{"id":1008882,"date":"2024-12-27T11:06:44","date_gmt":"2024-12-27T03:06:44","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1008882.html"},"modified":"2024-12-27T11:06:46","modified_gmt":"2024-12-27T03:06:46","slug":"python%e5%a6%82%e4%bd%95%e5%ae%9e%e7%8e%b0%e6%95%b0%e6%8d%ae%e6%8b%9f%e5%90%88","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1008882.html","title":{"rendered":"python\u5982\u4f55\u5b9e\u73b0\u6570\u636e\u62df\u5408"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25084028\/2191070d-c11c-4858-b50d-7701d12ce9f7.webp\" alt=\"python\u5982\u4f55\u5b9e\u73b0\u6570\u636e\u62df\u5408\" \/><\/p>\n<p><p> <strong>Python\u5b9e\u73b0\u6570\u636e\u62df\u5408\u7684\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u5305\u62ec\u7ebf\u6027\u56de\u5f52\u3001\u975e\u7ebf\u6027\u56de\u5f52\u3001\u66f2\u7ebf\u62df\u5408\u7b49\u3002\u53ef\u4ee5\u4f7f\u7528\u7684\u5e93\u6709numpy\u3001scipy\u3001pandas\u548cstatsmodels\u7b49\u3002\u6700\u5e38\u7528\u7684\u65b9\u6cd5\u662f\u901a\u8fc7scipy\u5e93\u4e2d\u7684curve_fit\u51fd\u6570\u8fdb\u884c\u975e\u7ebf\u6027\u62df\u5408\u3001\u901a\u8fc7numpy\u4e2d\u7684polyfit\u8fdb\u884c\u591a\u9879\u5f0f\u62df\u5408\u3001\u901a\u8fc7statsmodels\u8fdb\u884c\u7ebf\u6027\u56de\u5f52\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u5176\u4e2d\u7684curve_fit\u65b9\u6cd5\u3002<\/strong><\/p>\n<\/p>\n<p><p>\u4e00\u3001\u7ebf\u6027\u56de\u5f52<\/p>\n<\/p>\n<p><p>\u7ebf\u6027\u56de\u5f52\u662f\u6570\u636e\u62df\u5408\u4e2d\u6700\u57fa\u672c\u7684\u65b9\u6cd5\u4e4b\u4e00\uff0c\u9002\u7528\u4e8e\u7ebf\u6027\u5173\u7cfb\u7684\u6570\u636e\u96c6\u3002Python\u4e2d\u53ef\u4ee5\u4f7f\u7528statsmodels\u5e93\u6765\u5b9e\u73b0\u7ebf\u6027\u56de\u5f52\u3002\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u5c06\u6570\u636e\u5bfc\u5165Python\uff0c\u7136\u540e\u4f7f\u7528OLS\uff08Ordinary Least Squares\uff09\u65b9\u6cd5\u6765\u8fdb\u884c\u62df\u5408\u3002OLS\u65b9\u6cd5\u662f\u7ebf\u6027\u56de\u5f52\u7684\u4e00\u79cd\u57fa\u672c\u5b9e\u73b0\uff0c\u5b83\u901a\u8fc7\u6700\u5c0f\u5316\u6b8b\u5dee\u5e73\u65b9\u548c\u6765\u627e\u5230\u6700\u4f73\u62df\u5408\u53c2\u6570\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>import statsmodels.api as sm<\/p>\n<h2><strong>\u793a\u4f8b\u6570\u636e<\/strong><\/h2>\n<p>x = np.array([1, 2, 3, 4, 5])<\/p>\n<p>y = np.array([2, 4, 5, 4, 5])<\/p>\n<h2><strong>\u6dfb\u52a0\u5e38\u6570\u9879<\/strong><\/h2>\n<p>x = sm.add_constant(x)<\/p>\n<h2><strong>\u521b\u5efa\u6a21\u578b\u5e76\u62df\u5408<\/strong><\/h2>\n<p>model = sm.OLS(y, x)<\/p>\n<p>results = model.fit()<\/p>\n<h2><strong>\u8f93\u51fa\u7ed3\u679c<\/strong><\/h2>\n<p>print(results.summary())<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u521b\u5efa\u4e86\u4e00\u7ec4\u793a\u4f8b\u6570\u636e\uff0c\u7136\u540e\u4f7f\u7528statsmodels\u5e93\u4e2d\u7684OLS\u65b9\u6cd5\u6765\u62df\u5408\u8fd9\u4e9b\u6570\u636e\u3002\u6700\u540e\uff0c\u6211\u4eec\u4f7f\u7528summary()\u65b9\u6cd5\u6765\u67e5\u770b\u62df\u5408\u7ed3\u679c\uff0c\u5305\u62ec\u7cfb\u6570\u3001R-squared\u503c\u7b49\u3002<\/p>\n<\/p>\n<p><p>\u4e8c\u3001\u975e\u7ebf\u6027\u56de\u5f52<\/p>\n<\/p>\n<p><p>\u975e\u7ebf\u6027\u56de\u5f52\u9002\u7528\u4e8e\u590d\u6742\u5173\u7cfb\u7684\u6570\u636e\u96c6\uff0cPython\u4e2d\u53ef\u4ee5\u4f7f\u7528scipy\u5e93\u4e2d\u7684curve_fit\u51fd\u6570\u6765\u5b9e\u73b0\u975e\u7ebf\u6027\u56de\u5f52\u3002curve_fit\u51fd\u6570\u53ef\u4ee5\u62df\u5408\u4efb\u610f\u51fd\u6570\u5f62\u5f0f\u7684\u6570\u636e\u6a21\u578b\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">from scipy.optimize import curve_fit<\/p>\n<h2><strong>\u5b9a\u4e49\u6a21\u578b\u51fd\u6570<\/strong><\/h2>\n<p>def model_func(x, a, b, c):<\/p>\n<p>    return a * np.exp(-b * x) + c<\/p>\n<h2><strong>\u793a\u4f8b\u6570\u636e<\/strong><\/h2>\n<p>x_data = np.array([1, 2, 3, 4, 5])<\/p>\n<p>y_data = np.array([2.5, 3.6, 2.1, 5.8, 7.9])<\/p>\n<h2><strong>\u62df\u5408\u6570\u636e<\/strong><\/h2>\n<p>params, covariance = curve_fit(model_func, x_data, y_data)<\/p>\n<h2><strong>\u8f93\u51fa\u62df\u5408\u53c2\u6570<\/strong><\/h2>\n<p>print(params)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u5b9a\u4e49\u4e86\u4e00\u4e2a\u6a21\u578b\u51fd\u6570model_func\uff0c\u7136\u540e\u4f7f\u7528curve_fit\u51fd\u6570\u6765\u62df\u5408\u6570\u636e\u3002curve_fit\u51fd\u6570\u8fd4\u56de\u7684params\u662f\u62df\u5408\u53c2\u6570\uff0ccovariance\u662f\u53c2\u6570\u7684\u534f\u65b9\u5dee\u77e9\u9635\u3002<\/p>\n<\/p>\n<p><p>\u4e09\u3001\u591a\u9879\u5f0f\u62df\u5408<\/p>\n<\/p>\n<p><p>\u591a\u9879\u5f0f\u62df\u5408\u662f\u4e00\u79cd\u7b80\u5355\u4e14\u7075\u6d3b\u7684\u6570\u636e\u62df\u5408\u65b9\u6cd5\uff0c\u9002\u7528\u4e8e\u5177\u6709\u591a\u9879\u5f0f\u5173\u7cfb\u7684\u6570\u636e\u96c6\u3002Python\u4e2d\u53ef\u4ee5\u4f7f\u7528numpy\u5e93\u4e2d\u7684polyfit\u51fd\u6570\u6765\u5b9e\u73b0\u591a\u9879\u5f0f\u62df\u5408\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u793a\u4f8b\u6570\u636e<\/p>\n<p>x = np.array([1, 2, 3, 4, 5])<\/p>\n<p>y = np.array([2, 4, 5, 4, 5])<\/p>\n<h2><strong>\u591a\u9879\u5f0f\u62df\u5408<\/strong><\/h2>\n<p>coefficients = np.polyfit(x, y, 2)<\/p>\n<h2><strong>\u8f93\u51fa\u591a\u9879\u5f0f\u7cfb\u6570<\/strong><\/h2>\n<p>print(coefficients)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528polyfit\u51fd\u6570\u6765\u62df\u5408\u4e8c\u6b21\u591a\u9879\u5f0f\uff0c\u8fd4\u56de\u7684coefficients\u662f\u591a\u9879\u5f0f\u7684\u7cfb\u6570\u3002<\/p>\n<\/p>\n<p><p>\u56db\u3001\u66f2\u7ebf\u62df\u5408<\/p>\n<\/p>\n<p><p>\u66f2\u7ebf\u62df\u5408\u662f\u4e00\u79cd\u5e7f\u6cdb\u4f7f\u7528\u7684\u6570\u636e\u62df\u5408\u65b9\u6cd5\uff0c\u9002\u7528\u4e8e\u5404\u79cd\u66f2\u7ebf\u5173\u7cfb\u7684\u6570\u636e\u96c6\u3002Python\u4e2d\u53ef\u4ee5\u4f7f\u7528scipy\u5e93\u4e2d\u7684curve_fit\u51fd\u6570\u6765\u5b9e\u73b0\u66f2\u7ebf\u62df\u5408\u3002curve_fit\u51fd\u6570\u53ef\u4ee5\u62df\u5408\u4efb\u610f\u51fd\u6570\u5f62\u5f0f\u7684\u6570\u636e\u6a21\u578b\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u5b9a\u4e49\u6a21\u578b\u51fd\u6570<\/p>\n<p>def model_func(x, a, b, c):<\/p>\n<p>    return a * np.sin(b * x) + c<\/p>\n<h2><strong>\u793a\u4f8b\u6570\u636e<\/strong><\/h2>\n<p>x_data = np.array([1, 2, 3, 4, 5])<\/p>\n<p>y_data = np.array([2.5, 3.6, 2.1, 5.8, 7.9])<\/p>\n<h2><strong>\u62df\u5408\u6570\u636e<\/strong><\/h2>\n<p>params, covariance = curve_fit(model_func, x_data, y_data)<\/p>\n<h2><strong>\u8f93\u51fa\u62df\u5408\u53c2\u6570<\/strong><\/h2>\n<p>print(params)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u5b9a\u4e49\u4e86\u4e00\u4e2a\u6b63\u5f26\u51fd\u6570\u4f5c\u4e3a\u6a21\u578b\uff0c\u7136\u540e\u4f7f\u7528curve_fit\u51fd\u6570\u6765\u62df\u5408\u6570\u636e\u3002<\/p>\n<\/p>\n<p><p>\u4e94\u3001\u5b9e\u8df5\u4e2d\u7684\u6ce8\u610f\u4e8b\u9879<\/p>\n<\/p>\n<p><p>\u5728\u5b9e\u8df5\u4e2d\uff0c\u9009\u62e9\u5408\u9002\u7684\u62df\u5408\u65b9\u6cd5\u81f3\u5173\u91cd\u8981\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u5