{"id":1274,"date":"2023-07-27T01:24:14","date_gmt":"2023-07-27T01:24:14","guid":{"rendered":"https:\/\/statorials.org\/pl\/dfbetas-w-r\/"},"modified":"2023-07-27T01:24:14","modified_gmt":"2023-07-27T01:24:14","slug":"dfbetas-w-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/dfbetas-w-r\/","title":{"rendered":"Jak obliczy\u0107 dfbetas w r"},"content":{"rendered":"

<\/p>\n

\n

W statystyce cz\u0119sto chcemy wiedzie\u0107, jaki wp\u0142yw maj\u0105 r\u00f3\u017cne obserwacje<\/a> w modelach regresji.<\/span><\/p>\n

Jednym ze sposob\u00f3w obliczenia wp\u0142ywu obserwacji jest u\u017cycie metryki znanej jako DFBETAS<\/strong> , kt\u00f3ra informuje nas o standaryzowanym wp\u0142ywie na ka\u017cdy wsp\u00f3\u0142czynnik usuni\u0119cia ka\u017cdej indywidualnej obserwacji.<\/span><\/p>\n

Metryka ta daje nam wyobra\u017cenie o wp\u0142ywie ka\u017cdej obserwacji na ka\u017cde oszacowanie wsp\u00f3\u0142czynnika w danym modelu regresji.<\/span><\/p>\n

Ten samouczek pokazuje krok po kroku przyk\u0142ad obliczania i wizualizacji DFBETAS dla ka\u017cdej obserwacji w modelu w R.<\/span><\/p>\n

Krok 1: Utw\u00f3rz model regresji<\/strong><\/span><\/h3>\n

Najpierw utworzymy model regresji liniowej wielokrotnej<\/a> , korzystaj\u0105c ze zbioru danych mtcars<\/strong> wbudowanego w R:<\/span><\/p>\n

