ch07-逻辑回归/Z5-Logistic回归.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 逻辑回归-银行贷款违约问题"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_excel('datas/bankloan.xls')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data.iloc[:,:8].as_matrix()\n",
    "y = data.iloc[:,8].as_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>年龄</th>\n",
       "      <th>教育</th>\n",
       "      <th>工龄</th>\n",
       "      <th>地址</th>\n",
       "      <th>收入</th>\n",
       "      <th>负债率</th>\n",
       "      <th>信用卡负债</th>\n",
       "      <th>其他负债</th>\n",
       "      <th>违约</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>41</td>\n",
       "      <td>3</td>\n",
       "      <td>17</td>\n",
       "      <td>12</td>\n",
       "      <td>176</td>\n",
       "      <td>9.3</td>\n",
       "      <td>11.359392</td>\n",
       "      <td>5.008608</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>27</td>\n",
       "      <td>1</td>\n",
       "      <td>10</td>\n",
       "      <td>6</td>\n",
       "      <td>31</td>\n",
       "      <td>17.3</td>\n",
       "      <td>1.362202</td>\n",
       "      <td>4.000798</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>40</td>\n",
       "      <td>1</td>\n",
       "      <td>15</td>\n",
       "      <td>14</td>\n",
       "      <td>55</td>\n",
       "      <td>5.5</td>\n",
       "      <td>0.856075</td>\n",
       "      <td>2.168925</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>41</td>\n",
       "      <td>1</td>\n",
       "      <td>15</td>\n",
       "      <td>14</td>\n",
       "      <td>120</td>\n",
       "      <td>2.9</td>\n",
       "      <td>2.658720</td>\n",
       "      <td>0.821280</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>24</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>28</td>\n",
       "      <td>17.3</td>\n",
       "      <td>1.787436</td>\n",
       "      <td>3.056564</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   年龄  教育  工龄  地址   收入   负债率      信用卡负债      其他负债  违约\n",
       "0  41   3  17  12  176   9.3  11.359392  5.008608   1\n",
       "1  27   1  10   6   31  17.3   1.362202  4.000798   0\n",
       "2  40   1  15  14   55   5.5   0.856075  2.168925   0\n",
       "3  41   1  15  14  120   2.9   2.658720  0.821280   0\n",
       "4  24   2   2   0   28  17.3   1.787436  3.056564   1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression as LR\n",
    "from sklearn.linear_model import RandomizedLogisticRegression as RLR "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 随机逻辑回归\n",
