{"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\/lt\/regresine-analize\/","title":{"rendered":"Regresin\u0117s analiz\u0117s naudojimas sud\u0117tingiems ry\u0161iams suprasti"},"content":{"rendered":"<p>Regresin\u0117 analiz\u0117 - tai metodas, skirtas nustatyti ir analizuoti ry\u0161\u012f tarp vieno ar daugiau nepriklausom\u0173 kintam\u0173j\u0173 ir priklausomo kintamojo. \u0160is metodas pla\u010diai taikomas \u012fvairiose srityse, \u012fskaitant sveikatos prie\u017ei\u016br\u0105, socialinius mokslus, in\u017einerij\u0105, ekonomik\u0105 ir versl\u0105. Regresin\u0119 analiz\u0119 galite naudoti nor\u0117dami i\u0161tirti esminius duomen\u0173 ry\u0161ius ir sukurti prognozavimo modelius, kurie pad\u0117s jums priimti pagr\u012fstus sprendimus.<\/p>\n\n\n\n<p>\u0160iame straipsnyje i\u0161samiai ap\u017evelgiama regresin\u0117 analiz\u0117, pateikiama jos veikimo principas, lengvai suprantamas pavyzdys ir paai\u0161kinama, kuo ji skiriasi nuo koreliacin\u0117s analiz\u0117s.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-regression-analysis\">Kas yra regresin\u0117 analiz\u0117?<\/h2>\n\n\n\n<p>Regresin\u0117 analiz\u0117 yra statistinis metodas, skirtas nustatyti ir kiekybi\u0161kai \u012fvertinti priklausomo kintamojo ir vieno ar daugiau nepriklausom\u0173 kintam\u0173j\u0173 ry\u0161\u012f. Trumpai tariant, ji padeda suprasti, kaip vieno ar daugiau nepriklausom\u0173 kintam\u0173j\u0173 poky\u010diai susij\u0119 su priklausomo kintamojo poky\u010diais.<\/p>\n\n\n\n<p>Kad gerai suprastum\u0117te regresin\u0119 analiz\u0119, pirmiausia turite suprasti \u0161ias s\u0105vokas:<\/p>\n\n\n\n<ul>\n<li><strong>Priklausomas kintamasis: <\/strong>Tai kintamasis, kur\u012f norite analizuoti arba prognozuoti. Tai rezultato kintamasis, kur\u012f bandote suprasti ir paai\u0161kinti.<\/li>\n\n\n\n<li><strong>Nepriklausomi kintamieji: <\/strong>Tai kintamieji, kurie, j\u016bs\u0173 manymu, turi \u012ftakos priklausomam kintamajam. Jie da\u017enai vadinami predikciniais kintamaisiais, nes naudojami priklausomo kintamojo poky\u010diams prognozuoti arba paai\u0161kinti.<\/li>\n<\/ul>\n\n\n\n<p>Regresin\u0117 analiz\u0117 gali b\u016bti naudojama \u012fvairiomis aplinkyb\u0117mis, pavyzd\u017eiui, prognozuojant b\u016bsimas priklausomo kintamojo vertes, siekiant suprasti nepriklausom\u0173 kintam\u0173j\u0173 poveik\u012f priklausomam kintamajam ir ie\u0161kant i\u0161skir\u010di\u0173 ar ne\u012fprast\u0173 atvej\u0173 renkant duomenis.<\/p>\n\n\n\n<p>Regresin\u0117 analiz\u0117 gali b\u016bti skirstoma \u012f kelet\u0105 tip\u0173, \u012fskaitant vien\u0105 tiesin\u0119 regresij\u0105, logistin\u0119 regresij\u0105, polinomin\u0119 regresij\u0105 ir daugialyp\u0119 regresij\u0105. Tinkam\u0105 regresijos model\u012f lemia duomen\u0173 pob\u016bdis ir nagrin\u0117jamas tyrimo objektas.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-how-does-regression-analysis-work\">Kaip veikia regresin\u0117 analiz\u0117?<\/h2>\n\n\n\n<p>Regresin\u0117s analiz\u0117s tikslas - nustatyti geriausiai atitinkan\u010di\u0105 ties\u0119 arba kreiv\u0119, kuri atspindi ry\u0161\u012f tarp nepriklausom\u0173 kintam\u0173j\u0173 ir priklausomo kintamojo. \u0160i geriausiai tinkanti linija arba kreiv\u0117 sudaroma taikant statistinius metodus, kurie suma\u017eina tik\u0117tin\u0173 ir reali\u0173 duomen\u0173 rinkinio reik\u0161mi\u0173 skirtumus.