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href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_cs.wikipedia.org&uselang=cs" class=""><span>Podpořte Wikipedii</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speci%C3%A1ln%C3%AD:Vytvo%C5%99it_%C3%BA%C4%8Det&returnto=Korelace&returntoquery=oldid%3D23480683" title="Doporučujeme vytvořit si účet a přihlásit se, ovšem není to povinné" class=""><span>Vytvoření účtu</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speci%C3%A1ln%C3%AD:P%C5%99ihl%C3%A1sit&returnto=Korelace&returntoquery=oldid%3D23480683" title="Doporučujeme vám přihlásit se, ovšem není to povinné. 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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Přihlášení</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Stránky pro odhlášené editory <a href="/wiki/N%C3%A1pov%C4%9Bda:%C3%9Avod" aria-label="Více informací o editování"><span>dozvědět se více</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Moje_p%C5%99%C3%ADsp%C4%9Bvky" title="Seznam editací provedených z této IP adresy [y]" accesskey="y"><span>Příspěvky</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Moje_diskuse" title="Diskuse o editacích provedených z této IP adresy [n]" accesskey="n"><span>Diskuse</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Projekt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Obsah" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Obsah</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skrýt</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(úvod)</div> </a> </li> <li id="toc-Korelace_ve_statistice" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Korelace_ve_statistice"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Korelace ve statistice</span> </div> </a> <button aria-controls="toc-Korelace_ve_statistice-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Přepnout podsekci Korelace ve statistice</span> </button> <ul id="toc-Korelace_ve_statistice-sublist" class="vector-toc-list"> <li id="toc-Pearsonův_korelační_koeficient" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pearsonův_korelační_koeficient"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Pearsonův korelační koeficient</span> </div> </a> <ul id="toc-Pearsonův_korelační_koeficient-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Korelace_v_teorii_signálů" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Korelace_v_teorii_signálů"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Korelace v teorii signálů</span> </div> </a> <ul id="toc-Korelace_v_teorii_signálů-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Související_články" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Související_články"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Související články</span> </div> </a> <ul id="toc-Související_články-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externí_odkazy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Externí_odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Externí odkazy</span> </div> </a> <ul id="toc-Externí_odkazy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reference" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reference"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Reference</span> </div> </a> <ul id="toc-Reference-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Obsah" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Přepnout obsah" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Přepnout obsah</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Korelace</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Přejděte k článku v jiném jazyce. Je dostupný v 66 jazycích" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-66" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">66 jazyků</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D8%B1%D8%AA%D8%A8%D8%A7%D8%B7_(%D8%A5%D8%AD%D8%B5%D8%A7%D8%A1)" title="ارتباط (إحصاء) – arabština" lang="ar" hreflang="ar" data-title="ارتباط (إحصاء)" data-language-autonym="العربية" data-language-local-name="arabština" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%B8%E0%A6%B9-%E0%A6%B8%E0%A6%AE%E0%A7%8D%E0%A6%AC%E0%A6%A8%E0%A7%8D%E0%A6%A7" title="সহ-সম্বন্ধ – ásámština" lang="as" hreflang="as" data-title="সহ-সম্বন্ধ" data-language-autonym="অসমীয়া" data-language-local-name="ásámština" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Correlaci%C3%B3n" title="Correlación – asturština" lang="ast" hreflang="ast" data-title="Correlación" data-language-autonym="Asturianu" data-language-local-name="asturština" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Korrelyasiya" title="Korrelyasiya – ázerbájdžánština" lang="az" hreflang="az" data-title="Korrelyasiya" data-language-autonym="Azərbaycanca" data-language-local-name="ázerbájdžánština" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D0%B0%D1%80%D1%8D%D0%BB%D1%8F%D1%86%D1%8B%D1%8F" title="Карэляцыя – běloruština" lang="be" hreflang="be" data-title="Карэляцыя" data-language-autonym="Беларуская" data-language-local-name="běloruština" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9A%D0%B0%D1%80%D1%8D%D0%BB%D1%8F%D1%86%D1%8B%D1%8F" title="Карэляцыя – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Карэляцыя" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%BE%D1%80%D0%B5%D0%BB%D0%B0%D1%86%D0%B8%D1%8F" title="Корелация – bulharština" lang="bg" hreflang="bg" data-title="Корелация" data-language-autonym="Български" data-language-local-name="bulharština" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%95%E0%A5%8B%E0%A4%B0%E0%A4%BF%E0%A4%B2%E0%A5%87%E0%A4%B6%E0%A4%A8" title="कोरिलेशन – Bhojpuri" lang="bh" hreflang="bh" data-title="कोरिलेशन" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%82%E0%A6%B6%E0%A7%8D%E0%A6%B2%E0%A7%87%E0%A6%B7_%E0%A6%93_%E0%A6%A8%E0%A6%BF%E0%A6%B0%E0%A7%8D%E0%A6%AD%E0%A6%B0%E0%A6%B6%E0%A7%80%E0%A6%B2%E0%A6%A4%E0%A6%BE" title="সংশ্লেষ ও নির্ভরশীলতা – bengálština" lang="bn" hreflang="bn" data-title="সংশ্লেষ ও নির্ভরশীলতা" data-language-autonym="বাংলা" data-language-local-name="bengálština" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Koeficijent_korelacije" title="Koeficijent korelacije – bosenština" lang="bs" hreflang="bs" data-title="Koeficijent korelacije" data-language-autonym="Bosanski" data-language-local-name="bosenština" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Correlaci%C3%B3" title="Correlació – katalánština" lang="ca" hreflang="ca" data-title="Correlació" data-language-autonym="Català" data-language-local-name="katalánština" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Korrelation" title="Korrelation – dánština" lang="da" hreflang="da" data-title="Korrelation" data-language-autonym="Dansk" data-language-local-name="dánština" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Korrelation" title="Korrelation – němčina" lang="de" hreflang="de" data-title="Korrelation" data-language-autonym="Deutsch" data-language-local-name="němčina" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A3%CF%85%CF%83%CF%87%CE%AD%CF%84%CE%B9%CF%83%CE%B7_%CE%BA%CE%B1%CE%B9_%CE%B5%CE%BE%CE%AC%CF%81%CF%84%CE%B7%CF%83%CE%B7_(%CE%A3%CF%84%CE%B1%CF%84%CE%B9%CF%83%CF%84%CE%B9%CE%BA%CE%AE)" title="Συσχέτιση και εξάρτηση (Στατιστική) – řečtina" lang="el" hreflang="el" data-title="Συσχέτιση και εξάρτηση (Στατιστική)" data-language-autonym="Ελληνικά" data-language-local-name="řečtina" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Correlation" title="Correlation – angličtina" lang="en" hreflang="en" data-title="Correlation" data-language-autonym="English" data-language-local-name="angličtina" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Korelacio" title="Korelacio – esperanto" lang="eo" hreflang="eo" data-title="Korelacio" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Correlaci%C3%B3n" title="Correlación – španělština" lang="es" hreflang="es" data-title="Correlación" data-language-autonym="Español" data-language-local-name="španělština" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Korrelatsioon" title="Korrelatsioon – estonština" lang="et" hreflang="et" data-title="Korrelatsioon" data-language-autonym="Eesti" data-language-local-name="estonština" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Korrelazio" title="Korrelazio – baskičtina" lang="eu" hreflang="eu" data-title="Korrelazio" data-language-autonym="Euskara" data-language-local-name="baskičtina" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%87%D9%85%D8%A8%D8%B3%D8%AA%DA%AF%DB%8C_%D9%88_%D9%88%D8%A7%D8%A8%D8%B3%D8%AA%DA%AF%DB%8C" title="همبستگی و وابستگی – perština" lang="fa" hreflang="fa" data-title="همبستگی و وابستگی" data-language-autonym="فارسی" data-language-local-name="perština" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Korrelaatio" title="Korrelaatio – finština" lang="fi" hreflang="fi" data-title="Korrelaatio" data-language-autonym="Suomi" data-language-local-name="finština" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Corr%C3%A9lation_(statistiques)" title="Corrélation (statistiques) – francouzština" lang="fr" hreflang="fr" data-title="Corrélation (statistiques)" data-language-autonym="Français" data-language-local-name="francouzština" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Comhghaol%C3%BA" title="Comhghaolú – irština" lang="ga" hreflang="ga" data-title="Comhghaolú" data-language-autonym="Gaeilge" data-language-local-name="irština" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Correlaci%C3%B3n" title="Correlación – galicijština" lang="gl" hreflang="gl" data-title="Correlación" data-language-autonym="Galego" data-language-local-name="galicijština" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%AA%D7%90%D7%9D" title="מתאם – hebrejština" lang="he" hreflang="he" data-title="מתאם" data-language-autonym="עברית" data-language-local-name="hebrejština" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%B9%E0%A4%B8%E0%A4%AE%E0%A5%8D%E0%A4%AC%E0%A4%A8%E0%A5%8D%E0%A4%A7" title="सहसम्बन्ध – hindština" lang="hi" hreflang="hi" data-title="सहसम्बन्ध" data-language-autonym="हिन्दी" data-language-local-name="hindština" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Korelacija" title="Korelacija – chorvatština" lang="hr" hreflang="hr" data-title="Korelacija" data-language-autonym="Hrvatski" data-language-local-name="chorvatština" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Korrel%C3%A1ci%C3%B3" title="Korreláció – maďarština" lang="hu" hreflang="hu" data-title="Korreláció" data-language-autonym="Magyar" data-language-local-name="maďarština" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%B8%D5%BC%D5%A5%D5%AC%D5%B5%D5%A1%D6%81%D5%AB%D5%A1_(%D5%B4%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1)" title="Կոռելյացիա (մաթեմատիկա) – arménština" lang="hy" hreflang="hy" data-title="Կոռելյացիա (մաթեմատիկա)" data-language-autonym="Հայերեն" data-language-local-name="arménština" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Korelasi" title="Korelasi – indonéština" lang="id" hreflang="id" data-title="Korelasi" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéština" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Correlazione_(statistica)" title="Correlazione (statistica) – italština" lang="it" hreflang="it" data-title="Correlazione (statistica)" data-language-autonym="Italiano" data-language-local-name="italština" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%9B%B8%E9%96%A2" title="相関 – japonština" lang="ja" hreflang="ja" data-title="相関" data-language-autonym="日本語" data-language-local-name="japonština" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Analisis_kor%C3%A9lasi" title="Analisis korélasi – javánština" lang="jv" hreflang="jv" data-title="Analisis