LinearRegession-波士顿房价-MSE VS MAE  and R Square.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 加载数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = load_boston()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boston House Prices dataset\n",
      "===========================\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": [
    "data.keys()\n",
    "print(data.DESCR)\n",
    "data_RM = data.data[:,5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_y = data.target"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 数据可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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k3W6Xc5JC37zWmcWLa/X90KUCQi7wEnXq/wJ+PC1Xngt4RZcQ7DB0l6K1vzc1cGC4PGKX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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(data_RM,data_y,marker=\"+\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 去除边界值\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_RM = data_RM[data_y<50]\n",
    "data_y  = data_y[data_y<50]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RVY8ZOhFRyzFDJyIaGAZ0IqKeYEAnIuoJBnQiop5gQCci6gkGdCKinqi1bVFE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\nnvh/PC8tdTwK5NEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(data_RM,data_y,marker=\"+\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 划分数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from model_selection import train_test_split "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train,y_train,x_test,y_test = train_test_split(data_RM,data_y,seed=666)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(392,)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(98,)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 训练模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from SimpleLinearRegession import SimpleLinearRegression1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "SLR = SimpleLinearRegression1()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SimpleLinearRegression1()"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SLR.fit(x_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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j33gDDjwQHn54y66zp/WxvHtmxfxwODBFg2SlckWDW9z84nF5av/BUapmHicu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\nkZxQQBcRyYn/AYtA0eyNG08BAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_train,y_train,color =\"blue\",marker=\"+\")\n",
    "# plt.plot(np.array([3,4,5,6,7,8,9]),SLR.predict(np.array([3,4,5,6,7,8,9])),color =\"r\")\n",
    "plt.plot(x_train,SLR.predict(x_train),color=\"r\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-27.459342806705543"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SLR.b_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.8608543562689555"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SLR.w_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 评判模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.61293168039373225"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SLR.score(x_test,y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.156602134387441"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MSE = sum((y_test - SLR.predict(x_test))**2)/y_test.shape[0]\n",
    "MSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RMSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.9149366358466358"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RMSE = np.sqrt(MSE)\n",
    "RMSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MAE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.5430974409463873"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(np.absolute(y_test-SLR.predict(x_test)))/len(y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 自己实现的方法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "from metrics import mean_square_error,mean_absolute_error,root_mean_square_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_p = SLR.predict(x_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.5430974409463873"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_error(y_test,y_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.156602134387438"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_square_error(y_test,y_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.9149366358466349"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "root_mean_square_error(y_test,y_p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### sklearn中的ＭＳＥ  ＭＡＥ(没有RMSE 但是我们可以手动求)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_absolute_error,mean_squared_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.156602134387438"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_square_error(y_test,y_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.5430974409463873"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_error(y_test,y_p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### R Square"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_square = 1 - mean_square_error(y_test,y_p) / np.var(y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.61293168039373225"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_square"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "from metrics import r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.61293168039373225"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(y_test,y_p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### sklearn中的R Square"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.61293168039373236"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(y_test,y_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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