5.2 吸附中的线性回归.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c14fe03f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn import linear_model\n",
    "from pandas import read_csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "da1805ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>formula</th>\n",
       "      <th>db_center</th>\n",
       "      <th>ad_energy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Cu12Co</td>\n",
       "      <td>-1.33</td>\n",
       "      <td>-0.547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Cu12Rh</td>\n",
       "      <td>-1.57</td>\n",
       "      <td>-0.591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Cu12Ir</td>\n",
       "      <td>-1.74</td>\n",
       "      <td>-0.420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Cu12Ni</td>\n",
       "      <td>-1.21</td>\n",
       "      <td>-0.674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Cu12Pd</td>\n",
       "      <td>-2.01</td>\n",
       "      <td>-0.500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Cu12Pt</td>\n",
       "      <td>-1.78</td>\n",
       "      <td>-0.391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Cu13</td>\n",
       "      <td>-2.33</td>\n",
       "      <td>-0.316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Cu12Ag</td>\n",
       "      <td>-4.13</td>\n",
       "      <td>-0.201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Cu12Au</td>\n",
       "      <td>-3.12</td>\n",
       "      <td>-0.298</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  formula  db_center  ad_energy\n",
       "0  Cu12Co      -1.33     -0.547\n",
       "1  Cu12Rh      -1.57     -0.591\n",
       "2  Cu12Ir      -1.74     -0.420\n",
       "3  Cu12Ni      -1.21     -0.674\n",
       "4  Cu12Pd      -2.01     -0.500\n",
       "5  Cu12Pt      -1.78     -0.391\n",
       "6    Cu13      -2.33     -0.316\n",
       "7  Cu12Ag      -4.13     -0.201\n",
       "8  Cu12Au      -3.12     -0.298"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = open('db_center.csv', encoding = 'UTF-8')\n",
    "names = ['formula', 'db_center', 'ad_energy']\n",
    "data = read_csv(f, names = names)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3eb63b53",
   "metadata": {},
   "outputs": [],
   "source": [
    "f.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b31d6f0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\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>formula</th>\n",
       "      <th>db_center</th>\n",
       "      <th>ad_energy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Cu12Co</td>\n",
       "      <td>-1.33</td>\n",
       "      <td>-0.547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Cu12Rh</td>\n",