korélasi" data-language-autonym="Jawa" data-language-local-name="javánština" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%BE%D1%80%D1%80%D0%B5%D0%BB%D1%8F%D1%86%D0%B8%D1%8F" title="Корреляция – kazaština" lang="kk" hreflang="kk" data-title="Корреляция" data-language-autonym="Қазақша" data-language-local-name="kazaština" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%83%81%EA%B4%80_%EB%B6%84%EC%84%9D" title="상관 분석 – korejština" lang="ko" hreflang="ko" data-title="상관 분석" data-language-autonym="한국어" data-language-local-name="korejština" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9A%D0%BE%D1%80%D1%80%D0%B5%D0%BB%D1%8F%D1%86%D0%B8%D1%8F" title="Корреляция – kyrgyzština" lang="ky" hreflang="ky" data-title="Корреляция" data-language-autonym="Кыргызча" data-language-local-name="kyrgyzština" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Dependentia_(statistica)" title="Dependentia (statistica) – latina" lang="la" hreflang="la" data-title="Dependentia (statistica)" data-language-autonym="Latina" data-language-local-name="latina" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Koreliacija" title="Koreliacija – litevština" lang="lt" hreflang="lt" data-title="Koreliacija" data-language-autonym="Lietuvių" data-language-local-name="litevština" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Korel%C4%81cija" title="Korelācija – lotyština" lang="lv" hreflang="lv" data-title="Korelācija" data-language-autonym="Latviešu" data-language-local-name="lotyština" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%BE%D1%80%D0%B5%D0%BB%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Корелација – makedonština" lang="mk" hreflang="mk" data-title="Корелација" data-language-autonym="Македонски" data-language-local-name="makedonština" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Correlatie" title="Correlatie – nizozemština" lang="nl" hreflang="nl" data-title="Correlatie" data-language-autonym="Nederlands" data-language-local-name="nizozemština" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Korrelasjon" title="Korrelasjon – norština (nynorsk)" lang="nn" hreflang="nn" data-title="Korrelasjon" data-language-autonym="Norsk nynorsk" data-language-local-name="norština (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Korrelasjon" title="Korrelasjon – norština (bokmål)" lang="nb" hreflang="nb" data-title="Korrelasjon" data-language-autonym="Norsk bokmål" data-language-local-name="norština (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Zale%C5%BCno%C5%9B%C4%87_zmiennych_losowych" title="Zależność zmiennych losowych – polština" lang="pl" hreflang="pl" data-title="Zależność zmiennych losowych" data-language-autonym="Polski" data-language-local-name="polština" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Correla%C3%A7%C3%A3o" title="Correlação – portugalština" lang="pt" hreflang="pt" data-title="Correlação" data-language-autonym="Português" data-language-local-name="portugalština" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Corela%C8%9Bie" title="Corelație – rumunština" lang="ro" hreflang="ro" data-title="Corelație" data-language-autonym="Română" data-language-local-name="rumunština" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D1%80%D1%80%D0%B5%D0%BB%D1%8F%D1%86%D0%B8%D1%8F" title="Корреляция – ruština" lang="ru" hreflang="ru" data-title="Корреляция" data-language-autonym="Русский" data-language-local-name="ruština" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%DA%AF%DA%8F%D9%8A%D9%84_%D9%84%D8%A7%DA%B3%D8%A7%D9%BE%D9%88" title="گڏيل لاڳاپو – sindhština" lang="sd" hreflang="sd" data-title="گڏيل لاڳاپو" data-language-autonym="سنڌي" data-language-local-name="sindhština" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Korelacija" title="Korelacija – srbochorvatština" lang="sh" hreflang="sh" data-title="Korelacija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srbochorvatština" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Correlation" title="Correlation – Simple English" lang="en-simple" hreflang="en-simple" data-title="Correlation" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Korel%C3%A1cia_(%C5%A1tatistika)" title="Korelácia (štatistika) – slovenština" lang="sk" hreflang="sk" data-title="Korelácia (štatistika)" data-language-autonym="Slovenčina" data-language-local-name="slovenština" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Korelacija" title="Korelacija – slovinština" lang="sl" hreflang="sl" data-title="Korelacija" data-language-autonym="Slovenščina" data-language-local-name="slovinština" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Korrelacioni" title="Korrelacioni – albánština" lang="sq" hreflang="sq" data-title="Korrelacioni" data-language-autonym="Shqip" data-language-local-name="albánština" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%BE%D1%80%D0%B5%D0%BB%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Корелација – srbština" lang="sr" hreflang="sr" data-title="Корелација" data-language-autonym="Српски / srpski" data-language-local-name="srbština" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Kor%C3%A9lasi" title="Korélasi – sundština" lang="su" hreflang="su" data-title="Korélasi" data-language-autonym="Sunda" data-language-local-name="sundština" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Korrelation" title="Korrelation – švédština" lang="sv" hreflang="sv" data-title="Korrelation" data-language-autonym="Svenska" data-language-local-name="švédština" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Uhusiano_(Takwimu)" title="Uhusiano (Takwimu) – svahilština" lang="sw" hreflang="sw" data-title="Uhusiano (Takwimu)" data-language-autonym="Kiswahili" data-language-local-name="svahilština" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AA%E0%B8%AB%E0%B8%AA%E0%B8%B1%E0%B8%A1%E0%B8%9E%E0%B8%B1%E0%B8%99%E0%B8%98%E0%B9%8C" title="สหสัมพันธ์ – thajština" lang="th" hreflang="th" data-title="สหสัมพันธ์" data-language-autonym="ไทย" data-language-local-name="thajština" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Korelasyon_at_dependiyensiya" title="Korelasyon at dependiyensiya – tagalog" lang="tl" hreflang="tl" data-title="Korelasyon at dependiyensiya" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Korelasyon" title="Korelasyon – turečtina" lang="tr" hreflang="tr" data-title="Korelasyon" data-language-autonym="Türkçe" data-language-local-name="turečtina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%BE%D1%80%D0%B5%D0%BB%D1%8F%D1%86%D1%96%D1%8F" title="Кореляція – ukrajinština" lang="uk" hreflang="uk" data-title="Кореляція" data-language-autonym="Українська" data-language-local-name="ukrajinština" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D8%B1%D8%AA%D8%A8%D8%A7%D8%B7" title="ارتباط – urdština" lang="ur" hreflang="ur" data-title="ارتباط" data-language-autonym="اردو" data-language-local-name="urdština" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%E1%BB%87_s%E1%BB%91_t%C6%B0%C6%A1ng_quan" title="Hệ số tương quan – vietnamština" lang="vi" hreflang="vi" data-title="Hệ số tương quan" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamština" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%9B%B8%E5%85%B3" title="相关 – čínština (dialekty Wu)" lang="wuu" hreflang="wuu" data-title="相关" data-language-autonym="吴语" data-language-local-name="čínština (dialekty Wu)" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%9B%B8%E5%85%B3_(%E6%A6%82%E7%8E%87%E8%AE%BA)" title="相关 (概率论) – čínština" lang="zh" hreflang="zh" data-title="相关 (概率论)" data-language-autonym="中文" data-language-local-name="čínština" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%B5%B1%E8%A8%88%E7%9B%B8%E9%97%9C" title="統計相關 – kantonština" lang="yue" hreflang="yue" data-title="統計相關" data-language-autonym="粵語" data-language-local-name="kantonština" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q186290#sitelinks-wikipedia" title="Editovat mezijazykové odkazy" class="wbc-editpage">Upravit odkazy</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Jmenné prostory"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Korelace" title="Zobrazit obsahovou stránku [c]" accesskey="c"><span>Článek</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Diskuse:Korelace" rel="discussion" title="Diskuse ke stránce [t]" accesskey="t"><span>Diskuse</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Změnit variantu jazyka" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">čeština</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Zobrazení"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Korelace"><span>Číst</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Korelace&veaction=edit" title="Editovat tuto stránku [v]" accesskey="v"><span>Editovat</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Korelace&action=edit" title="Editovat zdrojový kód této stránky [e]" accesskey="e"><span>Editovat zdroj</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Korelace&action=history" title="Starší verze této stránky. [h]" accesskey="h"><span>Zobrazit historii</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Nástroje ke stránce"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Nástroje" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Nástroje</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Nástroje</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skrýt</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Další možnosti" > <div class="vector-menu-heading"> Akce </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Korelace"><span>Číst</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Korelace&veaction=edit" title="Editovat tuto stránku [v]" accesskey="v"><span>Editovat</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Korelace&action=edit" title="Editovat zdrojový kód této stránky [e]" accesskey="e"><span>Editovat zdroj</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Korelace&action=history"><span>Zobrazit historii</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Obecné </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Co_odkazuje_na/Korelace" title="Seznam všech wikistránek, které sem odkazují [j]" accesskey="j"><span>Odkazuje sem</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Souvisej%C3%ADc%C3%AD_zm%C4%9Bny/Korelace" rel="nofollow" title="Nedávné změny stránek, na které je odkazováno [k]" accesskey="k"><span>Související změny</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=cs" title="Nahrát obrázky či jiná multimédia [u]" accesskey="u"><span>Načíst soubor</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Speci%C3%A1ln%C3%AD_str%C3%A1nky" title="Seznam všech speciálních stránek [q]" accesskey="q"><span>Speciální stránky</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Korelace&oldid=23480683" title="Trvalý odkaz na současnou verzi této stránky"><span>Trvalý odkaz</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Korelace&action=info" title="Více informací o této stránce"><span>Informace o stránce</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:Citovat&page=Korelace&id=23480683&wpFormIdentifier=titleform" title="Informace o tom, jak citovat tuto stránku"><span>Citovat stránku</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:UrlShortener&url=https%3A%2F%2Fcs.wikipedia.org%2Fw%2Findex.php%3Ftitle%3DKorelace%26oldid%3D23480683"><span>Získat zkrácené URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:QrCode&url=https%3A%2F%2Fcs.wikipedia.org%2Fw%2Findex.php%3Ftitle%3DKorelace%26oldid%3D23480683"><span>Stáhnout QR kód</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Tisk/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:Kniha&bookcmd=book_creator&referer=Korelace"><span>Vytvořit