{"id":1291,"date":"2023-07-26T23:55:31","date_gmt":"2023-07-26T23:55:31","guid":{"rendered":"https:\/\/statorials.org\/de\/ruckstandsrechner\/"},"modified":"2023-07-26T23:55:31","modified_gmt":"2023-07-26T23:55:31","slug":"ruckstandsrechner","status":"publish","type":"post","link":"https:\/\/statorials.org\/de\/ruckstandsrechner\/","title":{"rendered":"R\u00fcckstandsrechner"},"content":{"rendered":"<p><script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjs\/5.1.1\/math.js\"><\/script><script src=\"https:\/\/cdn.jsdelivr.net\/npm\/jstat@latest\/dist\/jstat.min.js\"><\/script><\/p>\n<style>\n@import url('https:\/\/fonts.googleapis.com\/css?family=Droid+Serif|Raleway');<\/p>\n<p>h1 {\ntext-align: center;\nfont-size: 50px;\nmargin-bottom: 0px;\nfont-family: 'Raleway', serif;\n}<\/p>\n<p>p {\ncolor: black;\nmargin-bottom: 15px;\nmargin-top: 15px;\nfont-family: 'Raleway', sans-serif;\n}<\/p>\n<p>#words {\npadding-left: 30px;\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>#words_summary {\npadding-left: 70px;\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>#words_text {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>#words_text_area {\ndisplay:inline-block;\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 100px;\n}<\/p>\n<p>#calcTitle {\ntext-align: center;\nfont-size: 20px;\nmargin-bottom: 0px;\nfont-family: 'Raleway', serif;\n}<\/p>\n<p>#hr_top {\nwidth: 30%;\nmargin-bottom: 0px;\nborder: none;\nheight: 2px;\ncolor: black;\nbackground-color: black;\n}<\/p>\n<p>#hr_bottom {\nwidth: 30%;\nmargin-top: 15px;\nborder: none;\nheight: 2px;\ncolor: black;\nbackground-color: black;\n}<\/p>\n<p>#words_table label, #words_table input {\n    display: inline-block;\n    vertical-align: baseline;\n    width: 350px;\n}<\/p>\n<p>    #buttonCalc {\n      border: 1px solid;\n      border-radius: 10px;\n      margin-top: 20px;<\/p>\n<p>      cursor: pointer;\n      outline: none;\n      background-color: white;\n      color: black;\n      font-family: 'Work Sans', sans-serif;\n      border: 1px solid grey;\n      \/* Green *\/\n    }<\/p>\n<p>    #buttonCalc:hover {\n      background-color: #f6f6f6;\n      border: 1px solid black;\n    }<\/p>\n<p>\t#words_table {\ncolor: black;\nfont-family: Raleway;\nmax-width: 350px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>#summary_table {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 20px;\n}<\/p>\n<p>\t.label_radio {\n\ttext-align: center;\n    }<\/p>\n<p>td, tr, th {\n    border: 1px solid black;\n}\ntable {\n    border-collapse: collapse;\n}\ntd, th {\n    min-width: 50px;\n    height: 21px;\n}\n    .label_radio {\n\ttext-align: center;\n}<\/p>\n<p>#text_area_input {\n\tpadding-left: 35%;\n\tfloat: left;\n}<\/p>\n<p>svg:not(:root) {\n  overflow: visible;\n}<\/p>\n<\/style>\n<div id=\"words\">\n<p style=\"text-align: left\">Ein <b>Residuum<\/b> ist die Differenz zwischen einem beobachteten Wert und einem vorhergesagten Wert in einem Regressionsmodell. Es wird wie folgt berechnet:<\/p>\n<p style=\"text-align: left\"> Residuum = Beobachteter Wert \u2013 Vorhergesagter Wert<\/p>\n<p style=\"text-align: left\"> Dieser Rechner ermittelt die Residuen f\u00fcr jede Beobachtung in einem einfachen linearen Regressionsmodell.<\/p>\n<p style=\"text-align: left\"> Geben Sie einfach eine Werteliste f\u00fcr eine Pr\u00e4diktorvariable und eine Antwortvariable in die Felder unten ein und klicken Sie dann auf die Schaltfl\u00e4che \u201eBerechnen\u201c:<\/p>\n<\/div>\n<p style=\"text-align: center\"> <b>Vorhersagewerte:<\/b><\/p>\n<div id=\"words_table\"><textarea id=\"x\" rows=\"5\" cols=\"40\"> 1, 3, 3, 5, 7, 13, 15, 19<\/textarea><\/div>\n<p style=\"text-align: center\"> <b>Antwortwerte:<\/b><\/p>\n<div id=\"words_table\"><textarea id=\"y\" rows=\"5\" cols=\"40\"> 7, 7, 12, 13, 18, 24, 29, 33 <\/textarea><\/div>\n<div id=\"words_table\"><input type=\"button\" id=\"buttonCalc\" onclick=\"calc()\" value=\"Calculate\"><\/div>\n<div id=\"words_table\">\n<p> <b>Lineare Regressionsgleichung:<\/b><\/p>\n<\/div>\n<div id=\"words_table\">\n<p> \u0177 = <span id=\"b\">5,6631<\/span> + ( <span id=\"a\">1,4802<\/span> )*x<\/p>\n<\/div>\n<div id=\"words_table\">\n<p> <b>Liste der R\u00fcckst\u00e4nde:<\/b><\/p>\n<\/div>\n<div id=\"words_table\">\n<p style=\"text-align: left\"> <span id=\"resids_out\">-0,143<br \/> -3.104<br \/> 1.896<br \/> -0,064<br \/> 1.975<br \/> -0,906<br \/> 1.133<br \/> -0,787<\/span><\/p>\n<\/div>\n<div