{"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\/sv_se\/regressionsanalys\/","title":{"rendered":"Anv\u00e4nda regressionsanalys f\u00f6r att f\u00f6rst\u00e5 komplexa samband"},"content":{"rendered":"<p>Regressionsanalys \u00e4r en metod f\u00f6r att identifiera och analysera sambandet mellan en eller flera oberoende variabler och en beroende variabel. Metoden anv\u00e4nds flitigt inom en rad olika discipliner, t.ex. h\u00e4lso- och sjukv\u00e5rd, samh\u00e4llsvetenskap, teknik, ekonomi och f\u00f6retagsekonomi. Du kan anv\u00e4nda regressionsanalys f\u00f6r att unders\u00f6ka de grundl\u00e4ggande sambanden i data och utveckla prediktiva modeller som hj\u00e4lper dig att fatta v\u00e4lgrundade beslut.<\/p>\n\n\n\n<p>Den h\u00e4r artikeln ger dig en omfattande \u00f6versikt \u00f6ver regressionsanalys, inklusive hur den fungerar, ett l\u00e4ttbegripligt exempel och en f\u00f6rklaring av hur den skiljer sig fr\u00e5n korrelationsanalys.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-regression-analysis\">Vad \u00e4r regressionsanalys?<\/h2>\n\n\n\n<p>Regressionsanalys \u00e4r en statistisk metod f\u00f6r att identifiera och kvantifiera sambandet mellan en beroende variabel och en eller flera oberoende variabler. I ett n\u00f6tskal hj\u00e4lper den dig att f\u00f6rst\u00e5 hur f\u00f6r\u00e4ndringar i en eller flera oberoende variabler \u00e4r relaterade till f\u00f6r\u00e4ndringar i den beroende variabeln.<\/p>\n\n\n\n<p>F\u00f6r att f\u00e5 en grundlig f\u00f6rst\u00e5else av regressionsanalys m\u00e5ste du f\u00f6rst f\u00f6rst\u00e5 f\u00f6ljande termer:<\/p>\n\n\n\n<ul>\n<li><strong>Beroende variabel: <\/strong>Detta \u00e4r den variabel som du \u00e4r intresserad av att analysera eller f\u00f6ruts\u00e4ga. Det \u00e4r utfallsvariabeln som du f\u00f6rs\u00f6ker f\u00f6rst\u00e5 och f\u00f6rklara.<\/li>\n\n\n\n<li><strong>Oberoende variabler: <\/strong>Detta \u00e4r de variabler som du tror har en effekt p\u00e5 den beroende variabeln. De kallas ofta f\u00f6r prediktorvariabler, eftersom de anv\u00e4nds f\u00f6r att f\u00f6ruts\u00e4ga eller f\u00f6rklara f\u00f6r\u00e4ndringar i den beroende variabeln.<\/li>\n<\/ul>\n\n\n\n<p>Regressionsanalys kan anv\u00e4ndas under en rad omst\u00e4ndigheter, inklusive att f\u00f6ruts\u00e4ga framtida v\u00e4rden f\u00f6r den beroende variabeln, f\u00f6rst\u00e5 effekten av oberoende variabler p\u00e5 den beroende variabeln och hitta outliers eller ovanliga f\u00f6rekomster i datainsamlingen.<\/p>\n\n\n\n<p>Regressionsanalys kan klassificeras i flera typer, inklusive enkel linj\u00e4r regression, logistisk regression, polynomisk regression och multipel regression. Vilken regressionsmodell som \u00e4r l\u00e4mplig avg\u00f6rs av typen av data och det aktuella unders\u00f6kningsobjektet.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-how-does-regression-analysis-work\">Hur fungerar regressionsanalys?<\/h2>\n\n\n\n<p>Syftet med regressionsanalys \u00e4r att identifiera den b\u00e4st passande linjen eller kurvan som \u00e5terspeglar sambandet mellan de oberoende variablerna och den beroende variabeln. Denna linje eller kurva genereras med hj\u00e4lp av statistiska metoder som minskar skillnaderna mellan de f\u00f6rv\u00e4ntade och verkliga v\u00e4rdena i datainsamlingen.