{"id":781,"date":"2023-07-28T18:44:38","date_gmt":"2023-07-28T18:44:38","guid":{"rendered":"https:\/\/statorials.org\/pl\/regresja-kwadratowa-r\/"},"modified":"2023-07-28T18:44:38","modified_gmt":"2023-07-28T18:44:38","slug":"regresja-kwadratowa-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/regresja-kwadratowa-r\/","title":{"rendered":"Jak wykona\u0107 regresj\u0119 kwadratow\u0105 w r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Kiedy dwie zmienne maj\u0105 zwi\u0105zek liniowy, cz\u0119sto mo\u017cemy zastosowa\u0107 <a href=\"https:\/\/statorials.org\/pl\/prosta-regresja-liniowa-w-r\/\" target=\"_blank\" rel=\"noopener noreferrer\">prost\u0105 regresj\u0119 liniow\u0105<\/a> , aby okre\u015bli\u0107 ilo\u015bciowo ich zwi\u0105zek.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5772 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quadregstata1.png\" sizes=\"auto, \" srcset=\"\" alt=\"Przyk\u0142ad zale\u017cno\u015bci liniowej\" width=\"442\" height=\"318\"><\/p>\n<p> <span style=\"color: #000000;\">Je\u015bli jednak dwie zmienne maj\u0105 zwi\u0105zek kwadratowy, mo\u017cemy zastosowa\u0107 <strong>regresj\u0119 kwadratow\u0105<\/strong> do ilo\u015bciowego okre\u015blenia ich zwi\u0105zku.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5773 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quadregstata2.png\" sizes=\"auto, \" srcset=\"\" alt=\"Przyk\u0142ad zale\u017cno\u015bci kwadratowej\" width=\"441\" height=\"319\"><\/p>\n<p> <span style=\"color: #000000;\">W tym samouczku wyja\u015bniono, jak przeprowadzi\u0107 regresj\u0119 kwadratow\u0105 w j\u0119zyku R.<\/span><\/p>\n<h3> <strong>Przyk\u0142ad: regresja kwadratowa w R<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce chcemy zrozumie\u0107 zwi\u0105zek pomi\u0119dzy liczb\u0105 przepracowanych godzin a zg\u0142aszanym szcz\u0119\u015bciem. Mamy nast\u0119puj\u0105ce dane dotycz\u0105ce liczby godzin przepracowanych tygodniowo i zg\u0142aszanego poziomu szcz\u0119\u015bcia (w skali od 0 do 100) dla 11 r\u00f3\u017cnych os\u00f3b:<\/span> <\/p>\n<p data-slot-rendered-dynamic=\"true\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-6954 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quadti1.png\" sizes=\"auto, \" srcset=\"\" alt=\"\" width=\"150\" height=\"248\"><\/p>\n<p> <span style=\"color: #000000;\">Wykonaj poni\u017csze kroki, aby dopasowa\u0107 model regresji kwadratowej w R.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 1: Wprowad\u017a dane.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Najpierw utworzymy ramk\u0119 danych zawieraj\u0105c\u0105 nasze dane:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#createdata<\/span>\ndata &lt;- data.frame(hours=c(6, 9, 12, 14, 30, 35, 40, 47, 51, 55, 60),\n                   happiness=c(14, 28, 50, 70, 89, 94, 90, 75, 59, 44, 27))\n<span style=\"color: #008080;\">\n#viewdata<\/span> \ndata\n\n   hours happiness\n1 6 14\n2 9 28\n3 12 50\n4 14 70\n5 30 89\n6 35 94\n7 40 90\n8 47 75\n9 51 59\n10 55 44\n11 60 27\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>Krok 2: Wizualizuj dane.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie utworzymy prosty wykres rozrzutu do wizualizacji danych.<\/span> <\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create scatterplot<\/span>\nplot(data$hours, data$happiness, pch=16)<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8616 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quadratiquer1.png\" alt=\"Wykres rozrzutu w R\" width=\"370\" height=\"336\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Wyra\u017anie wida\u0107, \u017ce dane nie uk\u0142adaj\u0105 si\u0119 wed\u0142ug liniowego wzorca.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 3: Dopasuj prosty model regresji liniowej.