    "\n",
    "筛选有效 特征"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[False False  True  True False  True  True False]\n",
      "通过随机逻辑回归模型筛选特征结束------------\n",
      "工龄,地址,负债率,信用卡负债\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mgbook/.pyenv/versions/3.6.4rc1/lib/python3.6/site-packages/sklearn/utils/deprecation.py:58: DeprecationWarning: Class RandomizedLogisticRegression is deprecated; The class RandomizedLogisticRegression is deprecated in 0.19 and will be removed in 0.21.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "rlr = RLR() #建立随机逻辑回归模型，筛选变量\n",
    "rlr.fit(X, y) #训练模型\n",
    "print(rlr.get_support()) #获取特征筛选结果，也可以通过.scores_方法获取各个特征的分数\n",
    "print('通过随机逻辑回归模型筛选特征结束------------')\n",
    "suport_columns = np.append(rlr.get_support(), False)\n",
    "print(','.join(data.columns[suport_columns]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 逻辑回归\n",
    "![](images/logistic.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "逻辑回归模型训练结束------------\n",
      "模型的平均正确率为：0.8142857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mgbook/.pyenv/versions/3.6.4rc1/lib/python3.6/site-packages/sklearn/linear_model/logistic.py:432: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.\n",
      "  FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "#筛选好特征\n",
    "X = data[data.columns[suport_columns]].as_matrix()\n",
    "lr = LR() #建立逻辑回归模型\n",
    "lr.fit(X, y) #用筛选后的特征数据来训练模型\n",
    "print('逻辑回归模型训练结束------------')\n",
    "print(u'模型的平均正确率为：%s' % lr.score(X, y)) #给出模型的平均正确率，本例为81.4%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(700, 4)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 非线性回归\n",
    "\n",
    "销售额X 与 流通费率y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "from sklearn import metrics\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x10fd65b00>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fcd5f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = pd.DataFrame([1.5,2.8,4.5,7.5,10.5,13.5,15.1,16.5,19.5,22.5,24.5,26.5])\n",
    "y = pd.DataFrame([7.0,5.5,4.6,3.6,2.9,2.7,2.5,2.4,2.2,2.1,1.9,1.8])\n",
    "plt.scatter(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mgbook/.pyenv/versions/3.6.4rc1/lib/python3.6/site-packages/scipy/linalg/basic.py:1226: RuntimeWarning: internal gelsd driver lwork query error, required iwork dimension not returned. This is likely the result of LAPACK bug 0038, fixed in LAPACK 3.2.2 (released July 21, 2010). Falling back to 'gelss' driver.\n",