<\/p>\n\n\n\n<p>H\u00e4r f\u00f6ljer formlerna f\u00f6r de tv\u00e5 vanligaste typerna av regressionsanalys:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-single-linear-regression\">Enkel linj\u00e4r regression<\/h3>\n\n\n\n<p>I Enkel linj\u00e4r regression anv\u00e4nder du en linje med b\u00e4sta passform f\u00f6r att visa f\u00f6rh\u00e5llandet mellan tv\u00e5 variabler: den oberoende variabeln (x) och den beroende variabeln (y).<\/p>\n\n\n\n<p>Den linje som passar b\u00e4st kan representeras av ekvationen: y = a + bx.<\/p>\n\n\n\n<p>H\u00e4r \u00e4r a sk\u00e4rningspunkten och b linjens lutning. F\u00f6r att ber\u00e4kna lutningen anv\u00e4nder du formeln: b = (n\u03a3(xy) - \u03a3x\u03a3y) \/ (n\u03a3(x<sup>2<\/sup>) - (\u03a3x)<sup>2<\/sup>), d\u00e4r n \u00e4r antalet observationer, \u03a3xy \u00e4r summan av produkten av x och y, \u03a3x och \u03a3y \u00e4r summan av x respektive y, och \u03a3(x<sup>2<\/sup>) \u00e4r summan av kvadraterna f\u00f6r x.<\/p>\n\n\n\n<p>F\u00f6r att ber\u00e4kna sk\u00e4rningspunkten anv\u00e4nds formeln: a = (\u03a3y - b\u03a3x) \/ n.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-multiple-regression\">Multipel regression&nbsp;<\/h3>\n\n\n\n<p>Multipel linj\u00e4r regression:<\/p>\n\n\n\n<p>Formeln f\u00f6r ekvationen f\u00f6r den multipla linj\u00e4ra regressionsmodellen \u00e4r:<\/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>d\u00e4r y \u00e4r den beroende variabeln, x<sub>1<\/sub>, x<sub>2<\/sub>, ..., x<sub>n<\/sub> \u00e4r de oberoende variablerna, och b<sub>0<\/sub>, b<sub>1<\/sub>, b<sub>2<\/sub>, ..., bn \u00e4r koefficienterna f\u00f6r de oberoende variablerna.<\/p>\n\n\n\n<p>Formeln f\u00f6r att skatta koefficienterna med hj\u00e4lp av ordin\u00e4ra minsta kvadratmetoden \u00e4r<\/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>d\u00e4r \u03b2 \u00e4r en kolumnvektor av koefficienter, X \u00e4r designmatrisen av oberoende variabler, X' \u00e4r transponering av X, och y \u00e4r vektorn av observationer av den beroende variabeln.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-regression-analysis-example\">Exempel p\u00e5 regressionsanalys<\/h2>\n\n\n\n<p>Antag att du vill unders\u00f6ka sambandet mellan en individs betygsmedelv\u00e4rde (GPA) och antalet timmar de studerar per vecka. Du samlar in information fr\u00e5n en upps\u00e4ttning studenter, inklusive deras antal studietimmar och betygsmedelv\u00e4rde.<\/p>\n\n\n\n<p>Anv\u00e4nd sedan regressionsanalysen f\u00f6r att se om det finns ett linj\u00e4rt samband mellan de b\u00e5da variablerna och om s\u00e5 \u00e4r fallet kan du bygga en modell som f\u00f6ruts\u00e4ger en students GPA baserat p\u00e5 antalet timmar de studerar per vecka.<\/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>Bilden tillg\u00e4nglig 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\u00e4r data plottas p\u00e5 en spridningskarta verkar det som om det finns ett gynnsamt linj\u00e4rt samband mellan studietid och GPA. Lutningen och sk\u00e4rningspunkten f\u00f6r den linje som passar b\u00e4st uppskattas sedan med hj\u00e4lp av en enkel linj\u00e4r regressionsmodell. Den slutliga l\u00f6sningen kan se ut s\u00e5 h\u00e4r:<\/p>\n\n\n\n<p>GPA = 2,0 + 0,3 (studietimmar per vecka)<\/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>Bilden tillg\u00e4nglig 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>Denna ekvation s\u00e4ger att f\u00f6r varje extra studietimme per vecka kommer en elevs GPA att \u00f6ka med 0,3 po\u00e4ng, med allt annat likv\u00e4rdigt. Denna algoritm kan anv\u00e4ndas f\u00f6r att prognostisera en students GPA baserat p\u00e5 hur m\u00e5nga timmar de studerar per vecka, samt f\u00f6r att identifiera vilka studenter som riskerar att underprestera baserat p\u00e5 deras studierutiner.&nbsp;<\/p>\n\n\n\n<p>Med hj\u00e4lp av data fr\u00e5n exemplet, v\u00e4rdena f\u00f6r <strong>b<\/strong> och <strong>a<\/strong> \u00e4r f\u00f6ljande:<\/p>\n\n\n\n<p>n = 10 (antalet observationer)<\/p>\n\n\n\n<p>\u03a3x = 30 (summan av studietimmarna)<\/p>\n\n\n\n<p>\u03a3y = 25 (summan av GPA-v\u00e4rdena)<\/p>\n\n\n\n<p>\u03a3xy = 149 (summan av produkten av studietimmar och GPA)<\/p>\n\n\n\n<p>\u03a3(x)<sup>2<\/sup> = 102 (summan av kvadraterna f\u00f6r studietimmarna)<\/p>\n\n\n\n<p>Anv\u00e4nd dessa v\u00e4rden f\u00f6r att ber\u00e4kna <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>Och ber\u00e4kna <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>D\u00e4rf\u00f6r \u00e4r ekvationen f\u00f6r linjen f\u00f6r b\u00e4sta anpassning:&nbsp;<\/p>\n\n\n\n<p>GPA = 2,0 + 0,3 (studietimmar per vecka)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-the-difference-between-correlation-and-regression\">Vad \u00e4r skillnaden mellan korrelation och regression?<\/h2>\n\n\n\n<p>B\u00e5de korrelation och regression \u00e4r statistiska metoder f\u00f6r att unders\u00f6ka sambandet mellan tv\u00e5 variabler. De har olika syften och ger olika typer av information.<\/p>\n\n\n\n<p>Korrelation \u00e4r ett m\u00e5tt p\u00e5 styrkan och f\u00f6rloppet av ett samband mellan tv\u00e5 variabler. Det g\u00e5r fr\u00e5n -1 till +1, d\u00e4r -1 representerar en perfekt negativ korrelation, 0 representerar ingen korrelation och +1 representerar en perfekt positiv korrelation. Korrelationen anger i vilken grad tv\u00e5 variabler \u00e4r kopplade till varandra, men den anger inte orsak eller f\u00f6ruts\u00e4gbarhet.<\/p>\n\n\n\n<p>Regression, \u00e5 andra sidan, \u00e4r en metod f\u00f6r att modellera sambandet mellan tv\u00e5 variabler, vanligtvis i syfte att prognostisera eller f\u00f6rklara en variabel baserat p\u00e5 den andra. Regressionsanalys kan ge uppskattningar av sambandets storlek och riktning, samt statistiska signifikanstester, konfidensintervall och prognoser f\u00f6r framtida resultat.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-your-creations-ready-within-minutes\">Dina kreationer, klara inom n\u00e5gra minuter<\/h2>\n\n\n\n<p><a href=\"https:\/\/mindthegraph.com\" target=\"_blank\" rel=\"noreferrer noopener\">Mind the Graph<\/a> \u00e4r en onlineplattform som erbjuder dig ett omfattande bibliotek med vetenskapliga illustrationer och infografiska m\u00f6nster som enkelt kan modifieras f\u00f6r att uppfylla dina unika behov. Skapa professionella diagram, affischer och grafiska sammanfattningar p\u00e5 n\u00e5gra minuter med hj\u00e4lp av ett dra-och-sl\u00e4pp-gr\u00e4nssnitt och ett brett utbud av verktyg och funktioner.&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\">B\u00f6rja skapa 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>F\u00f6rst\u00e5 hur regressionsanalys fungerar enkelt med hj\u00e4lp av ett omfattande exempel och l\u00e4r dig de vanligaste formlerna. <\/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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