{"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\/cs\/regresni-analyza\/","title":{"rendered":"Vyu\u017eit\u00ed regresn\u00ed anal\u00fdzy k pochopen\u00ed slo\u017eit\u00fdch vztah\u016f"},"content":{"rendered":"<p>Regresn\u00ed anal\u00fdza je p\u0159\u00edstup k identifikaci a anal\u00fdze vztahu mezi jednou nebo v\u00edce nez\u00e1visl\u00fdmi prom\u011bnn\u00fdmi a z\u00e1vislou prom\u011bnnou. Tato metoda se hojn\u011b vyu\u017e\u00edv\u00e1 v r\u016fzn\u00fdch oborech, v\u010detn\u011b zdravotnictv\u00ed, soci\u00e1ln\u00edch v\u011bd, in\u017een\u00fdrstv\u00ed, ekonomie a podnik\u00e1n\u00ed. Pomoc\u00ed regresn\u00ed anal\u00fdzy m\u016f\u017eete zkoumat z\u00e1kladn\u00ed vztahy v datech a vytv\u00e1\u0159et prediktivn\u00ed modely, kter\u00e9 v\u00e1m pomohou p\u0159i p\u0159ij\u00edm\u00e1n\u00ed informovan\u00fdch rozhodnut\u00ed.<\/p>\n\n\n\n<p>Tento \u010dl\u00e1nek v\u00e1m poskytne ucelen\u00fd p\u0159ehled o regresn\u00ed anal\u00fdze, v\u010detn\u011b jej\u00edho fungov\u00e1n\u00ed, snadno pochopiteln\u00e9ho p\u0159\u00edkladu a vysv\u011btl\u00ed, jak se li\u0161\u00ed od korela\u010dn\u00ed anal\u00fdzy.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-regression-analysis\">Co je regresn\u00ed anal\u00fdza?<\/h2>\n\n\n\n<p>Regresn\u00ed anal\u00fdza je statistick\u00e1 metoda pro identifikaci a kvantifikaci vztahu mezi z\u00e1vislou prom\u011bnnou a jednou nebo v\u00edce nez\u00e1visl\u00fdmi prom\u011bnn\u00fdmi. Stru\u010dn\u011b \u0159e\u010deno, pom\u00e1h\u00e1 pochopit, jak zm\u011bny jedn\u00e9 nebo v\u00edce nez\u00e1visl\u00fdch prom\u011bnn\u00fdch souvisej\u00ed se zm\u011bnami z\u00e1visl\u00e9 prom\u011bnn\u00e9.<\/p>\n\n\n\n<p>Pro d\u016fkladn\u00e9 pochopen\u00ed regresn\u00ed anal\u00fdzy je t\u0159eba nejprve porozum\u011bt n\u00e1sleduj\u00edc\u00edm pojm\u016fm:<\/p>\n\n\n\n<ul>\n<li><strong>Z\u00e1visl\u00e1 prom\u011bnn\u00e1: <\/strong>Jedn\u00e1 se o prom\u011bnnou, kterou chcete analyzovat nebo p\u0159edpov\u00eddat. Je to v\u00fdsledn\u00e1 prom\u011bnn\u00e1, kterou se sna\u017e\u00edte pochopit a vysv\u011btlit.<\/li>\n\n\n\n<li><strong>Nez\u00e1visl\u00e9 prom\u011bnn\u00e9: <\/strong>Jedn\u00e1 se o prom\u011bnn\u00e9, o kter\u00fdch se domn\u00edv\u00e1te, \u017ee maj\u00ed vliv na z\u00e1vislou prom\u011bnnou. \u010casto se ozna\u010duj\u00ed jako prediktivn\u00ed prom\u011bnn\u00e9, proto\u017ee se pou\u017e\u00edvaj\u00ed k p\u0159edpov\u011bdi nebo vysv\u011btlen\u00ed zm\u011bn z\u00e1visl\u00e9 prom\u011bnn\u00e9.<\/li>\n<\/ul>\n\n\n\n<p>Regresn\u00ed anal\u00fdzu lze pou\u017e\u00edt za r\u016fzn\u00fdch okolnost\u00ed, v\u010detn\u011b p\u0159edpov\u011bdi budouc\u00edch hodnot z\u00e1visl\u00e9 prom\u011bnn\u00e9, pochopen\u00ed vlivu nez\u00e1visl\u00fdch prom\u011bnn\u00fdch na z\u00e1vislou prom\u011bnnou a zji\u0161t\u011bn\u00ed odlehl\u00fdch hodnot nebo neobvykl\u00fdch v\u00fdskyt\u016f p\u0159i sb\u011bru dat.