{"id":15149,"date":"2024-01-09T03:22:25","date_gmt":"2024-01-08T23:52:25","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7\/"},"modified":"2024-01-09T03:22:25","modified_gmt":"2024-01-08T23:52:25","slug":"%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7","status":"publish","type":"post","link":"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7\/","title":{"rendered":"\u0645\u062d\u0627\u0633\u0628\u0647 \u0636\u0631\u06cc\u0628 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>\u0645\u0639\u0631\u0641\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7\/#%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d8%b1%d8%aa%d8%a8%d9%87_%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86_%da%86%db%8c%d8%b3%d8%aa%d8%9f\" >\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0686\u06cc\u0633\u062a\u061f<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7\/#%d8%aa%d9%88%d8%a7%d8%a8%d8%b9_%db%8c%da%a9%d9%86%d9%88%d8%a7%d8%ae%d8%aa\" >\u062a\u0648\u0627\u0628\u0639 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7\/#%d8%a8%db%8c%d8%a7%d9%86_%d8%b1%db%8c%d8%a7%d8%b6%db%8c\" >\u0628\u06cc\u0627\u0646 \u0631\u06cc\u0627\u0636\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7\/#%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d8%a7%d8%aa_%d9%85%d8%ab%d8%a7%d9%84\" >\u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u062b\u0627\u0644<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7\/#%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87_%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d8%b1%d8%aa%d8%a8%d9%87_%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86_%d8%a8%d8%a7_%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_%d9%be%d8%a7%d9%86%d8%af%d8%a7%d9%87%d8%a7\" >\u0645\u062d\u0627\u0633\u0628\u0647 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u067e\u0627\u0646\u062f\u0627\u0647\u0627<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7\/#%d8%aa%d8%ac%d8%b3%d9%85_%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c\" >\u062a\u062c\u0633\u0645 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7\/#%d8%af%d8%b1%da%a9_%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86_%d8%b1%d9%88%db%8c_%d9%86%d9%85%d9%88%d9%86%d9%87_%d9%87%d8%a7%db%8c_%d9%85%d8%b5%d9%86%d9%88%d8%b9%db%8c\" >\u062f\u0631\u06a9 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0631\u0648\u06cc \u0646\u0645\u0648\u0646\u0647 \u0647\u0627\u06cc \u0645\u0635\u0646\u0648\u0639\u06cc<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7\/#%d8%aa%d9%88%d8%a7%d8%a8%d8%b9_%d8%a7%d9%81%d8%b2%d8%a7%db%8c%d8%b4_%d8%af%d9%87%d9%86%d8%af%d9%87_%db%8c%da%a9%d9%86%d9%88%d8%a7%d8%ae%d8%aa\" >\u062a\u0648\u0627\u0628\u0639 \u0627\u0641\u0632\u0627\u06cc\u0634 \u062f\u0647\u0646\u062f\u0647 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7\/#%d8%aa%d9%88%d8%a7%d8%a8%d8%b9_%da%a9%d8%a7%d9%87%d8%b4%db%8c_%db%8c%da%a9%d9%86%d9%88%d8%a7%d8%ae%d8%aa\" >\u062a\u0648\u0627\u0628\u0639 \u06a9\u0627\u0647\u0634\u06cc \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7\/#%d8%aa%d9%88%d8%a7%d8%a8%d8%b9_%d8%ba%db%8c%d8%b1_%db%8c%da%a9%d9%86%d9%88%d8%a7%d8%ae%d8%aa\" >\u062a\u0648\u0627\u0628\u0639 \u063a\u06cc\u0631 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7\/#%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86_%d8%b1%d9%88%db%8c_%d9%84%db%8c%d9%86%d8%b1%d9%88%d8%af_%d9%85%d8%ac%d9%85%d9%88%d8%b9%d9%87_%d8%af%d8%a7%d8%af%d9%87\" >\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0631\u0648\u06cc \u0644\u06cc\u0646\u0631\u0648\u062f \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/rasanegaar.com\/blog\/%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87-%d8%b6%d8%b1%db%8c%d8%a8-%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c-%d8%b1%d8%aa%d8%a8%d9%87-%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86-%d8%af%d8%b1-%d9%be%d8%a7\/#%d9%86%d8%aa%db%8c%d8%ac%d9%87_%da%af%db%8c%d8%b1%db%8c\" >\u0646\u062a\u06cc\u062c\u0647 \u06af\u06cc\u0631\u06cc<\/a><\/li><\/ul><\/nav><\/div>\n<span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 8<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span><p> <br \/>\n<\/p>\n<div><noscript><\/noscript><\/p>\n<h2 id=\"introduction\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%b9%d8%b1%d9%81%db%8c\"><\/span>\u0645\u0639\u0631\u0641\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0627\u06cc\u0646 \u0631\u0627\u0647\u0646\u0645\u0627 \u0645\u0642\u062f\u0645\u0647 \u0627\u06cc \u0627\u0633\u062a \u0628\u0631\u0627\u06cc <strong>\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646<\/strong>\u060c \u0645\u062d\u0627\u0633\u0628\u0647 \u0631\u06cc\u0627\u0636\u06cc \u0622\u0646 \u0648 \u0645\u062d\u0627\u0633\u0628\u0647 \u0622\u0646 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u067e\u0627\u06cc\u062a\u0648\u0646 <code>pandas<\/code> \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647  \u0645\u0627 \u0645\u062b\u0627\u0644\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u0645\u06cc\u200c\u0633\u0627\u0632\u06cc\u0645 \u062a\u0627 \u062f\u0631\u06a9 \u0627\u0633\u0627\u0633\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0636\u0631\u06cc\u0628 \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645 \u0648 \u0631\u0648\u0634 \u062a\u062c\u0633\u0645 \u0622\u0646 \u0631\u0627 \u0646\u0634\u0627\u0646 \u062f\u0647\u06cc\u0645 <strong>\u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc<\/strong> \u0627\u0632 \u0637\u0631\u06cc\u0642 <strong>\u0646\u0642\u0634\u0647 \u0647\u0627\u06cc \u062d\u0631\u0627\u0631\u062a\u06cc<\/strong>.