e38\u89c1\u7684\u6ce8\u610f\u4e8b\u9879\uff1a<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>\u6570\u636e\u9884\u5904\u7406<\/strong>\uff1a\u5728\u8fdb\u884c\u6570\u636e\u62df\u5408\u4e4b\u524d\uff0c\u901a\u5e38\u9700\u8981\u5bf9\u6570\u636e\u8fdb\u884c\u9884\u5904\u7406\uff0c\u5305\u62ec\u53bb\u9664\u5f02\u5e38\u503c\u3001\u5f52\u4e00\u5316\u7b49\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p><strong>\u9009\u62e9\u5408\u9002\u7684\u6a21\u578b<\/strong>\uff1a\u6839\u636e\u6570\u636e\u7684\u7279\u6027\u9009\u62e9\u5408\u9002\u7684\u62df\u5408\u6a21\u578b\uff0c\u907f\u514d\u8fc7\u62df\u5408\u6216\u6b20\u62df\u5408\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p><strong>\u8bc4\u4f30\u62df\u5408\u7ed3\u679c<\/strong>\uff1a\u4f7f\u7528R-squared\u3001\u6b8b\u5dee\u5206\u6790\u7b49\u65b9\u6cd5\u6765\u8bc4\u4f30\u62df\u5408\u7ed3\u679c\u7684\u8d28\u91cf\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p><strong>\u4ea4\u53c9\u9a8c\u8bc1<\/strong>\uff1a\u5728\u6570\u636e\u91cf\u8f83\u5927\u65f6\uff0c\u53ef\u4ee5\u4f7f\u7528\u4ea4\u53c9\u9a8c\u8bc1\u6765\u8bc4\u4f30\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n<p><p>\u901a\u8fc7\u4ee5\u4e0a\u65b9\u6cd5\u548c\u6ce8\u610f\u4e8b\u9879\uff0c\u60a8\u53ef\u4ee5\u5728Python\u4e2d\u5b9e\u73b0\u6570\u636e\u62df\u5408\uff0c\u5e76\u5728\u5b9e\u8df5\u4e2d\u5e94\u7528\u8fd9\u4e9b\u6280\u672f\u6765\u5206\u6790\u548c\u9884\u6d4b\u6570\u636e\u3002\u65e0\u8bba\u662f\u7b80\u5355\u7684\u7ebf\u6027\u5173\u7cfb\uff0c\u8fd8\u662f\u590d\u6742\u7684\u975e\u7ebf\u6027\u5173\u7cfb\uff0cPython\u63d0\u4f9b\u4e86\u4e30\u5bcc\u7684\u5de5\u5177\u548c\u5e93\u6765\u5e2e\u52a9\u60a8\u8fdb\u884c\u6570\u636e\u62df\u5408\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u5982\u4f55\u9009\u62e9\u5408\u9002\u7684\u62df\u5408\u6a21\u578b\u8fdb\u884c\u6570\u636e\u62df\u5408\uff1f<\/strong><br \/>\u9009\u62e9\u5408\u9002\u7684\u62df\u5408\u6a21\u578b\u662f\u6570\u636e\u62df\u5408\u7684\u5173\u952e\u6b65\u9aa4\u3002\u53ef\u4ee5\u901a\u8fc7\u5206\u6790\u6570\u636e\u7684\u5206\u5e03\u7279\u5f81\u6765\u51b3\u5b9a\u4f7f\u7528\u7ebf\u6027\u6a21\u578b\u3001\u975e\u7ebf\u6027\u6a21\u578b\u8fd8\u662f\u591a\u9879\u5f0f\u6a21\u578b\u3002\u901a\u5e38\uff0c\u53ef\u4ee5\u5229\u7528\u53ef\u89c6\u5316\u5de5\u5177\uff08\u5982\u6563\u70b9\u56fe\uff09\u6765\u89c2