      "  warnings.warn(mesg, RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linreg = LinearRegression()\n",
    "linreg.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.直线回归\n",
    "![](images/01.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: \n",
      " [[-0.17002988]]\n",
      "MSE: 0.494218627800241\n",
      "Variance score: 0.80\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10fd48630>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWwAAAD6CAYAAACF131TAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvAOZPmwAAHQZJREFUeJzt3Xt0lfW95/H3LxdIuEYItwRDkh2JgopAVCSQRFSQWi1F21ptVbCNycxaxx57cKTTnumsmR49UueM53ROABVKrVq1RWxrLV4wF+4EA4JYlJ0LEAQSIOGSC7n85o+dWIyBJLBvz96f11qstX14knz3evDDw7M/z+8x1lpERCT4RQR6ABER6R0FtoiIQyiwRUQcQoEtIuIQCmwREYdQYIuIOIQCW0TEIRTYIiIOocAWEXGIKG9+s/j4eJucnOzNbykiEvK2b99ea60d0dN+Xg3s5ORkSktLvfktRURCnjGmqjf76ZKIiIhDKLBFRBxCgS0i4hAKbBERh1Bgi4g4hAJbRMQheqz1GWNygP/d8Z/jgJ9aa1d5c4g1ZdUsWbuXQ3WNJMTFsmhOOvMmJ3rzR4iIOF6PgW2tLQRmABhj3gLKvDnAmrJqFq/eRWNLGwDVdY0sXr0LQKEtInKOXl8SMcYMANKstR95c4Ala/d+EdadGlvaWLJ2rzd/jIiI4/XlGvZtwPtdNxpjco0xpcaY0pqamj4PcKiusU/bRUTCVV8C+07gz103WmuXW2szrLUZI0b0eCv8VyTExfZpu4hIuOpVYBtjDHAzsM7bAyyak05sdOSXtsVGR7JoTrq3f5SIiKP1dvGn64GPrbVN3h6g84NFtURERC7MWGu99s0yMjKsVusTEekbY8x2a21GT/vpxhkREYdQYIuIOIQCW0TEIRTYIiIOocAWEXEIBbaIiEMosEVEHEKBLSLiEApsERGHUGCLiDiEAltExCEU2CIiDqHAFhFxCAW2iIhDKLBFRBxCgS0i4hAKbBERh1Bgi4g4hAJbRMQhFNgiIg6hwBYRcQgFtoiIQyiwRUQcQoEtIuIQCmwREYfoVWAbYx43xpQYY942xvTz9VAiIvJVPQa2MSYVmGitnQm8DYz1+VQiIvIVvTnDvgW4zBhTDMwEKnw7koiIdKc3gT0CqLHWZuE5u55x7m8aY3KNMaXGmNKamhpfzCgiIvQusE8CeztelwOJ5/6mtXa5tTbDWpsxYsQIb88nIiIdehPY24HrO16n4QltERHxsx4D21q7Cag1xmwD9lprt/p+LBER6SqqNztZa/N9PYiIiFyYbpwREXEIBbaIiEMosEVEHEKBLSLiEApsERGHUGCLiDiEAltExCEU2CIiDqHAFhFxiF7d6RjM1pRVs2TtXg7VNZIQF8uiOenMm5zY8xeKiDiMowN7TVk1i1fvorGlDYDqukYWr94FoNAWkZDj6EsiS9bu/SKsOzW2tLFk7d7zfIWIiHM5OrAP1TX2abuIiJM5OrAT4mL7tF1ExMkcHdiL5qQTGx35pW2x0ZEsmpMeoIlERHwnaD50bG1rJyqyb39/dH6wqJaIiISDoAjsqmNn+NbSTTxw0zi+Py2ZoQOie/218yYnKqBFJCwExSWRlrZ2JiQM4ZfvfMr0p97nF2/t4XB9U6DHEhEJKsZa67VvlpGRYUtLSy/66/ccOsmyYjd//uhzIgx8c3IiuVku0kYO8tqMIiLBxhiz3Vqb0eN+wRTYnQ4cb+C5knJe3XaAs23tzJ4wivycNK67PM4LU4qIBBdHB3an2tPNrNpYyaqNlZxsauWm1OHk5bjIuiIeY4zXfo6ISCCFRGB3Ot3cyu+27uf5kgoOn2xiwpgh5OW4+NrVo/vcLBERCTYhFdidzra2s2ZHNUuL3JTXnCFp2AB+mJXKt6aOJaZLH1tExClCMrA7tbdb3v3kCAWFbnYcqCN+UD8WZKbwvWnjGBrb+0qgiEgwCOnA7mStZUvFcQoK3RR9WsOg/lHcd2MSD89IYdSQGL/NISJyKbwW2MaY24HngcqOTQ9ba7tdDs/fgX2ujw/Vs6yonD9/dIioiAhPJTA7FdcIVQJFJLh5O7CnWmt/0dM3C2Rgd9p/zFMJfK3UUwmcM2E0+TkuJqkSKCJBytuB/S9AK3AAuMee54uCIbA71Z5u5tcbKvnNJk8lcLprOHnZLmaqEigiQcabgX0FMN5a+5YxZiPwE2ttYXf7BlNgdzrd3MorW/bz/PpyjpxsZmLCEPKyXcxVJVBEgoQ3A3s4cNpa22yMeRlYY6197ZzfzwVyAZKSkqZWVVVd2uQ+0tzaxptlh1ha/PdKYG5WKveoEigiAebNwP4F8CnwIrADuNdau6e7fYPxDLur9nbLO3uOUFDkZueBOuIH9WdBZrIqgSISMN4M7DHAK8BA4C/W2v9xvn2dENidrLVsKj/G0qJyijsqgfffmMRCVQJFxM/CooftLbur61lWXM5bHZXA+VMSyc1KJVWVQBHxAwX2Rag6dqajEniQlrZ2bp84mrxsVQJFxLcU2Jeg5lQzKzdU8OLmKk51VALzc1zMSFMlUES8T4HtBaeaWnilY5XAo6c8lcD8HBdzrx5DZISCW0S8Q4HtRc2tbawpq2ZZUTnltWcYN9xTCbx7iiqBInLpFNg+0NZueXfPYQoK3ew8WE/8oP4snOGpBA6JUSVQRC6OAtuHrLVsch+joMhNyWe1DO4fxX3Tkng4M4WRqgSKSB8psC/BmrJqlqzdy6G6RhLiYlk0J515kxO73Xd3dT1Li9z8ZdfnREVEcPdUz4ODU+IH+nlqEXEqBfZFWlNWzeLVu2hsaftiW2x0JE/Ov+a8oQ1QWeupBL6+3VMJnHu1pxJ47VhVAkXkwhTYFynzqXVU1zV+ZXtiXCwbnpjV49cfPdXErzdU8uKmKk41t5KZNpz87DQy04arEigi3eptYGu5ui4OdRPWF9re1cjBMTx++5VsXDyLxXOv5NMjp/neC1u461cbeOujz2lr995fkCISXhTYXSTExfZp+/kMjonmkWwXJY/fzJPzr+F0cyv/9eUPueWZQl7esp+mcy65iIj0hgK7i0Vz0ont0q2OjY5k0Zz0i/p+MdGRfPeGJN57LJv/vH8Kg2Oi+ckbu5j59AcUFLo52dTijbFFJAzoGnY3+tIS6StrLRvdx1h6TiXw/mnjWDgjmZGDVQkUCUf60NEBdh2sZ2mxm7d3fU5UZAR3TxnLI1mpJKsSKBJWFNgOUll7huUl5fy+9CCt7e3MvWYM+dkurk4cGujRRMQPFNgOdPRkEys2VPLSZk8lcOYV8eRlu5juUiVQJJQpsB3sZFMLL23ez4oNFdScaubasUPJy3YxZ+JorRIoEoIU2CGgqaWN1R9Ws7zYTeWxBlLiB5Kblcr8KYn0j9IqgSKhQoEdQtraLX/dfZiCon3srj7JyMH9eXhGCvfdmMRgrRIo4ngK7BBkrWXDvmMUFO1jw75jDI6J4vvTxrEgM4URg/sHejwRuUgK7BD30cE6lha5eXv3YaIjI/jW1LHkZqUybrgqgSJOo8AOE+U1p3mupJw/bK+mtb2dr10zhjxVAkUcRYEdZo6ebOKFDRW8tHk/pzsqgfnZLm5SJVAk6Cmww1R9YwsvbalixfpKak83M2nsUPJzXNw2QZVAkWClwA5zTS1t/OHDgywvLqfqWAOp8QN5JDuVeZNVCRQJNgpsATyVwLd3f87SIje7q08yaoinEvjdG1QJFAkWXg9sY8w/AndYa2893z4K7OBlrWX9vlqWFrm/qAQ+cNM4HpquSqBIoHk1sI0x44A/AjUKbOfbecBTCfzrx55K4LczxpI700XS8AGBHk0kLHk7sNcAy4HHFNiho7zmNMuLy1n9oacSeMe1CeRlpzIxQZVAEX/yWmAbY+4D0oGVwPNdA9sYkwvkAiQlJU2tqqq66KElMI6cbGLF+gpe2uKpBGaNH0F+totpqcNUCRTxA28G9stAEhCFJ7h/Zq39VXf76gzb2eobW/jt5ipWbqig9vRZJl0eR362i9kTRhGhSqCIz/jiQ8dkujnDPpcCOzQ0tbTx++2eSuD+4w2kjhhIXpaLb0xOUCVQxAd6G9h6CK98RUx0JN+bNo51P87mP747mZioSB7/w0dkPf0BzxWXc7q5NdAjioQl9bClR9ZaSj6rpaDQzabyYwyJieKBm5J5KDOZ+EGqBIpcKt04Iz6x40AdSwvdrN1zmH6REXw743Jys1K5fJgqgSIXS4EtPuWuOc3yonJWlx2k3cIdHasETkgYEujRRBxHgS1+cbi+iRUbKnhpcxVnzraRPX4E+TkubkxRJVCktxTY4lf1DS38dsvfK4HXXR7nWSXwKlUCRXqiwJaAaGpp4/XtB3muoxLoGjGQR7JdzLsukX5RKiWJdEeBHWLWlFWzZO1eDtU1khAXy6I56cybnBjosc6rta2dv+w+TEGhm08+P8noITH8YGYK996QxKD+UYEeTySoKLBDyJqyahav3kVjS9sX22KjI3ly/jVBHdrgqQQWf1ZLQeE+NpcfZ0hMFA9OT+ah6ckMVyVQBFBgh5TMp9ZRXdf4le2JcbFseGJWACa6OGX7T7C0yM07e47QP8pTCfzhTFUCRXob2Pq3qQMc6iasL7Q9WE1Ouoxl389g39HTLC9288rW/by0ZT9fv9ZTCbxqjCqBIheiT4EcICEutk/bg13ayEE8fc8kSh6fxcLMZN7bc4S5z5bw0MqtbCk/hjf/1ScSShTYDrBoTjqx0V9edCk2OpJFc9IDNJF3jB4aw3+/YwIbn7iFf5o9nl0H6/nO8s3ML9jIOx8fpr1dwS1yLl3DdgintUQuRlNLG6+XHmBZcTkHTzSSNnIQj2Sl8g1VAiXE6UNHcazWtnbe2vU5BYVu/nb4FGOGxnzx4OCBqgRKCFJgi+NZayn8tIalhW62VBxnaGw0D940jgdVCZQQo8CWkPLh/hMsLfRUAmOiI/hOxuX8QJVACREKbAlJ+46eYllROWt2VNNu4c5rx5CX4+LK0aoEinMpsCWkfV7fyAslFby8dT8NZ9u4OX0E+TlpXJ98mVYJFMdRYEtYqGs4y4ubqli5sZLjZ84yJSmO/Jw0brlypFYJFMdQYEtYaTzbxuvbD7CsqJzqukauGDmIR7Jd3DUpQZVACXoKbAlLXSuBCUNjeHhmKvdef7kqgRK0FNgS1qy1FO6toaDIzdaK48QNiPY8OHh6MsMG9gv0eCJfosAW6bC9yrNK4LsdlcB7r0/iBzNTGHuZKoESHBTYIl18duQUy4rLWVNWjQXumpTAI9mpqgRKwCmwRc7jUF0jz5dU8LttnkrgrCtHkp/j4vrkYYEeTcKUAlukB3UNZ/nNJs+Dg080tJAx7jLysl3MUiVQ/MxrgW2MiQJeARKAvdbahefbV4EtTtRwtpXXth3guZIKqusaGT9qEI9kubjrugSiI1UJFN/rbWD35k/jPGCntTYTGGOMue6SpxMJIgP6RfFQZgqFi3L4t+9MwmD48es7yVlSyIr1FTScbQ30iCJA786wBwHtwFmgBLjfWlve3b46w5ZQYK3lg71HKSh0s63yBJd1VAIfVCVQfMTr17CNMVuAz62187pszwVyAZKSkqZWVVVdxLgiwWl71XEKCst575MjxEZH8p3rL+eHWakkOvTxbBKcvHkNezhwGmgF1gE/t9Z+0N2+OsMOH+HwBJxzfXrEs0rgmzuqAbjrugTysl2MHzU4wJNJKPDmNewfA9+y1rYBDYBOLcLcmrJqFq/eRXVdIxaormtk8epdrCmrDvRoPjN+1GCe+fYkih6/me/fNI63dx1m9r8V84NV2yitPB7o8SRM9OYMOxF4EU9Qu4EHO8L7K3SGHR4yn1pHdV3jV7YnxsWy4YlZAZjI/06cOcuqTZWs2ljJiYYWrk/2VAJvTlclUPqut2fYPa6GY62tBsLj/0LplUPdhPWFtoeiywb240e3jic3K5VXtx3g+ZIKHl5VSvqowTySncqdk1QJFO/Tnyjps4TzfOB2vu2hbEC/KBZ0VAL/z7cnYbE89pqnErhygyqB4l0KbOmzRXPSiY2O/NK22OhIFs1JD9BEgRcdGcH8KWP566NZvPBgBglxMfzPP+0h86l1PPveZ5w4czbQI0oI0K3pclGCsSUSbDOVVh6noNDN+387Smx0JN+9wbNKYDj+S0QuTGuJSFjpbK40tvz98/DY6EienH9NwP8i2Xv4FMuK3Pxx5yEAvnFdInnZqVyhSqB0UGBLWHFCc+XgiQaeL6ng1W0HaGxp49arRpGfk8rUcVolMNx5s4ctEvSc0FwZe9kAfn7XRDY8MYtHb7mC0qrj3F2wiW8v3cS6vx3BmydPEpoU2BISnNRcGTawH/9423g2PjGLf/76BA6eaGDhr0uZ+2wJa8qqaW1rD/SIEqQU2BISnNhcGdAvioUzUih6/Gae+dYk2q3lR6/uIHtJIas2VtJ4ttv70ySM6Rq2hIxga4n0VXu7Zd3fjlJQ5GZ71QmGDezHQ9OTeeCmccQN0CqBoUwfOopcgkCH/7bK4yztqAQO6OepBD48Q5XAUKXAFrlIwVQR7KwEvrnzEAaYN9lTCUwbqUpgKFFgi1ykYKwIdlYCf7dtP00t7dw2YRT5OS6mJF0WkHnEu7y2+JNIuPFWRdCbl1U6K4H/cMsVrNpYyapNlbz7n0e4IWUY+TkucsaPwBitEhjq1BIR6cIbFUFfrRneWQnc8N86KoHHG1iwchtzny3hzR2qBIY6BbZIF96oCC5Zu/dL18ABGlvaWLJ2r1dmHNj/y5XAtnbLo7/bQc4vC/nNJlUCQ5UCW6SLeZMTeXL+NSTGxWLwXLvu6weO/rrzMjoygrunjmXtj7J4/oEMRg2J4Z/f/JjMf13Hf7z/GfUNLV79eRJYuoYt0o15kxMvqRGSEBfb7QeXvqrlRUQYbp0wilsnjGJbxyqBz7z7KUuL3J5K4MwUxgxVJdDpdIYt4gOBvPPy+uRhrHjoev76o5nMnjialRsryXr6Axa9vpN9R0/7/OeL76jWJ+Ijgb75ptOB4w28sN5TCWxubee2q0aRp0pgUFEPW0S+5NjpZn7yxi7e2XMEa6FfZAQLMpN5Yu6VqgQGmJZXFZEvKfmsluJPa+k8Rzvb1s6y4nIy/3WdKoEOocAWCRPdVQ0Bjp5s5tHf7eDmZwp5cVMlTd3sI8FBgS0SJs5XKWxttzz3QAYjBvXnZ29+TOZT6/jVOv9UAteUVZP51DpSnniLzKfWXfKNRaFOtT6RMHG+qmFiXCy3TRjFrVeNZFvlCQoK9/HLdz6loNDNfTcm8fCMVEYPjfH6PF0X2eq8GxRw1LK4/qQzbJEw0VPV0BjDDSnDWLngBt5+dCa3TRjFig2VzHx6HY//3vuVQF/fDRqKdIYtEiY6z1p7UzW8aswQ/u+9k/nx7HSeLynn1dIDvL79ILMnjCIv28VkL1QCnfAczmDTY63PePo+vwbSgaPAfGtta3f7qtYnEpqOnW7uWCWwivrGFqalDiMv20X2JawSGIzL2AaKN2t9mUCUtXYaMASYfanDiYizDB/Un8dmp7PxiVn89I6rqKxt4KGV2/jav6+/6EqgE5/DGWi9CewjwLMdr8/6cBYRCXID+0fxg5mpFD9+M0vuuZazrW0XXQn0xiJb4abXdzoaY74JPArcYq1tO2d7LpALkJSUNLWqqsoXc4pIEGpvt7z3yREKityU7a9j+MB+LMhM5vvTkhk6IDrQ4wXN8gA98eqt6caYu4DHgDuttafOt5+uYYuEJ2stWyuOU1DkpnBvDQP7RXL/tHEszEzxSSWwN4Lp2Zw98VpgG2NGA68Dt1trz1xoXwW2iOw5dJJlxW7+tPMQkRGGb05OJDfLRdrIQX6dw0kfanrzmY4PAmOAtR2fBq+w1q64xPlEJERNSBjCs/dO5p9mp/NcSTmvbvt7JTA/J43rLo/zyxz+qg3687KLVusTEZ+q7awEbqzkZFMrN6UOJy/HRdYV8T5dJdAfZ9jeuuyi1fpEJCjED+rPj2ens3HxLfz0jquoqD3Dgyu2cse/r+ePOw/5bJVAf9QG/X23pgJbRPxi0DmVwKfvuZam1jb+4ZUyZj1TxIubq7y+SqA/aoP+vltTl0REJCDa2y3vfnKEgkI3Ow7UET+oHwsyU/jetHEMjQ18JbA3vHXZRZdERCSoRUQY5kwczRv/ZTqv/HAaExOGsmTtXjKfWse//OUTjpxsCvSIPfL33Zo6wxaRoPHxoXqWFZXz548OERUR4akEZqfiGuHfSmBfeKMlomc6iohj7T/WwHMl5bxWeoCzbe3MmTCa/BwXk/xUCfQ3BbaIOF7t6WZ+vaGS32zyVAKnu4aTl+1ipo8rgf6mwBaRkHGqqYVXtu7nhfUVHDnZzMSEIeRlu/jaNWOIjHB+cCuwRSTkNLe2saasmmVF5ZTXnmHc8AHkZqVy95SxxHT58M9JFNgiErLa2i3v7jlMQaGbnQfriR/UnwWZyY6qBJ5LgS0iIc9ay6byYywtKqf40xoG9Y/i/huTWDgjhVFDArNK4MVQYItIWNldXc+y4nLe6qgE3j3Vs0pgSvzAQI/WIwW2iISlqmNnWF5czuvbD9LS1s7cq0eTl+3i2rHBWwlUYItIWKs51czKDRW8uLmKU02tZKYNJz87jcy04UFXCVRgi4jgqQS+vMVTCTx6qpmrE4eQn53G7VePDppKoAJbROQcza1tvPFhNcuKy6moPUPy8AHkZrmYPyUx4JVABbaISDfa2i3vfHyYgiI3Hx2sZ8Tg/izMTOH+aUkMiQlMJVCBLSJyAdZaNrmPUVDkpuSzWgb3j+p4cHAyI/1cCVRgi4j00u7qegqK3Ly96/OOSuBYHslKJdlPlUAFtohIH1XWnmF5STm/336Q1rZ25l49hrxsF9eMHerTn6vAFhG5SEdPNbFyQyW/3VTFqeZWZqTFk5/jYrrLN5VABbaIyCU6eU4lsOZUM9eOHUpetos5E71bCVRgi4h4SVNLG2+UVbOsyE3lsQZS4geSm5XK/CmJ9I+69EqgAltExMva2i1rP/asErirup6Rg/vz8IwU7rsxicGXUAlUYIuI+Ii1lo3uYxQUulm/r5bBMVH8r29c3ednOXbqbWBH9fKbRQOrrbV3XtQ0IiIhxBhDZlo8mWnx7DpYz9IiN5cPi/X5z+0xsI0xscAWYLzPpxERcZhrxg7l/90/xS8/K6KnHay1jdbaa4GDfphHRETOo8fA7okxJtcYU2qMKa2pqfHGTCIi0o1LDmxr7XJrbYa1NmPEiBHemElERLpxyYEtIiL+ocAWEXGIXge2tTbNl4OIiMiF6QxbRMQhFNgiIg7h1VvTjTE1QJXXvmHwigdqAz2En+k9h4dwe8/B8n7HWWt7rNl5NbDDhTGmtDf3/YcSvefwEG7v2WnvV5dEREQcQoEtIuIQCuyLszzQAwSA3nN4CLf37Kj3q2vYIiIOoTNsERGHUGD3gTHmdmPMQWPM+o5f6YGeyZeMMdHGmD91vI4xxvzZGLPTGPOi8cWjo4NAl/cc0sfbeKwyxmw2xvzRGDMo1I9xN+/56046xgrsviuw1s7o+LU30MP4SseDK7YDt3Vs+h5w0Fo7CbjsnO0ho5v3DKF9vDOBKGvtNGAIsJAQP8Z89T2346BjrMDuu7uNMVuNMX8IxTOQTt08uGIW8G7H63XAzQEZzIfO87COUD7eR4BnO16fBX5OiB9jvvqewUHHWIHdN27gZ9baG4AxQHaA5/Gn4UB9x+uTwLAAzuIvIX28rbWfWWu3GmO+CfTD86+LkD7G3bxnRx1jBXbfHAfe63hdCYwM3Ch+VwsM7Xg9lOC4ndfXQv54G2PuAh4F7gSOEgbHuMt7rsVBx1iB3TePAfcaYyKAq4HdAZ7Hn94HZne8ngV8EMBZ/CWkj7cxZjSwCLjDWnuKMDjG3bxnRx1jBXbf/ApYgOcp8m9Ya/cEeB5/eglINMZ8hOfM8/0Az+MPoX68H8RzGWCtMWY9EE3oH+Ou77kBBx1j3TgjIuIQOsMWEXEIBbaIiEMosEVEHEKBLSLiEApsERGHUGCLiDiEAltExCH+P2o6Y9Ovik89AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fd27710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The coefficients\n",
    "print('Coefficients: \\n', linreg.coef_)\n",
    "\n",
    "y_pred = linreg.predict(X)\n",
    "# The mean square error\n",
    "print(\"MSE:\", metrics.mean_squared_error(y, y_pred))\n",
    "\n",
    "# Explained variance score: 1 is perfect prediction\n",
    "print('Variance score: %.2f' % linreg.score(X, y))\n",
    "plt.scatter(X, y)\n",
    "plt.plot(X, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.多项式模型\n",
    "![](images/02.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: \n",
      " [[-0.4656313   0.01075704]]\n",
      "MSE: 0.11811957095094376\n",
      "Variance score: 0.95\n"
     ]
    }
   ],
   "source": [
    "x1 = X\n",
    "x2 = X**2\n",
    "x1['x2'] = x2\n",
    "\n",
    "linreg = LinearRegression()\n",
    "linreg.fit(x1, y)\n",
    "# The coefficients\n",
    "print('Coefficients: \\n', linreg.coef_)\n",
    "\n",
    "y_pred = linreg.predict(X)\n",
    "# The mean square error\n",
    "print(\"MSE:\",metrics.mean_squared_error(y, y_pred))\n",
    "print('Variance score: %.2f' % linreg.score(x1, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>x2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.5</td>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.8</td>\n",
       "      <td>7.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.5</td>\n",
       "      <td>20.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.5</td>\n",
       "      <td>56.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10.5</td>\n",
       "      <td>110.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>13.5</td>\n",
       "      <td>182.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>15.1</td>\n",
       "      <td>228.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>16.5</td>\n",
       "      <td>272.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>19.5</td>\n",
       "      <td>380.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>22.5</td>\n",
       "      <td>506.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>24.5</td>\n",
       "      <td>600.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>26.5</td>\n",
       "      <td>702.25</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       0      x2\n",
       "0    1.5    2.25\n",
       "1    2.8    7.84\n",
       "2    4.5   20.25\n",
       "3    7.5   56.25\n",
       "4   10.5  110.25\n",
       "5   13.5  182.25\n",
       "6   15.1  228.01\n",
       "7   16.5  272.25\n",
       "8   19.5  380.25\n",
       "9   22.5  506.25\n",
       "10  24.5  600.25\n",
       "11  26.5  702.25"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.对数模型\n",
    "![](images/03.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: \n",
      " [[-1.75683848]]\n",
      "MSE: 0.035512357185799176\n",
      "Variance score: 0.99\n"
     ]
    }
   ],
   "source": [
    "x2 = pd.DataFrame(np.log(X[0]))\n",
    "\n",
    "linreg = LinearRegression()\n",
    "linreg.fit(x2, y)\n",
    "\n",
    "# The coefficients\n",
    "print('Coefficients: \\n', linreg.coef_)\n",
    "\n",
    "y_pred = linreg.predict(x2)\n",
    "# The mean square error\n",
    "print(\"MSE:\", metrics.mean_squared_error(y, y_pred))\n",
    "print('Variance score: %.2f' % linreg.score(x2, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.指数\n",
    "![](images/04.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: \n",
      " [[-0.04880874]]\n",
      "MSE: 0.01474841988614977\n",
      "Variance score: 0.92\n"
     ]
    }
   ],
   "source": [
    "y2 = pd.DataFrame(np.log(y))\n",
    "\n",
    "linreg = LinearRegression()\n",
    "linreg.fit(pd.DataFrame(X[0]), y2)\n",
    "\n",
    "# The coefficients\n",
    "print('Coefficients: \\n', linreg.coef_)\n",
    "\n",
    "y_pred = linreg.predict(pd.DataFrame(X[0]))\n",
    "# The mean square error\n",
    "print(\"MSE:\", metrics.mean_squared_error(y2, y_pred))\n",
    "print('Variance score: %.2f' % linreg.score(pd.DataFrame(X[0]), y2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.幂函数\n",
    "![](images/05.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: \n",
      " [[-0.47242789]]\n",
      "MSE: 0.0010862101591600077\n",
      "Variance score: 0.99\n"
     ]
    }
   ],
   "source": [
    "linreg = LinearRegression()\n",
    "linreg.fit(x2, y2)\n",
    "\n",
    "# The coefficients\n",
    "print('Coefficients: \\n', linreg.coef_)\n",
    "\n",
    "y_pred = linreg.predict(x2)\n",
    "# The mean square error\n",
    "print(\"MSE:\",metrics.mean_squared_error(y2, y_pred))\n",
    "print('Variance score: %.2f' % linreg.score(x2, y2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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