<\/p>\n\n\n\n<p>Regresn\u00ed anal\u00fdzu lze rozd\u011blit na n\u011bkolik typ\u016f, v\u010detn\u011b jednoduch\u00e9 line\u00e1rn\u00ed regrese, logistick\u00e9 regrese, polynomi\u00e1ln\u00ed regrese a v\u00edcen\u00e1sobn\u00e9 regrese. Vhodn\u00fd regresn\u00ed model se ur\u010duje podle povahy dat a p\u0159edm\u011btu zkoum\u00e1n\u00ed.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-how-does-regression-analysis-work\">Jak funguje regresn\u00ed anal\u00fdza?<\/h2>\n\n\n\n<p>\u00da\u010delem regresn\u00ed anal\u00fdzy je ur\u010dit nejl\u00e9pe odpov\u00eddaj\u00edc\u00ed p\u0159\u00edmku nebo k\u0159ivku, kter\u00e1 odr\u00e1\u017e\u00ed souvislost mezi nez\u00e1visl\u00fdmi prom\u011bnn\u00fdmi a z\u00e1vislou prom\u011bnnou. Tato nejl\u00e9pe vyhovuj\u00edc\u00ed p\u0159\u00edmka nebo k\u0159ivka se vytv\u00e1\u0159\u00ed pomoc\u00ed statistick\u00fdch metod, kter\u00e9 sni\u017euj\u00ed rozd\u00edly mezi o\u010dek\u00e1van\u00fdmi a skute\u010dn\u00fdmi hodnotami v souboru dat.<\/p>\n\n\n\n<p>Zde jsou uvedeny vzorce pro dva nejb\u011b\u017en\u011bj\u0161\u00ed typy regresn\u00ed anal\u00fdzy:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-single-linear-regression\">Jednoduch\u00e1 line\u00e1rn\u00ed regrese<\/h3>\n\n\n\n<p>V jednoduch\u00e9 line\u00e1rn\u00ed regresi se k zobrazen\u00ed vztahu mezi dv\u011bma prom\u011bnn\u00fdmi: nez\u00e1vislou prom\u011bnnou (x) a z\u00e1vislou prom\u011bnnou (y) pou\u017e\u00edv\u00e1 p\u0159\u00edmka nejlep\u0161\u00ed shody.<\/p>\n\n\n\n<p>P\u0159\u00edmku nejlep\u0161\u00ed shody lze zn\u00e1zornit rovnic\u00ed: y = a + bx.<\/p>\n\n\n\n<p>Zde a je pr\u016fse\u010d\u00edk, b je sklon p\u0159\u00edmky. Pro v\u00fdpo\u010det sklonu se pou\u017eije vzorec: b = (n\u03a3(xy) - \u03a3x\u03a3y) \/ (n\u03a3(x<sup>2<\/sup>) - (\u03a3x)<sup>2<\/sup>), kde n je po\u010det pozorov\u00e1n\u00ed, \u03a3xy je sou\u010det sou\u010din\u016f x a y, \u03a3x a \u03a3y jsou sou\u010dty x a y a \u03a3(x<sup>2<\/sup>) je sou\u010det \u010dtverc\u016f x.<\/p>\n\n\n\n<p>Pro v\u00fdpo\u010det interceptu se pou\u017eije vzorec: a = (\u03a3y - b\u03a3x) \/ n.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-multiple-regression\">V\u00edcen\u00e1sobn\u00e1 regrese&nbsp;<\/h3>\n\n\n\n<p>V\u00edcen\u00e1sobn\u00e1 line\u00e1rn\u00ed regrese:<\/p>\n\n\n\n<p>Vzorec pro rovnici modelu v\u00edcen\u00e1sobn\u00e9 line\u00e1rn\u00ed regrese je:<\/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>kde y je z\u00e1visl\u00e1 prom\u011bnn\u00e1, x<sub>1<\/sub>, x<sub>2<\/sub>, ..., x<sub>n<\/sub> jsou nez\u00e1visl\u00e9 prom\u011bnn\u00e9 a b<sub>0<\/sub>, b<sub>1<\/sub>, b<sub>2<\/sub>, ..., bn jsou koeficienty nez\u00e1visl\u00fdch prom\u011bnn\u00fdch.