{"id":1128932,"date":"2025-01-08T20:25:02","date_gmt":"2025-01-08T12:25:02","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1128932.html"},"modified":"2025-01-08T20:25:06","modified_gmt":"2025-01-08T12:25:06","slug":"%e5%a6%82%e4%bd%95%e7%94%a8python%e8%bf%9b%e8%a1%8c%e4%b8%89%e9%a1%b9%e5%bc%8f%e6%8b%9f%e5%90%88","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1128932.html","title":{"rendered":"\u5982\u4f55\u7528python\u8fdb\u884c\u4e09\u9879\u5f0f\u62df\u5408"},"content":{"rendered":"

\"\u5982\u4f55\u7528python\u8fdb\u884c\u4e09\u9879\u5f0f\u62df\u5408\"<\/p>\n

\u5982\u4f55\u7528Python\u8fdb\u884c\u4e09\u9879\u5f0f\u62df\u5408<\/strong><\/p>\n<\/p>\n

\u5728\u4f7f\u7528Python\u8fdb\u884c\u4e09\u9879\u5f0f\u62df\u5408\u65f6\uff0c\u9009\u62e9\u5408\u9002\u7684\u5e93\u3001\u51c6\u5907\u6570\u636e\u3001\u4f7f\u7528polyfit\u51fd\u6570\u3001\u8bc4\u4f30\u62df\u5408\u6548\u679c<\/strong>\u662f\u5173\u952e\u6b65\u9aa4\u3002\u672c\u6587\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528Python\u8fdb\u884c\u4e09\u9879\u5f0f\u62df\u5408\uff0c\u5e76\u91cd\u70b9\u8bb2\u89e3\u5982\u4f55\u4f7f\u7528polyfit\u51fd\u6570\u8fdb\u884c\u591a\u9879\u5f0f\u62df\u5408\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u9009\u62e9\u5408\u9002\u7684\u5e93<\/h3>\n<\/p>\n

\u5728Python\u4e2d\uff0c\u6709\u591a\u4e2a\u5e93\u53ef\u4ee5\u7528\u4e8e\u6570\u636e\u62df\u5408\uff0c\u5176\u4e2d\u6700\u5e38\u7528\u7684\u5e93\u5305\u62ecNumPy\u3001SciPy\u548cSciKit-Learn\u3002\u5bf9\u4e8e\u4e09\u9879\u5f0f\u62df\u5408\uff0cNumPy\u5e93\u4e2d\u7684polyfit\u51fd\u6570\u662f\u4e00\u4e2a\u975e\u5e38\u65b9\u4fbf\u548c\u5f3a\u5927\u7684\u5de5\u5177\u3002<\/p>\n<\/p>\n

NumPy\u662f\u4e00\u4e2a\u5f3a\u5927\u7684\u79d1\u5b66\u8ba1\u7b97\u5e93\uff0c\u63d0\u4f9b\u4e86\u591a\u79cd\u591a\u9879\u5f0f\u62df\u5408\u51fd\u6570\u3002SciPy\u63d0\u4f9b\u4e86\u66f4\u591a\u9ad8\u7ea7\u7684\u7edf\u8ba1\u548c\u4f18\u5316\u5de5\u5177\uff0c\u800cSciKit-Learn\u5219\u662f\u673a\u5668\u5b66\u4e60<\/a>\u5e93\uff0c\u63d0\u4f9b\u4e86\u66f4\u9ad8\u7ea7\u7684\u56de\u5f52\u548c\u5206\u7c7b\u5de5\u5177\u3002<\/p>\n<\/p>\n

\u4e8c\u3001\u51c6\u5907\u6570\u636e<\/h3>\n<\/p>\n

\u5728\u8fdb\u884c\u4e09\u9879\u5f0f\u62df\u5408\u4e4b\u524d\uff0c\u9700\u8981\u5148\u51c6\u5907\u597d\u6570\u636e\u3002\u901a\u5e38\uff0c\u6570\u636e\u5305\u62ec\u81ea\u53d8\u91cf\u548c\u56e0\u53d8\u91cf\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\uff1a<\/p>\n<\/p>\n