<\/p>\n\n\n\n<p>Toliau pateikiamos dviej\u0173 labiausiai paplitusi\u0173 regresin\u0117s analiz\u0117s tip\u0173 formul\u0117s:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-single-linear-regression\">Viena tiesin\u0117 regresija<\/h3>\n\n\n\n<p>Taikant paprast\u0105j\u0105 tiesin\u0119 regresij\u0105, dviej\u0173 kintam\u0173j\u0173 - nepriklausomo kintamojo (x) ir priklausomo kintamojo (y) - ry\u0161iui parodyti naudojama geriausiai tinkanti ties\u0117.<\/p>\n\n\n\n<p>Geriausiai tinkan\u010di\u0105 ties\u0119 galima pavaizduoti lygtimi: y = a + bx.<\/p>\n\n\n\n<p>\u010cia a yra intercepcija, o b - ties\u0117s nuolydis. Norint apskai\u010diuoti ties\u0117s nuolyd\u012f, naudojama formul\u0117: b = (n\u03a3(xy) - \u03a3x\u03a3y) \/ (n\u03a3(x<sup>2<\/sup>) - (\u03a3x)<sup>2<\/sup>), kur n - steb\u0117jim\u0173 skai\u010dius, \u03a3xy - x ir y sandaugos suma, \u03a3x ir \u03a3y - atitinkamai x ir y sumos, o \u03a3(x<sup>2<\/sup>) yra x kvadrat\u0173 suma.<\/p>\n\n\n\n<p>Intercepcijai apskai\u010diuoti naudojama formul\u0117: a = (\u03a3y - b\u03a3x) \/ n.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-multiple-regression\">Daugialyp\u0117 regresija&nbsp;<\/h3>\n\n\n\n<p>Daugialyp\u0117 tiesin\u0117 regresija:<\/p>\n\n\n\n<p>Daugialyp\u0117s tiesin\u0117s regresijos modelio lygties formul\u0117 yra tokia:<\/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>kur y yra priklausomas kintamasis, x<sub>1<\/sub>, x<sub>2<\/sub>, ..., x<sub>n<\/sub> yra nepriklausomi kintamieji, o b<sub>0<\/sub>, b<sub>1<\/sub>, b<sub>2<\/sub>, ..., bn yra nepriklausom\u0173 kintam\u0173j\u0173 koeficientai.<\/p>\n\n\n\n<p>Koeficient\u0173 \u012fvertinimo formul\u0117, taikant paprast\u0173j\u0173 ma\u017eiausi\u0173j\u0173 kvadrat\u0173 metod\u0105, yra tokia:<\/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>kur \u03b2 yra stulpelinis koeficient\u0173 vektorius, X yra nepriklausom\u0173 kintam\u0173j\u0173 matrica, X' yra X transpozicija, o y yra priklausomo kintamojo steb\u0117jim\u0173 vektorius.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-regression-analysis-example\">Regresin\u0117s analiz\u0117s pavyzdys<\/h2>\n\n\n\n<p>Tarkime, kad norite i\u0161siai\u0161kinti ry\u0161\u012f tarp asmens pa\u017eymi\u0173 vidurkio (GPA) ir valand\u0173, kurias jis mokosi per savait\u0119, skai\u010diaus. Renkate informacij\u0105 i\u0161 student\u0173, \u012fskaitant j\u0173 studij\u0173 valand\u0173 skai\u010di\u0173 ir pa\u017eymi\u0173 vidurk\u012f.<\/p>\n\n\n\n<p>Tada naudokite regresin\u0119 analiz\u0119, kad pamatytum\u0117te, ar tarp abiej\u0173 kintam\u0173j\u0173 yra tiesinis ry\u0161ys, ir, jei taip, galite sukurti model\u012f, pagal kur\u012f b\u016bt\u0173 galima prognozuoti studento GPA, atsi\u017evelgiant \u012f jo mokymosi valand\u0173 skai\u010di\u0173 per savait\u0119.<\/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>Vaizdas prieinamas <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>Duomenis pavaizdavus sklaidos \u017eem\u0117lapyje, paai\u0161k\u0117ja, kad egzistuoja palankus tiesinis ry\u0161ys tarp mokymosi valand\u0173 ir GPA. Tuomet geriausio atitikimo ties\u0117s nuolydis ir interceptas \u012fvertinami taikant paprastosios tiesin\u0117s regresijos model\u012f. Galutinis sprendimas gal\u0117t\u0173 atrodyti taip:<\/p>\n\n\n\n<p>GPA = 2,0 + 0,3 (mokymosi valandos per savait\u0119)<\/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>Vaizdas prieinamas <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>Pagal \u0161i\u0105 lygt\u012f u\u017e kiekvien\u0105 papildom\u0105 mokymosi valand\u0105 per savait\u0119 studento vidurkis padid\u0117ja 0,3 balo, o visa kita yra lygiaverti\u0161ka. \u0160\u012f algoritm\u0105 galima naudoti norint prognozuoti studento GPA pagal tai, kiek valand\u0173 per savait\u0119 jis mokosi, taip pat nustatyti, kuriems studentams gresia prasti rezultatai, atsi\u017evelgiant \u012f j\u0173 mokymosi \u012fpro\u010dius.