{"id":880,"date":"2023-07-28T10:44:58","date_gmt":"2023-07-28T10:44:58","guid":{"rendered":"https:\/\/statorials.org\/ru\/%d0%bf%d0%be%d0%bb%d0%b8%d0%bd%d0%be%d0%bc%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0%d1%8f-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%81%d0%b8%d1%8f-python\/"},"modified":"2023-07-28T10:44:58","modified_gmt":"2023-07-28T10:44:58","slug":"%d0%bf%d0%be%d0%bb%d0%b8%d0%bd%d0%be%d0%bc%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0%d1%8f-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%81%d0%b8%d1%8f-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/ru\/%d0%bf%d0%be%d0%bb%d0%b8%d0%bd%d0%be%d0%bc%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0%d1%8f-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%81%d0%b8%d1%8f-python\/","title":{"rendered":"\u041a\u0430\u043a \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044e \u0432 python"},"content":{"rendered":"

<\/p>\n

\n

\u0420\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u043e\u043d\u043d\u044b\u0439 \u0430\u043d\u0430\u043b\u0438\u0437 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 \u043e\u0446\u0435\u043d\u043a\u0438 \u0432\u0437\u0430\u0438\u043c\u043e\u0441\u0432\u044f\u0437\u0438 \u043c\u0435\u0436\u0434\u0443 \u043e\u0434\u043d\u043e\u0439 \u0438\u043b\u0438 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u0438\u043c\u0438 \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u044e\u0449\u0438\u043c\u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438 \u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043e\u0442\u043a\u043b\u0438\u043a\u0430.<\/span><\/p>\n

\u041d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u043d\u044b\u043c \u0442\u0438\u043f\u043e\u043c \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u043e\u043d\u043d\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0440\u043e\u0441\u0442\u0430\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f<\/a> , \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0430\u044f, \u043a\u043e\u0433\u0434\u0430 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440 \u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f \u043e\u0442\u043a\u043b\u0438\u043a\u0430 \u0438\u043c\u0435\u044e\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0441\u0432\u044f\u0437\u044c.<\/span> <\/p>\n

\"\"<\/p>\n

\u041e\u0434\u043d\u0430\u043a\u043e \u0438\u043d\u043e\u0433\u0434\u0430 \u0441\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u043e\u043c \u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043e\u0442\u043a\u043b\u0438\u043a\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439.<\/span><\/p>\n

\u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0438\u0441\u0442\u0438\u043d\u043d\u0430\u044f \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\u0439:<\/span> <\/p>\n

\"\"<\/p>\n

\u0418\u043b\u0438 \u044d\u0442\u043e \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043a\u0443\u0431:<\/span> <\/p>\n

\"\"<\/p>\n

\u0412 \u044d\u0442\u0438\u0445 \u0441\u043b\u0443\u0447\u0430\u044f\u0445 \u0438\u043c\u0435\u0435\u0442 \u0441\u043c\u044b\u0441\u043b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044e<\/strong> , \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043c\u043e\u0436\u0435\u0442 \u0443\u0447\u0438\u0442\u044b\u0432\u0430\u0442\u044c \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0435 \u0441\u0432\u044f\u0437\u0438 \u043c\u0435\u0436\u0434\u0443 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438.<\/span><\/p>\n

\u0412 \u044d\u0442\u043e\u043c \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u0442\u0441\u044f, \u043a\u0430\u043a \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044e \u0432 Python.<\/span><\/p>\n

\u041f\u0440\u0438\u043c\u0435\u0440: \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u0432 Python<\/strong><\/span><\/h2>\n

\u041f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043c, \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440 (x) \u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f \u043e\u0442\u0432\u0435\u0442\u0430 (y) \u0432 Python:<\/span><\/p>\n

