{"id":28434,"date":"2023-06-20T18:17:37","date_gmt":"2023-06-20T21:17:37","guid":{"rendered":"https:\/\/mindthegraph.com\/blog\/psychedelic-medicine-copy\/"},"modified":"2023-07-03T18:36:10","modified_gmt":"2023-07-03T21:36:10","slug":"regression-analysis","status":"publish","type":"post","link":"https:\/\/mindthegraph.com\/blog\/nb\/regresjonsanalyse\/","title":{"rendered":"Bruk av regresjonsanalyse for \u00e5 forst\u00e5 komplekse sammenhenger"},"content":{"rendered":"<p>Regression analysis is an approach for identifying and analyzing the connection between one or more independent variables and a dependent variable. This method is extensively used in a variety of disciplines, including healthcare, social sciences, engineering, economics, and business. You can use regression analysis to investigate the fundamental relationships in data and develop predictive models that will assist you in making informed decisions.<\/p>\n\n\n\n<p>Denne artikkelen gir deg en omfattende oversikt over regresjonsanalyse, inkludert hvordan den fungerer, et lettfattelig eksempel og en forklaring p\u00e5 hvordan den skiller seg fra korrelasjonsanalyse.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-regression-analysis\">Hva er regresjonsanalyse?<\/h2>\n\n\n\n<p>Regresjonsanalyse er en statistisk metode for \u00e5 identifisere og kvantifisere sammenhengen mellom en avhengig variabel og en eller flere uavhengige variabler. Kort sagt hjelper den deg med \u00e5 forst\u00e5 hvordan endringer i en eller flere uavhengige variabler henger sammen med endringer i den avhengige variabelen.<\/p>\n\n\n\n<p>For \u00e5 f\u00e5 en grundig forst\u00e5else av regresjonsanalyse m\u00e5 du f\u00f8rst forst\u00e5 f\u00f8lgende begreper:<\/p>\n\n\n\n<ul>\n<li><strong>Avhengig variabel: <\/strong>Dette er variabelen du er interessert i \u00e5 analysere eller forutsi. Det er utfallsvariabelen du pr\u00f8ver \u00e5 forst\u00e5 og forklare.<\/li>\n\n\n\n<li><strong>Uavhengige variabler: <\/strong>Dette er de variablene som du tror har en effekt p\u00e5 den avhengige variabelen. De omtales ofte som prediktorvariabler, ettersom de brukes til \u00e5 forutsi eller forklare endringer i den avhengige variabelen.<\/li>\n<\/ul>\n\n\n\n<p>Regresjonsanalyse kan brukes i en rekke sammenhenger, blant annet for \u00e5 forutsi fremtidige verdier av den avhengige variabelen, forst\u00e5 effekten av uavhengige variabler p\u00e5 den avhengige variabelen og finne ekstremverdier eller uvanlige forekomster i datainnsamlingen.<\/p>\n\n\n\n<p>Regression analysis can be classified into several types, including single linear regression, logistic regression, polynomial regression, and multiple regression. The suitable regression model is determined by the nature of the data and the investigation&#8217;s subject under consideration.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-how-does-regression-analysis-work\">Hvordan fungerer regresjonsanalyse?<\/h2>\n\n\n\n<p>Form\u00e5let med regresjonsanalyse er \u00e5 identifisere den linjen eller kurven som passer best til sammenhengen mellom de uavhengige variablene og den avhengige variabelen. Denne linjen eller kurven som passer best, genereres ved hjelp av statistiske metoder som reduserer forskjellene mellom forventede og reelle verdier i datainnsamlingen.<\/p>\n\n\n\n<p>Her er formlene for de to vanligste typene regresjonsanalyse:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-single-linear-regression\">Enkel line\u00e6r regresjon<\/h3>\n\n\n\n<p>I enkel line\u00e6r regresjon bruker du en linje med best mulig tilpasning for \u00e5 vise sammenhengen mellom to variabler: den uavhengige variabelen (x) og den avhengige variabelen (y).<\/p>\n\n\n\n<p>Den beste tilpasningslinjen kan representeres ved ligningen: y = a + bx.<\/p>\n\n\n\n<p>Her er a skj\u00e6ringspunktet, mens b er linjens helning. For \u00e5 beregne helningen bruker du formelen: b = (n\u03a3(xy) - \u03a3x\u03a3y) \/ (n\u03a3(x<sup>2<\/sup>) - (\u03a3x)<sup>2<\/sup>), hvor n er antall observasjoner, \u03a3xy er summen av produktet av x og y, \u03a3x og \u03a3y er summen av henholdsvis x og y, og \u03a3(x<sup>2<\/sup>) er summen av kvadratene til x.