{"id":1649,"date":"2023-07-25T12:50:55","date_gmt":"2023-07-25T12:50:55","guid":{"rendered":"https:\/\/statorials.org\/cn\/python-%e6%9b%b2%e7%ba%bf%e6%8b%9f%e5%90%88\/"},"modified":"2023-07-25T12:50:55","modified_gmt":"2023-07-25T12:50:55","slug":"python-%e6%9b%b2%e7%ba%bf%e6%8b%9f%e5%90%88","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/python-%e6%9b%b2%e7%ba%bf%e6%8b%9f%e5%90%88\/","title":{"rendered":"Python \u4e2d\u7684\u66f2\u7ebf\u62df\u5408\uff08\u9644\u793a\u4f8b\uff09"},"content":{"rendered":"

<\/p>\n

\n

\u901a\u5e38\uff0c\u60a8\u53ef\u80fd\u5e0c\u671b\u5728 Python \u4e2d\u5c06\u66f2\u7ebf\u62df\u5408\u5230\u6570\u636e\u96c6\u3002<\/span> <\/p>\n

\"\"<\/p>\n

\u4ee5\u4e0b\u5206\u6b65\u793a\u4f8b\u8bf4\u660e\u4e86\u5982\u4f55\u4f7f\u7528numpy.polyfit()<\/a>\u51fd\u6570\u5728 Python \u4e2d\u5c06\u66f2\u7ebf\u62df\u5408\u5230\u6570\u636e\uff0c\u4ee5\u53ca\u5982\u4f55\u786e\u5b9a\u54ea\u6761\u66f2\u7ebf\u6700\u9002\u5408\u6570\u636e\u3002<\/span><\/p>\n

\u7b2c 1 \u6b65\uff1a\u521b\u5efa\u6570\u636e\u5e76\u53ef\u89c6\u5316<\/strong><\/span><\/h3>\n

\u8ba9\u6211\u4eec\u9996\u5148\u521b\u5efa\u4e00\u4e2a\u5047\u6570\u636e\u96c6\uff0c\u7136\u540e\u521b\u5efa\u4e00\u4e2a\u6563\u70b9\u56fe\u6765\u53ef\u89c6\u5316\u6570\u636e\uff1a<\/span> <\/p>\n

