05-Tutorial-Regressao-Linear-Simples-Numpy-com-libs-externas.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial Regressão Linear Simples usando o Numpy e Libs externas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from ml_libs import regressao_linear_simples\n",
    "from ml_libs import metrics\n",
    "from importlib import reload"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'ml_libs.metrics' from '/Users/regis/Dropbox/git/aulas-machine-learning-2019/ml_libs/metrics.py'>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reload(regressao_linear_simples)\n",
    "reload(metrics)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linha reta de uma regressão linear simples\n",
    "\n",
    "\n",
    "\n",
    "$$ y = w_0 + w_1 \\cdot x $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([ 1, 2, 4, 3, 5 ])\n",
    "y = np.array([ 1, 3, 3, 2, 5 ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = regressao_linear_simples.RegressaoLinearSimples()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.fit(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = model.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.2, 2. , 3.6, 2.8, 4.4])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.692820323027551"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.rmse(y, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Usando o algoritmo de Regressão Linear do Scikit Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2 = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [4],\n",
       "       [3],\n",
       "       [5]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_ = x.reshape((x.shape[0],1))\n",
    "x_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model2.fit(x_, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.2, 2. , 3.6, 2.8, 4.4])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred_ = model2.predict(x_)\n",
    "y_pred_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.47999999999999987"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mse_ = mean_squared_error(y, y_pred_)\n",
    "mse_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6928203230275508"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse_ = np.sqrt(mse_)\n",
    "rmse_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 4, 3, 5])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 3, 2, 5])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5,5))\n",
    "plt.title('Regressão Linear')\n",
    "plt.xlabel('rótulo do eixo x')\n",
    "plt.plot(x, y, 'o')\n",
    "plt.ylabel('rótulo do eixo y')\n",
    "plt.grid()\n",
    "plt.plot(x, y_pred, 'r-.')\n",
    "for i in range(x.shape[0]):\n",
    "    x_ = [ x[i], x[i] ]\n",
    "    y_ = [ y[i], y_pred[i] ]\n",
    "    plt.plot(x_, y_, 'm')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.8]), 0.39999999999999947)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model2.coef_, model2.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.2, 2. , 3.6, 2.8, 4.4])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}