import numpy as np<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
\u793a\u4f8b\u6570\u636e<\/strong><\/h2>\n
x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])<\/p>\n
y = np.array([1, 4, 9, 16, 25, 36, 49, 64, 81])<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u81ea\u53d8\u91cfx\u662f1\u52309\u7684\u6574\u6570\uff0c\u56e0\u53d8\u91cfy\u662fx\u7684\u5e73\u65b9\u3002<\/p>\n<\/p>\n
\u4e09\u3001\u4f7f\u7528polyfit\u51fd\u6570<\/h3>\n<\/p>\n
NumPy\u4e2d\u7684polyfit\u51fd\u6570\u53ef\u4ee5\u5f88\u65b9\u4fbf\u5730\u8fdb\u884c\u591a\u9879\u5f0f\u62df\u5408\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u4f7f\u7528polyfit\u8fdb\u884c\u4e09\u9879\u5f0f\u62df\u5408\u7684\u4f8b\u5b50\uff1a<\/p>\n<\/p>\n
# \u4f7f\u7528polyfit\u8fdb\u884c\u4e09\u9879\u5f0f\u62df\u5408<\/p>\n
coefficients = np.polyfit(x, y, 3)<\/p>\n
\u751f\u6210\u62df\u5408\u51fd\u6570<\/strong><\/h2>\n
polynomial = np.poly1d(coefficients)<\/p>\n
\u6253\u5370\u62df\u5408\u51fd\u6570\u7684\u7cfb\u6570<\/strong><\/h2>\n
print("\u4e09\u9879\u5f0f\u62df\u5408\u7684\u7cfb\u6570:", coefficients)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0cpolyfit\u51fd\u6570\u8fd4\u56de\u4e86\u4e09\u9879\u5f0f\u7684\u7cfb\u6570\u3002poly1d\u51fd\u6570\u751f\u6210\u4e86\u4e00\u4e2a\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u62df\u5408\u503c\u7684\u591a\u9879\u5f0f\u5bf9\u8c61\u3002<\/p>\n<\/p>\n
\u56db\u3001\u8bc4\u4f30\u62df\u5408\u6548\u679c<\/h3>\n<\/p>\n
\u8bc4\u4f30\u62df\u5408\u6548\u679c\u662f\u6570\u636e\u62df\u5408\u7684\u91cd\u8981\u6b65\u9aa4\u4e4b\u4e00\u3002\u53ef\u4ee5\u901a\u8fc7\u8ba1\u7b97\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\u6216\u51b3\u5b9a\u7cfb\u6570\uff08R\u00b2\uff09\u6765\u8bc4\u4f30\u62df\u5408\u6548\u679c\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u8ba1\u7b97MSE\u548cR\u00b2\u7684\u4f8b\u5b50\uff1a<\/p>\n<\/p>\n
# \u8ba1\u7b97\u62df\u5408\u503c<\/p>\n
y_fit = polynomial(x)<\/p>\n
\u8ba1\u7b97\u5747\u65b9\u8bef\u5dee<\/strong><\/h2>\n
mse = np.mean((y - y_fit)2)<\/p>\n
print("\u5747\u65b9\u8bef\u5dee (MSE):", mse)<\/p>\n
\u8ba1\u7b97\u51b3\u5b9a\u7cfb\u6570 (R\u00b2)<\/strong><\/h2>\n
ss_tot = np.sum((y - np.mean(y))2)<\/p>\n
ss_res = np.sum((y - y_fit)2)<\/p>\n
r2 = 1 - (ss_res \/ ss_tot)<\/p>\n
print("\u51b3\u5b9a\u7cfb\u6570 (R\u00b2):", r2)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e94\u3001\u7ed8\u5236\u62df\u5408\u7ed3\u679c<\/h3>\n<\/p>\n
\u7ed8\u5236\u62df\u5408\u7ed3\u679c\u6709\u52a9\u4e8e\u76f4\u89c2\u5730\u8bc4\u4f30\u62df\u5408\u6548\u679c\u3002\u53ef\u4ee5\u4f7f\u7528Matplotlib\u5e93\u8fdb\u884c\u7ed8\u56fe\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u7ed8\u5236\u62df\u5408\u7ed3\u679c\u7684\u4f8b\u5b50\uff1a<\/p>\n<\/p>\n
# \u7ed8\u5236\u539f\u59cb\u6570\u636e\u70b9<\/p>\n
plt.scatter(x, y, color='blue', label='\u539f\u59cb\u6570\u636e')<\/p>\n
\u7ed8\u5236\u62df\u5408\u66f2\u7ebf<\/strong><\/h2>\n
x_fit = np.linspace(min(x), max(x), 100)<\/p>\n
y_fit = polynomial(x_fit)<\/p>\n
plt.plot(x_fit, y_fit, color='red', label='\u62df\u5408\u66f2\u7ebf')<\/p>\n
\u6dfb\u52a0\u56fe\u4f8b\u548c\u6807\u7b7e<\/strong><\/h2>\n
plt.legend()<\/p>\n
plt.xlabel('x')<\/p>\n
plt.ylabel('y')<\/p>\n
plt.title('\u4e09\u9879\u5f0f\u62df\u5408')<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u516d\u3001\u5b9e\u9645\u5e94\u7528\u4e2d\u7684\u6ce8\u610f\u4e8b\u9879<\/h3>\n<\/p>\n
\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u4f7f\u7528Python\u8fdb\u884c\u4e09\u9879\u5f0f\u62df\u5408\u65f6\u9700\u8981\u6ce8\u610f\u4ee5\u4e0b\u51e0\u70b9\uff1a<\/p>\n<\/p>\n
    \n
  1. \u6570\u636e\u9884\u5904\u7406<\/strong>\uff1a\u5728\u8fdb\u884c\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\u6807\u51c6\u5316\u7b49\u3002<\/li>\n
  2. \u9009\u62e9\u5408\u9002\u7684\u6a21\u578b<\/strong>\uff1a\u867d\u7136\u4e09\u9879\u5f0f\u62df\u5408\u53ef\u4ee5\u5904\u7406\u5f88\u591a\u95ee\u9898\uff0c\u4f46\u5e76\u4e0d\u603b\u662f\u6700\u4f73\u9009\u62e9\u3002\u6839\u636e\u6570\u636e\u7279\u6027\u9009\u62e9\u5408\u9002\u7684\u62df\u5408\u6a21\u578b\u975e\u5e38\u91cd\u8981\u3002<\/li>\n
  3. \u8bc4\u4f30\u62df\u5408\u6548\u679c<\/strong>\uff1a\u4e0d\u4ec5\u4ec5\u8981\u770b\u62df\u5408\u66f2\u7ebf\u662f\u5426\u901a\u8fc7\u6570\u636e\u70b9\uff0c\u8fd8\u8981\u901a\u8fc7\u8ba1\u7b97\u8bef\u5dee\u548c\u5176\u4ed6\u8bc4\u4f30\u6307\u6807\u6765\u5168\u9762\u8bc4\u4f30\u62df\u5408\u6548\u679c\u3002<\/li>\n
  4. \u907f\u514d\u8fc7\u62df\u5408<\/strong>\uff1a\u5728\u62df\u5408\u8fc7\u7a0b\u4e2d\uff0c\u4f7f\u7528\u8fc7\u9ad8\u9636\u7684\u591a\u9879\u5f0f\u53ef\u80fd\u4f1a\u5bfc\u81f4\u8fc7\u62df\u5408\uff0c\u5373\u6a21\u578b\u5728\u8bad\u7ec3\u6570\u636e\u4e0a\u8868\u73b0\u5f88\u597d\uff0c\u4f46\u5728\u65b0\u6570\u636e\u4e0a\u8868\u73b0\u4e0d\u4f73\u3002\u9009\u62e9\u9002\u5f53\u7684\u591a\u9879\u5f0f\u9636\u6570\u5f88\u91cd\u8981\u3002<\/li>\n<\/ol>\n
    \u4e03\u3001\u6269\u5c55\u9605\u8bfb<\/h3>\n<\/p>\n
    \u5bf9\u4e8e\u6709\u5174\u8da3\u6df1\u5165\u4e86\u89e3\u6570\u636e\u62df\u5408\u548c\u56de\u5f52\u6280\u672f\u7684\u8bfb\u8005\uff0c\u53ef\u4ee5\u53c2\u8003\u4ee5\u4e0b\u8d44\u6e90\uff1a<\/p>\n<\/p>\n
      \n
    1. \u300aPython\u6570\u636e\u79d1\u5b66\u624b\u518c\u300b<\/strong>\uff1a\u5168\u9762\u4ecb\u7ecd\u4e86\u4f7f\u7528Python\u8fdb\u884c\u6570\u636e\u5206\u6790\u548c\u79d1\u5b66\u8ba1\u7b97\u7684\u5404\u79cd\u6280\u672f\u548c\u5de5\u5177\u3002<\/li>\n
    2. \u300a\u673a\u5668\u5b66\u4e60\u5b9e\u6218\u300b<\/strong>\uff1a\u8be6\u7ec6\u8bb2\u89e3\u4e86\u5404\u79cd\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\uff0c\u5305\u62ec\u56de\u5f52\u548c\u5206\u7c7b\u6280\u672f\u3002<\/li>\n
    3. NumPy\u548cSciPy\u5b98\u65b9\u6587\u6863<\/strong>\uff1a\u63d0\u4f9b\u4e86\u8be6\u7ec6\u7684\u51fd\u6570\u8bf4\u660e\u548c\u793a\u4f8b\u4ee3\u7801\u3002<\/li>\n<\/ol>\n
      \u516b\u3001\u7ed3\u8bba<\/h3>\n<\/p>\n
      \u4f7f\u7528Python\u8fdb\u884c\u4e09\u9879\u5f0f\u62df\u5408\u662f\u6570\u636e\u5206\u6790\u548c\u79d1\u5b66\u8ba1\u7b97\u4e2d\u7684\u5e38\u89c1\u4efb\u52a1\u3002\u901a\u8fc7\u9009\u62e9\u5408\u9002\u7684\u5e93\u3001\u51c6\u5907\u6570\u636e\u3001\u4f7f\u7528polyfit\u51fd\u6570\u3001\u8bc4\u4f30\u62df\u5408\u6548\u679c\uff0c\u53ef\u4ee5\u9ad8\u6548\u5730\u8fdb\u884c\u4e09\u9879\u5f0f\u62df\u5408\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6ce8\u610f\u6570\u636e\u9884\u5904\u7406\u3001\u6a21\u578b\u9009\u62e9\u548c\u8bc4\u4f30\u6307\u6807\uff0c\u53ef\u4ee5\u8fdb\u4e00\u6b65\u63d0\u9ad8\u62df\u5408\u6548\u679c\u548c\u6a21\u578b\u7684\u9c81\u68d2\u6027\u3002\u5e0c\u671b\u672c\u6587\u80fd\u591f\u5e2e\u52a9\u60a8\u66f4\u597d\u5730\u7406\u89e3\u548c\u5e94\u7528Python\u8fdb\u884c\u4e09\u9879\u5f0f\u62df\u5408\u3002<\/p>\n<\/p>\n
      \u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
       \u5982\u4f55\u9009\u62e9\u5408\u9002\u7684\u4e09\u9879\u5f0f\u6a21\u578b\u8fdb\u884c\u62df\u5408\uff1f<\/strong>
      \u9009\u62e9\u5408\u9002\u7684\u4e09\u9879\u5f0f\u6a21\u578b\u901a\u5e38\u53d6\u51b3\u4e8e\u6570\u636e\u7684\u7279\u6027\u4ee5\u53ca\u62df\u5408\u7684\u76ee\u7684\u3002\u53ef\u4ee5\u901a\u8fc7\u53ef\u89c6\u5316\u6570\u636e\u70b9\uff0c\u89c2\u5bdf\u6570\u636e\u7684\u8d8b\u52bf\u6765\u51b3\u5b9a\u4e09\u9879\u5f0f\u7684\u9636\u6570\u3002\u5982\u679c\u6570\u636e\u5448\u73b0\u51fa\u660e\u663e\u7684\u975e\u7ebf\u6027\u7279\u5f81\uff0c\u53ef\u80fd\u9700\u8981\u4f7f\u7528\u9ad8\u9636\u4e09\u9879\u5f0f\u3002\u8fd8\u53ef\u4ee5\u5229\u7528\u4ea4\u53c9\u9a8c\u8bc1\u7b49\u65b9\u6cd5\u5bf9\u4e0d\u540c\u6a21\u578b\u8fdb\u884c\u6bd4\u8f83\uff0c\u4ee5\u627e\u5230\u6700\u4f73\u62df\u5408\u6548\u679c\u3002<\/p>\n
      \u7528Python\u8fdb\u884c\u4e09\u9879\u5f0f\u62df\u5408\u65f6\u6709\u54ea\u4e9b\u5e38\u7528\u7684\u5e93\u548c\u5de5\u5177\uff1f<\/strong>
      \u5728Python\u4e2d\uff0c\u5e38\u7528\u7684\u5e93\u5305\u62ecNumPy\u548cSciPy\uff0c\u5206\u522b\u63d0\u4f9b\u4e86\u6570\u7ec4\u64cd\u4f5c\u548c\u79d1\u5b66\u8ba1\u7b97\u529f\u80fd\u3002\u5bf9\u4e8e\u6570\u636e\u53ef\u89c6\u5316\uff0cMatplotlib\u548cSeaborn\u662f\u975e\u5e38\u53d7\u6b22\u8fce\u7684\u9009\u62e9\u3002\u6b64\u5916\uff0c\u4f7f\u7528Scikit-learn\u5e93\u4e2d\u7684PolynomialFeatures\u7c7b\u4e5f\u975e\u5e38\u65b9\u4fbf\uff0c\u53ef\u4ee5\u65b9\u4fbf\u5730\u751f\u6210\u591a\u9879\u5f0f\u7279\u5f81\u5e76\u8fdb\u884c\u7ebf\u6027\u56de\u5f52\u3002<\/p>\n
      \u4e09\u9879\u5f0f\u62df\u5408\u7684\u7ed3\u679c\u5982\u4f55\u8bc4\u4f30\u548c\u9a8c\u8bc1\uff1f<\/strong>
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