{"id":1749,"date":"2023-07-25T03:30:46","date_gmt":"2023-07-25T03:30:46","guid":{"rendered":"https:\/\/statorials.org\/pl\/aic-w-pythonie\/"},"modified":"2023-07-25T03:30:46","modified_gmt":"2023-07-25T03:30:46","slug":"aic-w-pythonie","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/aic-w-pythonie\/","title":{"rendered":"Jak obliczy\u0107 aic modeli regresji w pythonie"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Kryterium informacyjne Akaike (AIC) to metryka u\u017cywana do por\u00f3wnywania dopasowania r\u00f3\u017cnych modeli 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;\">AIC = 2K \u2013 2 <em>ln<\/em> (L)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>K:<\/strong> Liczba parametr\u00f3w modelu. Domy\u015blna warto\u015b\u0107 K wynosi 2, zatem model z tylko jedn\u0105 zmienn\u0105 predykcyjn\u0105 b\u0119dzie mia\u0142 warto\u015b\u0107 K wynosz\u0105c\u0105 2+1 = 3.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><em>ln<\/em> (L)<\/strong> : Logarytm wiarygodno\u015bci modelu. To m\u00f3wi nam o prawdopodobie\u0144stwie modelu na podstawie danych.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Celem AIC jest znalezienie modelu wyja\u015bniaj\u0105cego najwi\u0119ksze zr\u00f3\u017cnicowanie danych, przy jednoczesnym karaniu modeli wykorzystuj\u0105cych nadmiern\u0105 liczb\u0119 parametr\u00f3w.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Po dopasowaniu wielu modeli regresji mo\u017cna por\u00f3wna\u0107<\/span> <span style=\"color: #000000;\">warto\u015b\u0107 AIC ka\u017cdego modelu. Model z najni\u017cszym AIC zapewnia najlepsze dopasowanie.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Aby obliczy\u0107 AIC 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 <strong>aic<\/strong> , kt\u00f3ra informuje nas o warto\u015bci AIC 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 AIC dla r\u00f3\u017cnych modeli regresji w Pythonie.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad: oblicz i zinterpretuj AIC 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 zestaw 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;\">Oto zmienne predykcyjne, kt\u00f3rych b\u0119dziemy u\u017cywa\u0107 w ka\u017cdym modelu:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Zmienne predykcyjne w modelu 1: disp, hp, wt, qsec<\/span><\/li>\n<li> <span style=\"color: #000000;\">Zmienne predykcyjne w modelu 2: disp, qsec<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak dopasowa\u0107 pierwszy model i obliczy\u0107 AIC:<\/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', 'hp', 'wt', '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 AIC of model\n<\/span><span style=\"color: #993300;\">print<\/span> (model. <span style=\"color: #3366ff;\">aic<\/span> )\n\n157.06960941462438<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">AIC tego modelu okazuje si\u0119 wynosi\u0107 <strong>157,07<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie dopasujemy drugi model i obliczymy AIC:<\/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 AIC of model\n<\/span><span style=\"color: #993300;\">print<\/span> (model. <span style=\"color: #3366ff;\">aic<\/span> )\n\n169.84184864154588<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">AIC tego modelu okazuje si\u0119 wynosi\u0107 <strong>169,84<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poniewa\u017c pierwszy model ma ni\u017csz\u0105 warto\u015b\u0107 AIC, 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> <a href=\"https:\/\/statorials.org\/pl\/python-regresji-liniowej\/\" target=\"_blank\" rel=\"noopener\">Kompletny przewodnik po regresji liniowej 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>Kryterium informacyjne Akaike (AIC) to metryka u\u017cywana do por\u00f3wnywania dopasowania r\u00f3\u017cnych modeli regresji. Oblicza si\u0119 go w nast\u0119puj\u0105cy spos\u00f3b: AIC = 2K \u2013 2 ln (L) Z\u0142oto: K: Liczba parametr\u00f3w modelu. Domy\u015blna warto\u015b\u0107 K wynosi 2, zatem model z tylko jedn\u0105 zmienn\u0105 predykcyjn\u0105 b\u0119dzie mia\u0142 warto\u015b\u0107 K wynosz\u0105c\u0105 2+1 = 3. ln (L) : Logarytm [&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-1749","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 AIC modeli regresji w Pythonie<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 warto\u015b\u0107 kryterium informacyjnego Akaike (AIC) modeli regresji w j\u0119zyku Python.\" \/>\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\/aic-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 AIC modeli regresji w Pythonie\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 warto\u015b\u0107 kryterium informacyjnego Akaike (AIC) modeli regresji w j\u0119zyku Python.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/aic-w-pythonie\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-25T03:30:46+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\/aic-w-pythonie\/\",\"url\":\"https:\/\/statorials.org\/pl\/aic-w-pythonie\/\",\"name\":\"Jak obliczy\u0107 AIC modeli regresji w Pythonie\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-25T03:30:46+00:00\",\"dateModified\":\"2023-07-25T03:30:46+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 warto\u015b\u0107 kryterium informacyjnego Akaike (AIC) modeli regresji w j\u0119zyku Python.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/aic-w-pythonie\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/aic-w-pythonie\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/aic-w-pythonie\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak obliczy\u0107 aic modeli regresji 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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