 x = [2, 3, 4, 5, 6, 7, 7, 8, 9, 11, 12]\ny = [18, 16, 15, 17, 20, 23, 25, 28, 31, 30, 29]\n<\/strong><\/pre>\n
 \u0415\u0441\u043b\u0438 \u043c\u044b \u0441\u043e\u0437\u0434\u0430\u0434\u0438\u043c \u043f\u0440\u043e\u0441\u0442\u0443\u044e \u0434\u0438\u0430\u0433\u0440\u0430\u043c\u043c\u0443 \u0440\u0430\u0441\u0441\u0435\u044f\u043d\u0438\u044f \u044d\u0442\u0438\u0445 \u0434\u0430\u043d\u043d\u044b\u0445, \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e \u0441\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 x \u0438 y \u044f\u0432\u043d\u043e \u043d\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u0430:<\/span> <\/p>\n
 import<\/span> matplotlib.pyplot as<\/span> plt\n\n#create scatterplot<\/span> \nplt.scatter(x, y)\n<\/strong><\/pre>\n
\"\"<\/p>\n
 import<\/span> numpy as<\/span> np\n\n#polynomial fit with degree = 3\n<\/span>model = np.poly1d(np.polyfit(x, y, 3))\n\n#add fitted polynomial line to scatterplot\n<\/span>polyline = np.linspace(1, 12, 50)\nplt.scatter(x, y)\nplt.plot(polyline, model(polyline))\nplt.show()<\/strong> <\/pre>\n
\"\u041b\u0438\u043d\u0438\u044f<\/p>\n
 \u041c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438, \u0440\u0430\u0441\u043f\u0435\u0447\u0430\u0442\u0430\u0432 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u043c\u043e\u0434\u0435\u043b\u0438:<\/span><\/p>\n
 print(model)\n\npoly1d([ -0.10889554, 2.25592957, -11.83877127, 33.62640038])\n<\/strong><\/pre>\n
 \u041f\u043e\u0434\u043e\u0431\u0440\u0430\u043d\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438:<\/span><\/p>\n
 \u0443 = -0,109\u0445 3<\/sup> + 2,256\u0445 2<\/sup> \u2013 11,839\u0445 + 33,626<\/strong><\/span><\/p>\n
 \u042d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0434\u043b\u044f \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u043e\u0436\u0438\u0434\u0430\u0435\u043c\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043e\u0442\u043a\u043b\u0438\u043a\u0430 \u043f\u0440\u0438 \u0437\u0430\u0434\u0430\u043d\u043d\u043e\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0438 \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u044e\u0449\u0435\u0439 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439.<\/span><\/p>\n
 \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043c, \u0447\u0442\u043e x = 4. \u041e\u0436\u0438\u0434\u0430\u0435\u043c\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043e\u0442\u0432\u0435\u0442\u0430 y \u0431\u0443\u0434\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c:<\/span><\/p>\n
 \u0443 = -0,109(4) 3<\/sup> + 2,256(4) 2<\/sup> \u2013 11,839(4) + 33,626= 15,39<\/b> .<\/span><\/p>\n
 \u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u043c \u043d\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u043a\u043e\u0440\u043e\u0442\u043a\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c R-\u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u043c\u043e\u0434\u0435\u043b\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u0434\u043e\u043b\u044e \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0438\u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043e\u0442\u043a\u043b\u0438\u043a\u0430, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u043e\u0436\u043d\u043e \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u0442\u044c \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u0430\u043c\u0438.<\/span><\/p>\n
 #define function to calculate r-squared<\/span>\ndef<\/span> polyfit(x, y, degree):\n    results = {}\n    coeffs = numpy.polyfit(x, y, degree)\n    p = numpy.poly1d(coeffs)\n    #calculate r-squared<\/span>\n    yhat = p(x)\n    ybar = numpy.sum(y)\/len(y)\n    ssreg = numpy.sum((yhat-ybar)**2)\n    sstot = numpy.sum((y - ybar)**2)\n    results['r_squared'] = ssreg \/ sstot\n\n    return<\/span> results\n\n#find r-squared of polynomial model with degree = 3\n<\/span>polyfit(x, y, 3)\n\n{'r_squared': 0.9841113454245183}\n<\/strong><\/pre>\n
 \u0412 \u044d\u0442\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 R \u043c\u043e\u0434\u0435\u043b\u0438 \u0440\u0430\u0432\u0435\u043d 0,9841<\/strong> .<\/span><\/p>\n
 \u042d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e 98,41%<\/strong> \u0432\u0430\u0440\u0438\u0430\u0446\u0438\u0439 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043e\u0442\u0432\u0435\u0442\u0430 \u043c\u043e\u0436\u043d\u043e \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u0442\u044c \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u0430\u043c\u0438.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"
\u0420\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u043e\u043d\u043d\u044b\u0439 \u0430\u043d\u0430\u043b\u0438\u0437 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 \u043e\u0446\u0435\u043d\u043a\u0438 \u0432\u0437\u0430\u0438\u043c\u043e\u0441\u0432\u044f\u0437\u0438 \u043c\u0435\u0436\u0434\u0443 \u043e\u0434\u043d\u043e\u0439 \u0438\u043b\u0438 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u0438\u043c\u0438 \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u044e\u0449\u0438\u043c\u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438 \u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043e\u0442\u043a\u043b\u0438\u043a\u0430. \u041d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u043d\u044b\u043c \u0442\u0438\u043f\u043e\u043c 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