{"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\/sl\/regresijska-analiza\/","title":{"rendered":"Uporaba regresijske analize za razumevanje zapletenih odnosov"},"content":{"rendered":"<p>Regresijska analiza je pristop za ugotavljanje in analiziranje povezave med eno ali ve\u010d neodvisnimi spremenljivkami in odvisno spremenljivko. Ta metoda se pogosto uporablja na razli\u010dnih podro\u010djih, vklju\u010dno z zdravstvom, dru\u017eboslovjem, in\u017eenirstvom, ekonomijo in poslovanjem. Z regresijsko analizo lahko raziskujete temeljne povezave v podatkih in razvijate napovedne modele, ki vam bodo pomagali pri sprejemanju utemeljenih odlo\u010ditev.<\/p>\n\n\n\n<p>V tem \u010dlanku boste na\u0161li celovit pregled regresijske analize, vklju\u010dno z njenim delovanjem, razumljivim primerom in razlago, kako se razlikuje od korelacijske analize.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-regression-analysis\">Kaj je regresijska analiza?<\/h2>\n\n\n\n<p>Regresijska analiza je statisti\u010dna metoda za ugotavljanje in koli\u010dinsko opredelitev povezave med odvisno spremenljivko in eno ali ve\u010d neodvisnimi spremenljivkami. Na kratko, pomaga vam razumeti, kako so spremembe ene ali ve\u010d neodvisnih spremenljivk povezane s spremembami odvisne spremenljivke.<\/p>\n\n\n\n<p>Za temeljito razumevanje regresijske analize morate najprej razumeti naslednje izraze:<\/p>\n\n\n\n<ul>\n<li><strong>Odvisna spremenljivka: <\/strong>To je spremenljivka, ki jo \u017eelite analizirati ali napovedati. To je spremenljivka rezultata, ki jo posku\u0161ate razumeti in razlo\u017eiti.<\/li>\n\n\n\n<li><strong>Neodvisne spremenljivke: <\/strong>To so spremenljivke, za katere menite, da vplivajo na odvisno spremenljivko. Pogosto jih imenujemo napovedne spremenljivke, saj se uporabljajo za napovedovanje ali pojasnjevanje sprememb v odvisni spremenljivki.<\/li>\n<\/ul>\n\n\n\n<p>Regresijska analiza se lahko uporablja v razli\u010dnih okoli\u0161\u010dinah, vklju\u010dno z napovedovanjem prihodnjih vrednosti odvisne spremenljivke, razumevanjem vpliva neodvisnih spremenljivk na odvisno spremenljivko ter iskanjem odstopanj ali nenavadnih pojavov pri zbiranju podatkov.<\/p>\n\n\n\n<p>Regresijsko analizo lahko razdelimo na ve\u010d vrst, med drugim na eno linearno regresijo, logisti\u010dno regresijo, polinomsko regresijo in multiplo regresijo. Ustrezen regresijski model je odvisen od narave podatkov in predmeta obravnavane preiskave.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-how-does-regression-analysis-work\">Kako deluje regresijska analiza?<\/h2>\n\n\n\n<p>Namen regresijske analize je ugotoviti, katera \u010drta ali krivulja najbolje ustreza povezavi med neodvisnimi spremenljivkami in odvisno spremenljivko. Ta najbolje ustrezajo\u010da \u010drta ali krivulja se ustvari z uporabo statisti\u010dnih metod, ki zmanj\u0161ujejo razlike med pri\u010dakovanimi in dejanskimi vrednostmi v zbirki podatkov.<\/p>\n\n\n\n<p>Tukaj so formule za dve najpogostej\u0161i vrsti regresijske analize:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-single-linear-regression\">Enotna linearna regresija<\/h3>\n\n\n\n<p>Pri preprosti linearni regresiji uporabite premico najbolj\u0161e skladnosti za prikaz povezave med dvema spremenljivkama: neodvisno spremenljivko (x) in odvisno spremenljivko (y).<\/p>\n\n\n\n<p>Najustreznej\u0161o premico lahko predstavimo z ena\u010dbo: y = a + bx.<\/p>\n\n\n\n<p>Pri tem je a prese\u010di\u0161\u010de, b pa naklon premice. Za izra\u010dun naklona uporabite formulo: b = (n\u03a3(xy) - \u03a3x\u03a3y) \/ (n\u03a3(x<sup>2<\/sup>) - (\u03a3x)<sup>2<\/sup>), kjer je n \u0161tevilo opazovanj, \u03a3xy je vsota produkta x in y, \u03a3x in \u03a3y sta vsoti x oziroma y, \u03a3(x<sup>2<\/sup>) je vsota kvadratov x.<\/p>\n\n\n\n<p>Za izra\u010dun intercepcije uporabite formulo: a = (\u03a3y - b\u03a3x) \/ n.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-multiple-regression\">Ve\u010dkratna regresija&nbsp;<\/h3>\n\n\n\n<p>Ve\u010dkratna linearna regresija:<\/p>\n\n\n\n<p>Ena\u010dba modela ve\u010dkratne linearne regresije je naslednja:<\/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>kjer je y odvisna spremenljivka, x<sub>1<\/sub>, x<sub>2<\/sub>, ..., x<sub>n<\/sub> sta neodvisni spremenljivki, b<sub>0<\/sub>, b<sub>1<\/sub>, b<sub>2<\/sub>, ..., bn so koeficienti neodvisnih spremenljivk.<\/p>\n\n\n\n<p>Formula za oceno koeficientov z uporabo navadnih najmanj\u0161ih kvadratov je:<\/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>kjer je \u03b2 stolp\u010dni vektor koeficientov, X je matrika neodvisnih spremenljivk, X' je transpozicija X, y pa je vektor opazovanj odvisne spremenljivke.