>\n",
       "      <td>0.56</td>\n",
       "      <td>0.732</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.542</td>\n",
       "      <td>0.831</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      OLS  OLS - CV  LASSO  LASSO - CV  LASSO - CV (α selection)  OLS X²\n",
       "MSE  21.9      37.2   22.7        35.5                      38.6    14.3\n",
       "R²  0.741      0.56  0.732        0.58                     0.542   0.831"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mse_ls = mean_squared_error(y, lr.predict(x2))\n",
    "r2_ls = r2_score(y, lr.predict(x2))\n",
    "\n",
    "result_df['OLS X\\u00b2'] = [mse_ls, r2_ls]\n",
    "result_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JUBUGypgitffQiU4IeOohb4U+xfW9P6nqyE7g8wQeHJgYvdV6ZeUMMaZMjCkX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\n1ASxnkheTYOIwAzfPQeD3tI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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11adb0240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatterPlot(y, lr.predict(x2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Conforme esperado, vemos que o modelo de segunda ordem se encaixa melhor. Porém, faremos mais a frente a validação cruzada para verificar se não está ocorrendo *overfitting*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regressão LASSO com termos de segunda ordem\n",
    "\n",
    "Dessa vez escolhemos um valor maior para $\\alpha$, visto que há agora um maior número de variáveis a serem eliminadas pelo modelo.\n",
    "\n",
    "Observamos um maior número de coeficientes iguais a 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OLS X²</th>\n",
       "      <th>LASSO X²</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>18.7</td>\n",
       "      <td>21.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>-2.96</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>-0.988</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>0.0311</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>0.0536</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOX</th>\n",
       "      <td>-2.62</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>1.89</td>\n",
       "      <td>2.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>0.0627</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>-3.24</td>\n",
       "      <td>-0.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>3.83</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>-2.23</td>\n",
       "      <td>-0.216</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>-1.32</td>\n",
       "      <td>-1.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>-0.36</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>-5.32</td>\n",
       "      <td>-4.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CRIM²</th>\n",
       "      <td>0.213</td>\n",
       "      <td>-0.108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN²</th>\n",
       "      <td>0.397</td>\n",
       "      <td>0.145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS²</th>\n",
       "      <td>0.331</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS²</th>\n",
       "      <td>0.182</td>\n",
       "      <td>0.215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOX²</th>\n",
       "      <td>-0.0441</td>\n",
       "      <td>-0.619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM²</th>\n",
       "      <td>0.859</td>\n",
       "      <td>1.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE²</th>\n",
       "      <td>0.13</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS²</th>\n",
       "      <td>0.599</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD²</th>\n",
       "      <td>-0.667</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX²</th>\n",
       "      <td>0.427</td>\n",
       "      <td>0.053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO²</th>\n",
       "      <td>0.58</td>\n",
       "      <td>0.0311</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B²</th>\n",
       "      <td>-0.318</td>\n",
       "      <td>-0.236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT²</th>\n",
       "      <td>1.15</td>\n",
       "      <td>0.808</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           OLS X²  LASSO X²\n",
       "Intercept    18.7      21.2\n",
       "CRIM        -2.96        -0\n",
       "ZN         -0.988         0\n",
       "INDUS      0.0311        -0\n",
       "CHAS       0.0536         0\n",
       "NOX         -2.62        -0\n",
       "RM           1.89      2.23\n",
       "AGE        0.0627        -0\n",
       "DIS         -3.24     -0.74\n",
       "RAD          3.83         0\n",
       "TAX         -2.23    -0.216\n",
       "PTRATIO     -1.32     -1.39\n",
       "B           -0.36         0\n",
       "LSTAT       -5.32     -4.97\n",
       "CRIM²       0.213    -0.108\n",
       "ZN²         0.397     0.145\n",
       "INDUS²      0.331         0\n",
       "CHAS²       0.182     0.215\n",
       "NOX²      -0.0441    -0.619\n",
       "RM²         0.859      1.03\n",
       "AGE²         0.13         0\n",
       "DIS²        0.599        -0\n",
       "RAD²       -0.667        -0\n",
       "TAX²        0.427     0.053\n",
       "PTRATIO²     0.58    0.0311\n",
       "B²         -0.318    -0.236\n",
       "LSTAT²       1.15     0.808"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha = 0.20\n",
    "\n",
    "las = Lasso(alpha=alpha)\n",
    "las.fit(x2, y)\n",
    "\n",
    "coef_df_2['LASSO X\\u00b2'] = np.append([las.intercept_], las.coef_) \n",
