{"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\/ro\/analiza-de-regresie\/","title":{"rendered":"Utilizarea analizei de regresie pentru \u00een\u021belegerea rela\u021biilor complexe"},"content":{"rendered":"<p>Analiza de regresie este o metod\u0103 de identificare \u0219i analiz\u0103 a leg\u0103turii dintre una sau mai multe variabile independente \u0219i o variabil\u0103 dependent\u0103. Aceast\u0103 metod\u0103 este utilizat\u0103 pe scar\u0103 larg\u0103 \u00eentr-o varietate de discipline, inclusiv \u00een domeniul s\u0103n\u0103t\u0103\u021bii, al \u0219tiin\u021belor sociale, al ingineriei, al economiei \u0219i al afacerilor. Pute\u021bi utiliza analiza de regresie pentru a investiga rela\u021biile fundamentale din date \u0219i pentru a dezvolta modele predictive care v\u0103 vor ajuta s\u0103 lua\u021bi decizii \u00een cuno\u0219tin\u021b\u0103 de cauz\u0103.<\/p>\n\n\n\n<p>Acest articol v\u0103 va oferi o prezentare cuprinz\u0103toare a analizei de regresie, inclusiv modul \u00een care func\u021bioneaz\u0103, un exemplu u\u0219or de \u00een\u021beles \u0219i va explica \u00een ce fel difer\u0103 de analiza de corela\u021bie.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-regression-analysis\">Ce este analiza de regresie?<\/h2>\n\n\n\n<p>Analiza de regresie este o metod\u0103 statistic\u0103 de identificare \u0219i cuantificare a leg\u0103turii dintre o variabil\u0103 dependent\u0103 \u0219i una sau mai multe variabile independente. Pe scurt, aceasta v\u0103 ajut\u0103 s\u0103 \u00een\u021belege\u021bi modul \u00een care modific\u0103rile uneia sau mai multor variabile independente sunt legate de modific\u0103rile variabilei dependente.<\/p>\n\n\n\n<p>Pentru a ob\u021bine o \u00een\u021belegere aprofundat\u0103 a analizei de regresie, trebuie mai \u00eent\u00e2i s\u0103 \u00een\u021belege\u021bi urm\u0103torii termeni:<\/p>\n\n\n\n<ul>\n<li><strong>Variabila dependent\u0103: <\/strong>Aceasta este variabila pe care v\u0103 intereseaz\u0103 s\u0103 o analiza\u021bi sau s\u0103 o prezice\u021bi. Este variabila de rezultat pe care \u00eencerca\u021bi s\u0103 o \u00een\u021belege\u021bi \u0219i s\u0103 o explica\u021bi.<\/li>\n\n\n\n<li><strong>Variabile independente: <\/strong>Acestea sunt variabilele care crede\u021bi c\u0103 au un efect asupra variabilei dependente. Acestea sunt adesea denumite variabile predictive, deoarece sunt utilizate pentru a prezice sau explica schimb\u0103rile variabilei dependente.<\/li>\n<\/ul>\n\n\n\n<p>Analiza de regresie poate fi utilizat\u0103 \u00eentr-o serie de situa\u021bii, inclusiv pentru a prezice valorile viitoare ale variabilei dependente, pentru a \u00een\u021belege efectul variabilelor independente asupra variabilei dependente \u0219i pentru a g\u0103si valori aberante sau evenimente neobi\u0219nuite \u00een colectarea datelor.<\/p>\n\n\n\n<p>Analiza de regresie poate fi clasificat\u0103 \u00een mai multe tipuri, inclusiv regresia liniar\u0103 simpl\u0103, regresia logistic\u0103, regresia polinomial\u0103 \u0219i regresia multipl\u0103. Modelul de regresie adecvat este determinat de natura datelor \u0219i de subiectul investiga\u021biei \u00een cauz\u0103.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-how-does-regression-analysis-work\">Cum func\u021bioneaz\u0103 analiza de regresie?<\/h2>\n\n\n\n<p>Scopul analizei de regresie este de a identifica linia sau curba care se potrive\u0219te cel mai bine \u0219i care reflect\u0103 leg\u0103tura dintre variabilele independente \u0219i variabila dependent\u0103. Aceast\u0103 linie sau curb\u0103 cea mai bine adaptat\u0103 este generat\u0103 cu ajutorul unor metode statistice care reduc diferen\u021bele dintre valorile a\u0219teptate \u0219i cele reale din colectarea datelor.