&nbsp;<\/p>\n\n\n\n<p>Naudojant pavyzd\u017eio duomenis, vert\u0117s <strong>b<\/strong> ir <strong>a<\/strong> yra \u0161ie:<\/p>\n\n\n\n<p>n = 10 (steb\u0117jim\u0173 skai\u010dius)<\/p>\n\n\n\n<p>\u03a3x = 30 (studij\u0173 valand\u0173 suma)<\/p>\n\n\n\n<p>\u03a3y = 25 (GPA suma)<\/p>\n\n\n\n<p>\u03a3xy = 149 (studij\u0173 valand\u0173 ir GPA sandaugos suma)<\/p>\n\n\n\n<p>\u03a3(x)<sup>2<\/sup> = 102 (studij\u0173 valand\u0173 kvadrat\u0173 suma)<\/p>\n\n\n\n<p>Remdamiesi \u0161iomis vert\u0117mis, apskai\u010diuokite <strong>b<\/strong> kaip:<\/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>Ir apskai\u010diuokite <strong>a <\/strong>kaip:<\/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>Tod\u0117l geriausiai tinkan\u010dios ties\u0117s lygtis yra:&nbsp;<\/p>\n\n\n\n<p>GPA = 2,0 + 0,3 (mokymosi valandos per savait\u0119)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-the-difference-between-correlation-and-regression\">Kuo skiriasi koreliacija nuo regresijos?<\/h2>\n\n\n\n<p>Ir koreliacija, ir regresija yra statistiniai metodai, skirti dviej\u0173 kintam\u0173j\u0173 ry\u0161iui tirti. Jie naudojami skirtingiems tikslams ir teikia skirting\u0105 informacij\u0105.<\/p>\n\n\n\n<p>Koreliacija yra dviej\u0173 kintam\u0173j\u0173 ry\u0161io stiprumo ir eigos matas. Jis svyruoja nuo -1 iki +1, kai -1 rei\u0161kia tobul\u0105 neigiam\u0105 koreliacij\u0105, 0 - jokio ry\u0161io, o +1 - tobul\u0105 teigiam\u0105 koreliacij\u0105. Koreliacija parodo dviej\u0173 kintam\u0173j\u0173 ry\u0161io laipsn\u012f, ta\u010diau ji nenurodo prie\u017easties ar nusp\u0117jamumo.<\/p>\n\n\n\n<p>Kita vertus, regresija - tai dviej\u0173 kintam\u0173j\u0173 ry\u0161io modeliavimo metodas, paprastai siekiant prognozuoti arba paai\u0161kinti vien\u0105 kintam\u0105j\u012f remiantis kitu. Regresin\u0117 analiz\u0117 gali pad\u0117ti \u012fvertinti ry\u0161io dyd\u012f ir krypt\u012f, taip pat atlikti statistinio reik\u0161mingumo testus, nustatyti patikimumo intervalus ir b\u016bsim\u0173 rezultat\u0173 prognozes.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-your-creations-ready-within-minutes\">J\u016bs\u0173 k\u016briniai, paruo\u0161ti per kelias minutes<\/h2>\n\n\n\n<p><a href=\"https:\/\/mindthegraph.com\" target=\"_blank\" rel=\"noreferrer noopener\">Mind the Graph<\/a> tai internetin\u0117 platforma, kurioje rasite pla\u010di\u0105 mokslini\u0173 iliustracij\u0173 ir infografikos dizain\u0173 bibliotek\u0105, kuri\u0105 galima lengvai modifikuoti, kad ji atitikt\u0173 j\u016bs\u0173 unikalius poreikius. Naudodamiesi \"drag-and-drop\" s\u0105saja ir \u012fvairiais \u012frankiais bei funkcijomis, per kelias minutes sukurkite profesionaliai atrodan\u010dias diagramas, plakatus ir grafines santraukas.&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\">Prad\u0117kite kurti su 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>Remdamiesi i\u0161samiu pavyzd\u017eiu lengvai supraskite, kaip veikia regresin\u0117 analiz\u0117, ir i\u0161mokite da\u017eniausiai pasitaikan\u010dias formules. <\/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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