{"id":698,"date":"2023-07-29T01:26:46","date_gmt":"2023-07-29T01:26:46","guid":{"rendered":"https:\/\/statorials.org\/de\/linearer-regressionsrechner\/"},"modified":"2023-07-29T01:26:46","modified_gmt":"2023-07-29T01:26:46","slug":"linearer-regressionsrechner","status":"publish","type":"post","link":"https:\/\/statorials.org\/de\/linearer-regressionsrechner\/","title":{"rendered":"Linearer regressionsrechner"},"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 label, input {\n    display: inline-block;\n    vertical-align: baseline;\n    width: 350px;\n}<\/p>\n<p>    #button {\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>    #button: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\">Dieser Rechner erstellt eine lineare Regressionsgleichung basierend auf den Werten einer Pr\u00e4diktorvariablen und einer Antwortvariablen.<\/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\"> 6, 7, 7, 8, 12, 14, 15, 16, 16, 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\"> 14, 15, 15, 17, 18, 18, 19, 24, 25, 29 <\/textarea><\/div>\n<div id=\"words_table\"><input type=\"button\" id=\"button\" onclick=\"calc()\" value=\"Calculate\"><\/div>\n<div id=\"words_table\">\n<p style=\"text-align: center\"> <b>Lineare Regressionsgleichung:<\/b><\/p>\n<\/div>\n<div id=\"words_table\">\n<p style=\"text-align: center\"> \u0177 = <span id=\"b\">0,9694<\/span> + ( <span id=\"a\">7,7673<\/span> )*x<\/p>\n<\/div>\n<div id=\"words_table\">\n<p style=\"text-align: center\"> <b>Passformqualit\u00e4t:<\/b><\/p>\n<\/div>\n<div id=\"words_table\">\n<p style=\"text-align: center\"> R-Quadrat: <span id=\"r2\">0,8282<\/span><\/p>\n<\/div>\n<div id=\"words_table\">\n<p style=\"text-align: center\"> <b>Deutung:<\/b><\/p>\n<\/div>\n<div id=\"words_table\">\n<p style=\"text-align: left\"> Wenn die Pr\u00e4diktorvariable gleich 0 ist, betr\u00e4gt der Durchschnittswert der Antwortvariablen <span id=\"interceptOut\">0,9694<\/span> .<\/p>\n<p style=\"text-align: left\"> Jeder Anstieg der Pr\u00e4diktorvariablen um eine Einheit ist mit einer durchschnittlichen \u00c4nderung der Antwortvariablen um ( <span id=\"slopeOut\">7,7673<\/span> ) verbunden.<\/p>\n<p style=\"text-align: left\"> <span id=\"r2Out\">82,82<\/span> % der Variation der Antwortvariablen k\u00f6nnen durch die Pr\u00e4diktorvariable erkl\u00e4rt werden.<\/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><\/p>\n<p>function 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\n            sum_x += x[i];\n            sum_y += 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{\ndocument.getElementById('error_msg').innerHTML = 'The two lists must be of equal length.';\n}\n\t  \n} \/\/end calc function\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dieser Rechner erstellt eine lineare Regressionsgleichung basierend auf den Werten einer Pr\u00e4diktorvariablen und einer Antwortvariablen. 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: Vorhersagewerte: 6, 7, 7, 8, 12, 14, 15, 16, 16, 19 Antwortwerte: 14, 15, 15, 17, [&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>Linearer Regressionsrechner \u2013 Statistik<\/title>\n<meta name=\"description\" content=\"Dieser Rechner ermittelt die am besten geeignete Linie f\u00fcr einen bestimmten Datensatz.\" \/>\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\/linearer-regressionsrechner\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Linearer Regressionsrechner \u2013 Statistik\" \/>\n<meta property=\"og:description\" content=\"Dieser Rechner ermittelt die am besten geeignete Linie f\u00fcr einen bestimmten Datensatz.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/de\/linearer-regressionsrechner\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T01:26:46+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\/linearer-regressionsrechner\/\",\"url\":\"https:\/\/statorials.org\/de\/linearer-regressionsrechner\/\",\"name\":\"Linearer Regressionsrechner \u2013 Statistik\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/de\/#website\"},\"datePublished\":\"2023-07-29T01:26:46+00:00\",\"dateModified\":\"2023-07-29T01:26:46+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/de\/#\/schema\/person\/ec75c4d6365f2708f8a0ad3a42121aa0\"},\"description\":\"Dieser Rechner ermittelt die am besten geeignete Linie f\u00fcr einen bestimmten Datensatz.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/de\/linearer-regressionsrechner\/#breadcrumb\"},\"inLanguage\":\"de-DE\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/de\/linearer-regressionsrechner\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/de\/linearer-regressionsrechner\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Heim\",\"item\":\"https:\/\/statorials.org\/de\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Linearer regressionsrechner\"}]},{\"@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. 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