{"id":1336,"date":"2023-07-26T19:53:42","date_gmt":"2023-07-26T19:53:42","guid":{"rendered":"https:\/\/statorials.org\/pl\/pozostala-suma-kwadratow-w-pythonie\/"},"modified":"2023-07-26T19:53:42","modified_gmt":"2023-07-26T19:53:42","slug":"pozostala-suma-kwadratow-w-pythonie","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/pozostala-suma-kwadratow-w-pythonie\/","title":{"rendered":"Jak obliczy\u0107 pozosta\u0142\u0105 sum\u0119 kwadrat\u00f3w w pythonie"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/pl\/pozosta\u0142osc\/\" target=\"_blank\" rel=\"noopener\">Reszta<\/a> to r\u00f3\u017cnica mi\u0119dzy warto\u015bci\u0105 obserwowan\u0105 a warto\u015bci\u0105 przewidywan\u0105 w modelu regresji.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Oblicza si\u0119 go w nast\u0119puj\u0105cy spos\u00f3b:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Warto\u015b\u0107 rezydualna = Warto\u015b\u0107 obserwowana \u2013 Warto\u015b\u0107 przewidywana<\/span><\/p>\n<p> <span style=\"color: #000000;\">Jednym ze sposob\u00f3w sprawdzenia, jak dobrze model regresji pasuje do zbioru danych, jest obliczenie <strong>resztowej sumy kwadrat\u00f3w<\/strong> , kt\u00f3r\u0105 oblicza si\u0119 w nast\u0119puj\u0105cy spos\u00f3b:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Pozosta\u0142a suma kwadrat\u00f3w = \u03a3(e <sub>i<\/sub> ) <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : Grecki symbol oznaczaj\u0105cy \u201esum\u0119\u201d<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>e <sub>i<\/sub><\/strong> : i- <sup>ta<\/sup> reszta<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Im ni\u017csza warto\u015b\u0107, tym lepiej model pasuje do zbioru danych.<\/span><\/p>\n<p> <span style=\"color: #000000;\">W tym samouczku przedstawiono krok po kroku przyk\u0142ad obliczenia pozosta\u0142ej sumy kwadrat\u00f3w dla modelu regresji w j\u0119zyku Python.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 1: Wprowad\u017a dane<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">W tym przyk\u0142adzie wprowadzimy dane dotycz\u0105ce liczby godzin sp\u0119dzonych na nauce, \u0142\u0105cznej liczby zdanych egzamin\u00f3w przygotowawczych oraz wynik\u00f3w egzamin\u00f3w uzyskanych przez 14 r\u00f3\u017cnych student\u00f3w:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> pandas <span style=\"color: #107d3f;\">as<\/span> pd\n\n<span style=\"color: #008080;\">#createDataFrame<\/span>\ndf = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #008000;\">hours<\/span> ': [1, 2, 2, 4, 2, 1, 5, 4, 2, 4, 4, 3, 6, 5],\n                   ' <span style=\"color: #008000;\">exams<\/span> ': [1, 3, 3, 5, 2, 2, 1, 1, 0, 3, 4, 3, 2, 4],\n                   ' <span style=\"color: #008000;\">score<\/span> ': [76, 78, 85, 88, 72, 69, 94, 94, 88, 92, 90, 75, 96, 90]})\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Krok 2: Dopasuj model regresji<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie u\u017cyjemy<\/span> <a href=\"https:\/\/www.statsmodels.org\/devel\/generated\/statsmodels.regression.linear_model.OLS.html\" target=\"_blank\" rel=\"noopener noreferrer\">funkcji OLS()<\/a> <span style=\"color: #000000;\">z biblioteki statsmodels do przeprowadzenia zwyk\u0142ej regresji metod\u0105 najmniejszych kwadrat\u00f3w, u\u017cywaj\u0105c \u201egodzin\u201d i \u201eegzamin\u00f3w\u201d jako zmiennych predykcyjnych oraz \u201ewyniku\u201d jako zmiennej odpowiedzi:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008000;\">import<\/span> statsmodels. <span style=\"color: #3366ff;\">api<\/span> <span style=\"color: #008000;\">as<\/span> sm\n\n<span style=\"color: #008080;\">#define response variable\n<\/span>y = df[' <span style=\"color: #008000;\">score<\/span> ']\n\n<span style=\"color: #008080;\">#define predictor variables\n<\/span>x = df[[' <span style=\"color: #008000;\">hours<\/span> ', ' <span style=\"color: #008000;\">exams<\/span> ']]\n\n<span