\u5bdf\u6570\u636e\u7684\u8d8b\u52bf\u3002\u6b64\u5916\uff0c\u4f7f\u7528\u7edf\u8ba1\u6307\u6807\uff08\u5982R\u00b2\u503c\u3001\u5747\u65b9\u8bef\u5dee\u7b49\uff09\u6765\u8bc4\u4f30\u6a21\u578b\u7684\u62df\u5408\u6548\u679c\uff0c\u4e5f\u80fd\u5e2e\u52a9\u9009\u62e9\u6700\u4f18\u6a21\u578b\u3002<\/p>\n<p><strong>\u5728Python\u4e2d\u6709\u54ea\u4e9b\u5e93\u53ef\u4ee5\u8fdb\u884c\u6570\u636e\u62df\u5408\uff1f<\/strong><br \/>Python\u63d0\u4f9b\u4e86\u591a\u4e2a\u5f3a\u5927\u7684\u5e93\u7528\u4e8e\u6570\u636e\u62df\u5408\uff0c\u5176\u4e2d\u6700\u5e38\u7528\u7684\u5305\u62ecNumPy\u3001SciPy\u548cPandas\u3002NumPy\u53ef\u4ee5\u7528\u4e8e\u7b80\u5355\u7684\u7ebf\u6027\u62df\u5408\uff0cSciPy\u5219\u63d0\u4f9b\u4e86\u66f4\u590d\u6742\u7684\u4f18\u5316\u548c\u975e\u7ebf\u6027\u62df\u5408\u529f\u80fd\uff0c\u800cPandas\u5219\u5728\u6570\u636e\u5904\u7406\u548c\u9884\u5904\u7406\u4e0a\u975e\u5e38\u65b9\u4fbf\u3002\u6b64\u5916\uff0cMatplotlib\u53ef\u4ee5\u7528\u4e8e\u53ef\u89c6\u5316\u62df\u5408\u7ed3\u679c\uff0c\u5e2e\u52a9\u7406\u89e3\u6a21\u578b\u8868\u73b0\u3002<\/p>\n<p><strong>\u5982\u4f55\u8bc4\u4f30\u62df\u5408\u6a21\u578b\u7684\u6548\u679c\uff1f<\/strong><br \/>\u8bc4\u4f30\u62df\u5408\u6a21\u578b\u6548\u679c\u7684\u65b9\u6cd5\u6709\u5f88\u591a\u3002\u5e38\u7528\u7684\u6307\u6807\u5305\u62ecR\u00b2\uff08\u51b3\u5b9a\u7cfb\u6570\uff09\u3001\u5747\u65b9\u6839\u8bef\u5dee\uff08RMSE\uff09\u548c\u6b8b\u5dee\u5206\u6790\u3002R\u00b2\u503c\u8d8a\u63a5\u8fd11\uff0c\u8bf4\u660e\u6a21\u578b\u5bf9\u6570\u636e\u7684\u89e3\u91ca\u80fd\u529b\u8d8a\u5f3a\u3002\u5747\u65b9\u6839\u8bef\u5dee\u5219\u7528\u4e8e\u8861\u91cf\u9884\u6d4b\u503c\u4e0e\u5b9e\u9645\u503c\u7684\u504f\u5dee\uff0c\u6570\u503c\u8d8a\u5c0f\u8868\u793a\u62df\u5408\u6548\u679c\u8d8a\u597d\u3002\u6b8b\u5dee\u5206\u6790\u53ef\u4ee5\u5e2e\u52a9\u53d1\u73b0\u6a21\u578b\u7684\u4e0d\u8db3\u4e4b\u5904\uff0c\u6307\u5bfc\u8fdb\u4e00\u6b65\u7684\u6a21\u578b\u6539\u8fdb\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"Python\u5b9e\u73b0\u6570\u636e\u62df\u5408\u7684\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u5305\u62ec\u7ebf\u6027\u56de\u5f52\u3001\u975e\u7ebf\u6027\u56de\u5f52\u3001\u66f2\u7ebf\u62df\u5408\u7b49\u3002\u53ef\u4ee5\u4f7f\u7528\u7684\u5e93\u6709numpy\u3001scip 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