 import<\/span> pandas as<\/span> pd\nimport<\/span> matplotlib. pyplot<\/span> as<\/span> plt\n\n#createDataFrame\n<\/span>df = pd. DataFrame<\/span> ({' x<\/span> ': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],\n                   ' y<\/span> ': [3, 14, 23, 25, 23, 15, 9, 5, 9, 13, 17, 24, 32, 36, 46]})\n\n#create scatterplot of x vs. y\n<\/span>plt. scatter<\/span> (df. x<\/span> , df. y<\/span> )<\/strong> <\/pre>\n
\"\"<\/p>\n
\u7b2c2\u6b65\uff1a\u8c03\u6574\u591a\u6761\u66f2\u7ebf<\/strong><\/span><\/h3>\n
\u7136\u540e\uff0c\u8ba9\u6211\u4eec\u5c06\u51e0\u4e2a\u591a\u9879\u5f0f\u56de\u5f52\u6a21\u578b\u62df\u5408\u5230\u6570\u636e\uff0c\u5e76\u5728\u540c\u4e00\u56fe\u4e2d\u53ef\u89c6\u5316\u6bcf\u4e2a\u6a21\u578b\u7684\u66f2\u7ebf\uff1a<\/span> <\/p>\n
 import<\/span> numpy as<\/span> np\n\n#fit polynomial models up to degree 5\n<\/span>model1 = np. poly1d<\/span> (np. polyfit<\/span> (df. x<\/span> , df. y<\/span> , 1))\nmodel2 = np. poly1d<\/span> (np. polyfit<\/span> (df. x<\/span> , df. y<\/span> , 2))\nmodel3 = np. poly1d<\/span> (np. polyfit<\/span> (df. x<\/span> , df. y<\/span> , 3))\nmodel4 = np. poly1d<\/span> (np. polyfit<\/span> (df. x<\/span> , df. y<\/span> , 4))\nmodel5 = np. poly1d<\/span> (np. polyfit<\/span> (df. x<\/span> , df. y<\/span> , 5))\n\n#create scatterplot\n<\/span>polyline = np. linspace<\/span> (1, 15, 50)\nplt. scatter<\/span> (df. x<\/span> , df. y<\/span> )\n\n#add fitted polynomial lines to scatterplot \n<\/span>plt. plot<\/span> (polyline, model1(polyline), color=' green<\/span> ')\nplt. plot<\/span> (polyline, model2(polyline), color=' red<\/span> ')\nplt. plot<\/span> (polyline, model3(polyline), color=' purple<\/span> ')\nplt. plot<\/span> (polyline, model4(polyline), color=' blue<\/span> ')\nplt. plot<\/span> (polyline, model5(polyline), color=' orange<\/span> ')\nplt. show<\/span> ()\n<\/span><\/span><\/strong><\/pre>\n
\"\"<\/p>\n
\u8be5\u503c\u544a\u8bc9\u6211\u4eec\u53ef\u4ee5\u7531\u6a21\u578b\u4e2d\u7684\u9884\u6d4b\u53d8\u91cf\u89e3\u91ca\u7684\u54cd\u5e94\u53d8\u91cf\u7684\u53d8\u5316\u767e\u5206\u6bd4\uff0c\u5e76\u6839\u636e\u9884\u6d4b\u53d8\u91cf\u7684\u6570\u91cf\u8fdb\u884c\u8c03\u6574\u3002<\/span><\/p>\n
 #define function to calculate adjusted r-squared\ndef<\/span> adjR(x, y, degree):\n    results = {}\n    coeffs = np. polyfit<\/span> (x, y, degree)\n    p = np. poly1d<\/span> (coeffs)\n    yhat = p(x)\n    ybar = np. sum<\/span> (y)\/len(y)\n    ssreg = np. sum<\/span> ((yhat-ybar)**2)\n    sstot = np. sum<\/span> ((y - ybar)**2)\n    results[' r_squared<\/span> '] = 1- (((1-(ssreg\/sstot))*(len(y)-1))\/(len(y)-degree-1))\n\n    return<\/span> results<\/span>\n\n#calculated adjusted R-squared of each model\n<\/span>adjR(df. x<\/span> , df. y<\/span> , 1)\nadjR(df. x<\/span> , df. y<\/span> , 2)\nadjR(df. x<\/span> , df. y<\/span> , 3)\nadjR(df. x<\/span> , df. y<\/span> , 4)\nadjR(df. x<\/span> , df. y<\/span> , 5)\n\n{'r_squared': 0.3144819}\n{'r_squared': 0.5186706}\n{'r_squared': 0.7842864}\n{'r_squared': 0.9590276}\n{'r_squared': 0.9549709}\n<\/strong><\/pre>\n
\u4ece\u7ed3\u679c\u4e2d\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u8c03\u6574 R \u5e73\u65b9\u6700\u9ad8\u7684\u6a21\u578b\u662f\u56db\u6b21\u591a\u9879\u5f0f\uff0c\u5176\u8c03\u6574 R \u5e73\u65b9\u4e3a0.959<\/strong> \u3002<\/span><\/p>\n
\u7b2c 3 \u6b65\uff1a\u53ef\u89c6\u5316\u6700\u7ec8\u66f2\u7ebf<\/strong><\/span><\/h3>\n
\u6700\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u56db\u6b21\u591a\u9879\u5f0f\u6a21\u578b\u7684\u66f2\u7ebf\u521b\u5efa\u6563\u70b9\u56fe\uff1a<\/span> <\/p>\n
 #fit fourth-degree polynomial\n<\/span>model4 = np. poly1d<\/span> (np. polyfit<\/span> (df. x<\/span> , df. y<\/span> , 4))\n\n#define scatterplot\n<\/span>polyline = np. linspace<\/span> (1, 15, 50)\nplt. scatter<\/span> (df. x<\/span> , df. y<\/span> )\n\n#add fitted polynomial curve to scatterplot\n<\/span>plt. plot<\/span> (polyline, model4(polyline), ' --<\/span> ', color=' red<\/span> ')\nplt. show<\/span> ()\n<\/strong><\/pre>\n
\"\"<\/p>\n
\u6211\u4eec\u8fd8\u53ef\u4ee5\u4f7f\u7528print()<\/strong>\u51fd\u6570\u5f97\u5230\u8be5\u884c\u7684\u65b9\u7a0b\uff1a<\/span><\/p>\n
 print<\/span> (model4)\n\n          4 3 2\n-0.01924x + 0.7081x - 8.365x + 35.82x - 26.52\n<\/strong><\/pre>\n
\u66f2\u7ebf\u65b9\u7a0b\u5982\u4e0b\uff1a<\/span><\/p>\n
 y = -0.01924x 4<\/sup> + 0.7081x 3<\/sup> \u2013 8.365x 2<\/sup> + 35.82x \u2013 26.52<\/span><\/p>\n
\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u8be5\u65b9\u7a0b\u6839\u636e\u6a21\u578b\u4e2d\u7684\u9884\u6d4b\u53d8\u91cf\u6765\u9884\u6d4b\u54cd\u5e94\u53d8\u91cf<\/a>\u7684\u503c\u3002\u4f8b\u5982\uff0c\u5982\u679cx<\/em> = 4 \u90a3\u4e48\u6211\u4eec\u5c06\u9884\u6d4by<\/em> = 23.32<\/strong> \uff1a<\/span><\/p>\n
 y = -0.0192(4) 4<\/sup> + 0.7081(4) 3<\/sup> \u2013 8.365(4) 2<\/sup> + 35.82(4) \u2013 26.52 = 23.32<\/span><\/p>\n
\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h3>\n
\u591a\u9879\u5f0f\u56de\u5f52\u7b80\u4ecb
<\/a>\u5982\u4f55\u5728 Python \u4e2d\u6267\u884c\u591a\u9879\u5f0f\u56de\u5f52<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
\u901a\u5e38\uff0c\u60a8\u53ef\u80fd\u5e0c\u671b\u5728 Python \u4e2d\u5c06\u66f2\u7ebf\u62df\u5408\u5230\u6570\u636e\u96c6\u3002 \u4ee5\u4e0b\u5206\u6b65\u793a\u4f8b\u8bf4\u660e\u4e86\u5982\u4f55\u4f7f\u7528numpy.polyfit […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1649","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"\nPython \u4e2d\u7684\u66f2\u7ebf\u62df\u5408\uff08\u5e26\u6709\u793a\u4f8b\uff09-Statorials<\/title>\n<meta name=\"description\" content=\"\u672c\u6559\u7a0b\u901a\u8fc7\u51e0\u4e2a\u793a\u4f8b\u89e3\u91ca\u4e86\u5982\u4f55\u5728 Python \u4e2d\u62df\u5408\u66f2\u7ebf\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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