{"id":2137,"date":"2023-07-23T13:02:12","date_gmt":"2023-07-23T13:02:12","guid":{"rendered":"https:\/\/statorials.org\/pl\/python-bic\/"},"modified":"2023-07-23T13:02:12","modified_gmt":"2023-07-23T13:02:12","slug":"python-bic","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/python-bic\/","title":{"rendered":"Jak obliczy\u0107 bic w pythonie"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Bayesowskie kryterium informacyjne<\/strong> , cz\u0119sto w skr\u00f3cie <strong>BIC<\/strong> , jest miar\u0105 stosowan\u0105 do por\u00f3wnywania dobroci dopasowania r\u00f3\u017cnych modeli regresji.<\/span><\/p>\n<p> <span style=\"color: #000000;\">W praktyce dopasowujemy modele regresji wielokrotnej do tego samego zbioru danych i wybieramy model o najni\u017cszej warto\u015bci BIC jako model najlepiej pasuj\u0105cy do danych.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Do obliczenia BIC u\u017cywamy nast\u0119puj\u0105cego wzoru:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>BIC:<\/strong> (RSS+log(n)d\u03c3\u0302 <sup>2<\/sup> ) \/ n<\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>d:<\/strong> Liczba predyktor\u00f3w<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> Ca\u0142kowita liczba obserwacji<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03c3\u0302:<\/strong> Oszacowanie wariancji b\u0142\u0119du zwi\u0105zanej z ka\u017cd\u0105 miar\u0105 odpowiedzi w modelu regresji<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>RSS:<\/strong> Pozosta\u0142a suma kwadrat\u00f3w z modelu regresji<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>TSS:<\/strong> Ca\u0142kowita suma kwadrat\u00f3w modelu regresji<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Aby obliczy\u0107 BIC modeli regresji wielokrotnej w Pythonie, mo\u017cemy u\u017cy\u0107 funkcji <strong>statsmodels.regression.linear_model.OLS()<\/strong> , kt\u00f3ra ma w\u0142a\u015bciwo\u015b\u0107 zwan\u0105 bic, kt\u00f3ra informuje nas o warto\u015bci BIC dla danego modelu.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017cszy przyk\u0142ad pokazuje, jak u\u017cywa\u0107 tej funkcji do obliczania i interpretowania BIC dla r\u00f3\u017cnych modeli regresji w Pythonie.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad: oblicz BIC modeli regresji w Pythonie<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce chcemy dopasowa\u0107 dwa r\u00f3\u017cne <a href=\"https:\/\/statorials.org\/pl\/wielokrotna-regresja-liniowa\/\" target=\"_blank\" rel=\"noopener\">modele regresji liniowej wielokrotnej,<\/a> u\u017cywaj\u0105c zmiennych ze zbioru danych <strong>mtcars<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Najpierw za\u0142adujemy ten zbi\u00f3r danych:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">from<\/span> sklearn. <span style=\"color: #3366ff;\">linear_model<\/span> <span style=\"color: #008000;\">import<\/span> LinearRegression\n<span style=\"color: #008000;\">import<\/span> statsmodels. <span style=\"color: #3366ff;\">api<\/span> <span style=\"color: #008000;\">as<\/span> sm\n<span style=\"color: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd\n\n<span style=\"color: #008080;\">#define URL where dataset is located\n<\/span>url = \"https:\/\/raw.githubusercontent.com\/Statorials\/Python-Guides\/main\/mtcars.csv\"\n\n<span style=\"color: #008080;\">#read in data\n<\/span>data = pd. <span style=\"color: #3366ff;\">read_csv<\/span> (url)\n\n<span style=\"color: #008080;\">#view head of data\n<\/span>data. <span style=\"color: #3366ff;\">head<\/span> ()\n\n        model mpg cyl disp hp drat wt qsec vs am gear carb\n0 Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4\n1 Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4\n2 Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1\n3 Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1\n4 Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie dopasujemy nast\u0119puj\u0105ce dwa modele regresji:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Model 1<\/strong> : mpg = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> (disp) + \u03b2 <sub>2<\/sub> (qsec)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Model 2<\/strong> : mpg = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> (dost\u0119pny) + \u03b2 <sub>2<\/sub> (wagowo)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak dopasowa\u0107 pierwszy model i obliczy\u0107 BIC:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#define response variable\n<\/span>y = data['mpg']\n\n<span style=\"color: #008080;\">#define predictor variables\n<\/span>x = data[['disp', 'qsec']]\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 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 BIC of model\n<\/span><span style=\"color: #993300;\">print<\/span> (model. <span style=\"color: #3366ff;\">bic<\/span> )\n\n174.23905634994506<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">BIC