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie dopasujemy prosty model regresji liniowej, aby sprawdzi\u0107, jak dobrze pasuje on do danych:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit linear model<\/span>\nlinearModel &lt;- lm(happiness ~ hours, data=data)\n\n<span style=\"color: #008080;\">#view model summary<\/span>\nsummary(linearModel)\n\nCall:\nlm(formula = happiness ~ hours)\n\nResiduals:\n   Min 1Q Median 3Q Max \n-39.34 -21.99 -2.03 23.50 35.11 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)  \n(Intercept) 48.4531 17.3288 2.796 0.0208 *\nhours 0.2981 0.4599 0.648 0.5331  \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 28.72 on 9 degrees of freedom\nMultiple R-squared: 0.0446, Adjusted R-squared: -0.06156 \nF-statistic: 0.4201 on 1 and 9 DF, p-value: 0.5331\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Ca\u0142kowita wariancja szcz\u0119\u015bcia wyja\u015bniona przez model wynosi tylko <strong>4,46%<\/strong> , jak pokazuje wielokrotna warto\u015b\u0107 R-kwadrat.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 4: Dopasuj model regresji kwadratowej.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie dopasujemy model regresji kwadratowej.<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create a new variable for hours <sup>2<\/sup><\/span>\ndata$hours2 &lt;- data$hours^2\n\n<span style=\"color: #008080;\">#fit quadratic regression model<\/span>\nquadraticModel &lt;- lm(happiness ~ hours + hours2, data=data)\n\n<span style=\"color: #008080;\">#view model summary\n<\/span>summary(quadraticModel)\n\nCall:\nlm(formula = happiness ~ hours + hours2, data = data)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-6.2484 -3.7429 -0.1812 1.1464 13.6678 \n\nCoefficients:\n             Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) -18.25364 6.18507 -2.951 0.0184 *  \nhours 6.74436 0.48551 13.891 6.98e-07 ***\nhours2 -0.10120 0.00746 -13.565 8.38e-07 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 6.218 on 8 degrees of freedom\nMultiple R-squared: 0.9602, Adjusted R-squared: 0.9502 \nF-statistic: 96.49 on 2 and 8 DF, p-value: 2.51e-06\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Ca\u0142kowita wariancja szcz\u0119\u015bcia wyja\u015bniona przez model wzros\u0142a do <b>96,02%<\/b> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Mo\u017cemy u\u017cy\u0107 poni\u017cszego kodu, aby zwizualizowa\u0107 stopie\u0144 dopasowania modelu do danych:<\/span> <\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create sequence of hour values<\/span>\nhourValues &lt;- seq(0, 60, 0.1)\n\n<span style=\"color: #008080;\">#create list of predicted happiness levels using quadratic model\n<\/span>happinessPredict &lt;- predict(quadraticModel, list(hours=hourValues, hours2=hourValues^2))\n\n<span style=\"color: #008080;\">#create scatterplot of original data values\n<\/span>plot(data$hours, data$happiness, pch=16)\n<span style=\"color: #008080;\">#add predicted lines based on quadratic regression model<\/span>\nlines(hourValues, happinessPredict, col='blue')\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8619 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quadratiquer2.png\" alt=\"Wykres rozproszenia regresji kwadratowej w R\" width=\"399\" height=\"368\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Widzimy, \u017ce linia regresji kwadratowej ca\u0142kiem dobrze pasuje do warto\u015bci danych.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 5: Interpretacja modelu regresji kwadratowej.