<\/p>\n\n\n\n<p>Vzorec pro odhad koeficient\u016f pomoc\u00ed oby\u010dejn\u00fdch nejmen\u0161\u00edch \u010dtverc\u016f je n\u00e1sleduj\u00edc\u00ed:<\/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>kde \u03b2 je sloupcov\u00fd vektor koeficient\u016f, X je n\u00e1vrhov\u00e1 matice nez\u00e1visl\u00fdch prom\u011bnn\u00fdch, X' je transpozice X a y je vektor pozorov\u00e1n\u00ed z\u00e1visl\u00e9 prom\u011bnn\u00e9.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-regression-analysis-example\">P\u0159\u00edklad regresn\u00ed anal\u00fdzy<\/h2>\n\n\n\n<p>P\u0159edpokl\u00e1dejme, \u017ee chcete zjistit souvislost mezi pr\u016fm\u011brn\u00fdm prosp\u011bchem (GPA) a po\u010dtem hodin studia t\u00fddn\u011b. Shrom\u00e1\u017ed\u00edte informace od souboru student\u016f, v\u010detn\u011b jejich po\u010dtu studijn\u00edch hodin a pr\u016fm\u011bru zn\u00e1mek.<\/p>\n\n\n\n<p>Pot\u00e9 pomoc\u00ed regresn\u00ed anal\u00fdzy zjist\u011bte, zda mezi ob\u011bma prom\u011bnn\u00fdmi existuje line\u00e1rn\u00ed souvislost, a pokud ano, m\u016f\u017eete sestavit model, kter\u00fd p\u0159edpov\u00edd\u00e1 pr\u016fm\u011brn\u00fd prosp\u011bch studenta na z\u00e1klad\u011b po\u010dtu hodin studia t\u00fddn\u011b.<\/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>Obr\u00e1zek je k dispozici 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>P\u0159i vynesen\u00ed dat do mapy rozptylu se ukazuje, \u017ee mezi po\u010dtem hodin studia a GPA existuje p\u0159\u00edzniv\u00e1 line\u00e1rn\u00ed souvislost. Sklon a pr\u016fse\u010d\u00edk p\u0159\u00edmky nejlep\u0161\u00ed shody jsou pak odhadnuty pomoc\u00ed jednoduch\u00e9ho line\u00e1rn\u00edho regresn\u00edho modelu. Kone\u010dn\u00e9 \u0159e\u0161en\u00ed by mohlo vypadat n\u00e1sledovn\u011b:<\/p>\n\n\n\n<p>GPA = 2,0 + 0,3 (po\u010det hodin t\u00fddn\u011b)<\/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>Obr\u00e1zek je k dispozici 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>Tato rovnice \u0159\u00edk\u00e1, \u017ee za ka\u017edou hodinu studia t\u00fddn\u011b nav\u00edc se student\u016fv pr\u016fm\u011br zv\u00fd\u0161\u00ed o 0,3 bodu, p\u0159i\u010dem\u017e v\u0161e ostatn\u00ed je rovnocenn\u00e9. Tento algoritmus lze pou\u017e\u00edt k p\u0159edpov\u011bdi GPA studenta na z\u00e1klad\u011b toho, kolik hodin t\u00fddn\u011b studuje, a tak\u00e9 k identifikaci student\u016f, u kter\u00fdch hroz\u00ed, \u017ee budou m\u00edt hor\u0161\u00ed v\u00fdsledky, na z\u00e1klad\u011b jejich studijn\u00edch n\u00e1vyk\u016f.&nbsp;<\/p>\n\n\n\n<p>Na z\u00e1klad\u011b \u00fadaj\u016f z p\u0159\u00edkladu jsou hodnoty pro <strong>b<\/strong> a <strong>a<\/strong> jsou n\u00e1sleduj\u00edc\u00ed:<\/p>\n\n\n\n<p>n = 10 (po\u010det pozorov\u00e1n\u00ed)<\/p>\n\n\n\n<p>\u03a3x = 30 (sou\u010det studijn\u00edch hodin)<\/p>\n\n\n\n<p>\u03a3y = 25 (sou\u010det pr\u016fm\u011br\u016f)<\/p>\n\n\n\n<p>\u03a3xy = 149 (sou\u010det sou\u010dinu studijn\u00edch hodin a pr\u016fm\u011brn\u00fdch studijn\u00edch v\u00fdsledk\u016f)<\/p>\n\n\n\n<p>\u03a3(x)<sup>2<\/sup> = 102 (sou\u010det \u010dtverc\u016f