id=\"words_table\">\n<p style=\"text-align: center\"><span id=\"error_msg\"><\/span><\/p>\n<\/div>\n<p><script>\nfunction calc() {<\/p>\n<p>\/\/get input data\nvar x = document.getElementById('x').value.split(',').map(Number);\nvar y = document.getElementById('y').value.split(',').map(Number);<\/p>\n<p>\/\/check that both lists are equal length\nif (x.length - y.length == 0) {\ndocument.getElementById('error_msg').innerHTML = '';<\/p>\n<p>function linearRegression(y,x){\n        var lr = {};\n        var n = y.length;\n        var sum_x = 0;\n        var sum_y = 0;\n        var sum_xy = 0;\n        var sum_xx = 0;\n        var sum_yy = 0;<\/p>\n<p>        for (var i = 0; i < y.length; i++) {\n            sum_x += x[i];\n            sum_y += y[i];\n            sum_xy += (x[i]*y[i]);\n            sum_xx += (x[i]*x[i]);\n            sum_yy += (y[i]*y[i]);\n        } \n\n        lr['slope'] = (n * sum_xy - sum_x * sum_y) \/ (n*sum_xx - sum_x * sum_x);\n        lr['intercept'] = (sum_y - lr.slope * sum_x)\/n;\n        return lr;\n}\n\nvar lr = linearRegression(y, x);\nvar a = lr.slope;\nvar b = lr.intercept;\n\n\/\/calculate residuals\nresiduals = [];\n\nfor (var obs = 0; obs < y.length; obs++) {\nthis_resid = (y[obs] - (b - (-1*a*x[obs]))).toFixed(3);\nresiduals.push(this_resid);\n}\n\ndocument.getElementById('a').innerHTML = a.toFixed(4);\ndocument.getElementById('b').innerHTML = b.toFixed(4);\ndocument.getElementById('resids_out').innerHTML = residuals.toString().split(',').join(\"<br \/>\");\n}<\/p>\n<p>\/\/output error message if both lists are not equal\nelse {\ndocument.getElementById('error_msg').innerHTML = 'The two lists must be of equal length.';\n}<\/p>\n<p>} \/\/end calc function\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ein Residuum ist die Differenz zwischen einem beobachteten Wert und einem vorhergesagten Wert in einem Regressionsmodell. Es wird wie folgt berechnet: Residuum = Beobachteter Wert \u2013 Vorhergesagter Wert Dieser Rechner ermittelt die Residuen f\u00fcr jede Beobachtung in einem einfachen linearen Regressionsmodell. Geben Sie einfach eine Werteliste f\u00fcr eine Pr\u00e4diktorvariable und eine Antwortvariable in die Felder [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>R\u00fcckstandsrechner - Statistik<\/title>\n<meta name=\"description\" content=\"Dieser Rechner ermittelt die Residuen f\u00fcr ein bestimmtes lineares Regressionsmodell.\" \/>\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\/de\/ruckstandsrechner\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"R\u00fcckstandsrechner - Statistik\" \/>\n<meta property=\"og:description\" content=\"Dieser Rechner ermittelt die Residuen f\u00fcr ein bestimmtes lineares Regressionsmodell.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/de\/ruckstandsrechner\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-26T23:55:31+00:00\" \/>\n<meta name=\"author\" content=\"Dr. Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Verfasst von\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr. Benjamin Anderson\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/de\/ruckstandsrechner\/\",\"url\":\"https:\/\/statorials.org\/de\/ruckstandsrechner\/\",\"name\":\"R\u00fcckstandsrechner - Statistik\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/de\/#website\"},\"datePublished\":\"2023-07-26T23:55:31+00:00\",\"dateModified\":\"2023-07-26T23:55:31+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/de\/#\/schema\/person\/ec75c4d6365f2708f8a0ad3a42121aa0\"},\"description\":\"Dieser Rechner ermittelt die Residuen f\u00fcr ein bestimmtes lineares Regressionsmodell.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/de\/ruckstandsrechner\/#breadcrumb\"},\"inLanguage\":\"de-DE\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/de\/ruckstandsrechner\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/de\/ruckstandsrechner\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Heim\",\"item\":\"https:\/\/statorials.org\/de\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"R\u00fcckstandsrechner\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/de\/#website\",\"url\":\"https:\/\/statorials.org\/de\/\",\"name\":\"Statorials\",\"description\":\"Ihr Leitfaden f\u00fcr statistische Kompetenz !