    "coef_df_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OLS</th>\n",
       "      <th>OLS - CV</th>\n",
       "      <th>LASSO</th>\n",
       "      <th>LASSO - CV</th>\n",
       "      <th>LASSO - CV (α selection)</th>\n",
       "      <th>OLS X²</th>\n",
       "      <th>LASSO X²</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>MSE</th>\n",
       "      <td>21.9</td>\n",
       "      <td>37.2</td>\n",
       "      <td>22.7</td>\n",
       "      <td>35.5</td>\n",
       "      <td>38.6</td>\n",
       "      <td>14.3</td>\n",
       "      <td>16.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R²</th>\n",
       "      <td>0.741</td>\n",
       "      <td>0.56</td>\n",
       "      <td>0.732</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.542</td>\n",
       "      <td>0.831</td>\n",
       "      <td>0.807</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      OLS  OLS - CV  LASSO  LASSO - CV  LASSO - CV (α selection)  OLS X²  \\\n",
       "MSE  21.9      37.2   22.7        35.5                      38.6    14.3   \n",
       "R²  0.741      0.56  0.732        0.58                     0.542   0.831   \n",
       "\n",
       "     LASSO X²  \n",
       "MSE      16.3  \n",
       "R²      0.807  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mse_lasso = mean_squared_error(y, las.predict(x2))\n",
    "r2_lasso = r2_score(y, las.predict(x2))\n",
    "\n",
    "result_df['LASSO X\\u00b2'] = [mse_lasso, r2_lasso]\n",
    "result_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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2ptogcp1p1pLeWpk8KEU6CntfgsBctwXyfUihmwqD0jPZg9O1114XV8VAyHkK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\n/A9XXXVlWfqhKIpSKDVvQB7PKJyNXbt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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a8911d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatterPlot(y, las.predict(x2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Validação Cruzada\n",
    "\n",
    "Faremos agora o teste de validação cruzada para o modelo com termos de segunda ordem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Fold 1] R²: 0.68\n",
      "[Fold 2] R²: 0.53\n",
      "[Fold 3] R²: 0.82\n",
      "[Fold 4] R²: 0.42\n",
      "[Fold 5] R²: -0.25\n",
      "-------------------\n",
      "[Fold 1] α: 0.20, R²: 0.80\n",
      "[Fold 2] α: 0.20, R²: 0.83\n",
      "[Fold 3] α: 0.20, R²: 0.81\n",
      "[Fold 4] α: 0.20, R²: 0.36\n",
      "[Fold 5] α: 0.20, R²: 0.50\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OLS</th>\n",
       "      <th>OLS - CV</th>\n",
       "      <th>LASSO</th>\n",
       "      <th>LASSO - CV</th>\n",
       "      <th>LASSO - CV (α selection)</th>\n",
       "      <th>OLS X²</th>\n",
       "      <th>LASSO X²</th>\n",
       "      <th>OLS X² - CV</th>\n",
       "      <th>LASSO X² - CV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>MSE</th>\n",
       "      <td>21.9</td>\n",
       "      <td>37.2</td>\n",
       "      <td>22.7</td>\n",
       "      <td>35.5</td>\n",
       "      <td>38.6</td>\n",
       "      <td>14.3</td>\n",
       "      <td>16.3</td>\n",
       "      <td>30.6</td>\n",
       "      <td>21.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R²</th>\n",
       "      <td>0.741</td>\n",
       "      <td>0.56</td>\n",
       "      <td>0.732</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.542</td>\n",
       "      <td>0.831</td>\n",
       "      <td>0.807</td>\n",
       "      <td>0.638</td>\n",
       "      <td>0.746</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      OLS  OLS - CV  LASSO  LASSO - CV  LASSO - CV (α selection)  OLS X²  \\\n",
       "MSE  21.9      37.2   22.7        35.5                      38.6    14.3   \n",
       "R²  0.741      0.56  0.732        0.58                     0.542   0.831   \n",
       "\n",
       "     LASSO X²  OLS X² - CV  LASSO X² - CV  \n",
       "MSE      16.3         30.6           21.4  \n",
       "R²      0.807        0.638          0.746  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kf = KFold(len(x2), n_folds=5)\n",
    "p = np.zeros_like(y)\n",
    "for k, (train, test) in enumerate(kf):\n",
    "    lr.fit(x2.ix[train], y[train])\n",
    "    p[test] = lr.predict(x2.ix[test])\n",
    "    print(\"[Fold {0}] R\\u00b2: {1:.2f}\".\n",
    "          format(k+1, lr.score(x2.ix[test], y[test])))\n",
    "\n",
    "mse_ls_cv = mean_squared_error(y, p)\n",
    "r2_ls_cv = r2_score(y, p)\n",
    "\n",
    "result_df['OLS X\\u00b2 - CV'] = [mse_ls_cv, r2_ls_cv]\n",
    "\n",
    "print('-------------------')\n",
    "\n",
    "p = np.zeros_like(y)\n",
    "for k, (train, test) in enumerate(kf):\n",
    "    las.fit(x2.ix[train], y[train])\n",
    "    p[test] = las.predict(x2.ix[test])\n",
    "    print(\"[Fold {0}] \\u03b1: {1:.2f}, R\\u00b2: {2:.2f}\".\n",
    "          format(k+1, alpha, las.score(x2.ix[test], y[test])))\n",
    "\n",
    "mse_lasso_cv = mean_squared_error(y, p)\n",
    "r2_lasso_cv = r2_score(y, p)\n",
    "\n",
    "result_df['LASSO X\\u00b2 - CV'] = [mse_lasso_cv, r2_lasso_cv]\n",
    "\n",
    "result_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusão\n",
    "\n",
    "Observamos na tabela anterior que nos testes de validação cruzada a regressão LASSO teve um desempenho superior em relação ao método dos mínimos quadrados ordinários. Podemos concluir, portanto, que a seleção de variáveis feita pela regularização melhorou o modelo para previsões (dados fora da amostra)."
   ]
  }
 ],
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