<\/p>\n\n\n\n<p>Iat\u0103 formulele pentru cele mai frecvente dou\u0103 tipuri de analiz\u0103 de regresie:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-single-linear-regression\">Regresie liniar\u0103 unic\u0103<\/h3>\n\n\n\n<p>\u00cen Regresia liniar\u0103 simpl\u0103, utiliza\u021bi o linie de cea mai bun\u0103 potrivire pentru a ar\u0103ta rela\u021bia dintre dou\u0103 variabile: variabila independent\u0103 (x) \u0219i variabila dependent\u0103 (y).<\/p>\n\n\n\n<p>Linia de cea mai bun\u0103 potrivire poate fi reprezentat\u0103 prin ecua\u021bia: y = a + bx.<\/p>\n\n\n\n<p>Aici, a este intercep\u021bia, iar b este panta dreptei. Pentru a calcula panta, se folose\u0219te formula: b = (n\u03a3(xy) - \u03a3x\u03a3y) \/ (n\u03a3(x<sup>2<\/sup>) - (\u03a3x)<sup>2<\/sup>), unde n este num\u0103rul de observa\u021bii, \u03a3xy este suma produsului dintre x \u0219i y, \u03a3x \u0219i \u03a3y sunt sumele lui x \u0219i respectiv y, iar \u03a3(x<sup>2<\/sup>) este suma p\u0103tratelor lui x.<\/p>\n\n\n\n<p>Pentru a calcula intercep\u021bia, se folose\u0219te formula: a = (\u03a3y - b\u03a3x) \/ n.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-multiple-regression\">Regresie multipl\u0103&nbsp;<\/h3>\n\n\n\n<p>Regresie liniar\u0103 multipl\u0103:<\/p>\n\n\n\n<p>Formula pentru ecua\u021bia modelului de regresie liniar\u0103 multipl\u0103 este:<\/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>unde y este variabila dependent\u0103, x<sub>1<\/sub>, x<sub>2<\/sub>, ..., x<sub>n<\/sub> sunt variabilele independente, iar b<sub>0<\/sub>, b<sub>1<\/sub>, b<sub>2<\/sub>, ..., bn sunt coeficien\u021bii variabilelor independente.<\/p>\n\n\n\n<p>Formula de estimare a coeficien\u021bilor prin metoda celor mai mici p\u0103trate ordinare este:<\/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>unde \u03b2 este un vector coloan\u0103 de coeficien\u021bi, X este matricea de proiectare a variabilelor independente, X' este transpunerea lui X, iar y este vectorul de observa\u021bii ale variabilei dependente.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-regression-analysis-example\">Exemplu de analiz\u0103 de regresie<\/h2>\n\n\n\n<p>S\u0103 presupunem c\u0103 dori\u021bi s\u0103 analiza\u021bi leg\u0103tura dintre media unei persoane \u0219i num\u0103rul de ore de studiu pe s\u0103pt\u0103m\u00e2n\u0103. Aduna\u021bi informa\u021bii de la un set de studen\u021bi, inclusiv num\u0103rul de ore de studiu \u0219i media lor.<\/p>\n\n\n\n<p>Apoi, utiliza\u021bi analiza de regresie pentru a vedea dac\u0103 exist\u0103 o leg\u0103tur\u0103 liniar\u0103 \u00eentre cele dou\u0103 variabile \u0219i, dac\u0103 da, pute\u021bi construi un model care s\u0103 prezic\u0103 media general\u0103 a unui student pe baza num\u0103rului de ore de studiu pe s\u0103pt\u0103m\u00e2n\u0103.<\/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>Imagine disponibil\u0103 pe <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>Atunci c\u00e2nd datele sunt reprezentate pe o hart\u0103 de dispersie, se pare c\u0103 exist\u0103 o leg\u0103tur\u0103 liniar\u0103 favorabil\u0103 \u00eentre orele de studiu \u0219i media general\u0103. Panta \u0219i interceptarea liniei de cea mai bun\u0103 potrivire sunt apoi estimate cu ajutorul unui model de regresie liniar\u0103 simpl\u0103. Solu\u021bia final\u0103 ar putea ar\u0103ta astfel:<\/p>\n\n\n\n<p>GPA = 2.0 + 0.3 (ore studiate pe s\u0103pt\u0103m\u00e2n\u0103)<\/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>Imagine disponibil\u0103 pe <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>Aceast\u0103 ecua\u021bie spune c\u0103 pentru fiecare or\u0103 suplimentar\u0103 de studiu pe s\u0103pt\u0103m\u00e2n\u0103, media unui student va cre\u0219te cu 0,3 puncte, restul fiind echivalent. Acest algoritm poate fi folosit pentru a prognoza media general\u0103 a unui student \u00een func\u021bie de c\u00e2te ore studiaz\u0103 pe s\u0103pt\u0103m\u00e2n\u0103, precum \u0219i pentru a identifica studen\u021bii care risc\u0103 s\u0103 aib\u0103 rezultate slabe pe baza rutinei lor de studiu.