{ "cells": [ { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0. , 0.52631579, 1.05263158, 1.57894737, 2.10526316,\n", " 2.63157895, 3.15789474, 3.68421053, 4.21052632, 4.73684211,\n", " 5.26315789, 5.78947368, 6.31578947, 6.84210526, 7.36842105,\n", " 7.89473684, 8.42105263, 8.94736842, 9.47368421, 10. ])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np # 导入包\n", "import matplotlib.pyplot as plt\n", "import statsmodels.api as sm\n", "\n", "nsample = 20 #生成20个样本点\n", "x = np.linspace(0, 10, nsample) # 从0-10之间生成20个数\n", "x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**一元线性回归**" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 1. , 0. ],\n", " [ 1. , 0.52631579],\n", " [ 1. , 1.05263158],\n", " [ 1. , 1.57894737],\n", " [ 1. , 2.10526316],\n", " [ 1. , 2.63157895],\n", " [ 1. , 3.15789474],\n", " [ 1. , 3.68421053],\n", " [ 1. , 4.21052632],\n", " [ 1. , 4.73684211],\n", " [ 1. , 5.26315789],\n", " [ 1. , 5.78947368],\n", " [ 1. , 6.31578947],\n", " [ 1. , 6.84210526],\n", " [ 1. , 7.36842105],\n", " [ 1. , 7.89473684],\n", " [ 1. , 8.42105263],\n", " [ 1. , 8.94736842],\n", " [ 1. , 9.47368421],\n", " [ 1. , 10. ]])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = sm.add_constant(x) # 生成第一列都是1，第二列是原始数据\n", "X" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([2, 5])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#β0，β1分别设置成2，5\n", "beta = np.array([2,5])\n", "beta" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-0.44917782, -0.7881134 , -0.41908437, 0.03441592, -1.52404766,\n", " -0.00416825, -0.65333685, 1.67840733, 1.52347633, -0.43867697,\n", " 0.22222029, 0.61150455, -2.23946729, 1.22670988, 0.17836627,\n", " 0.66150276, -1.77887457, 0.37328361, 1.94511935, -0.05179077])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#构造一个高斯分布的误差项\n", "e = np.random.normal(size = nsample)\n", "e" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1.55082218, 3.84346555, 6.84407352, 9.92915276, 11.00226813,\n", " 15.15372648, 17.13613683, 22.09945996, 24.57610791, 25.24553356,\n", " 28.53800976, 31.55887297, 31.33948008, 37.4372362 , 39.02047153,\n", " 42.13518697, 42.32638858, 47.11012572, 51.3135404 , 51.94820923])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#实际值y\n", "y = np.dot(X, beta) + e\n", "y" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "#最小二乘法\n", "model = sm.OLS(y, X)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "#拟合数据\n", "res = model.fit()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1.58035731, 5.08501122])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#回归系数\n", "res.params # 求出的结果就是β0和β1，会有一些差距，因为数据点比较少，可以早多点数据点" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: y R-squared: 0.995
Model: OLS Adj. R-squared: 0.995
Method: Least Squares F-statistic: 3853.
Date: Mon, 09 Nov 2020 Prob (F-statistic): 1.89e-22
Time: 21:52:46 Log-Likelihood: -29.445
No. Observations: 20 AIC: 62.89
Df Residuals: 18 BIC: 64.88
Df Model: 1
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
const 1.5804 0.479 3.298 0.004 0.574 2.587
x1 5.0850 0.082 62.075 0.000 4.913 5.257
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 1.296 Durbin-Watson: 2.429
Prob(Omnibus): 0.523 Jarque-Bera (JB): 0.560
Skew: -0.408 Prob(JB): 0.756
Kurtosis: 3.073 Cond. No. 11.5


Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.995\n", "Model: OLS Adj. R-squared: 0.995\n", "Method: Least Squares F-statistic: 3853.\n", "Date: Mon, 09 Nov 2020 Prob (F-statistic): 1.89e-22\n", "Time: 21:52:46 Log-Likelihood: -29.445\n", "No. Observations: 20 AIC: 62.89\n", "Df Residuals: 18 BIC: 64.88\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const 1.5804 0.479 3.298 0.004 0.574 2.587\n", "x1 5.0850 0.082 62.075 0.000 4.913 5.257\n", "==============================================================================\n", "Omnibus: 1.296 Durbin-Watson: 2.429\n", "Prob(Omnibus): 0.523 Jarque-Bera (JB): 0.560\n", "Skew: -0.408 Prob(JB): 0.756\n", "Kurtosis: 3.073 Cond. No. 11.5\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "\"\"\"" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#全部结果\n", "res.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "R-squared:R方值，评估线性回归方程好不好，主要看R方\n", "Adj. R-squared:\t调整后R方值\n", "Prob (F-statistic):检验是否可用线性回归方程，越小线性关系越强\n", "No. Observations:\t观察的样本\n", "const：常数项，对应β0\n", "x1：对应β1" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1.58035731, 4.256679 , 6.9330007 , 9.60932239, 12.28564409,\n", " 14.96196578, 17.63828748, 20.31460918, 22.99093087, 25.66725257,\n", " 28.34357426, 31.01989596, 33.69621766, 36.37253935, 39.04886105,\n", " 41.72518274, 44.40150444, 47.07782614, 49.75414783, 52.43046953])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#拟合的估计值\n", "y_ = res.fittedvalues\n", "y_" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8,6))\n", "ax.plot(x,y,'o',label='data') # 原始数据\n", "ax.plot(x,y_,'r--.',label='test') #拟合数据\n", "ax.legend(loc='best')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "可以看到非常接近原始值" ] }, { "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }