{"id":1077053,"date":"2025-01-08T11:58:47","date_gmt":"2025-01-08T03:58:47","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1077053.html"},"modified":"2025-01-08T11:58:49","modified_gmt":"2025-01-08T03:58:49","slug":"python%e5%a6%82%e4%bd%95%e5%ae%9e%e7%8e%b0%e4%b8%80%e5%85%83%e7%ba%bf%e6%80%a7%e5%9b%9e%e5%bd%92-2","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1077053.html","title":{"rendered":"python\u5982\u4f55\u5b9e\u73b0\u4e00\u5143\u7ebf\u6027\u56de\u5f52"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/24181320\/45ed50ec-20f4-419a-b66e-b93b227b0ec2.webp\" alt=\"python\u5982\u4f55\u5b9e\u73b0\u4e00\u5143\u7ebf\u6027\u56de\u5f52\" \/><\/p>\n<p><p> <strong>Python\u5b9e\u73b0\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u7684\u65b9\u6cd5\u4e3b\u8981\u5305\u62ec\uff1a\u4f7f\u7528numpy\u548cscipy\u5e93\u624b\u52a8\u8ba1\u7b97\u3001\u4f7f\u7528scikit-learn\u5e93\u8fdb\u884c\u5efa\u6a21\u3001\u4f7f\u7528statsmodels\u5e93\u8fdb\u884c\u5efa\u6a21\u3002<\/strong> \u5176\u4e2d\uff0c<strong>\u4f7f\u7528scikit-learn\u5e93\u5efa\u6a21<\/strong>\u662f\u6700\u5e38\u89c1\u4e14\u63a8\u8350\u7684\u65b9\u5f0f\uff0c\u56e0\u4e3a\u5b83\u7b80\u5355\u3001\u76f4\u89c2\uff0c\u5e76\u4e14\u529f\u80fd\u5f3a\u5927\u3002\u63a5\u4e0b\u6765\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u8fd9\u51e0\u79cd\u65b9\u6cd5\u3002<\/p>\n<\/p>\n<p><p>\u4e00\u3001\u4f7f\u7528numpy\u548cscipy\u5e93\u624b\u52a8\u8ba1\u7b97<\/p>\n<\/p>\n<p><p>\u4f7f\u7528numpy\u548cscipy\u5e93\u624b\u52a8\u8ba1\u7b97\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u7684\u8fc7\u7a0b\u4e3b\u8981\u5305\u62ec\u4ee5\u4e0b\u51e0\u4e2a\u6b65\u9aa4\uff1a<\/p>\n<\/p>\n<ol>\n<li>\u6570\u636e\u51c6\u5907\uff1a\u51c6\u5907\u597d\u81ea\u53d8\u91cf\uff08X\uff09\u548c\u56e0\u53d8\u91cf\uff08Y\uff09\u3002<\/li>\n<li>\u8ba1\u7b97\u7ebf\u6027\u56de\u5f52\u7cfb\u6570\uff1a\u4f7f\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u516c\u5f0f\u8ba1\u7b97\u622a\u8ddd\u548c\u659c\u7387\u3002<\/li>\n<li>\u7ed8\u5236\u56de\u5f52\u76f4\u7ebf\uff1a\u4f7f\u7528matplotlib\u5e93\u7ed8\u5236\u56de\u5f52\u76f4\u7ebf\u5e76\u5c55\u793a\u7ed3\u679c\u3002<\/li>\n<\/ol>\n<p><p>\u4ee5\u4e0b\u662f\u5177\u4f53\u5b9e\u73b0\u4ee3\u7801\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>import matplotlib.pyplot as plt<\/p>\n<h2><strong>1. \u6570\u636e\u51c6\u5907<\/strong><\/h2>\n<p>X = np.array([1, 2, 3, 4, 5])<\/p>\n<p>Y = np.array([2, 3, 5, 7, 11])<\/p>\n<h2><strong>2. \u8ba1\u7b97\u7ebf\u6027\u56de\u5f52\u7cfb\u6570<\/strong><\/h2>\n<p>n = len(X)<\/p>\n<p>X_mean = np.mean(X)<\/p>\n<p>Y_mean = np.mean(Y)<\/p>\n<p>XY_mean = np.mean(X * Y)<\/p>\n<p>XX_mean = np.mean(X * X)<\/p>\n<h2><strong>\u659c\u7387\u548c\u622a\u8ddd\u516c\u5f0f<\/strong><\/h2>\n<p>slope = (XY_mean - X_mean * Y_mean) \/ (XX_mean - X_mean * X_mean)<\/p>\n<p>intercept = Y_mean - slope * X_mean<\/p>\n<h2><strong>3. \u7ed8\u5236\u56de\u5f52\u76f4\u7ebf<\/strong><\/h2>\n<p>plt.scatter(X, Y, color=&#39;blue&#39;, label=&#39;Data points&#39;)<\/p>\n<p>plt.plot(X, slope * X + intercept, color=&#39;red&#39;, label=&#39;Regression line&#39;)<\/p>\n<p>plt.xlabel(&#39;X&#39;)<\/p>\n<p>plt.ylabel(&#39;Y&#39;)<\/p>\n<p>plt.legend()<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u4e8c\u3001\u4f7f\u7528scikit-learn\u5e93\u8fdb\u884c\u5efa\u6a21<\/p>\n<\/p>\n<p><p>scikit-learn\u5e93\u662f\u4e00\u4e2a\u5f3a\u5927\u7684<a href=\"https:\/\/docs.pingcode.com\/ask\/59192.html\" target=\"_blank\">\u673a\u5668\u5b66\u4e60<\/a>\u5e93\uff0c\u5b83\u7b80\u5316\u4e86\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u7684\u5b9e\u73b0\u8fc7\u7a0b\u3002\u4e3b\u8981\u6b65\u9aa4\u5305\u62ec\uff1a<\/p>\n<\/p>\n<ol>\n<li>\u6570\u636e\u51c6\u5907\uff1a\u51c6\u5907\u597d\u81ea\u53d8\u91cf\uff08X\uff09\u548c\u56e0\u53d8\u91cf\uff08Y\uff09\u3002<\/li>\n<li>\u6a21\u578b\u8bad\u7ec3\uff1a\u4f7f\u7528LinearRegression\u7c7b\u8bad\u7ec3\u6a21\u578b\u3002<\/li>\n<li>\u6a21\u578b\u9884\u6d4b\uff1a\u4f7f\u7528\u8bad\u7ec3\u597d\u7684\u6a21\u578b\u8fdb\u884c\u9884\u6d4b\u3002<\/li>\n<li>\u6a21\u578b\u8bc4\u4f30\uff1a\u4f7f\u7528R\u5e73\u65b9\uff08R^2\uff09\u7b49\u6307\u6807\u8bc4\u4f30\u6a21\u578b\u6027\u80fd\u3002<\/li>\n<\/ol>\n<p><p>\u4ee5\u4e0b\u662f\u5177\u4f53\u5b9e\u73b0\u4ee3\u7801\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>import matplotlib.pyplot as plt<\/p>\n<p>from sklearn.linear_model import LinearRegression<\/p>\n<h2><strong>1. \u6570\u636e\u51c6\u5907<\/strong><\/h2>\n<p>X = np.array([1, 2, 3, 4, 5]).reshape(-1, 1)<\/p>\n<p>Y = np.array([2, 3, 5, 7, 11])<\/p>\n<h2><strong>2. \u6a21\u578b\u8bad\u7ec3<\/strong><\/h2>\n<p>model = LinearRegression()<\/p>\n<p>model.fit(X, Y)<\/p>\n<h2><strong>3. \u6a21\u578b\u9884\u6d4b<\/strong><\/h2>\n<p>Y_pred = model.predict(X)<\/p>\n<h2><strong>4. \u6a21\u578b\u8bc4\u4f30<\/strong><\/h2>\n<p>r_squared = model.score(X, Y)<\/p>\n<p>print(f&#39;R^2: {r_squared}&#39;)<\/p>\n<h2><strong>5. \u7ed8\u5236\u56de\u5f52\u76f4\u7ebf<\/strong><\/h2>\n<p>plt.scatter(X, Y, color=&#39;blue&#39;, label=&#39;Data points&#39;)<\/p>\n<p>plt.plot(X, Y_pred, color=&#39;red&#39;, label=&#39;Regression line&#39;)<\/p>\n<p>plt.xlabel(&#39;X&#39;)<\/p>\n<p>plt.ylabel(&#39;Y&#39;)<\/p>\n<p>plt.legend()<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u4e09\u3001\u4f7f\u7528statsmodels\u5e93\u8fdb\u884c\u5efa\u6a21<\/p>\n<\/p>\n<p><p>statsmodels\u5e93\u4e5f\u53ef\u4ee5\u7528\u4e8e\u8fdb\u884c\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u5206\u6790\uff0c\u5b83\u63d0\u4f9b\u4e86\u66f4\u8be6\u7ec6\u7684\u7edf\u8ba1\u7ed3\u679c\u548c\u8bca\u65ad\u5de5\u5177\u3002\u4e3b\u8981\u6b65\u9aa4\u5305\u62ec\uff1a<\/p>\n<\/p>\n<ol>\n<li>\u6570\u636e\u51c6\u5907\uff1a\u51c6\u5907\u597d\u81ea\u53d8\u91cf\uff08X\uff09\u548c\u56e0\u53d8\u91cf\uff08Y\uff09\u3002<\/li>\n<li>\u6a21\u578b\u8bad\u7ec3\uff1a\u4f7f\u7528OLS\u7c7b\u8bad\u7ec3\u6a21\u578b\u3002<\/li>\n<li>\u6a21\u578b\u8bc4\u4f30\uff1a\u83b7\u53d6\u8be6\u7ec6\u7684\u7edf\u8ba1\u7ed3\u679c\uff0c\u5305\u62ec\u7cfb\u6570\u3001\u6807\u51c6\u8bef\u5dee\u3001t\u503c\u3001p\u503c\u7b49\u3002<\/li>\n<\/ol>\n<p><p>\u4ee5\u4e0b\u662f\u5177\u4f53\u5b9e\u73b0\u4ee3\u7801\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>import statsmodels.api as sm<\/p>\n<p>import matplotlib.pyplot as plt<\/p>\n<h2><strong>1. \u6570\u636e\u51c6\u5907<\/strong><\/h2>\n<p>X = np.array([1, 2, 3, 4, 5])<\/p>\n<p>Y = np.array([2, 3, 5, 7, 11])<\/p>\n<h2><strong>2. \u6a21\u578b\u8bad\u7ec3<\/strong><\/h2>\n<p>X = sm.add_constant(X)  # \u6dfb\u52a0\u5e38\u6570\u9879\u622a\u8ddd<\/p>\n<p>model = sm.OLS(Y, X).fit()<\/p>\n<h2><strong>3. \u6a21\u578b\u8bc4\u4f30<\/strong><\/h2>\n<p>print(model.summary())<\/p>\n<h2><strong>4. \u7ed8\u5236\u56de\u5f52\u76f4\u7ebf<\/strong><\/h2>\n<p>plt.scatter(X[:, 1], Y, color=&#39;blue&#39;, label=&#39;Data points&#39;)<\/p>\n<p>plt.plot(X[:, 1], model.predict(X), color=&#39;red&#39;, label=&#39;Regression line&#39;)<\/p>\n<p>plt.xlabel(&#39;X&#39;)<\/p>\n<p>plt.ylabel(&#39;Y&#39;)<\/p>\n<p>plt.legend()<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u603b\u7ed3\uff1a<\/p>\n<p><strong>\u4f7f\u7528numpy\u548cscipy\u5e93\u624b\u52a8\u8ba1\u7b97<\/strong>\u9002\u7528\u4e8e\u7406\u89e3\u7ebf\u6027\u56de\u5f52\u7684\u57fa\u7840\u539f\u7406\u548c\u5b9e\u73b0\u8fc7\u7a0b\u3002<strong>\u4f7f\u7528scikit-learn\u5e93\u8fdb\u884c\u5efa\u6a21<\/strong>\u662f\u6700\u5e38\u89c1\u4e14\u63a8\u8350\u7684\u65b9\u5f0f\uff0c\u9002\u7528\u4e8e\u5feb\u901f\u5b9e\u73b0\u548c\u5e94\u7528\u3002<strong>\u4f7f\u7528statsmodels\u5e93\u8fdb\u884c\u5efa\u6a21<\/strong>\u9002\u7528\u4e8e\u9700\u8981\u8be6\u7ec6\u7edf\u8ba1\u7ed3\u679c\u548c\u8bca\u65ad\u5de5\u5177\u7684\u573a\u666f\u3002<\/p>\n<\/p>\n<p><p>\u65e0\u8bba\u9009\u62e9\u54ea\u79cd\u65b9\u6cd5\uff0c\u90fd\u9700\u8981\u6ce8\u610f\u6570\u636e\u7684\u9884\u5904\u7406\u548c\u53ef\u89c6\u5316\uff0c\u4ee5\u786e\u4fdd\u6a21\u578b\u7684\u51c6\u786e\u6027\u548c\u89e3\u91ca\u6027\u3002\u5e0c\u671b\u901a\u8fc7\u672c\u6587\u7684\u8be6\u7ec6\u4ecb\u7ecd\uff0c\u5927\u5bb6\u80fd\u591f\u638c\u63e1Python\u5b9e\u73b0\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u7684\u591a\u79cd\u65b9\u6cd5\uff0c\u5e76\u6839\u636e\u5b9e\u9645\u9700\u6c42\u9009\u62e9\u5408\u9002\u7684\u5de5\u5177\u548c\u65b9\u6cd5\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u7684\u57fa\u672c\u6982\u5ff5\u662f\u4ec0\u4e48\uff1f<\/strong><br \/>\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u662f\u4e00\u79cd\u7edf\u8ba1\u65b9\u6cd5\uff0c\u7528\u4e8e\u63cf\u8ff0\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u7ebf\u6027\u5173\u7cfb\u3002\u5728\u8fd9\u79cd\u6a21\u578b\u4e2d\uff0c\u4e00\u4e2a\u81ea\u53d8\u91cf\uff08\u72ec\u7acb\u53d8\u91cf\uff09\u7528\u6765\u9884\u6d4b\u4e00\u4e2a\u56e0\u53d8\u91cf\uff08\u4f9d\u8d56\u53d8\u91cf\uff09\u3002\u901a\u8fc7\u62df\u5408\u4e00\u6761\u76f4\u7ebf\uff0c\u6a21\u578b\u80fd\u591f\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u81ea\u53d8\u91cf\u7684\u53d8\u5316\u5982\u4f55\u5f71\u54cd\u56e0\u53d8\u91cf\u3002<\/p>\n<p><strong>\u5728Python\u4e2d\u5b9e\u73b0\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u9700\u8981\u54ea\u4e9b\u5e93\uff1f<\/strong><br \/>\u5728Python\u4e2d\uff0c\u5e38\u7528\u7684\u5e93\u5305\u62ecNumPy\u3001Pandas\u548cScikit-learn\u3002NumPy\u7528\u4e8e\u9ad8\u6548\u7684\u6570\u503c\u8ba1\u7b97\uff0cPandas\u7528\u4e8e\u6570\u636e\u5904\u7406\u548c\u5206\u6790\uff0c\u800cScikit-learn\u5219\u63d0\u4f9b\u4e86\u4e00\u7cfb\u5217\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\uff0c\u5305\u62ec\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u5b9e\u73b0\u3002\u8fd9\u4e9b\u5e93\u7ed3\u5408\u4f7f\u7528\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u8fdb\u884c\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u5206\u6790\u3002<\/p>\n<p><strong>\u5982\u4f55\u8bc4\u4f30\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u6027\u80fd\uff1f<\/strong><br \/>\u8bc4\u4f30\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u6027\u80fd\u901a\u5e38\u4f7f\u7528\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\u548c\u51b3\u5b9a\u7cfb\u6570\uff08R\u00b2\uff09\u7b49\u6307\u6807\u3002\u5747\u65b9\u8bef\u5dee\u8861\u91cf\u9884\u6d4b\u503c\u4e0e\u771f\u5b9e\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u800c\u51b3\u5b9a\u7cfb\u6570\u5219\u8868\u793a\u6a21\u578b\u5bf9\u6570\u636e\u53d8\u5f02\u6027\u7684\u89e3\u91ca\u80fd\u529b\u3002\u901a\u8fc7\u8fd9\u4e9b\u6307\u6807\uff0c\u53ef\u4ee5\u5224\u65ad\u6a21\u578b\u7684\u9884\u6d4b\u80fd\u529b\u548c\u51c6\u786e\u6027\uff0c\u4ece\u800c\u4f18\u5316\u6a21\u578b\u53c2\u6570\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"Python\u5b9e\u73b0\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u7684\u65b9\u6cd5\u4e3b\u8981\u5305\u62ec\uff1a\u4f7f\u7528numpy\u548cscipy\u5e93\u624b\u52a8\u8ba1\u7b97\u3001\u4f7f\u7528scikit-learn [&hellip;]","protected":false},"author":3,"featured_media":1077064,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1077053"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=1077053"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1077053\/revisions"}],"predecessor-version":[{"id":1077065,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1077053\/revisions\/1077065"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1077064"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1077053"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1077053"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1077053"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}