tego modelu okazuje si\u0119 wynosi\u0107 <strong>174.239<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie dopasujemy drugi model i obliczymy BIC:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#define response variable\n<\/span>y = data['mpg']\n\n<span style=\"color: #008080;\">#define predictor variables\n<\/span>x = data[['disp', 'wt']]\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 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 BIC of model\n<\/span><span style=\"color: #993300;\">print<\/span> (model. <span style=\"color: #3366ff;\">bic<\/span> )\n\n166.56499196301334<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">BIC tego modelu okazuje si\u0119 wynosi\u0107 <strong>166,565<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poniewa\u017c drugi model ma ni\u017csz\u0105 warto\u015b\u0107 BIC, jest to model najlepiej dopasowany.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Gdy uznamy ten model za najlepszy, mo\u017cemy przyst\u0105pi\u0107 do jego dopasowywania i przeanalizowa\u0107 wyniki, w tym warto\u015b\u0107 R-kwadrat i wsp\u00f3\u0142czynniki beta, aby okre\u015bli\u0107 dok\u0142adny zwi\u0105zek pomi\u0119dzy zestawem zmiennych predykcyjnych a<a href=\"https:\/\/statorials.org\/pl\/zmienne-odpowiedzi-wyjasniajace\/\" target=\"_blank\" rel=\"noopener\">zmienn\u0105 odpowiedzi<\/a> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Dwie inne powszechnie stosowane metryki do por\u00f3wnywania dopasowania modeli regresji to <strong>AIC<\/strong> i <strong>skorygowana warto\u015b\u0107 R-kwadrat<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017csze samouczki wyja\u015bniaj\u0105, jak obliczy\u0107 ka\u017cd\u0105 z tych metryk dla modeli regresji w Pythonie:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/pl\/aic-w-pythonie\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 AIC modeli regresji w Pythonie<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/r-kwadrat-w-pythonie-dostosowuje-sie\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 skorygowany R-kwadrat w Pythonie<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bayesowskie kryterium informacyjne , cz\u0119sto w skr\u00f3cie BIC , jest miar\u0105 stosowan\u0105 do por\u00f3wnywania dobroci dopasowania r\u00f3\u017cnych modeli regresji. W praktyce dopasowujemy modele regresji wielokrotnej do tego samego zbioru danych i wybieramy model o najni\u017cszej warto\u015bci BIC jako model najlepiej pasuj\u0105cy do danych. Do obliczenia BIC u\u017cywamy nast\u0119puj\u0105cego wzoru: BIC: (RSS+log(n)d\u03c3\u0302 2 ) \/ n [&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-2137","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 BIC w Pythonie - Statologia<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 warto\u015bci BIC dla modeli regresji w Pythonie, z kilkoma przyk\u0142adami.\" \/>\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\/python-bic\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak obliczy\u0107 BIC w Pythonie - Statologia\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 warto\u015bci BIC dla modeli regresji w Pythonie, z kilkoma przyk\u0142adami.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/python-bic\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-23T13:02:12+00:00\" \/>\n<meta name=\"author\" content=\"Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisane przez\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/python-bic\/\",\"url\":\"https:\/\/statorials.org\/pl\/python-bic\/\",\"name\":\"Jak obliczy\u0107 BIC w Pythonie - Statologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-23T13:02:12+00:00\",\"dateModified\":\"2023-07-23T13:02:12+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 warto\u015bci BIC dla modeli regresji w Pythonie, z kilkoma przyk\u0142adami.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/python-bic\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/python-bic\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/python-bic\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak obliczy\u0107 bic w pythonie\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pl\/#website\",\"url\":\"https:\/\/statorials.org\/pl\/\",\"name\":\"Statorials\",\"description\":\"Tw\u00f3j przewodnik po kompetencjach statystycznych!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pl\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pl-PL\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\",\"name\":\"Benjamin Anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pl-PL\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin Anderson\"},\"description\":\"Cze\u015b\u0107, jestem Benjamin i jestem emerytowanym profesorem statystyki, kt\u00f3ry zosta\u0142 oddanym nauczycielem Statorials. 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