studijn\u00edch hodin)<\/p>\n\n\n\n<p>Na z\u00e1klad\u011b t\u011bchto hodnot vypo\u010d\u00edtejte <strong>b<\/strong> jako:<\/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>A vypo\u010d\u00edtat <strong>a <\/strong>jako:<\/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>Rovnice p\u0159\u00edmky nejlep\u0161\u00ed shody je tedy:&nbsp;<\/p>\n\n\n\n<p>GPA = 2,0 + 0,3 (po\u010det hodin t\u00fddn\u011b)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-the-difference-between-correlation-and-regression\">Jak\u00fd je rozd\u00edl mezi korelac\u00ed a regres\u00ed?<\/h2>\n\n\n\n<p>Korelace i regrese jsou statistick\u00e9 metody pro zkoum\u00e1n\u00ed vztahu mezi dv\u011bma prom\u011bnn\u00fdmi. Slou\u017e\u00ed k r\u016fzn\u00fdm \u00fa\u010del\u016fm a poskytuj\u00ed r\u016fzn\u00e9 typy informac\u00ed.<\/p>\n\n\n\n<p>Korelace je m\u011b\u0159\u00edtkem s\u00edly a pr\u016fb\u011bhu vztahu mezi dv\u011bma prom\u011bnn\u00fdmi. Pohybuje se od -1 do +1, p\u0159i\u010dem\u017e -1 p\u0159edstavuje dokonalou z\u00e1pornou korelaci, 0 p\u0159edstavuje \u017e\u00e1dnou korelaci a +1 p\u0159edstavuje dokonalou kladnou korelaci. Korelace ud\u00e1v\u00e1 m\u00edru propojen\u00ed dvou prom\u011bnn\u00fdch, ale nevypov\u00edd\u00e1 o p\u0159\u00ed\u010din\u011b nebo p\u0159edv\u00eddatelnosti.<\/p>\n\n\n\n<p>Regrese je naopak metoda modelov\u00e1n\u00ed vztahu mezi dv\u011bma prom\u011bnn\u00fdmi, obvykle za \u00fa\u010delem p\u0159edpov\u011bdi nebo vysv\u011btlen\u00ed jedn\u00e9 prom\u011bnn\u00e9 na z\u00e1klad\u011b druh\u00e9. Regresn\u00ed anal\u00fdza m\u016f\u017ee poskytnout odhady velikosti a sm\u011bru vztahu, stejn\u011b jako testy statistick\u00e9 v\u00fdznamnosti, rozsahy spolehlivosti a progn\u00f3zy budouc\u00edch v\u00fdsledk\u016f.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-your-creations-ready-within-minutes\">Va\u0161e v\u00fdtvory p\u0159ipraven\u00e9 b\u011bhem n\u011bkolika minut<\/h2>\n\n\n\n<p><a href=\"https:\/\/mindthegraph.com\" target=\"_blank\" rel=\"noreferrer noopener\">Mind the Graph<\/a> je online platforma, kter\u00e1 nab\u00edz\u00ed rozs\u00e1hlou knihovnu v\u011bdeck\u00fdch ilustrac\u00ed a infografik, kter\u00e9 lze jednodu\u0161e upravit podle va\u0161ich jedine\u010dn\u00fdch pot\u0159eb. Vytv\u00e1\u0159ejte profesion\u00e1ln\u011b vypadaj\u00edc\u00ed grafy, plak\u00e1ty a grafick\u00e9 abstrakty b\u011bhem n\u011bkolika minut pomoc\u00ed rozhran\u00ed drag-and-drop a \u0161irok\u00e9 \u0161k\u00e1ly n\u00e1stroj\u016f a funkc\u00ed.&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\u010dn\u011bte tvo\u0159it s 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>Pochopte, jak funguje regresn\u00ed anal\u00fdza, na komplexn\u00edm p\u0159\u00edkladu a nau\u010dte se nejb\u011b\u017en\u011bj\u0161\u00ed vzorce. <\/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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