<\/p>\n<h2 id=\"whatisthespearmanrankcorrelationcoefficient\"><span class=\"ez-toc-section\" id=\"%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d8%b1%d8%aa%d8%a8%d9%87_%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86_%da%86%db%8c%d8%b3%d8%aa%d8%9f\"><\/span>\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0686\u06cc\u0633\u062a\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646<\/strong> \u0627\u0631\u062a\u0628\u0627\u0637 \u0646\u0632\u062f\u06cc\u06a9\u06cc \u0628\u0627 <strong>\u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646<\/strong>\u060c \u0648 \u0647\u0631 \u062f\u0648 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 \u0645\u062d\u062f\u0648\u062f \u0647\u0633\u062a\u0646\u062f\u060c \u0627\u0632 <code>-1<\/code> \u0628\u0647 <code>1<\/code> \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 a <strong>\u0647\u0645\u0628\u0633\u062a\u06af\u06cc<\/strong> \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631<\/p>\n<blockquote>\n<p>\u0627\u06af\u0631 \u0645\u0627\u06cc\u0644\u06cc\u062f \u062f\u0631 \u0645\u0648\u0631\u062f \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0628\u06cc\u0634\u062a\u0631 \u0628\u062e\u0648\u0627\u0646\u06cc\u062f &#8211; \u0631\u0627\u0647\u0646\u0645\u0627\u06cc \u0645\u0627 \u0628\u0631\u0627\u06cc \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0631\u0627 \u0628\u062e\u0648\u0627\u0646\u06cc\u062f.<\/p>\n<\/blockquote>\n<p>\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u0642\u0627\u062f\u06cc\u0631 \u062f\u0627\u062f\u0647 \u062e\u0627\u0645 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u0634\u0648\u062f\u060c \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0627\u0632 <em>\u0631\u062a\u0628\u0647 \u0647\u0627<\/em> \u0627\u0632 \u0627\u0631\u0632\u0634 \u0647\u0627\u06cc \u0641\u0631\u062f\u06cc  \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0645\u0639\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0631\u0627\u0628\u0637\u0647 \u062e\u0637\u06cc \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0627\u0633\u062a\u060c \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0631\u0627\u0628\u0637\u0647 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u0628\u06cc\u0646 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u0631\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0645\u06cc \u06a9\u0646\u062f. <em>\u062c\u0641\u062a \u0645\u062a\u063a\u06cc\u0631<\/em>.  \u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646\u060c \u0645\u0627 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u062f\u0631\u06a9 \u0627\u0633\u0627\u0633\u06cc \u062f\u0627\u0631\u06cc\u0645 <strong>\u062a\u0648\u0627\u0628\u0639 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a<\/strong>.<\/p>\n<h3 id=\"monotonicfunctions\"><span class=\"ez-toc-section\" id=\"%d8%aa%d9%88%d8%a7%d8%a8%d8%b9_%db%8c%da%a9%d9%86%d9%88%d8%a7%d8%ae%d8%aa\"><\/span>\u062a\u0648\u0627\u0628\u0639 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<blockquote>\n<p>\u062a\u0648\u0627\u0628\u0639 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u0627\u0641\u0632\u0627\u06cc\u0634\u06cc\u060c \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u06a9\u0627\u0647\u0634\u06cc \u0648 \u063a\u06cc\u0631 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f.<\/p>\n<\/blockquote>\n<p>\u0628\u0631\u0627\u06cc \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0627\u0641\u0632\u0627\u06cc\u0634 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a\u060c \u0628\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 X\u060c Y \u0646\u06cc\u0632 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f (\u0648 \u0644\u0627\u0632\u0645 \u0646\u06cc\u0633\u062a \u062e\u0637\u06cc \u0628\u0627\u0634\u062f).  \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0646\u0632\u0648\u0644\u06cc \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a\u060c \u0628\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631\u060c \u0645\u062a\u063a\u06cc\u0631 \u062f\u06cc\u06af\u0631 \u06a9\u0627\u0647\u0634 \u0645\u06cc \u06cc\u0627\u0628\u062f (\u0647\u0645\u0686\u0646\u06cc\u0646 \u0644\u0627\u0632\u0645 \u0646\u06cc\u0633\u062a \u062e\u0637\u06cc \u0628\u0627\u0634\u062f).  \u062a\u0627\u0628\u0639 \u063a\u06cc\u0631 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u062c\u0627\u06cc\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u0642\u062f\u0627\u0631 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u06af\u0627\u0647\u06cc \u0645\u0646\u062c\u0631 \u0628\u0647 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0648 \u06af\u0627\u0647\u06cc \u0628\u0647 \u06a9\u0627\u0647\u0634 \u0645\u0642\u062f\u0627\u0631 \u0645\u062a\u063a\u06cc\u0631 \u062f\u06cc\u06af\u0631 \u0634\u0648\u062f.<\/p>\n<p>\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0645\u06cc \u0634\u0648\u062f <strong>\u0631\u0627\u0628\u0637\u0647 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631<\/strong>.  \u0645\u0642\u0627\u062f\u06cc\u0631 \u0622\u0646 \u0627\u0632 -1 \u062a\u0627 +1 \u0645\u062a\u063a\u06cc\u0631 \u0627\u0633\u062a \u0648 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062a\u0641\u0633\u06cc\u0631 \u06a9\u0631\u062f:<\/p>\n<ul>\n<li><strong>+1:<\/strong> \u0631\u0627\u0628\u0637\u0647 \u06a9\u0627\u0645\u0644\u0627\u064b \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u062f\u0631 \u062d\u0627\u0644 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0627\u0633\u062a<\/li>\n<li><strong>+0.8:<\/strong> \u0631\u0627\u0628\u0637\u0647 \u0642\u0648\u06cc \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u062f\u0631 \u062d\u0627\u0644 \u0627\u0641\u0632\u0627\u06cc\u0634<\/li>\n<li><strong>+0.2:<\/strong> \u0631\u0627\u0628\u0637\u0647 \u0636\u0639\u06cc\u0641 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u062f\u0631 \u062d\u0627\u0644 \u0627\u0641\u0632\u0627\u06cc\u0634<\/li>\n<li><strong>0:<\/strong> \u0631\u0627\u0628\u0637\u0647 \u063a\u06cc\u0631 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a<\/li>\n<li><strong>-0.2:<\/strong> \u0631\u0627\u0628\u0637\u0647 \u0636\u0639\u06cc\u0641 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u062f\u0631 \u062d\u0627\u0644 \u06a9\u0627\u0647\u0634<\/li>\n<li><strong>-0.8:<\/strong> \u0631\u0627\u0628\u0637\u0647 \u0642\u0648\u06cc \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u062f\u0631 \u062d\u0627\u0644 \u06a9\u0627\u0647\u0634<\/li>\n<li><strong>-1:<\/strong> \u0631\u0627\u0628\u0637\u0647 \u06a9\u0627\u0645\u0644\u0627\u064b \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u062f\u0631 \u062d\u0627\u0644 \u06a9\u0627\u0647\u0634 \u0627\u0633\u062a<\/li>\n<\/ul>\n<h3 id=\"mathematicalexpression\"><span class=\"ez-toc-section\" id=\"%d8%a8%db%8c%d8%a7%d9%86_%d8%b1%db%8c%d8%a7%d8%b6%db%8c\"><\/span>\u0628\u06cc\u0627\u0646 \u0631\u06cc\u0627\u0636\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0645\u0634\u0627\u0647\u062f\u0647 \\(n\\) \u0627\u0632 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u062a\u0635\u0627\u062f\u0641\u06cc \\(X\\) \u0648 \\(Y\\) \u062f\u0627\u0631\u06cc\u0645.  \u0627\u0628\u062a\u062f\u0627 \u062a\u0645\u0627\u0645 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0647\u0631 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0631\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \\(X_r\\) \u0648 \\(Y_r\\) \u0631\u062a\u0628\u0647 \u0628\u0646\u062f\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0628\u0627 \\(r_s\\) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f \u0648 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u0634\u0648\u062f:<\/p>\n<p>$$<br \/>r_s = \\rho_{X_r,Y_r} = \\frac{\\text{COV}(X_r,Y_r)}{\\text{STD}(X_r)\\text{STD}(Y_r)} = \\frac{n\\sum\\ limits_{x_r\\in X_r, y_r \\in Y_r} x_r y_r &#8211; \\sum\\limits_{x_r\\in X_r}x_r\\sum\\limits_{y_r\\in Y_r}y_r}{\\sqrt{\\Big(n\\sum\\limits_ {x_r \\in X_r} x_r^2 -(\\sum\\limits_{x_r\\in X_r}x_r)^2\\Big)}\\sqrt{\\Big(n\\sum\\limits_{y_r \\in Y_r} y_r^2 &#8211; (\\sum\\limits_{y_r\\in Y_r}y_r)^2 \\Big)}}<br \/>$$<\/p>\n<p>\u0627\u06cc\u0646\u062c\u0627\u060c <code>COV()<\/code> \u06a9\u0648\u0648\u0627\u0631\u06cc\u0627\u0646\u0633 \u0627\u0633\u062a \u0648 <code>STD()<\/code> \u0627\u0646\u062d\u0631\u0627\u0641 \u0645\u0639\u06cc\u0627\u0631 \u0627\u0633\u062a.  \u0642\u0628\u0644 \u0627\u0632 \u0627\u06cc\u0646\u06a9\u0647 \u062a\u0648\u0627\u0628\u0639 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0627\u06cc\u0646 \u0636\u0631\u06cc\u0628 \u0628\u0628\u06cc\u0646\u06cc\u0645\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u06cc\u06a9 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u062b\u0627\u0644\u06cc \u0628\u0627 \u062f\u0633\u062a \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645 \u062a\u0627 \u0627\u06cc\u0646 \u0639\u0628\u0627\u0631\u062a \u0631\u0627 \u0628\u0641\u0647\u0645\u06cc\u0645 \u0648 \u0622\u0646 \u0631\u0627 \u062f\u0631\u06a9 \u06a9\u0646\u06cc\u0645.<\/p>\n<h3 id=\"examplecomputation\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d8%a7%d8%aa_%d9%85%d8%ab%d8%a7%d9%84\"><\/span>\u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u062b\u0627\u0644<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0645\u0634\u0627\u0647\u062f\u0627\u062a\u06cc \u0627\u0632 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \\(X\\) \u0648 \\(Y\\) \u0628\u0647 \u0645\u0627 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.  \u0627\u0648\u0644\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u062a\u0628\u062f\u06cc\u0644 \\(X\\) \u0648 \\(Y\\) \u0628\u0647 \\(X_r\\) \u0648 \\(Y_r\\) \u0627\u0633\u062a \u06a9\u0647 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0631\u062a\u0628\u0647 \u0647\u0627\u06cc \u0645\u0631\u0628\u0648\u0637 \u0628\u0647 \u0622\u0646\u0647\u0627 \u0627\u0633\u062a.  \u0686\u0646\u062f \u0645\u0642\u062f\u0627\u0631 \u0645\u06cc\u0627\u0646\u06cc \u0646\u06cc\u0632 \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mtable columnalign=\"left center center center center center center center center\" rowspacing=\"4pt\" columnspacing=\"1em\">\n    <mtr>\n      <mtd>\n        <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">(<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo>&#8211;<\/mo>\n        <mn>2<\/mn>\n      <\/mtd>\n      <mtd>\n        <mo>&#8211;<\/mo>\n        <mn>1<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>0<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>1<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>2<\/mn>\n      <\/mtd>\n      <mtd>\n        <msup>\n          <mo stretchy=\"false\">)<\/mo>\n          <mi>\u062a\u06cc<\/mi>\n        <\/msup>\n      <\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd>\n        <mi>Y<\/mi>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">(<\/mo>\n      <\/mtd>\n      <mtd>\n        <mn>4<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>1<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>3<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>2<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>0<\/mn>\n      <\/mtd>\n      <mtd>\n        <msup>\n          <mo stretchy=\"false\">)<\/mo>\n          <mi>\u062a\u06cc<\/mi>\n        <\/msup>\n      <\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd>\n        <msub>\n          <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n          <mi>r<\/mi>\n        <\/msub>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">(<\/mo>\n      <\/mtd>\n      <mtd>\n        <mn>1<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>2<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>3<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>4<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>5<\/mn>\n      <\/mtd>\n      <mtd>\n        <msup>\n          <mo stretchy=\"false\">)<\/mo>\n          <mi>\u062a\u06cc<\/mi>\n        <\/msup>\n      <\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd>\n        <msub>\n          <mi>Y<\/mi>\n          <mi>r<\/mi>\n        <\/msub>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">(<\/mo>\n      <\/mtd>\n      <mtd>\n        <mn>5<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>2<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>4<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>3<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>1<\/mn>\n      <\/mtd>\n      <mtd>\n        <msup>\n          <mo stretchy=\"false\">)<\/mo>\n          <mi>\u062a\u06cc<\/mi>\n        <\/msup>\n      <\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd>\n        <msubsup>\n          <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n          <mi>r<\/mi>\n          <mn>2<\/mn>\n        <\/msubsup>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">(<\/mo>\n      <\/mtd>\n      <mtd>\n        <mn>1<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>4<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>9<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>16<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>25<\/mn>\n      <\/mtd>\n      <mtd>\n        <msup>\n          <mo stretchy=\"false\">)<\/mo>\n          <mi>\u062a\u06cc<\/mi>\n        <\/msup>\n      <\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd>\n        <msubsup>\n          <mi>Y<\/mi>\n          <mi>r<\/mi>\n          <mn>2<\/mn>\n        <\/msubsup>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">(<\/mo>\n      <\/mtd>\n      <mtd>\n        <mn>25<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>4<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>16<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>9<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>1<\/mn>\n      <\/mtd>\n      <mtd>\n        <msup>\n          <mo stretchy=\"false\">)<\/mo>\n          <mi>\u062a\u06cc<\/mi>\n        <\/msup>\n      <\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd>\n        <msub>\n          <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n          <mi>r<\/mi>\n        <\/msub>\n        <msub>\n          <mi>Y<\/mi>\n          <mi>r<\/mi>\n        <\/msub>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">(<\/mo>\n      <\/mtd>\n      <mtd>\n        <mn>5<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>4<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>12<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>12<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>5<\/mn>\n      <\/mtd>\n      <mtd>\n        <msup>\n          <mo stretchy=\"false\">)<\/mo>\n          <mi>\u062a\u06cc<\/mi>\n        <\/msup>\n      <\/mtd>\n    <\/mtr>\n  <\/mtable>\n<\/math><\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u0632 \u0641\u0631\u0645\u0648\u0644 \u0642\u0628\u0644\u06cc \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <msub>\n    <mi>r<\/mi>\n    <mi>\u0633<\/mi>\n  <\/msub>\n  <mo>=<\/mo>\n  <mfrac>\n    <mrow>\n      <mn>5<\/mn>\n      <mo>\u2217<\/mo>\n      <mn>38<\/mn>\n      <mo>&#8211;<\/mo>\n      <mo stretchy=\"false\">(<\/mo>\n      <mn>15<\/mn>\n      <mo stretchy=\"false\">)<\/mo>\n      <mo stretchy=\"false\">(<\/mo>\n      <mn>15<\/mn>\n      <mo stretchy=\"false\">)<\/mo>\n    <\/mrow>\n    <mrow>\n      <msqrt>\n        <mo stretchy=\"false\">(<\/mo>\n        <mn>5<\/mn>\n        <mo>\u2217<\/mo>\n        <mn>55<\/mn>\n        <mo>&#8211;<\/mo>\n        <msup>\n          <mn>15<\/mn>\n          <mn>2<\/mn>\n        <\/msup>\n        <mo stretchy=\"false\">)<\/mo>\n      <\/msqrt>\n      <msqrt>\n        <mo stretchy=\"false\">(<\/mo>\n        <mn>5<\/mn>\n        <mo>\u2217<\/mo>\n        <mn>55<\/mn>\n        <mo>&#8211;<\/mo>\n        <msup>\n          <mn>15<\/mn>\n          <mn>2<\/mn>\n        <\/msup>\n        <mo stretchy=\"false\">)<\/mo>\n      <\/msqrt>\n    <\/mrow>\n  <\/mfrac>\n  <mo>=<\/mo>\n  <mfrac>\n    <mn>181<\/mn>\n    <mn>532<\/mn>\n  <\/mfrac>\n  <mo>=<\/mo>\n  <mo>&#8211;<\/mo>\n  <mn>0.7<\/mn>\n<\/math><\/p>\n<p>\u0639\u0627\u0644\u06cc!  \u0627\u06af\u0631\u0686\u0647\u060c \u0645\u062d\u0627\u0633\u0628\u0647 \u0627\u06cc\u0646 \u0628\u0647 \u0635\u0648\u0631\u062a \u062f\u0633\u062a\u06cc \u0632\u0645\u0627\u0646 \u0628\u0631 \u0627\u0633\u062a\u060c \u0648 \u0628\u0647\u062a\u0631\u06cc\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0627\u06cc\u0627\u0646\u0647\u060c \u0645\u062d\u0627\u0633\u0628\u0647 \u0686\u06cc\u0632\u0647\u0627 \u0628\u0631\u0627\u06cc \u0645\u0627 \u0627\u0633\u062a.  \u0645\u062d\u0627\u0633\u0628\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc Spearman \u0628\u0627 \u062a\u0648\u0627\u0628\u0639 \u062f\u0627\u062e\u0644\u06cc \u062f\u0631 \u067e\u0627\u0646\u062f\u0627\u0647\u0627 \u0648\u0627\u0642\u0639\u0627\u064b \u0622\u0633\u0627\u0646 \u0648 \u0633\u0627\u062f\u0647 \u0627\u0633\u062a.<\/p>\n<h2 id=\"computingthespearmanrankcorrelationcoefficientusingpandas\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87_%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d8%b1%d8%aa%d8%a8%d9%87_%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86_%d8%a8%d8%a7_%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_%d9%be%d8%a7%d9%86%d8%af%d8%a7%d9%87%d8%a7\"><\/span>\u0645\u062d\u0627\u0633\u0628\u0647 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <em>\u067e\u0627\u0646\u062f\u0627\u0647\u0627<\/em><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<blockquote>\n<p>\u0636\u0631\u0627\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062e\u062a\u0644\u0641\u060c \u0627\u0632 \u062c\u0645\u0644\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646\u060c \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0631\u062f <code>corr()<\/code> \u0631\u0648\u0634 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u067e\u0627\u0646\u062f\u0627.<\/p>\n<\/blockquote>\n<p>\u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0622\u0631\u06af\u0648\u0645\u0627\u0646 \u0648\u0631\u0648\u062f\u06cc \u060c <code>corr()<\/code> \u062a\u0627\u0628\u0639 \u0631\u0648\u0634 \u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u0627 \u0645\u06cc \u067e\u0630\u06cc\u0631\u062f (<code>spearman<\/code> \u062f\u0631 \u0645\u0648\u0631\u062f \u0645\u0627).  \u0631\u0648\u0634 \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f \u0631\u0648\u06cc \u0622 <code>DataFrame<\/code>\u060c \u0645\u06cc \u06af\u0648\u06cc\u0646\u062f \u0627\u0632 \u0627\u0646\u062f\u0627\u0632\u0647 <code>mxn<\/code>\u060c \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0647\u0631 \u0633\u062a\u0648\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u062a\u0635\u0627\u062f\u0641\u06cc \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u0648 <code>m<\/code> \u0646\u0645\u0648\u0646\u0647 \u0647\u0627\u06cc \u06a9\u0644 \u0647\u0631 \u0645\u062a\u063a\u06cc\u0631 \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<p>\u0628\u0631\u0627\u06cc <code>n<\/code> \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u060c \u0622\u0646 \u0631\u0627 \u0628\u0631\u0645\u06cc \u06af\u0631\u062f\u0627\u0646\u062f <code>nxn<\/code> \u0645\u0627\u062a\u0631\u06cc\u0633 \u0645\u0631\u0628\u0639 <code>R<\/code>. <code>R(i,j)<\/code> \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631 \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u0633\u062a <code>i<\/code> \u0648 <code>j<\/code>.  \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0628\u06cc\u0646 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u0648 \u062e\u0648\u062f\u0634 1 \u0627\u0633\u062a\u060c \u062a\u0645\u0627\u0645 \u0648\u0631\u0648\u062f\u06cc \u0647\u0627\u06cc \u0645\u0648\u0631\u0628 <code>(i,i)<\/code> \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0648\u062d\u062f\u062a \u0647\u0633\u062a\u0646\u062f.  \u0628\u0647 \u0627\u062e\u062a\u0635\u0627\u0631:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mi>\u0622\u0631<\/mi>\n  <mo stretchy=\"false\">(<\/mo>\n  <mi>\u0645\u0646<\/mi>\n  <mo>\u060c<\/mo>\n  <mi>j<\/mi>\n  <mo stretchy=\"false\">)<\/mo>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>{<\/mo>\n    <mtable columnalign=\"left left\" rowspacing=\".2em\" columnspacing=\"1em\" displaystyle=\"false\">\n      <mtr>\n        <mtd>\n          <msub>\n            <mi>r<\/mi>\n            <mrow class=\"MJX-TeXAtom-ORD\">\n              <mi>\u0645\u0646<\/mi>\n              <mo>\u060c<\/mo>\n              <mi>j<\/mi>\n            <\/mrow>\n          <\/msub>\n        <\/mtd>\n        <mtd>\n          <mtext> \u0627\u06af\u0631 <\/mtext>\n          <mi>\u0645\u0646<\/mi>\n          <mo>\u2260<\/mo>\n          <mi>j<\/mi>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mtext>\u062f\u0631 \u063a\u06cc\u0631 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a<\/mtext>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n  <\/mrow>\n<\/math><\/p>\n<p>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062a\u0642\u0627\u0631\u0646 \u0627\u0633\u062a \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062a\u0642\u0627\u0631\u0646 \u0627\u0633\u062a\u060c \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c <code>M(i,j)=M(j,i)<\/code>.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0645\u062b\u0627\u0644 \u0633\u0627\u062f\u0647 \u062e\u0648\u062f \u0631\u0627 \u0627\u0632 \u0628\u062e\u0634 \u0642\u0628\u0644 \u0628\u06af\u06cc\u0631\u06cc\u0645 \u0648 \u0631\u0648\u0634 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u067e\u0627\u0646\u062f\u0627\u0647\u0627 \u0631\u0627 \u0628\u0628\u06cc\u0646\u06cc\u0645. <code>corr()<\/code> \u062a\u0627\u0628\u0639:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> numpy <span class=\"hljs-keyword\">as<\/span> np\n<span class=\"hljs-keyword\">import<\/span> pandas <span class=\"hljs-keyword\">as<\/span> pd\n<span class=\"hljs-keyword\">import<\/span> seaborn <span class=\"hljs-keyword\">as<\/span> sns \n<span class=\"hljs-keyword\">import<\/span> matplotlib.pyplot <span class=\"hljs-keyword\">as<\/span> plt\n<\/code><\/pre>\n<p>\u0645\u0627 \u0627\u0632 Pandas \u0628\u0631\u0627\u06cc \u062e\u0648\u062f \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u060c Matplotlib \u0628\u0627 Seaborn \u0628\u0631\u0627\u06cc \u062a\u062c\u0633\u0645 \u0648 NumPy \u0628\u0631\u0627\u06cc \u0639\u0645\u0644\u06cc\u0627\u062a \u0627\u0636\u0627\u0641\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f. \u0631\u0648\u06cc \u062f\u0627\u062f\u0647.<\/p>\n<p>\u06a9\u062f \u0632\u06cc\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u06a9\u0646\u062f \u0631\u0648\u06cc \u0686\u0627\u0631\u0686\u0648\u0628 \u062f\u0627\u062f\u0647 <code>x_simple<\/code>.  \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 <strong>\u0622\u0646\u0647\u0627\u06cc\u06cc \u06a9\u0647<\/strong> \u0631\u0648\u06cc  \u0642\u0637\u0631\u0647\u0627\u060c \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u0628\u0627 \u062e\u0648\u062f\u0634 \u0628\u0647 \u0637\u0648\u0631 \u0637\u0628\u06cc\u0639\u06cc \u0627\u0633\u062a\u060c <strong>\u06cc\u06a9\u06cc<\/strong>:<\/p>\n<pre><code class=\"hljs\">x_simple = pd.DataFrame(((-<span class=\"hljs-number\">2<\/span>,<span class=\"hljs-number\">4<\/span>),(-<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">1<\/span>),(<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">3<\/span>),(<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">2<\/span>),(<span class=\"hljs-number\">2<\/span>,<span class=\"hljs-number\">0<\/span>)),\n                        columns=(<span class=\"hljs-string\">\"X\"<\/span>,<span class=\"hljs-string\">\"Y\"<\/span>))\nmy_r = x_simple.corr(method=<span class=\"hljs-string\">\"spearman\"<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(my_r)\n<\/code><\/pre>\n<pre><code class=\"hljs\">     X    Y\nX  1.0 -0.7\nY -0.7  1.0\n<\/code><\/pre>\n<h2 id=\"visualizingthecorrelationcoefficient\"><span class=\"ez-toc-section\" id=\"%d8%aa%d8%ac%d8%b3%d9%85_%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c\"><\/span>\u062a\u062c\u0633\u0645 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0633\u0627\u062e\u062a\u0627\u0631 \u062c\u062f\u0648\u0644 \u0645\u0627\u0646\u0646\u062f \u0634\u062f\u062a \u0647\u0627\u06cc \u0645\u062d\u062f\u0648\u062f\u060c <code>(-1, 1)<\/code> &#8211; \u06cc\u06a9 \u0631\u0648\u0634 \u0637\u0628\u06cc\u0639\u06cc \u0648 \u0631\u0627\u062d\u062a <em>\u062a\u062c\u0633\u0645 \u06a9\u0631\u062f\u0646<\/em> \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u06cc\u06a9 \u0627\u0633\u062a <strong>\u0646\u0642\u0634\u0647 \u062d\u0631\u0627\u0631\u062a<\/strong>.<\/p>\n<blockquote>\n<p>\u0627\u06af\u0631 \u0645\u06cc\u200c\u062e\u0648\u0627\u0647\u06cc\u062f \u062f\u0631\u0628\u0627\u0631\u0647 \u0646\u0642\u0634\u0647\u200c\u0647\u0627\u06cc \u062d\u0631\u0627\u0631\u062a\u06cc \u062f\u0631 Seaborn \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631\u06cc \u06a9\u0633\u0628 \u06a9\u0646\u06cc\u062f\u060c \u0631\u0627\u0647\u0646\u0645\u0627\u06cc \u0646\u0647\u0627\u06cc\u06cc \u0645\u0627 \u0628\u0631\u0627\u06cc \u0646\u0642\u0634\u0647\u200c\u0647\u0627\u06cc \u062d\u0631\u0627\u0631\u062a\u06cc \u062f\u0631 Seaborn \u0628\u0627 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0631\u0627 \u0628\u062e\u0648\u0627\u0646\u06cc\u062f!<\/p>\n<\/blockquote>\n<p>\u0646\u0642\u0634\u0647 \u062d\u0631\u0627\u0631\u062a\u06cc \u0634\u0628\u06a9\u0647\u200c\u0627\u06cc \u0627\u0632 \u0633\u0644\u0648\u0644\u200c\u0647\u0627 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0628\u0647 \u0647\u0631 \u0633\u0644\u0648\u0644 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0645\u0642\u062f\u0627\u0631\u0634 \u0631\u0646\u06af\u06cc \u0627\u062e\u062a\u0635\u0627\u0635 \u062f\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u0648 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0635\u0631\u06cc \u062a\u0641\u0633\u06cc\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633\u200c\u0647\u0627\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0628\u0631\u0627\u06cc \u0645\u0627 \u0628\u0633\u06cc\u0627\u0631 \u0622\u0633\u0627\u0646\u200c\u062a\u0631 \u0627\u0632 \u062a\u062c\u0632\u06cc\u0647 \u0627\u0639\u062f\u0627\u062f \u0627\u0633\u062a.  \u0628\u0631\u0627\u06cc \u0645\u06cc\u0632\u0647\u0627\u06cc \u06a9\u0648\u0686\u06a9\u06cc \u0645\u0627\u0646\u0646\u062f \u0645\u06cc\u0632\u0647\u0627\u06cc \u0642\u0628\u0644\u06cc &#8211; \u06a9\u0627\u0645\u0644\u0627\u064b \u062e\u0648\u0628 \u0627\u0633\u062a.  \u0627\u0645\u0627 \u0628\u0627 <em>\u0632\u06cc\u0627\u062f<\/em> \u0627\u0632 \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u060c \u062a\u0641\u0633\u06cc\u0631 \u0648\u0627\u0642\u0639\u06cc \u0622\u0646\u0686\u0647 \u062f\u0631 \u062d\u0627\u0644 \u0627\u0646\u062c\u0627\u0645 \u0627\u0633\u062a \u0628\u0633\u06cc\u0627\u0631 \u062f\u0634\u0648\u0627\u0631\u062a\u0631 \u0627\u0633\u062a \u0631\u0648\u06cc.<\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f a \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0646\u06cc\u0645 <code>display_correlation()<\/code> \u062a\u0627\u0628\u0639\u06cc \u06a9\u0647 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u06a9\u0646\u062f \u0648 \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0646\u0642\u0634\u0647 \u062d\u0631\u0627\u0631\u062a\u06cc \u0646\u0645\u0627\u06cc\u0634 \u0645\u06cc \u062f\u0647\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">display_correlation<\/span>(<span class=\"hljs-params\">df<\/span>):<\/span>\n    r = df.corr(method=<span class=\"hljs-string\">\"spearman\"<\/span>)\n    plt.figure(figsize=(<span class=\"hljs-number\">10<\/span>,<span class=\"hljs-number\">6<\/span>))\n    heatmap = sns.heatmap(df.corr(), vmin=-<span class=\"hljs-number\">1<\/span>, \n                      vmax=<span class=\"hljs-number\">1<\/span>, annot=<span class=\"hljs-literal\">True<\/span>)\n    plt.title(<span class=\"hljs-string\">\"Spearman Correlation\"<\/span>)\n    <span class=\"hljs-keyword\">return<\/span>(r)\n<\/code><\/pre>\n<p>\u0628\u06cc\u0627 \u062a\u0645\u0627\u0633 \u0628\u06af\u06cc\u0631\u06cc\u0645 <code>display_correlation()<\/code> \u0631\u0648\u06cc  \u0645\u0627 <code>r_simple<\/code> DataFrame \u0628\u0631\u0627\u06cc \u062a\u062c\u0633\u0645 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc Spearman:<\/p>\n<pre><code class=\"hljs\">r_simple=display_correlation(x_simple)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/calculating-spearmans-rank-correlation-coefficient-in-python-with-pandas-1.png\" alt=\"\u0645\u0642\u0627\u062f\u06cc\u0631 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc\" title=\"\"><\/p>\n<h2 id=\"understandingthespearmanscorrelationcoefficientonsyntheticexamples\"><span class=\"ez-toc-section\" id=\"%d8%af%d8%b1%da%a9_%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86_%d8%b1%d9%88%db%8c_%d9%86%d9%85%d9%88%d9%86%d9%87_%d9%87%d8%a7%db%8c_%d9%85%d8%b5%d9%86%d9%88%d8%b9%db%8c\"><\/span>\u062f\u0631\u06a9 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0631\u0648\u06cc \u0646\u0645\u0648\u0646\u0647 \u0647\u0627\u06cc \u0645\u0635\u0646\u0648\u0639\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646\u060c \u0627\u062c\u0627\u0632\u0647 \u062f\u0647\u06cc\u062f \u0686\u0646\u062f \u0645\u062b\u0627\u0644 \u0645\u0635\u0646\u0648\u0639\u06cc \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0631\u0648\u0634 \u0639\u0645\u0644\u06a9\u0631\u062f \u0636\u0631\u06cc\u0628 \u0631\u0627 \u0628\u0631\u062c\u0633\u062a\u0647 \u0645\u06cc \u06a9\u0646\u062f &#8211; \u0642\u0628\u0644 \u0627\u0632 \u0627\u06cc\u0646\u06a9\u0647 \u0628\u0647 \u0646\u0645\u0648\u0646\u0647 \u0647\u0627\u06cc \u0637\u0628\u06cc\u0639\u06cc \u062a\u0631 \u0628\u067e\u0631\u062f\u0627\u0632\u06cc\u0645.  \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644\u200c\u0647\u0627 \u0628\u0647 \u0645\u0627 \u06a9\u0645\u06a9 \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f \u0628\u0641\u0647\u0645\u06cc\u0645 \u0627\u06cc\u0646 \u0636\u0631\u06cc\u0628 \u0628\u0631\u0627\u06cc \u0686\u0647 \u0646\u0648\u0639 \u0631\u0648\u0627\u0628\u0637\u06cc +1\u060c -1 \u06cc\u0627 \u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647 \u0635\u0641\u0631 \u0627\u0633\u062a.<\/p>\n<p>\u0642\u0628\u0644 \u0627\u0632 \u062a\u0648\u0644\u06cc\u062f \u0645\u062b\u0627\u0644\u200c\u0647\u0627\u060c \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u06a9\u0645\u06a9\u06cc \u062c\u062f\u06cc\u062f \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645\u060c <code>plot_data_corr()<\/code>\u060c \u06a9\u0647 \u062a\u0645\u0627\u0633 \u0645\u06cc \u06af\u06cc\u0631\u062f <code>display_correlation()<\/code> \u0648 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u062f\u0631 \u0628\u0631\u0627\u0628\u0631 <code>X<\/code> \u0645\u062a\u063a\u06cc\u0631:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">plot_data_corr<\/span>(<span class=\"hljs-params\">df,title,color=<span class=\"hljs-string\">\"green\"<\/span><\/span>):<\/span>    \n    r = display_correlation(df)\n    fig, ax = plt.subplots(nrows=<span class=\"hljs-number\">1<\/span>, ncols=<span class=\"hljs-built_in\">len<\/span>(df.columns)-<span class=\"hljs-number\">1<\/span>,figsize=(<span class=\"hljs-number\">14<\/span>,<span class=\"hljs-number\">3<\/span>))\n    <span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-built_in\">len<\/span>(df.columns)):\n        ax(i-<span class=\"hljs-number\">1<\/span>).scatter(df(<span class=\"hljs-string\">\"X\"<\/span>),df.values(:,i),color=color)\n        ax(i-<span class=\"hljs-number\">1<\/span>).title.set_text(title(i) +<span class=\"hljs-string\">'\\n r = '<\/span> + \n                             <span class=\"hljs-string\">\"{:.2f}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(r.values(<span class=\"hljs-number\">0<\/span>,i)))\n        ax(i-<span class=\"hljs-number\">1<\/span>).