<\/p>\n\n\n\n<p>For \u00e5 beregne skj\u00e6ringspunktet bruker du formelen: a = (\u03a3y - b\u03a3x) \/ n.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-multiple-regression\">Multippel regresjon&nbsp;<\/h3>\n\n\n\n<p>Multippel line\u00e6r regresjon:<\/p>\n\n\n\n<p>Formelen for ligningen til den multiple line\u00e6re regresjonsmodellen er:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote\">\n<p><strong>y = b<sub>0<\/sub> + b<sub>1<\/sub>x<sub>1<\/sub> + b<sub>2<\/sub>x<sub>2<\/sub> + ... + b<sub>n<\/sub>x<sub>n<\/sub><\/strong><\/p>\n<\/blockquote>\n\n\n\n<p>der y er den avhengige variabelen, x<sub>1<\/sub>, x<sub>2<\/sub>, ..., x<sub>n<\/sub> er de uavhengige variablene, og b<sub>0<\/sub>, b<sub>1<\/sub>, b<sub>2<\/sub>, ..., bn er koeffisientene til de uavhengige variablene.<\/p>\n\n\n\n<p>Formelen for estimering av koeffisientene ved hjelp av minste kvadraters metode er:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote\">\n<p><strong>\u03b2 = (X'X)<sup>(-1)<\/sup>X'y<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p>der \u03b2 er en kolonnevektor av koeffisienter, X er designmatrisen av uavhengige variabler, X' er transponering av X, og y er vektoren av observasjoner av den avhengige variabelen.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-regression-analysis-example\">Eksempel p\u00e5 regresjonsanalyse<\/h2>\n\n\n\n<p>Anta at du \u00f8nsker \u00e5 unders\u00f8ke sammenhengen mellom en persons karaktersnitt (GPA) og antall timer vedkommende studerer per uke. Du samler inn informasjon fra et sett med studenter, inkludert antall studietimer og karaktersnitt.<\/p>\n\n\n\n<p>Deretter kan du bruke regresjonsanalysen til \u00e5 se om det er en line\u00e6r sammenheng mellom de to variablene, og i s\u00e5 fall kan du lage en modell som forutsier en students GPA basert p\u00e5 antall timer de studerer per uke.<\/p>\n\n\n\n<div style=\"height:21px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/lh5.googleusercontent.com\/jY2vs2UsuRYMfVS7ZwPuk_epkVR-Yl7jnG8al1mDmUs6L8YsZ_X3WwNFy40jDCareFFtyOzL6b_DXIhO8FrJR1CMyVwg_rHyE1jycXX-LGWLsUf4LTzWV4L35ObUSidK1EsF136nqG-tHj_zjStgbbA\" alt=\"\" width=\"505\" height=\"263\"\/><figcaption class=\"wp-element-caption\"><em>Bildet er tilgjengelig p\u00e5 <a href=\"https:\/\/www.alchemer.com\" target=\"_blank\" rel=\"noreferrer noopener\">alchemer.com<\/a><\/em><\/figcaption><\/figure><\/div>\n\n\n<p><a href=\"https:\/\/www.alchemer.com\/wp-content\/uploads\/2019\/04\/regression-analysis-1.png\"><\/a><\/p>\n\n\n\n<div style=\"height:21px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>N\u00e5r dataene plottes inn p\u00e5 et spredningskart, ser det ut til at det er en gunstig line\u00e6r sammenheng mellom studietid og GPA. Helling og skj\u00e6ringspunkt for linjen med best mulig tilpasning estimeres deretter ved hjelp av en enkel line\u00e6r regresjonsmodell. Den endelige l\u00f8sningen kan se slik ut:<\/p>\n\n\n\n<p>GPA = 2,0 + 0,3 (timer studert per uke)<\/p>\n\n\n\n<div style=\"height:21px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/lh6.googleusercontent.com\/plMkcFRz9dE-xiHm7wkzhCBplbaGIBdvzy4y8LmGqBEaFAMV72IUx7DRx8uvaU_TVMkcOlwcgH_s12NMZFjni4gWrlANjcBH2RqyoFKzrks9q3SGUDpnd_ILZZ4ookIPxD-PJ2T5L-HS3GaWCJf8yEE\" alt=\"\" width=\"505\" height=\"263\"\/><figcaption class=\"wp-element-caption\"><em><em>Bildet er tilgjengelig p\u00e5 <a href=\"https:\/\/www.alchemer.com\" target=\"_blank\" rel=\"noreferrer noopener\">alchemer.com<\/a><\/em><\/em><\/figcaption><\/figure><\/div>\n\n\n<p><a href=\"https:\/\/www.alchemer.com\/wp-content\/uploads\/2019\/04\/regression-analysis-2.png\"><\/a><\/p>\n\n\n\n<div style=\"height:21px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Denne ligningen sier at for hver ekstra time en student studerer per uke, vil karaktersnittet stige med 0,3 poeng, med alt annet likt. Denne algoritmen kan brukes til \u00e5 forutsi en students GPA basert p\u00e5 hvor mange timer de studerer per uke, samt til \u00e5 identifisere hvilke studenter som er i faresonen for \u00e5 underprestere basert p\u00e5 studierutinene deres.