&nbsp;<\/p>\n\n\n\n<p>Utiliz\u00e2nd datele din exemplu, valorile pentru <strong>b<\/strong> \u0219i <strong>a<\/strong> sunt urm\u0103toarele:<\/p>\n\n\n\n<p>n = 10 (num\u0103rul de observa\u021bii)<\/p>\n\n\n\n<p>\u03a3x = 30 (suma orelor de studiu)<\/p>\n\n\n\n<p>\u03a3y = 25 (suma mediilor medii)<\/p>\n\n\n\n<p>\u03a3xy = 149 (suma produsului dintre orele de studiu \u0219i media general\u0103)<\/p>\n\n\n\n<p>\u03a3(x)<sup>2<\/sup> = 102 (suma p\u0103tratelor orelor de studiu)<\/p>\n\n\n\n<p>Folosind aceste valori, se calculeaz\u0103 <strong>b<\/strong> ca:<\/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>\u0218i calcula\u021bi <strong>a <\/strong>ca:<\/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>Prin urmare, ecua\u021bia liniei de cea mai bun\u0103 potrivire este:&nbsp;<\/p>\n\n\n\n<p>GPA = 2.0 + 0.3 (ore studiate pe s\u0103pt\u0103m\u00e2n\u0103)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-the-difference-between-correlation-and-regression\">Care este diferen\u021ba dintre corela\u021bie \u0219i regresie?<\/h2>\n\n\n\n<p>At\u00e2t corela\u021bia, c\u00e2t \u0219i regresia sunt metode statistice de examinare a leg\u0103turii dintre dou\u0103 variabile. Acestea au scopuri diferite \u0219i ofer\u0103 tipuri diferite de informa\u021bii.<\/p>\n\n\n\n<p>Corela\u021bia este o m\u0103sur\u0103 a puterii \u0219i a cursului unei leg\u0103turi \u00eentre dou\u0103 variabile. Aceasta variaz\u0103 de la -1 la +1, -1 reprezent\u00e2nd o corela\u021bie negativ\u0103 perfect\u0103, 0 reprezent\u00e2nd absen\u021ba corela\u021biei, iar +1 reprezent\u00e2nd o corela\u021bie pozitiv\u0103 perfect\u0103. Corela\u021bia indic\u0103 gradul \u00een care dou\u0103 variabile sunt conectate, dar nu indic\u0103 cauza sau predictibilitatea.<\/p>\n\n\n\n<p>Pe de alt\u0103 parte, regresia este o metod\u0103 de modelare a leg\u0103turii dintre dou\u0103 variabile, de obicei pentru a prognoza sau explica o variabil\u0103 pe baza celeilalte. Analiza de regresie poate furniza estim\u0103ri ale m\u0103rimii \u0219i direc\u021biei rela\u021biei, precum \u0219i teste de semnifica\u021bie statistic\u0103, intervale de \u00eencredere \u0219i previziuni ale rezultatelor viitoare.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-your-creations-ready-within-minutes\">Crea\u021biile tale, gata \u00een c\u00e2teva minute<\/h2>\n\n\n\n<p><a href=\"https:\/\/mindthegraph.com\" target=\"_blank\" rel=\"noreferrer noopener\">Mind the Graph<\/a> este o platform\u0103 online care v\u0103 ofer\u0103 o bibliotec\u0103 extins\u0103 de ilustra\u021bii \u0219tiin\u021bifice \u0219i modele infografice care pot fi modificate simplu pentru a r\u0103spunde nevoilor dumneavoastr\u0103 unice. Realiza\u021bi diagrame, postere \u0219i rezumate grafice cu aspect profesional \u00een c\u00e2teva minute, utiliz\u00e2nd o interfa\u021b\u0103 drag-and-drop \u0219i o gam\u0103 larg\u0103 de instrumente \u0219i func\u021bii.&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\">\u00cencepe\u021bi s\u0103 crea\u021bi cu 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>\u00cen\u021belege\u021bi cu u\u0219urin\u021b\u0103 cum func\u021bioneaz\u0103 analiza de regresie cu ajutorul unui exemplu cuprinz\u0103tor \u0219i \u00eenv\u0103\u021ba\u021bi cele mai frecvente formule. <\/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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