knihu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:DownloadAsPdf&page=Korelace&action=show-download-screen"><span>Stáhnout jako PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Korelace&printable=yes" title="Tato stránka v podobě vhodné k tisku [p]" accesskey="p"><span>Verze k tisku</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Na jiných projektech </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li 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Pokud se jedna z <a href="/wiki/N%C3%A1hodn%C3%A1_veli%C4%8Dina" title="Náhodná veličina">náhodných veličin</a> mění, mění se i druhá a naopak. Pokud se mezi dvěma náhodnými procesy identifikuje korelace, je pravděpodobné, že na sobě závisejí. Z korelovanosti náhodných procesů nebo náhodných veličin však nelze usuzovat na příčinný vztah. Tedy jeden z nich nemusí být <a href="/wiki/Kauzalita" title="Kauzalita">příčinou</a> a druhý <a href="/wiki/N%C3%A1sledek" class="mw-redirect" title="Následek">následkem</a>. Toto samotná korelace nedovoluje rozhodnout, jelikož <a href="/wiki/Korelace_neimplikuje_kauzalitu" title="Korelace neimplikuje kauzalitu">korelace neimplikuje kauzalitu</a> a ani směr kauzality.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Nejmenovaný-20231103185542_2-0" class="reference"><a href="#cite_note-Nejmenovaný-20231103185542-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Ve <a href="/wiki/Statistika" title="Statistika">statistice</a> se pojem korelace užívá pro vyjádření lineárního vztahu mezi náhodnými veličinami <i>X</i> a <i>Y</i>. Sílu korelace pak vyjadřuje korelační koeficient, který nabývá hodnoty −1 až +1.<sup id="cite_ref-Nejmenovaný-20231103185542_2-1" class="reference"><a href="#cite_note-Nejmenovaný-20231103185542-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Nejmenovaný_2-20231103185542_3-0" class="reference"><a href="#cite_note-Nejmenovaný_2-20231103185542-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Korelace_ve_statistice">Korelace ve statistice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Korelace&veaction=edit&section=1" title="Editace sekce: Korelace ve statistice" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Korelace&action=edit&section=1" title="Editovat zdrojový kód sekce Korelace ve statistice"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Soubor:Correlation_examples2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Correlation_examples2.svg/460px-Correlation_examples2.svg.png" decoding="async" width="460" height="210" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Correlation_examples2.svg/690px-Correlation_examples2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Correlation_examples2.svg/920px-Correlation_examples2.svg.png 2x" data-file-width="506" data-file-height="231" /></a><figcaption>Na obrázku je několik příkladů grafického zobrazení dat a koeficienty jejich korelace s funkcí y = x</figcaption></figure> <p>Vztah mezi znaky či náhodnými veličinami <i>X</i> a <i>Y</i> může být kladný, pokud (přibližně) platí <i>Y</i> = <i>kX</i>, nebo záporný (<i>Y</i> = -<i>kX</i>). Hodnota korelačního koeficientu −1 značí zcela nepřímou závislost (antikorelaci), tedy čím více se zvětší hodnoty v první skupině znaků, tím více se zmenší hodnoty v druhé skupině znaků, např. vztah mezi uplynulým a zbývajícím časem. Hodnota korelačního koeficientu +1 značí zcela přímou závislost, např. vztah mezi rychlostí bicyklu a frekvencí otáček kola bicyklu. Pokud je korelační koeficient roven 0 (nekorelovanost), pak mezi znaky není žádná statisticky zjistitelná lineární závislost. Je dobré si uvědomit, že i při nulovém korelačním koeficientu na sobě veličiny mohou záviset, pouze tento vztah nelze vyjádřit <a href="/wiki/Line%C3%A1rn%C3%AD_funkce" title="Lineární funkce">lineární funkcí</a> (např.<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y=X^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> <mo>=</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y=X^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/164fd6721c56072e02ca8627ae6c18b1efa64e71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.923ex; height:2.676ex;" alt="{\displaystyle Y=X^{2}}"></span> ), a to ani přibližně.<sup id="cite_ref-Nejmenovaný-20231103185542_2-2" class="reference"><a href="#cite_note-Nejmenovaný-20231103185542-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Nejmenovaný_2-20231103185542_3-1" class="reference"><a href="#cite_note-Nejmenovaný_2-20231103185542-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Pearsonův_korelační_koeficient"><span id="Pearson.C5.AFv_korela.C4.8Dn.C3.AD_koeficient"></span>Pearsonův korelační koeficient</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Korelace&veaction=edit&section=2" title="Editace sekce: Pearsonův korelační koeficient" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Korelace&action=edit&section=2" title="Editovat zdrojový kód sekce Pearsonův korelační koeficient"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pearsonův korelační koeficient je definován, pokud jsou druhé mocniny náhodných veličin X a Y <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E(X^{2}),E(Y^{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>,</mo> <mi>E</mi> <mo stretchy="false">(</mo> <msup> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(X^{2}),E(Y^{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2521ee08cd83bd4a8c887203a5f9769ca2eae96b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.209ex; height:3.176ex;" alt="{\displaystyle E(X^{2}),E(Y^{2})}"></span> konečné a jejich rozptyly nenulové. Vypočte se normováním <a href="/wiki/Kovariance" title="Kovariance">kovariance</a> tak, že ji podělíme směrodatnými odchylkami obou proměnných na bezrozměrné číslo nabývající hodnoty -1 až 1: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{X,Y}={\mathrm {cov} (X,Y) \over \sigma _{X}\sigma _{Y}}={E((X-\mu _{X})(Y-\mu _{Y})) \over \sigma _{X}\sigma _{Y}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">v</mi> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>E</mi> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo>−</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>Y</mi> <mo>−</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mrow> <mrow> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{X,Y}={\mathrm {cov} (X,Y) \over \sigma _{X}\sigma _{Y}}={E((X-\mu _{X})(Y-\mu _{Y})) \over \sigma _{X}\sigma _{Y}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb39f772010b8f3b6afe345bb0af63c855a4a541" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:44.993ex; height:6.009ex;" alt="{\displaystyle \rho _{X,Y}={\mathrm {cov} (X,Y) \over \sigma _{X}\sigma _{Y}}={E((X-\mu _{X})(Y-\mu _{Y})) \over \sigma _{X}\sigma _{Y}}}"></span></dd></dl> <p>Jelikož <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{X}=E(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo>=</mo> <mi>E</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{X}=E(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d889bd192ef195a3c839037a434d934de150759" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.697ex; height:2.843ex;" alt="{\displaystyle \mu _{X}=E(X)}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{X}^{2}=E(X^{2})-E^{2}(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <mi>E</mi> <mo stretchy="false">(</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>−</mo> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{X}^{2}=E(X^{2})-E^{2}(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ffb8a72219cb6a07e2e0dc29fa73042e0fa31df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:22.172ex; height:3.343ex;" alt="{\displaystyle \sigma _{X}^{2}=E(X^{2})-E^{2}(X)}"></span> a obdobně pro <i>Y</i>, lze výše uvedený vzorec upravit do přehlednějšího výpočetního tvaru: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{X,Y}={\frac {E(XY)-E(X)E(Y)}{{\sqrt {E(X^{2})-E^{2}(X)}}~{\sqrt {E(Y^{2})-E^{2}(Y)}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>E</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mi>Y</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>E</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mi>E</mi> <mo stretchy="false">(</mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>E</mi> <mo stretchy="false">(</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>−</mo> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>E</mi> <mo stretchy="false">(</mo> <msup> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>−</mo> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>Y</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{X,Y}={\frac {E(XY)-E(X)E(Y)}{{\sqrt {E(X^{2})-E^{2}(X)}}~{\sqrt {E(Y^{2})-E^{2}(Y)}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c22fc0fe0e7b664eb276a03bdd0cfb3961b3b4b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:45.633ex; height:7.009ex;" alt="{\displaystyle \rho _{X,Y}={\frac {E(XY)-E(X)E(Y)}{{\sqrt {E(X^{2})-E^{2}(X)}}~{\sqrt {E(Y^{2})-E^{2}(Y)}}}}}"></span></dd></dl> <p>Korelační koeficient nabývá hodnot z intervalu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle -1,1\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle -1,1\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb50d4b38df26b6a48739505de6a68e3a9747ae9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.976ex; height:2.843ex;" alt="{\displaystyle \langle -1,1\rangle }"></span>. Při nezávislosti náhodných veličin <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span> je korelační koeficient roven 0. Nulový korelační koeficient však neznamená, že jsou náhodné veličiny <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span> nezávislé. Nulový korelační koeficient má například dvojice náhodných veličin <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y=X^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> <mo>=</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y=X^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/164fd6721c56072e02ca8627ae6c18b1efa64e71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.923ex; height:2.676ex;" alt="{\displaystyle Y=X^{2}}"></span>. </p><p>Tuto míru asociace jako první odvodil anglický psycholog a antropolog sir <a href="/wiki/Francis_Galton" title="Francis Galton">Francis Galton</a>. </p><p>Existují nicméně i jiné koeficienty asociace, například <a href="/wiki/Spearman%C5%AFv_koeficient_po%C5%99adov%C3%A9_korelace" title="Spearmanův koeficient pořadové korelace">Spearmanovo rhó</a> či <a href="/wiki/Kendall%C5%AFv_test" title="Kendallův test">Kendallovo tau</a> pro <a href="/wiki/Ordin%C3%A1ln%C3%AD_%C4%8D%C3%ADslo" title="Ordinální číslo">ordinální</a> (pořadová) data. </p> <div class="mw-heading mw-heading2"><h2 id="Korelace_v_teorii_signálů"><span id="Korelace_v_teorii_sign.C3.A1l.C5.AF"></span>Korelace v teorii signálů</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Korelace&veaction=edit&section=3" title="Editace sekce: Korelace v teorii signálů" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Korelace&action=edit&section=3" title="Editovat zdrojový kód sekce Korelace v teorii signálů"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><div class="uvodni-upozorneni hatnote">Související informace naleznete také v článku <a href="/wiki/Korelace_(zpracov%C3%A1n%C3%AD_sign%C3%A1lu)" title="Korelace (zpracování signálu)">korelace (zpracování signálu)</a>.