&nbsp;<\/p>\n\n\n\n<p>Ved hjelp av dataene fra eksemplet kan verdiene for <strong>b<\/strong> og <strong>a<\/strong> er som f\u00f8lger:<\/p>\n\n\n\n<p>n = 10 (antall observasjoner)<\/p>\n\n\n\n<p>\u03a3x = 30 (summen av studietimene)<\/p>\n\n\n\n<p>\u03a3y = 25 (summen av GPA)<\/p>\n\n\n\n<p>\u03a3xy = 149 (summen av produktet av studietimer og GPA)<\/p>\n\n\n\n<p>\u03a3(x)<sup>2<\/sup> = 102 (summen av kvadratet av studietimene)<\/p>\n\n\n\n<p>Bruk disse verdiene til \u00e5 beregne <strong>b<\/strong> som:<\/p>\n\n\n\n<p>b = (n\u03a3(xy) - \u03a3x\u03a3y) \/ (n\u03a3(x<sup>2<\/sup>) - (\u03a3x)<sup>2<\/sup>)<\/p>\n\n\n\n<p>= (10 * 149 &#8211; 30 * 25) \/ (10 * 102 &#8211; 30<sup>2<\/sup>)<\/p>\n\n\n\n<p>= 0.3<\/p>\n\n\n\n<p>Og beregne <strong>a <\/strong>som:<\/p>\n\n\n\n<p>a = (\u03a3y - b\u03a3x) \/ n<\/p>\n\n\n\n<p>= (25 &#8211; 0.3 * 30) \/ 10<\/p>\n\n\n\n<p>= 2.0<\/p>\n\n\n\n<p>Derfor er likningen for linjen med best mulig tilpasning:&nbsp;<\/p>\n\n\n\n<p>GPA = 2,0 + 0,3 (timer studert per uke)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-the-difference-between-correlation-and-regression\">Hva er forskjellen mellom korrelasjon og regresjon?<\/h2>\n\n\n\n<p>B\u00e5de korrelasjon og regresjon er statistiske metoder for \u00e5 unders\u00f8ke sammenhengen mellom to variabler. De tjener ulike form\u00e5l og gir ulike typer informasjon.<\/p>\n\n\n\n<p>Korrelasjon er et m\u00e5l p\u00e5 styrken og forl\u00f8pet av en sammenheng mellom to variabler. Den g\u00e5r fra -1 til +1, der -1 representerer en perfekt negativ korrelasjon, 0 representerer ingen korrelasjon og +1 representerer en perfekt positiv korrelasjon. Korrelasjon indikerer i hvilken grad to variabler henger sammen, men sier ikke noe om \u00e5rsak eller forutsigbarhet.<\/p>\n\n\n\n<p>Regression, on the other hand, is a method for modeling the connection between two variables, typically in order to forecast or explain one variable based on the other. Regression analysis can provide estimations of the size and direction of the relationship, as well as statistical significance tests, confidence ranges, and future result forecasts.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-your-creations-ready-within-minutes\">Dine kreasjoner, klare i l\u00f8pet av f\u00e5 minutter<\/h2>\n\n\n\n<p><a href=\"https:\/\/mindthegraph.com\" target=\"_blank\" rel=\"noreferrer noopener\">Mind the Graph<\/a> is an online platform that offers you an extensive library of scientific illustrations and infographic designs that can be simply modified to meet your unique needs. Make professional-looking charts, posters, and graphical abstracts in minutes by using a drag-and-drop interface and a wide range of tools and features.&nbsp;<\/p>\n\n\n\n<div style=\"height:21px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"800\" height=\"500\" src=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2023\/05\/banco.gif\" alt=\"\" class=\"wp-image-28087\"\/><\/figure><\/div>\n\n\n<div style=\"height:21px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"is-layout-flex wp-block-buttons\">\n<div class=\"wp-block-button aligncenter\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/mindthegraph.com\/\" style=\"border-radius:50px;background-color:#dc1866\" target=\"_blank\" rel=\"noreferrer noopener\">Begynn \u00e5 skape med Mind the Graph<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:44px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>","protected":false},"excerpt":{"rendered":"<p>Forst\u00e5 hvordan regresjonsanalyse fungerer ved hjelp av et omfattende eksempel, og l\u00e6r deg de vanligste formlene. <\/p>","protected":false},"author":28,"featured_media":28437,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[959,28],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.9 - 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