       "      <td>-1.57</td>\n",
       "      <td>-0.591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Cu12Ir</td>\n",
       "      <td>-1.74</td>\n",
       "      <td>-0.420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Cu12Ni</td>\n",
       "      <td>-1.21</td>\n",
       "      <td>-0.674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Cu12Pd</td>\n",
       "      <td>-2.01</td>\n",
       "      <td>-0.500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  formula  db_center  ad_energy\n",
       "0  Cu12Co      -1.33     -0.547\n",
       "1  Cu12Rh      -1.57     -0.591\n",
       "2  Cu12Ir      -1.74     -0.420\n",
       "3  Cu12Ni      -1.21     -0.674\n",
       "4  Cu12Pd      -2.01     -0.500"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a342608b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.547, -0.591, -0.42 , -0.674, -0.5  , -0.391, -0.316, -0.201,\n",
       "       -0.298])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = data['ad_energy'].values\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3ae54d7c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   db_center\n",
      "0      -1.33\n",
      "1      -1.57\n",
      "2      -1.74\n",
      "3      -1.21\n",
      "4      -2.01\n",
      "5      -1.78\n",
      "6      -2.33\n",
      "7      -4.13\n",
      "8      -3.12\n"
     ]
    }
   ],
   "source": [
    "excluded = ['formula', 'ad_energy']\n",
    "X = data.drop(excluded, axis = 1)\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1146529f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "#from sklearn.metrics import mean_squared_error\n",
    "\n",
    "lr = LinearRegression()\n",
    "lr.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "22883e64",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.42839089]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\base.py:441: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "predicts = lr.predict([[-2.2]])\n",
    "print(predicts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "05663398",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2=0.7646612597264624\n"
     ]
    }
   ],
   "source": [
    "R2 = lr.score(X,y)\n",
    "print('R2='+str(R2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a8201419",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.14221031]\n",
      "-0.7412535628655474\n"
     ]
    }
   ],
   "source": [
    "coef = lr.coef_\n",
    "intercept = lr.intercept_\n",
    "print(coef)\n",
    "print(intercept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "03f0fa7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei']\n",
    "plt.rcParams['axes.unicode_minus'] = False\n",
    "\n",
    "y = data.iloc[:,2]\n",
    "x = data.iloc[:,1]\n",