</div></dd></dl> <p>Zkrácený výraz pro <a href="/w/index.php?title=Korela%C4%8Dn%C3%AD_funkce&action=edit&redlink=1" class="new" title="Korelační funkce (stránka neexistuje)">korelační funkci</a>. </p><p>Pro spojité signály <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bf044fe2fbfc4bd8d6d7230f4108430263f9fd6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.927ex; height:2.843ex;" alt="{\displaystyle f(t)}"></span> a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b84f700860ee7af27797d11ddfad3d185eb7af0e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.765ex; height:2.843ex;" alt="{\displaystyle g(t)}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (f\star g)(t)\ {\stackrel {\mathrm {def} }{=}}\int _{-\infty }^{\infty }f^{*}(\tau )\cdot g(t+\tau )\,{\rm {d}}\tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>f</mi> <mo>⋆</mo> <mi>g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo>=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </mover> </mrow> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo stretchy="false">(</mo> <mi>τ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo>+</mo> <mi>τ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (f\star g)(t)\ {\stackrel {\mathrm {def} }{=}}\int _{-\infty }^{\infty }f^{*}(\tau )\cdot g(t+\tau )\,{\rm {d}}\tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0374e6dde07d85472d1382686e8e7775361595cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:34.858ex; height:6.009ex;" alt="{\displaystyle (f\star g)(t)\ {\stackrel {\mathrm {def} }{=}}\int _{-\infty }^{\infty }f^{*}(\tau )\cdot g(t+\tau )\,{\rm {d}}\tau }"></span></dd></dl> <p>Pro diskrétní signály <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a585492f646ca803bc408103a0c705dd67ab8b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.228ex; height:2.509ex;" alt="{\displaystyle f_{k}}"></span> a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de363eb168fab5e16a5acc74d8b0288e07a23aca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.198ex; height:2.009ex;" alt="{\displaystyle g_{k}}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (f\star g)_{k}\ {\stackrel {\mathrm {def} }{=}}\sum _{i=-\infty }^{\infty }f_{i}^{*}\ g_{k+i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>f</mi> <mo>⋆</mo> <mi>g</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo>=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </mover> </mrow> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <msubsup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mtext> </mtext> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>+</mo> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (f\star g)_{k}\ {\stackrel {\mathrm {def} }{=}}\sum _{i=-\infty }^{\infty }f_{i}^{*}\ g_{k+i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bb1d086544f5b4cc8b4a898fb1d6f76fe15882f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:22.865ex; height:7.009ex;" alt="{\displaystyle (f\star g)_{k}\ {\stackrel {\mathrm {def} }{=}}\sum _{i=-\infty }^{\infty }f_{i}^{*}\ g_{k+i}}"></span></dd></dl> <p>U komplexních signálů <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/190a73fde235865b8d2a783334f90194331c7f19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.375ex; height:2.676ex;" alt="{\displaystyle f^{*}}"></span> představuje <a href="/wiki/Komplexn%C4%9B_sdru%C5%BEen%C3%A9_%C4%8D%C3%ADslo" title="Komplexně sdružené číslo">komplexně sdružené číslo</a> k <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span>. </p><p>Velmi se podobá <a href="/wiki/Konvoluce" title="Konvoluce">konvoluci</a>. Rozdíl je hlavně v časovém překlopení druhé funkce <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.116ex; height:2.009ex;" alt="{\displaystyle g}"></span>. </p><p><b>Autokorelací</b> se rozumí korelace <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (f\star f)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>f</mi> <mo>⋆</mo> <mi>f</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (f\star f)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb58ec18cc099e266c5ffabcea0f73f28b33d308" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.561ex; height:2.843ex;" alt="{\displaystyle (f\star f)}"></span>. Lze tak určit tzv. soběpodobnost signálu, tedy zda se např. signál v určitých periodách opakuje. </p> <div class="mw-heading mw-heading2"><h2 id="Související_články"><span id="Souvisej.C3.ADc.C3.AD_.C4.8Dl.C3.A1nky"></span>Související články</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Korelace&veaction=edit&section=4" title="Editace sekce: Související články" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Korelace&action=edit&section=4" title="Editovat zdrojový kód sekce Související články"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Charakteristika_n%C3%A1hodn%C3%A9_veli%C4%8Diny" title="Charakteristika náhodné veličiny">Charakteristika náhodné veličiny</a></li> <li><a href="/wiki/Korelace_neimplikuje_kauzalitu" title="Korelace neimplikuje kauzalitu">Korelace neimplikuje kauzalitu</a></li> <li><a href="/wiki/Spearman%C5%AFv_koeficient_po%C5%99adov%C3%A9_korelace" title="Spearmanův koeficient pořadové korelace">Spearmanův koeficient pořadové korelace</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Externí_odkazy"><span id="Extern.C3.AD_odkazy"></span>Externí odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Korelace&veaction=edit&section=5" title="Editace sekce: Externí odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Korelace&action=edit&section=5" title="Editovat zdrojový kód sekce Externí odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="wd"><span class="sisterproject sisterproject-commons"><span class="sisterproject_image"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons"><img alt="Logo Wikimedia Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></span> <span class="sisterproject_text">Obrázky, zvuky či videa k tématu <span class="sisterproject_text_target"><a href="https://commons.wikimedia.org/wiki/Category:Correlation" class="extiw" title="c:Category:Correlation">korelace</a></span> na <a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a></span></span></span><i> </i></li></ul> <table class="plainlinks metadata noprint pahyl" cellpadding="2" style="background: transparent;"> <tbody><tr> <td><figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/Soubor:Wiki_letter_w.svg" class="mw-file-description" title="Pahýl"><img alt="Pahýl" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/40px-Wiki_letter_w.