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">W poprzednim kroku widzieli\u015bmy, \u017ce wynikiem modelu regresji kwadratowej by\u0142:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>Coefficients:\n             Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) -18.25364 6.18507 -2.951 0.0184 *  \nhours 6.74436 0.48551 13.891 6.98e-07 ***\nhours2 -0.10120 0.00746 -13.565 8.38e-07 ***\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">W oparciu o przedstawione tutaj wsp\u00f3\u0142czynniki skorygowana regresja kwadratowa b\u0119dzie wynosi\u0107:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Szcz\u0119\u015bcie = -0,1012 (godziny) <sup>2<\/sup> + 6,7444 (godziny) \u2013 18,2536<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Mo\u017cemy u\u017cy\u0107 tego r\u00f3wnania, aby znale\u017a\u0107 przewidywane szcz\u0119\u015bcie danej osoby, bior\u0105c pod uwag\u0119 liczb\u0119 godzin przepracowanych w tygodniu.<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\">Na przyk\u0142ad osoba pracuj\u0105ca 60 godzin tygodniowo mia\u0142aby poziom szcz\u0119\u015bcia r\u00f3wny <strong>22,09<\/strong> :<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\">Szcz\u0119\u015bcie = -0,1012(60) <sup>2<\/sup> + 6,7444(60) \u2013 18,2536 = 22,09<\/span><\/p>\n<p> <span style=\"color: #000000;\">I odwrotnie, osoba pracuj\u0105ca 30 godzin tygodniowo powinna mie\u0107 poziom szcz\u0119\u015bcia na poziomie <strong>92,99<\/strong> :<\/span><\/p>\n<p> <span style=\"color: #000000;\">Szcz\u0119\u015bcie = -0,1012(30) <sup>2<\/sup> + 6,7444(30) \u2013 18,2536 = 92,99<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Kiedy dwie zmienne maj\u0105 zwi\u0105zek liniowy, cz\u0119sto mo\u017cemy zastosowa\u0107 prost\u0105 regresj\u0119 liniow\u0105 , aby okre\u015bli\u0107 ilo\u015bciowo ich zwi\u0105zek. Je\u015bli jednak dwie zmienne maj\u0105 zwi\u0105zek kwadratowy, mo\u017cemy zastosowa\u0107 regresj\u0119 kwadratow\u0105 do ilo\u015bciowego okre\u015blenia ich zwi\u0105zku. W tym samouczku wyja\u015bniono, jak przeprowadzi\u0107 regresj\u0119 kwadratow\u0105 w j\u0119zyku R. Przyk\u0142ad: regresja kwadratowa w R Za\u0142\u00f3\u017cmy, \u017ce chcemy zrozumie\u0107 zwi\u0105zek [&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-781","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 wykona\u0107 regresj\u0119 kwadratow\u0105 w R - Statology<\/title>\n<meta name=\"description\" content=\"Proste wyja\u015bnienie, jak przeprowadzi\u0107 regresj\u0119 kwadratow\u0105 w R, \u0142\u0105cznie z przyk\u0142adem krok po kroku.\" \/>\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\/regresja-kwadratowa-r\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak wykona\u0107 regresj\u0119 kwadratow\u0105 w R - Statology\" \/>\n<meta property=\"og:description\" content=\"Proste wyja\u015bnienie, jak przeprowadzi\u0107 regresj\u0119 kwadratow\u0105 w R, \u0142\u0105cznie z przyk\u0142adem krok po kroku.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/regresja-kwadratowa-r\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T18:44:38+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quadregstata1.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\/regresja-kwadratowa-r\/\",\"url\":\"https:\/\/statorials.org\/pl\/regresja-kwadratowa-r\/\",\"name\":\"Jak wykona\u0107 regresj\u0119 kwadratow\u0105 w R - Statology\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-28T18:44:38+00:00\",\"dateModified\":\"2023-07-28T18:44:38+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"Proste wyja\u015bnienie, jak przeprowadzi\u0107 regresj\u0119 kwadratow\u0105 w R, \u0142\u0105cznie z przyk\u0142adem krok po kroku.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/regresja-kwadratowa-r\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/regresja-kwadratowa-r\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/regresja-kwadratowa-r\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak wykona\u0107 regresj\u0119 kwadratow\u0105 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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