<span class=\"hljs-built_in\">set<\/span>(xlabel=df.columns(<span class=\"hljs-number\">0<\/span>),ylabel=df.columns(i))\n    fig.subplots_adjust(wspace=<span class=\"hljs-number\">.7<\/span>)    \n    plt.show()\n<\/code><\/pre>\n<h3 id=\"monotonicallyincreasingfunctions\"><span class=\"ez-toc-section\" id=\"%d8%aa%d9%88%d8%a7%d8%a8%d8%b9_%d8%a7%d9%81%d8%b2%d8%a7%db%8c%d8%b4_%d8%af%d9%87%d9%86%d8%af%d9%87_%db%8c%da%a9%d9%86%d9%88%d8%a7%d8%ae%d8%aa\"><\/span>\u062a\u0648\u0627\u0628\u0639 \u0627\u0641\u0632\u0627\u06cc\u0634 \u062f\u0647\u0646\u062f\u0647 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 NumPy \u0686\u0646\u062f \u062a\u0648\u0627\u0628\u0639 \u0627\u0641\u0632\u0627\u06cc\u0634\u200c\u062f\u0647\u0646\u062f\u0647 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u0645 \u0648 \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u0622\u0646 \u0628\u06cc\u0646\u062f\u0627\u0632\u06cc\u0645 <code>DataFrame<\/code> \u067e\u0633 \u0627\u0632 \u067e\u0631 \u0634\u062f\u0646 \u0628\u0627 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0635\u0646\u0648\u0639\u06cc:<\/p>\n<pre><code class=\"hljs\">seed = <span class=\"hljs-number\">11<\/span>\nrand = np.random.RandomState(seed)\n\nx_incr = pd.DataFrame({<span class=\"hljs-string\">\"X\"<\/span>:rand.uniform(<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">10<\/span>,<span class=\"hljs-number\">100<\/span>)})\nx_incr(<span class=\"hljs-string\">\"Line+\"<\/span>) = x_incr.X*<span class=\"hljs-number\">2<\/span>+<span class=\"hljs-number\">1<\/span>\nx_incr(<span class=\"hljs-string\">\"Sq+\"<\/span>) = x_incr.X**<span class=\"hljs-number\">2<\/span>\nx_incr(<span class=\"hljs-string\">\"Exp+\"<\/span>) = np.exp(x_incr.X)\nx_incr(<span class=\"hljs-string\">\"Cube+\"<\/span>) = (x_incr.X-<span class=\"hljs-number\">5<\/span>)**<span class=\"hljs-number\">3<\/span>\n\n<span class=\"hljs-built_in\">print<\/span>(x_incr.head())\n<\/code><\/pre>\n<table class=\"table table-striped\">\n<thead>\n<tr>\n<th><\/th>\n<th>\u0627\u06cc\u06a9\u0633<\/th>\n<th>\u062e\u0637 +<\/th>\n<th>\u0645\u0631\u0628\u0639 +<\/th>\n<th>Exp+<\/th>\n<th>\u0645\u06a9\u0639\u0628 +<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>0<\/th>\n<td>1.802697<\/td>\n<td>4.605394<\/td>\n<td>3.249716<\/td>\n<td>6.065985<\/td>\n<td>-32.685221<\/td>\n<\/tr>\n<tr>\n<th>1<\/th>\n<td>0.194752<\/td>\n<td>1.389505<\/td>\n<td>0.037929<\/td>\n<td>1.215010<\/td>\n<td>-110.955110<\/td>\n<\/tr>\n<tr>\n<th>2<\/th>\n<td>4.632185<\/td>\n<td>10.264371<\/td>\n<td>21.457140<\/td>\n<td>102.738329<\/td>\n<td>-0.049761<\/td>\n<\/tr>\n<tr>\n<th>3<\/th>\n<td>7.249339<\/td>\n<td>15.498679<\/td>\n<td>52.552920<\/td>\n<td>1407.174809<\/td>\n<td>11.380593<\/td>\n<\/tr>\n<tr>\n<th>4<\/th>\n<td>4.202036<\/td>\n<td>9.404072<\/td>\n<td>17.657107<\/td>\n<td>66.822246<\/td>\n<td>-0.508101<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u062d\u0627\u0644\u0627 \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0647 \u0646\u0642\u0634\u0647 \u062d\u0631\u0627\u0631\u062a\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0648 \u0646\u0645\u0648\u062f\u0627\u0631 \u062a\u0648\u0627\u0628\u0639 \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u0628\u0631\u0627\u0628\u0631 \u0622\u0646 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645 <code>X<\/code>:<\/p>\n<pre><code class=\"hljs\">plot_data_corr(x_incr,(<span class=\"hljs-string\">\"X\"<\/span>,<span class=\"hljs-string\">\"2X+1\"<\/span>,<span class=\"hljs-string\">\"$X^2$\"<\/span>,<span class=\"hljs-string\">\"$e^X$\"<\/span>,<span class=\"hljs-string\">\"$(X-5)^3$\"<\/span>))\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/calculating-spearmans-rank-correlation-coefficient-in-python-with-pandas-2.png\" alt=\"\u0646\u0642\u0634\u0647 \u062d\u0631\u0627\u0631\u062a\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/calculating-spearmans-rank-correlation-coefficient-in-python-with-pandas-3.png\" alt=\"\u0627\u0641\u0632\u0627\u06cc\u0634 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u062a\u0648\u0627\u0628\u0639\" title=\"\"><\/p>\n<p>\u0645\u0627 \u0645\u06cc \u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0647\u0627\u060c \u06cc\u06a9 \u0631\u0627\u0628\u0637\u0647 \u06a9\u0627\u0645\u0644\u0627\u064b \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f.  \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u06cc\u06a9 +1 \u0627\u0633\u062a\u060c \u0635\u0631\u0641 \u0646\u0638\u0631 \u0627\u0632 \u0627\u06cc\u0646\u06a9\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0631\u0627\u0628\u0637\u0647 \u062e\u0637\u06cc \u06cc\u0627 \u063a\u06cc\u0631\u062e\u0637\u06cc \u062f\u0627\u0631\u0646\u062f.<\/p>\n<p><strong>\u067e\u06cc\u0631\u0633\u0648\u0646<\/strong> \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0645\u062d\u0627\u0633\u0628\u0647 \u0627\u0633\u062a\u060c \u0646\u062a\u0627\u06cc\u062c \u0628\u0633\u06cc\u0627\u0631 \u0645\u062a\u0641\u0627\u0648\u062a\u06cc \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u0634\u0648\u062f \u0631\u0648\u06cc \u0631\u0627 <strong>\u062e\u0637\u06cc<\/strong> \u0631\u0627\u0628\u0637\u0647 \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627<\/p>\n<blockquote>\n<p>\u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 Y \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u06cc \u06cc\u0627\u0628\u062f \u0628\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 X\u060c <em>\u0628\u062f\u0648\u0646 \u0634\u06a9\u0633\u062a<\/em>\u060c \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f <strong>1<\/strong>.