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/60px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/80px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a><figcaption>Pahýl</figcaption></figure> </td> <td><i>Tento článek je příliš stručný nebo <a href="/wiki/Wikipedie:Pah%C3%BDl" title="Wikipedie:Pahýl">postrádá důležité informace</a>.<br />Pomozte Wikipedii tím, že jej vhodně <a class="external text" href="https://cs.wikipedia.org/w/index.php?title=Korelace&action=edit">rozšíříte</a>. Nevkládejte však <a href="/wiki/Wikipedie:Autorsk%C3%A9_pr%C3%A1vo#Publikování_cizích_autorských_děl" title="Wikipedie:Autorské právo">bez oprávnění</a> cizí texty.</i> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Reference">Reference</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Korelace&veaction=edit&section=6" title="Editace sekce: Reference" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Korelace&action=edit&section=6" title="Editovat zdrojový kód sekce Reference"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><cite class="book" style="font-style:normal;"> <i>13 - Korelace (MAT - Statistika)</i>. [s.l.]: [s.n.] <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=CLXb-4nYLeQ">Dostupné online</a>.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/cs.wikipedia.org:templatecitacemonografie&rft.btitle=13+-+Korelace+%28MAT+-+Statistika%29&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DCLXb-4nYLeQ"><span style="display:none"> </span></span></span> </li> <li id="cite_note-Nejmenovaný-20231103185542-2"><span class="mw-cite-backlink">↑ <a href="#cite_ref-Nejmenovaný-20231103185542_2-0"><sup style="font-style: italic; font-weight: bold; vertical-align: top">a</sup></a> <a href="#cite_ref-Nejmenovaný-20231103185542_2-1"><sup style="font-style: italic; font-weight: bold; vertical-align: top">b</sup></a> <a href="#cite_ref-Nejmenovaný-20231103185542_2-2"><sup style="font-style: italic; font-weight: bold; vertical-align: top">c</sup></a></span> <span class="reference-text"><cite class="book" style="font-style:normal;"> <i>Co je to korelace a kauzalita? - Vědecké kladivo AK 14</i>. [s.l.]: [s.n.] <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=mo33sE9v9h8">Dostupné online</a>.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/cs.wikipedia.org:templatecitacemonografie&rft.btitle=Co+je+to+korelace+a+kauzalita%3F+-+V%C4%9Bdeck%C3%A9+kladivo+AK+14&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3Dmo33sE9v9h8"><span style="display:none"> </span></span></span> </li> <li id="cite_note-Nejmenovaný_2-20231103185542-3"><span class="mw-cite-backlink">↑ <a href="#cite_ref-Nejmenovaný_2-20231103185542_3-0"><sup style="font-style: italic; font-weight: bold; vertical-align: top">a</sup></a> <a href="#cite_ref-Nejmenovaný_2-20231103185542_3-1"><sup style="font-style: italic; font-weight: bold; vertical-align: top">b</sup></a></span> <span class="reference-text"><cite class="book" style="font-style:normal;"> <i>Korelace – co to je korelace a co znamená korelační koeficient</i> [online]. 2021-01-03 [cit. 2023-06-09]. <a rel="nofollow" class="external text" href="https://exceltown.com/navody/pokrocila-analyza-regrese-korelace/korelace-co-to-vlastne-je/">Dostupné online</a>.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/cs.wikipedia.org:templatecitaceelmonografie&rft.btitle=Korelace+%E2%80%93+co+to+je+korelace+a+co+znamen%C3%A1+korela%C4%8Dn%C3%AD+koeficient&rft_id=https%3A%2F%2Fexceltown.com%2Fnavody%2Fpokrocila-analyza-regrese-korelace%2Fkorelace-co-to-vlastne-je%2F"><span style="display:none"> </span></span></span> </li> </ol></div> <style data-mw-deduplicate="TemplateStyles:r23078045">.mw-parser-output .navbox2{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox2 .navbox2{margin-top:0}.mw-parser-output .navbox2+.navbox2{margin-top:-1px}.mw-parser-output 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class="printfooter" data-nosnippet="">Citováno z „<a dir="ltr" href="https://cs.wikipedia.org/w/index.php?title=Korelace&oldid=23480683">https://cs.wikipedia.org/w/index.php?title=Korelace&oldid=23480683</a>“</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/N%C3%A1pov%C4%9Bda:Kategorie" title="Nápověda:Kategorie">Kategorie</a>: <ul><li><a href="/wiki/Kategorie:Statistika" title="Kategorie:Statistika">Statistika</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Skryté kategorie: <ul><li><a href="/wiki/Kategorie:%C3%9Adr%C5%BEba:%C4%8Cl%C3%A1nky_k_ov%C4%9B%C5%99en%C3%AD" title="Kategorie:Údržba:Články k ověření">Údržba:Články k ověření</a></li><li><a href="/wiki/Kategorie:Pah%C3%BDly" title="Kategorie:Pahýly">Pahýly</a></li><li><a href="/wiki/Kategorie:Monitoring:%C4%8Cl%C3%A1nky_s_identifik%C3%A1torem_BNF" title="Kategorie:Monitoring:Články s identifikátorem BNF">Monitoring:Články s identifikátorem BNF</a></li><li><a href="/wiki/Kategorie:Monitoring:%C4%8Cl%C3%A1nky_s_identifik%C3%A1torem_GND" title="Kategorie:Monitoring:Články s identifikátorem GND">Monitoring:Články s identifikátorem GND</a></li><li><a href="/wiki/Kategorie:Monitoring:%C4%8Cl%C3%A1nky_s_identifik%C3%A1torem_LCCN" title="Kategorie:Monitoring:Články s identifikátorem LCCN">Monitoring:Články s identifikátorem LCCN</a></li><li><a href="/wiki/Kategorie:Monitoring:%C4%8Cl%C3%A1nky_s_identifik%C3%A1torem_NLI" title="Kategorie:Monitoring:Články s identifikátorem NLI">Monitoring:Články s identifikátorem NLI</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Stránka byla naposledy editována 20. 12. 2023 v 08:38.</li> <li id="footer-info-copyright">Text je dostupný pod <a rel="nofollow" class="external text" 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