    "plt.scatter(x, y, label='实际值')\n",
    "plt.plot(x, lr.predict(X), color = 'red', label = '预测值')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "f19e8372",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tK2fass0KeZFWEHXAm9lCM1tnZjPqmXMssAI4G1hjZhnNqFESTZjOlX9+fAYlvxnNifs+obyikjmFW30sUCQ5RBXwZjYWSHHODQS6m9kpEaaeCdzsnLsLKAT6N69MSUg9e5J16wpG/+je6qEX51/FjBf+i4Ol6nMjEmtto5yfCyyuuv8sMBh4t+4k59yLAGZ2Lt5W/K/DvZmZTQGmAHTt2jXKUiQRdE5P4y1OptutK+jy+Yfc8Mpj/Hjjcia+WQgd3/YuJ3jssX6XKRJI9W7Bm9lDZlYUugHXA6Gdp58BJ9TzWgPGA3uBinBznHPznXM5zrmcjAztxQmi/OHZpKWmALCr0wn831E3Mfqah/gs9/veoZVZWTBzJuzf73OlIsFTb8A75652zuWGbsB9QFrV08fU93rnuRZ4E/hBC9UrCSavXyazxvYmMz0NAzLT07j6qpF0KXwSNm3y2hXffrt3mOXcuVBe7nfJIoER7S6ajXi7ZdYDfYCw35SZ2a3AHufcI0A6UNb0EiXR5fXLJK9f5jefOPNMePJJ71j622/3jqH/3e+8+1dcAUcd1frFxrGC4lLmFG5ld1k5ndPTyB+eHf7fVaRKtEfRFACTzWwuMA5YaWanmdnMOvPmV817CUjB218vEt73vgfPPutdXSorC376U+/Sgn/6kxqaVSkoLmXass2UlpXrcFNptKgC3jm3D++L1vXA+c65z51zbzvnZtSZt9c5d6Fz7lzn3P9xTt2opBHOOw/WroWnn/a+eL38cjjjDFi82OtomcTmFG6lvOLIX3Y63FQaEvVx8FXhvdg590EsCpIkZwYjR3oXBX/iCa+R2fjx3jVkV6xI2s6Vu8vCfzcRaVwE1KpA4pUZjB3rXWjk0Udh3z7vsoKDBsELL/hdXavrnJ4W1bgIKOAl3qWkeJcR3LIF5s+HXbtg2DC44AJYt87v6lpN7cNNQ9JSU8gfnu1TRZIIFPCSGFJT4aqr4N134d574f/9P29rfvRoKC72u7qYC3e46ayxvXUUjdTL4uX7z5ycHLdhwwa/y5BE8eWXcP/98Nvfeg3OLrkEfv1r6NXL78pEWpWZbXTO5YR7Tlvwkpi+9S2YOhV27PCOm3/mGe+Imx/9yBsTEQW8JLj0dG/LfccOuPlm75DK7GzvWrG7dvldnYivFPASDBkZMGeOd+GRKVO8K0qdfLIX+h995Hd1Ir5QwEuwdO4Mf/gD/OMfMHEi/P73Xp+b6dO9ffUiSUQBL8HUrZu3Ff/2296RNnff7QX9XXfBF1/4XZ1Iq1DAS7BlZ8Nf/wpvvAFDhsCMGV6/G3WulCSggJfk0KcPPPUUrF8Pfft6nStPPhn++Ef4+mu/qxOJCQW8JJfvfQ+eew7WrPF246hzpQSYAl6SU24uvPzyNztXLlmS9J0rJTgU8JK8aneuXLrU61w5blzSd66U4FDAi5jBxRd/s3PlOefA6tV+VyfSZAp4kZDanSsfegjefx+GDvVuSdS5UoJDAS9SV2qqdzZsqHPlW28lVedKCQ4FvEgk7dvDjTd67Q/uvhteeQX694dLL4V33vG7OpEGKeBFGnLMMTBtGuzcqc6VklAU8CKNVbtz5c9+ps6VEvcU8CLRysiAe+5R50qJewp4kaaq3blywoSazpUzZqhzpcQFBbxIc3XrBg8/7F0ndvRor2OlOldKHFDAi7SUnj3VuVLiigJepKWF61x5yinqXNkIBcWlnDN7NVlTV3LO7NUUFJf6XVJCU8CLxErtzpUnnaTOlQ0oKC5l2rLNlJaV44DSsnKmLduskG8GBbxIrKlzZaPMKdxKecWRv/jKKyqZU7jVp4oSnwJepDXU17ly5Up1rgR2l4X/niLSuDRMAS/SmsJ1rhw9Wp0rgc7paVGNS8OiDngzW2hm68xsRiPmnmBm6s4kUpc6V35D/vBs0lJTjhhLS00hf3i2TxUlvqgC3szGAinOuYFAdzM7pYGX3APo169IJPV1rnzjDb+ra1V5/TKZNbY3melpGJCZnsassb3J65fpd2kJy1wU+/7M7D7gGefc02Z2GZDmnHs4wtwLgHFAT+dcboQ5U4ApAF27dj3rvffei7J8kYD54gu4/3747W+hrMzrXPmrX0GvXn5XJnHKzDY653LCPVfvFryZPWRmRaEbcD0QOmbpM+CECK87CrgdmFrf+zvn5jvncpxzORkZGQ0shkgSqNu5ctUqda6UJqs34J1zVzvnckM34D5qdrkcU8/rpwIPOufKWqpQkaQSqXPlT38KpTouXBon2i9ZNwKDq+73AUoizBsGXFu11d/XzBY0qTqRZFe7c+VVV8HChdCjhzpXSqNEuw++I7AWeAEYCQwAMoGJzrmwR9WYWVGkffC15eTkuA0bNjS6FpGktHOnt2X/yCOQlgY33QQ//7m3xR9QBcWlzCncyu6ycjqnp5E/PFtfvNbS5H3wdTnn9gG5wHrgfOfc5865tyOFe9VrcqP5DBGpR1bWNztXZmUFtnOl2hc0T9THwTvn9jrnFjvnPohFQSLSCOE6V3bvDvPmBapzpdoXNI/OZBVJZKHOlevWefdvvjlQnSvVvqB5FPAiQTBgQPjOlY88ktCdK9W+oHkU8CJBEupcuXKl98Xrj36U0J0r1b6geRTwIkFjBqNG1XSuNEvYzpVqX9A8UR0mGUs6TFIkRior4S9/gTvu8E6cGjgQZs6ECy7wuzJpAS12mKSIJKCUFJg8uaZz5T//WdO5cv16v6uTGFLAiySLUOfKbdu8wyk3b/a25seMSbrOlclCAS+SbNq3986A3bED7r7b+1K2Xz9vP/2WLX5XJy1IAS+SrGp3rpwxw+tcefrp3jVjd+70uzppAQp4kWSXng533ult0d90k3eG7KmnqnNlACjgRcSTkQG/+11N58oFC+Dkk+GWW+Djj/2uTppAAS8iR8rMhAcfhH/8Ay67zLuUYFaWtxunrMzv6iQKCngRCa9258p/+7eazpV33x3IzpVBpIAXkfr17AmPPw7FxTB4MEyfDh06eGfIfqCmsvFMAS8ijdO3LyxfDs88UzP2ne94Qf/5576VJZEp4EUkOsOHe/1sBg+uGUtP94I+QL3og0ABLyJNs3at16Gye/easaOP9s6YPXTIv7qkmgJeRJrOzDussqIC2rb1xg4d8kK+e/eE6lwZRAp4EWm+tm29kP/qq5qxnTuhTRs491z/6kpyCngRaTlpad5We+3j5deu9bb0J070raxkpYAXkZbXqZMX9Hv21Iw99pgX9Dff7F9dSUYBLyKxc+KJXtBv21YzNm+eF/S/+Y1/dSUJBbyIxF6PHl7QFxfXjE2d6gX9ww/7V1fAKeBFpPX07esFfVFRzdgVV3hB/9RTflUVWAp4EWl9553nBf3f/lYzdtFFXtC/9JJ/dQWMAl5E/JOX5wX9ggU1Y+ed5wW9Olc2mwJeRPx35ZVe0M+aVTOWmanOlc2kgBeR+DF1as2XsRdc4HWu7NEDxo5V58omUMCLSKMVFJdyzuzVZE1dyTmzV1NQHKNL+oU6V65b53Ws/Nvf1LmyCaIOeDNbaGbrzGxGPXPamtk/zayo6ta7eWWKiN8KikuZtmwzpWXlOKC0rJxpyzbHLuQBBgyAN96A3NyasVDnygMHYve5ARFVwJvZWCDFOTcQ6G5mp0SYeibwmHMut+q2ubmFioi/5hRupbyi8oix8opK5hRujf2Hr1njda7MyqoZS0tT58oGRLsFnwssrrr/LDA4wrwBwGgz+9+qLf624SaZ2RQz22BmGz7WRX1F4trusvC93iONtzgz2LFDnSujUG/Am9lDtXazFAHXA6G/xz4DTojw0teBYc65s4FUYFS4Sc65+c65HOdcTkZGRpMWQERaR+f0tKjGY0adKxut3oB3zl1dazdLLnAfEFqbx9Tz+jedc6EuQxuASLtyRCRB5A/PJi015YixtNQU8odn+1OQOlc2KNpdNBup2S3TByiJMO9RM+tjZilAHrCpSdWJSNzI65fJrLG9yUxPw4DM9DRmje1NXr9MfwtT58qIzEWx38rMOgJrgReAkXj72jOBic65GbXmnQH8BTDgKefc9IbeOycnx23YsCG66kVE6tq+HU4++cix2bPh1lv9qSfGzGyjcy4n7HPRBHzVmx0LXAi85JxrsTMPFPAi0qLeeAP69TtybOFCr7lZgNQX8FEfB++c2+ucW9yS4S4i0uLCda688kpv182TT/pVVavSmawiEmzhOlfm5SVF50oFvIgkh/o6V24K5nEgCngRSS7hOlf27VtzIlWAKOBFJDmFOlfedFPNWI8eXtAHpHOlAl5Ektu8eV7QjxtXMxaQzpUKeBERgMcf94J+cK0WWwneuVIBLyJS29q1XufKk06qGUvQzpUKeBGRusygpMRrapZS1X8n1LmyR4+E6VwZto2viIjgda48dAjKy+Hoo72xHTtqOle++GL11ILiUuYUbmV3WTmd09PIH57te58ebcGLiDQk1Lly796asZde8rb0J03y52pXjaCAFxFprPR0L+h3764Z+8tfyOvfhZsLHzpiaqtd7aoeCngRkWh95zte0L/7bvXQVa8XUPKb0Ux57YnqsVa72lUECngRkaY6+WRwjsuv/2P10G1FD1Pym9EMfO/N1r/aVR36klVEpJnyfjyaXp1W0Wd7MX997DYAHvvrbfBXYNjrkBO2m2/MKeBFRJopdLTMnMKjyOq6gqH732PBg9d6T373u97Pt9+GXr1ata6oL/gRK7rgh4gEzgsvwLBhR46VlBx5ElUztegFP0REpJGGDvW+jF22rGasWzfo2BE+/DDmH6+AFxGJtX//dy/oFy3yHu/fDyeeCFlZUFYWs49VwIuItJYf/9gL+rlzvcclJXDssfDaazH5OAW8iEhr+9nPvKCfPt17/MUXMfkYBbyIiF9mzvSCfujQmLy9Al5EJKAU8CIiAaWAFxEJKJ3JKiKBF4+92luDAl5EAi3Uq728ohKo6dUOBD7ktYtGRAJtTuHW6nAPiYde7a1BAS8igRapJ7vfvdpbgwJeRAItUk92v3u1t4aoA97MFprZOjOb0Yi5D5rZmKaVJiLSfPnDs0lLTTliLC01hfzh2T5V1HqiCngzGwukOOcGAt3N7JR65g4BTnTOLW9mjSIiTZbXL5NZY3uTmZ6GAZnpacwa2zvwX7BC9EfR5AKLq+4/CwwG3q07ycxSgf8Cnjazi5xzT4Z7MzObAkwB6Nq1a5SliIg0Tl6/zKQI9Lrq3YI3s4fMrCh0A64HSque/gw4IcJL/wN4G/gtcLaZXR9uknNuvnMuxzmXk5GR0aQFEBGR8OrdgnfOXV37sZn9Hgh9M3EMkX9B9APmO+c+MLP/Ae4C7m9mrSIiEoVov2TdiLdbBqAPUBJh3jage9X9HOC9qCsTEZFmiXYffAGw1sw6AyOBAWZ2GjDROVf7qJqFwCIzuwxIBS5piWJFRKTxogp459w+M8sFLgR+65z7HPgcmFFn3n7g0haqUUREmiDqXjTOub3UHEkjIiJxSmeyiogElAJeRCSgFPAiIgGlgBcRCSgFvIhIQCngRUQCSgEvIhJQCngRkYBSwIuIBJQCXkQkoBTwIiIBpYAXEQkoBbyISEAp4EVEAkoBLyISUAp4EZGAUsCLiASUAl5EJKCivmSfiIi0jILiUuYUbmV3WTmd09PIH55NXr/MFnt/BbyIiA8KikuZtmwz5RWVAJSWlTNt2WaAFgt57aIREfHBnMKt1eEeUl5RyZzCrS32GQp4EREf7C4rj2q8KRTwIiI+6JyeFtV4UyjgRUR8kD88m7TUlCPG0lJTyB+e3WKfoS9ZRUR8EPoiVUfRiIgEUF6/zBYN9Lq0i0ZEJKAU8CIiAaWAFxEJqKgD3swWmtk6M5tRz5yfmllR1e0NM3uoeWWKiEi0ogp4MxsLpDjnBgLdzeyUcPOcc//pnMt1zuUCa4H/analIiISlWiPoskFFlfdfxYYDLwbabKZZQInOOc2RHh+CjCl6uEXZtZy5+g2zvHAJ638mbGk5YlvWp74l4jLdFKkJ+oN+KpdK7WPuj8PWFh1/zOgfwMffC3wn5GedM7NB+Y38B4xY2YbnHM5fn1+S9PyxDctT/wL2jLVG/DOuatrPzaz3wOh82iPoZ5dPGbWBjgfmN7MGkVEpAmi/ZJ1I95uGYA+QEk9c4cArznnXBPqEhGRZop2H3wBsNbMOgMjgQFmdhow0TlX96ia4cBLzS8xpnzbPRQjWp74puWJf4FaJot2A9vMjgUuBF5yzn0Qk6pERKTZog54ERFJDDqTNUGZ2bfN7EIzO97vWlpC0JZHJB4kVcCb2QlmVtzAnAbP1PVb1W6yFcDZwBozy4gwr62Z/bPWWcW9W7XQRmrs8lTNjfv1A2BmncxslZk9a2Z/M7OjIsxLlHXUqOWpmpso6+gEM1vbwJyEWD+RJFXAA/dQc5jnNzT2TN04cCZws3PuLqCQyOcjnAk8Fjqr2Dm3udUqjE6jlieB1g/AJGCuc+77wAfAiAjzEmUdNWp5EmUdVW1U/An4VgNTE2X9hJU0AW9mFwBf4v3njCSXb56pG3eccy8659ab2bl4W73rIkwdAIw2s/+t2qqKy/7/USxPLgmwfgCccw86556repgBfBRhaqKso8YuTy6JsY4qgfHAvgbmJcT6iSShim2sMGfgrsY76erf8Q71jORbQGnV/cacqdsqIizPnXj/QfcCFRFe+jowzDm3x8weAUYBT8Wy1sZoxvLE5fqB8MvknPu1mQ0EjnXOrY/w0oRZR41cnrhcR/UsT0Mvjcv101iBDPgwZ+D+AnjQOVfWwAr9gkaeqdua6i5PLdea2Z3AD4DHwzz/pnPuYNX9DUBc/LncjOWJy/UD4ZfJzL4N3A9cXM9LE2YdNXJ54nId1fN/riFxuX4aKy7+8VvBMLzwKAL6mtmCCPOiOVPXN2Z2q5n9R9XDdKAswtRHzayPmaUAecCm2FcXvSiWJyHWD0DVl5BLgGnOuffqmZoo66ixy5Mw66iREmL9ROScS6obUFT18zRgZp3nOuKtwLnAO0Anv+uNsAzHAs/hnSn8IGARlucM4E1gM3CX33W3wPIkxPqpqvWneLubiqpu4xN8HTV2eRJmHVXVW1TrfsKun0g3nehUh87UjW9aP/FP6yh+KOBFRAIqWfbBi4gkHQW8iEhAKeBFRAJKAS8iElAKeBGRgPr/jIfoAY46dGIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei']\n",
    "plt.rcParams['axes.unicode_minus'] = False\n",
    "\n",
    "y = data.iloc[:,2]\n",
    "x = data.iloc[:,1]\n",
    "plt.scatter(x, y, label='实际值')\n",
    "plt.plot(x, lr.predict(x.to_frame()), color = 'red', label = '预测值')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "1099ae98",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\base.py:441: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei']\n",
    "plt.rcParams['axes.unicode_minus'] = False\n",
    "\n",
    "y = data.iloc[:,2]\n",
    "x = data.iloc[:,1]\n",
    "plt.scatter(x, y, label='实际值')\n",
    "x = np.array(x)\n",
    "plt.plot(x, lr.predict(x.reshape(-1,1)), color = 'red', label = '预测值')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "17ca6933",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}