 #fit a regression model<\/span>\nmodel <- lm(mpg~disp+hp, data=mtcars)\n\n#view model summary\n<\/span>summary(model)\n\nCoefficients:\n             Estimate Std. Error t value Pr(>|t|)    \n(Intercept) 30.735904 1.331566 23.083 < 2nd-16 ***\navailable -0.030346 0.007405 -4.098 0.000306 ***\nhp -0.024840 0.013385 -1.856 0.073679 .  \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 3.127 on 29 degrees of freedom\nMultiple R-squared: 0.7482, Adjusted R-squared: 0.7309 \nF-statistic: 43.09 on 2 and 29 DF, p-value: 2.062e-09\n<\/strong><\/pre>\n
 Krok 2: Oblicz DFBETAS dla ka\u017cdej obserwacji<\/strong><\/span><\/h3>\n
 Nast\u0119pnie skorzystamy z wbudowanej funkcji dfbetas()<\/strong> do obliczenia warto\u015bci DFBETAS dla ka\u017cdej obserwacji w modelu:<\/span><\/p>\n
 #calculate DFBETAS for each observation in the model\n<\/span>dfbetas <- as<\/span> . data<\/span> . frame<\/span> (dfbetas(model))\n\n#display DFBETAS for each observation\n<\/span>dfbetas\n\n                      (Intercept) disp hp\nMazda RX4 -0.1174171253 0.030760632 1.748143e-02\nMazda RX4 Wag -0.1174171253 0.030760632 1.748143e-02\nDatsun 710 -0.1694989349 0.086630144 -3.332781e-05\nHornet 4 Drive 0.0577309674 0.078971334 -8.705488e-02\nHornet Sportabout -0.0204333878 0.237526523 -1.366155e-01\nValiant -0.1711908285 -0.139135639 1.829038e-01\nDuster 360 -0.0312338677 -0.005356209 3.581378e-02\nMerc 240D -0.0312259577 -0.010409922 2.433256e-02\nMerc 230 -0.0865872595 0.016428917 2.287867e-02\nMerc 280 -0.1560683502 0.078667906 -1.911180e-02\nMerc 280C -0.2254489597 0.113639937 -2.760800e-02\nMerc 450SE 0.0022844093 0.002966155 -2.855985e-02\nMerc 450SL 0.0009062022 0.001176644 -1.132941e-02\nMerc 450SLC 0.0041566755 0.005397169 -5.196706e-02\nCadillac Fleetwood 0.0388832216 -0.134511133 7.277283e-02\nLincoln Continental 0.0483781688 -0.121146607 5.326220e-02\nChrysler Imperial -0.1645266331 0.236634429 -3.917771e-02\nFiat 128 0.5720358325 -0.181104179 -1.265475e-01\nHonda Civic 0.3490872162 -0.053660545 -1.326422e-01\nToyota Corolla 0.7367058819 -0.268512348 -1.342384e-01\nToyota Corona -0.2181110386 0.101336902 5.945352e-03\nDodge Challenger -0.0270169005 -0.123610713 9.441241e-02\nAMC Javelin -0.0406785103 -0.141711468 1.074514e-01\nCamaro Z28 0.0390139262 0.012846225 -5.031588e-02\nPontiac Firebird -0.0549059340 0.574544346 -3.689584e-01\nFiat X1-9 0.0565157245 -0.017751582 -1.262221e-02\nPorsche 914-2 0.0839169111 -0.028670987 -1.240452e-02\nLotus Europa 0.3444562478 -0.402678927 2.135224e-01\nFord Pantera L -0.1598854695 -0.094184733 2.320845e-01\nFerrari Dino -0.0343997122 0.248642444 -2.344154e-01\nMaserati Bora -0.3436265545 -0.511285637 7.319066e-01\nVolvo 142E -0.1784974091 0.132692956 -4.433915e-02\n<\/strong><\/pre>\n
 Dla ka\u017cdej obserwacji mo\u017cemy zobaczy\u0107 r\u00f3\u017cnic\u0119 w oszacowaniu wsp\u00f3\u0142czynnika pochodzenia, zmiennej disp<\/em> i zmiennej hp<\/em> , kt\u00f3ra pojawia si\u0119 po usuni\u0119ciu tej konkretnej obserwacji.<\/span><\/p>\n
 Og\u00f3lnie rzecz bior\u0105c, uwa\u017camy, \u017ce obserwacja ma du\u017cy wp\u0142yw na estymacj\u0119 danego wsp\u00f3\u0142czynnika, je\u015bli ma warto\u015b\u0107 DBETAS wi\u0119ksz\u0105 ni\u017c pr\u00f3g 2\/\u221a n<\/span> , gdzie n<\/em> jest liczb\u0105 obserwacji.<\/span><\/p>\n
 W tym przyk\u0142adzie pr\u00f3g b\u0119dzie wynosi\u0107 0,3535534<\/strong> :<\/span><\/p>\n
 #find number of observations<\/span>\nn <- nrow<\/span> (mtcars)\n\n#calculate DFBETAS threshold value<\/span>\nthresh <- 2\/ sqrt<\/span> (n)\n\nthresh\n\n[1] 0.3535534\n<\/strong><\/pre>\n
 Krok 3: Wizualizuj DFBETAS<\/strong><\/p>\n
 Na koniec mo\u017cemy utworzy\u0107 wykresy wizualizuj\u0105ce warto\u015b\u0107 DFBETAS dla ka\u017cdej obserwacji i ka\u017cdego predyktora w modelu:<\/span> <\/p>\n
 #specify 2 rows and 1 column in plotting region<\/span>\nby(mfrow=c(2,1))\n\n#plot DFBETAS for disp<\/em> with threshold lines<\/span>\nplot(dfbetas$disp, type=' h<\/span> ')\nabline(h = thresh, lty = 2)\nabline(h = -thresh, lty = 2)\n\n#plot DFBETAS for hp<\/em> with threshold lines<\/span> \nplot(dfbetas$hp, type=' h<\/span> ')\nabline(h = thresh, lty = 2)\nabline(h = -thresh, lty = 2)\n<\/strong><\/pre>\n
\"DFBETAS<\/p>\n
 Na ka\u017cdym wykresie o\u015b x przedstawia indeks ka\u017cdej obserwacji w zbiorze danych, a warto\u015b\u0107 y przedstawia odpowiednie warto\u015bci DFBETAS dla ka\u017cdej obserwacji i ka\u017cdego predyktora.<\/span><\/p>\n
 Na pierwszym wykresie wida\u0107, \u017ce trzy obserwacje przekraczaj\u0105 bezwzgl\u0119dn\u0105 warto\u015b\u0107 progow\u0105 0,3535534<\/strong> , a na drugim wykresie wida\u0107, \u017ce dwie obserwacje przekraczaj\u0105 bezwzgl\u0119dn\u0105 warto\u015b\u0107 progow\u0105.<\/span><\/p>\n
 Mo\u017cemy zdecydowa\u0107 si\u0119 na dok\u0142adniejsze przestudiowanie tych obserwacji, aby ustali\u0107, czy maj\u0105 one nadmierny wp\u0142yw na estymacj\u0119 wsp\u00f3\u0142czynnik\u00f3w modelu.<\/span><\/p>\n
 Dodatkowe zasoby<\/strong><\/span><\/h3>\n
 Jak wykona\u0107 prost\u0105 regresj\u0119 liniow\u0105 w R<\/a>
 Jak wykona\u0107 wielokrotn\u0105 regresj\u0119 liniow\u0105 w R<\/a>
 Jak obliczy\u0107 statystyki d\u017awigni w R<\/a>
 Jak obliczy\u0107 DFFITS w R<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
W statystyce cz\u0119sto chcemy wiedzie\u0107, jaki wp\u0142yw maj\u0105 r\u00f3\u017cne obserwacje w modelach regresji. Jednym ze sposob\u00f3w obliczenia wp\u0142ywu obserwacji jest u\u017cycie metryki znanej jako DFBETAS , kt\u00f3ra informuje nas o standaryzowanym wp\u0142ywie na ka\u017cdy wsp\u00f3\u0142czynnik usuni\u0119cia ka\u017cdej indywidualnej obserwacji. Metryka ta daje nam wyobra\u017cenie o wp\u0142ywie ka\u017cdej obserwacji na ka\u017cde oszacowanie wsp\u00f3\u0142czynnika w danym modelu […]<\/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-1274","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"\nJak obliczy\u0107 DFBETAS w R - Statology<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 DFBETAS w R, na przyk\u0142adzie.\" \/>\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\/dfbetas-w-r\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak obliczy\u0107 DFBETAS w R - Statology\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 DFBETAS w R, na przyk\u0142adzie.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/dfbetas-w-r\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-27T01:24:14+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/dfbetas1.png\" \/>\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=\"3 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/dfbetas-w-r\/\",\"url\":\"https:\/\/statorials.org\/pl\/dfbetas-w-r\/\",\"name\":\"Jak obliczy\u0107 DFBETAS w R - Statology\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-27T01:24:14+00:00\",\"dateModified\":\"2023-07-27T01:24:14+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 DFBETAS w R, na przyk\u0142adzie.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/dfbetas-w-r\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/dfbetas-w-r\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/dfbetas-w-r\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak obliczy\u0107 dfbetas w r\"}]},{\"@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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