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-regression-analysis-example\">Primer regresijske analize<\/h2>\n\n\n\n<p>Recimo, da \u017eelite preu\u010diti povezavo med posameznikovo povpre\u010dno oceno (GPA) in \u0161tevilom ur u\u010denja na teden. Zberete informacije od skupine \u0161tudentov, vklju\u010dno z njihovim \u0161tevilom \u0161tudijskih ur in povpre\u010djem ocen.<\/p>\n\n\n\n<p>Nato s pomo\u010djo regresijske analize preverite, ali med spremenljivkama obstaja linearna povezava, in \u010de je, lahko sestavite model, ki napoveduje povpre\u010dno oceno \u0161tudenta na podlagi \u0161tevila ur \u0161tudija na teden.<\/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>Slika je na voljo na <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>Ko podatke prika\u017eemo na zemljevidu razpr\u0161itve, se zdi, da obstaja ugodna linearna povezava med \u0161tudijskimi urami in povpre\u010dno oceno \u0161tudija. Naklon in prese\u010di\u0161\u010de najbolj primerne premice se nato ocenita s preprostim linearnim regresijskim modelom. Kon\u010dna re\u0161itev je lahko videti takole:<\/p>\n\n\n\n<p>Povpre\u010dna ocena uspeha = 2,0 + 0,3 (\u0161tevilo ur \u0161tudija na teden)<\/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>Slika je na voljo na <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>Ta ena\u010dba pravi, da se za vsako dodatno uro u\u010denja na teden povpre\u010dna ocena \u0161tudenta pove\u010da za 0,3 to\u010dke, pri \u010demer je vse ostalo enako. Ta algoritem se lahko uporabi za napovedovanje povpre\u010dne ocene \u0161tudenta glede na to, koliko ur na teden \u0161tudira, in za ugotavljanje, kateri \u0161tudenti so glede na svoje \u0161tudijske navade izpostavljeni tveganju, da bodo dosegli slab\u0161e rezultate.&nbsp;<\/p>\n\n\n\n<p>Na podlagi podatkov iz primera so vrednosti za <strong>b<\/strong> in . <strong>a<\/strong> so naslednji:<\/p>\n\n\n\n<p>n = 10 (\u0161tevilo opazovanj)<\/p>\n\n\n\n<p>\u03a3x = 30 (vsota ur \u0161tudija)<\/p>\n\n\n\n<p>\u03a3y = 25 (vsota povpre\u010dnih povpre\u010dnih ocen)<\/p>\n\n\n\n<p>\u03a3xy = 149 (vsota zmno\u017eka \u0161tudijskih ur in povpre\u010dne ocene \u0161tudija)<\/p>\n\n\n\n<p>\u03a3(x)<sup>2<\/sup> = 102 (vsota kvadratov \u0161tudijskih ur)<\/p>\n\n\n\n<p>Na podlagi teh vrednosti izra\u010dunajte <strong>b<\/strong> kot:<\/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>In izra\u010dunajte <strong>a <\/strong>kot:<\/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>Zato je ena\u010dba najbolj primerne premice naslednja:&nbsp;<\/p>\n\n\n\n<p>Povpre\u010dna ocena uspeha = 2,0 + 0,3 (\u0161tevilo ur \u0161tudija na teden)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-the-difference-between-correlation-and-regression\">Kak\u0161na je razlika med korelacijo in regresijo?<\/h2>\n\n\n\n<p>Korelacija in regresija sta statisti\u010dni metodi za preu\u010devanje povezave med dvema spremenljivkama. Uporabljata se za razli\u010dne namene in zagotavljata razli\u010dne vrste informacij.<\/p>\n\n\n\n<p>Korelacija je merilo za mo\u010d in potek povezave med dvema spremenljivkama. Njena vrednost je od -1 do +1, pri \u010demer -1 pomeni popolno negativno korelacijo, 0 pomeni brez korelacije, +1 pa pomeni popolno pozitivno korelacijo. Korelacija ozna\u010duje stopnjo povezanosti dveh spremenljivk, ne ka\u017ee pa na vzrok ali predvidljivost.<\/p>\n\n\n\n<p>Regresija pa je metoda za modeliranje povezave med dvema spremenljivkama, obi\u010dajno za napovedovanje ali pojasnjevanje ene spremenljivke na podlagi druge. Regresijska analiza lahko zagotovi ocene velikosti in smeri povezave ter teste statisti\u010dne pomembnosti, obmo\u010dja zaupanja in napovedi prihodnjih rezultatov.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-your-creations-ready-within-minutes\">Va\u0161e kreacije, pripravljene v nekaj minutah<\/h2>\n\n\n\n<p><a href=\"https:\/\/mindthegraph.com\" target=\"_blank\" rel=\"noreferrer noopener\">Mind the Graph<\/a> je spletna platforma, ki vam ponuja obse\u017eno knji\u017enico znanstvenih ilustracij in infografik, ki jih lahko preprosto prilagodite svojim edinstvenim potrebam. S pomo\u010djo vmesnika povleci in spusti ter \u0161tevilnih orodij in funkcij v nekaj minutah izdelajte profesionalno oblikovane diagrame, plakate in grafi\u010dne izvle\u010dke.&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\">Za\u010dnite ustvarjati z 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>Na iz\u010drpnem primeru razumite delovanje regresijske analize in se nau\u010dite najpogostej\u0161ih formul. <\/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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