\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/de\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"de-DE\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/de\/#\/schema\/person\/ec75c4d6365f2708f8a0ad3a42121aa0\",\"name\":\"Dr. Benjamin Anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"de-DE\",\"@id\":\"https:\/\/statorials.org\/de\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/de\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/de\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr. Benjamin Anderson\"},\"description\":\"Hallo, ich bin Benjamin, ein pensionierter Statistikprofessor, der sich zum engagierten Statorials-Lehrer entwickelt hat. Mit umfassender Erfahrung und Fachwissen auf dem Gebiet der Statistik bin ich bestrebt, mein Wissen zu teilen, um Studenten durch Statorials zu bef\u00e4higen. Mehr wissen\",\"sameAs\":[\"https:\/\/statorials.org\/de\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"R\u00fcckstandsrechner - Statistik","description":"Dieser Rechner ermittelt die Residuen f\u00fcr ein bestimmtes lineares Regressionsmodell.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/statorials.org\/de\/ruckstandsrechner\/","og_locale":"de_DE","og_type":"article","og_title":"R\u00fcckstandsrechner - Statistik","og_description":"Dieser Rechner ermittelt die Residuen f\u00fcr ein bestimmtes lineares Regressionsmodell.","og_url":"https:\/\/statorials.org\/de\/ruckstandsrechner\/","og_site_name":"Statorials","article_published_time":"2023-07-26T23:55:31+00:00","author":"Dr. Benjamin Anderson","twitter_card":"summary_large_image","twitter_misc":{"Verfasst von":"Dr. Benjamin Anderson"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/statorials.org\/de\/ruckstandsrechner\/","url":"https:\/\/statorials.org\/de\/ruckstandsrechner\/","name":"R\u00fcckstandsrechner - Statistik","isPartOf":{"@id":"https:\/\/statorials.org\/de\/#website"},"datePublished":"2023-07-26T23:55:31+00:00","dateModified":"2023-07-26T23:55:31+00:00","author":{"@id":"https:\/\/statorials.org\/de\/#\/schema\/person\/ec75c4d6365f2708f8a0ad3a42121aa0"},"description":"Dieser Rechner ermittelt die Residuen f\u00fcr ein bestimmtes lineares Regressionsmodell.","breadcrumb":{"@id":"https:\/\/statorials.org\/de\/ruckstandsrechner\/#breadcrumb"},"inLanguage":"de-DE","potentialAction":[{"@type":"ReadAction","target":["https:\/\/statorials.org\/de\/ruckstandsrechner\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/statorials.org\/de\/ruckstandsrechner\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Heim","item":"https:\/\/statorials.org\/de\/"},{"@type":"ListItem","position":2,"name":"R\u00fcckstandsrechner"}]},{"@type":"WebSite","@id":"https:\/\/statorials.org\/de\/#website","url":"https:\/\/statorials.org\/de\/","name":"Statorials","description":"Ihr Leitfaden f\u00fcr statistische Kompetenz !","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/statorials.org\/de\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"de-DE"},{"@type":"Person","@id":"https:\/\/statorials.org\/de\/#\/schema\/person\/ec75c4d6365f2708f8a0ad3a42121aa0","name":"Dr. Benjamin Anderson","image":{"@type":"ImageObject","inLanguage":"de-DE","@id":"https:\/\/statorials.org\/de\/#\/schema\/person\/image\/","url":"https:\/\/statorials.org\/de\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg","contentUrl":"https:\/\/statorials.org\/de\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg","caption":"Dr. Benjamin Anderson"},"description":"Hallo, ich bin Benjamin, ein pensionierter Statistikprofessor, der sich zum engagierten Statorials-Lehrer entwickelt hat. Mit umfassender Erfahrung und Fachwissen auf dem Gebiet der Statistik bin ich bestrebt, mein Wissen zu teilen, um Studenten durch Statorials zu bef\u00e4higen. Mehr wissen","sameAs":["https:\/\/statorials.org\/de"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/de\/wp-json\/wp\/v2\/posts\/1291"}],"collection":[{"href":"https:\/\/statorials.org\/de\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/de\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/de\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/de\/wp-json\/wp\/v2\/comments?post=1291"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/de\/wp-json\/wp\/v2\/posts\/1291\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/de\/wp-json\/wp\/v2\/media?parent=1291"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/de\/wp-json\/wp\/v2\/categories?post=1291"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/de\/wp-json\/wp\/v2\/tags?post=1291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}