style=\"color: #008080;\">#add constant to predictor variables\n<\/span>x = sm. <span style=\"color: #3366ff;\">add_constant<\/span> (x)\n\n<span style=\"color: #008080;\">#fit linear regression model\n<\/span>model = sm. <span style=\"color: #3366ff;\">OLS<\/span> (y,x). <span style=\"color: #3366ff;\">fit<\/span> ()\n\n<span style=\"color: #008080;\">#view model summary\n<\/span><span style=\"color: #993300;\">print<\/span> ( <span style=\"color: #3366ff;\">model.summary<\/span> ())\n\n                            OLS Regression Results                            \n==================================================== ============================\nDept. Variable: R-squared score: 0.722\nModel: OLS Adj. R-squared: 0.671\nMethod: Least Squares F-statistic: 14.27\nDate: Sat, 02 Jan 2021 Prob (F-statistic): 0.000878\nTime: 15:58:35 Log-Likelihood: -41.159\nNo. Comments: 14 AIC: 88.32\nDf Residuals: 11 BIC: 90.24\nModel: 2                                         \nCovariance Type: non-robust                                         \n==================================================== ============================\n                 coef std err t P&gt;|t| [0.025 0.975]\n-------------------------------------------------- ----------------------------\nconst 71.8144 3.680 19.517 0.000 63.716 79.913\nhours 5.0318 0.942 5.339 0.000 2.958 7.106\nexams -1.3186 1.063 -1.240 0.241 -3.658 1.021\n==================================================== ============================\nOmnibus: 0.976 Durbin-Watson: 1.270\nProb(Omnibus): 0.614 Jarque-Bera (JB): 0.757\nSkew: -0.245 Prob(JB): 0.685\nKurtosis: 1.971 Cond. No. 12.1\n==================================================== ============================\n<\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Krok 3: Oblicz pozosta\u0142\u0105 sum\u0119 kwadrat\u00f3w<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Do obliczenia pozosta\u0142ej sumy kwadrat\u00f3w modelu mo\u017cemy u\u017cy\u0107 nast\u0119puj\u0105cego kodu:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #993300;\">print<\/span> ( <span style=\"color: #3366ff;\">model.ssr<\/span> )\n\n293.25612951525414\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">Pozosta\u0142a suma kwadrat\u00f3w wynosi <strong>293 256<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pl\/prosta-regresja-liniowa-w-pythonie\/\" target=\"_blank\" rel=\"noopener\">Jak wykona\u0107 prost\u0105 regresj\u0119 liniow\u0105 w Pythonie<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/python-regresji-liniowej\/\" target=\"_blank\" rel=\"noopener\">Jak wykona\u0107 wielokrotn\u0105 regresj\u0119 liniow\u0105 w Pythonie<\/a><br \/> Kalkulator pozosta\u0142ej sumy kwadrat\u00f3w<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Reszta to r\u00f3\u017cnica mi\u0119dzy warto\u015bci\u0105 obserwowan\u0105 a warto\u015bci\u0105 przewidywan\u0105 w modelu regresji. Oblicza si\u0119 go w nast\u0119puj\u0105cy spos\u00f3b: Warto\u015b\u0107 rezydualna = Warto\u015b\u0107 obserwowana \u2013 Warto\u015b\u0107 przewidywana Jednym ze sposob\u00f3w sprawdzenia, jak dobrze model regresji pasuje do zbioru danych, jest obliczenie resztowej sumy kwadrat\u00f3w , kt\u00f3r\u0105 oblicza si\u0119 w nast\u0119puj\u0105cy spos\u00f3b: Pozosta\u0142a suma kwadrat\u00f3w = \u03a3(e [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1336","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Jak obliczy\u0107 pozosta\u0142\u0105 sum\u0119 kwadrat\u00f3w w Pythonie - Statorials<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, na przyk\u0142adzie, jak obliczy\u0107 rezydualn\u0105 sum\u0119 kwadrat\u00f3w dla modelu regresji w Pythonie.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/pl\/pozostala-suma-kwadratow-w-pythonie\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak obliczy\u0107 pozosta\u0142\u0105 sum\u0119 kwadrat\u00f3w w Pythonie - 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