<\/p>\n<\/blockquote>\n<h3 id=\"monotonicallydecreasingfunctions\"><span class=\"ez-toc-section\" id=\"%d8%aa%d9%88%d8%a7%d8%a8%d8%b9_%da%a9%d8%a7%d9%87%d8%b4%db%8c_%db%8c%da%a9%d9%86%d9%88%d8%a7%d8%ae%d8%aa\"><\/span>\u062a\u0648\u0627\u0628\u0639 \u06a9\u0627\u0647\u0634\u06cc \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0647\u0645\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0647\u0627 \u0631\u0627 \u062a\u06a9\u0631\u0627\u0631 \u06a9\u0646\u06cc\u0645 \u0631\u0648\u06cc \u062a\u0648\u0627\u0628\u0639 \u062f\u0631 \u062d\u0627\u0644 \u06a9\u0627\u0647\u0634 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a  \u0645\u0627 \u062f\u0648\u0628\u0627\u0631\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0635\u0646\u0648\u0639\u06cc \u062a\u0648\u0644\u06cc\u062f \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u0627\u0628\u062a\u062f\u0627\u060c \u0627\u062c\u0627\u0632\u0647 \u062f\u0647\u06cc\u062f \u0628\u0647 4 \u0631\u062f\u06cc\u0641 \u0627\u0648\u0644 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645 <code>DataFrame<\/code>:<\/p>\n<pre><code class=\"hljs\">\nx_decr = pd.DataFrame({<span class=\"hljs-string\">\"X\"<\/span>:rand.uniform(<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">10<\/span>,<span class=\"hljs-number\">100<\/span>)})\nx_decr(<span class=\"hljs-string\">\"Line-\"<\/span>) = -x_decr.X*<span class=\"hljs-number\">2<\/span>+<span class=\"hljs-number\">1<\/span>\nx_decr(<span class=\"hljs-string\">\"Sq-\"<\/span>) = -x_decr.X**<span class=\"hljs-number\">2<\/span>\nx_decr(<span class=\"hljs-string\">\"Exp-\"<\/span>) = np.exp(-x_decr.X)\nx_decr(<span class=\"hljs-string\">\"Cube-\"<\/span>) = -(x_decr.X-<span class=\"hljs-number\">5<\/span>)**<span class=\"hljs-number\">3<\/span>\nx_decr.head()\n<\/code><\/pre>\n<table class=\"table table-striped\">\n<thead>\n<tr>\n<th><\/th>\n<th>\u0627\u06cc\u06a9\u0633<\/th>\n<th>\u062e\u0637-<\/th>\n<th>\u0645\u0631\u0628\u0639<\/th>\n<th>\u0627\u0646\u0642\u0636\u0627-<\/th>\n<th>\u0645\u06a9\u0639\u0628-<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>0<\/th>\n<td>3.181872<\/td>\n<td>-5.363744<\/td>\n<td>-10.124309<\/td>\n<td>0.041508<\/td>\n<td>6.009985<\/td>\n<\/tr>\n<tr>\n<th>1<\/th>\n<td>2.180034<\/td>\n<td>-3.360068<\/td>\n<td>-4.752547<\/td>\n<td>0.113038<\/td>\n<td>22.424963<\/td>\n<\/tr>\n<tr>\n<th>2<\/th>\n<td>8.449385<\/td>\n<td>-15.898771<\/td>\n<td>-71.392112<\/td>\n<td>0.000214<\/td>\n<td>-41.041680<\/td>\n<\/tr>\n<tr>\n<th>3<\/th>\n<td>3.021647<\/td>\n<td>-5.043294<\/td>\n<td>-9.130350<\/td>\n<td>0.048721<\/td>\n<td>7.743039<\/td>\n<\/tr>\n<tr>\n<th>4<\/th>\n<td>4.382207<\/td>\n<td>-7.764413<\/td>\n<td>-19.203736<\/td>\n<td>0.012498<\/td>\n<td>0.235792<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u0646\u0642\u0634\u0647 \u062d\u0631\u0627\u0631\u062a\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0648 \u0646\u0645\u0648\u062f\u0627\u0631 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u062f\u0631 \u0632\u06cc\u0631 \u0622\u0648\u0631\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">plot_data_corr(x_decr,(<span class=\"hljs-string\">\"X\"<\/span>,<span class=\"hljs-string\">\"-2X+1\"<\/span>,<span class=\"hljs-string\">\"$-X^2$\"<\/span>,<span class=\"hljs-string\">\"$-e^X$\"<\/span>,<span class=\"hljs-string\">\"$-(X-5)^3$\"<\/span>),<span class=\"hljs-string\">\"blue\"<\/span>)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/calculating-spearmans-rank-correlation-coefficient-in-python-with-pandas-4.png\" alt=\"\u0646\u0642\u0634\u0647 \u062d\u0631\u0627\u0631\u062a\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/calculating-spearmans-rank-correlation-coefficient-in-python-with-pandas-5.png\" alt=\"\u062a\u0648\u0627\u0628\u0639 \u062f\u0631 \u062d\u0627\u0644 \u06a9\u0627\u0647\u0634 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a\" title=\"\"><\/p>\n<h3 id=\"nonmonotonicfunctions\"><span class=\"ez-toc-section\" id=\"%d8%aa%d9%88%d8%a7%d8%a8%d8%b9_%d8%ba%db%8c%d8%b1_%db%8c%da%a9%d9%86%d9%88%d8%a7%d8%ae%d8%aa\"><\/span>\u062a\u0648\u0627\u0628\u0639 \u063a\u06cc\u0631 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0645\u062b\u0627\u0644 \u0647\u0627\u06cc \u0632\u06cc\u0631 \u0628\u0631\u0627\u06cc \u062a\u0648\u0627\u0628\u0639 \u0645\u062e\u062a\u0644\u0641 \u063a\u06cc\u0631 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u0647\u0633\u062a\u0646\u062f.  \u0622\u062e\u0631\u06cc\u0646 \u0633\u062a\u0648\u0646 \u0628\u0647 <code>DataFrame<\/code> \u0645\u062a\u063a\u06cc\u0631 \u0645\u0633\u062a\u0642\u0644 \u0627\u0633\u062a <code>Rand<\/code>\u060c \u06a9\u0647 \u0647\u06cc\u0686 \u0627\u0631\u062a\u0628\u0627\u0637\u06cc \u0628\u0627 <code>X<\/code>.<\/p>\n<p>\u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0647\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0627\u06cc\u062f \u0631\u0648\u0634\u0646 \u06a9\u0646\u0646\u062f \u06a9\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0645\u0639\u06cc\u0627\u0631\u06cc \u0628\u0631\u0627\u06cc \u0633\u0646\u062c\u0634 \u0627\u0633\u062a <strong><em>\u06cc\u06a9\u0646\u0648\u0627\u062e\u062a\u06cc<\/em><\/strong>  \u0631\u0627\u0628\u0637\u0647 \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631  \u0636\u0631\u06cc\u0628 \u0635\u0641\u0631 \u0644\u0632\u0648\u0645\u0627\u064b \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0639\u062f\u0645 \u0648\u062c\u0648\u062f \u0631\u0627\u0628\u0637\u0647 \u0646\u06cc\u0633\u062a\u060c \u0627\u0645\u0627 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0639\u062f\u0645 \u0648\u062c\u0648\u062f \u0631\u0627\u0628\u0637\u0647 \u0627\u0633\u062a <strong><em>\u06cc\u06a9\u0646\u0648\u0627\u062e\u062a\u06cc<\/em><\/strong>  \u0628\u06cc\u0646 \u0622\u0646\u0647\u0627.<\/p>\n<p>\u0642\u0628\u0644 \u0627\u0632 \u062a\u0648\u0644\u06cc\u062f \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0635\u0646\u0648\u0639\u06cc\u060c \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u06a9\u0645\u06a9\u06cc \u062f\u06cc\u06af\u0631 \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u06a9\u0646\u06cc\u0645\u060c <code>display_corr_pairs()<\/code>\u060c \u06a9\u0647 \u062a\u0645\u0627\u0633 \u0645\u06cc \u06af\u06cc\u0631\u062f <code>display_correlation()<\/code> \u0628\u0631\u0627\u06cc \u0646\u0645\u0627\u06cc\u0634 \u0646\u0642\u0634\u0647 \u062d\u0631\u0627\u0631\u062a\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0648 \u0633\u067e\u0633 \u0631\u0633\u0645 \u062a\u0645\u0627\u0645 \u062c\u0641\u062a \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u062f\u0631 <code>DataFrame<\/code> \u062f\u0631 \u0645\u0642\u0627\u0628\u0644 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 Seaborn.<\/p>\n<p>\u062f\u0631 \u0645\u0648\u0631\u0628 \u0647\u0627\u060c \u0647\u06cc\u0633\u062a\u0648\u06af\u0631\u0627\u0645 \u0647\u0631 \u0645\u062a\u063a\u06cc\u0631 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0646\u06af \u0632\u0631\u062f \u0646\u0634\u0627\u0646 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u062f <code>map_diag()<\/code>.  \u062f\u0631 \u0632\u06cc\u0631 \u0645\u0648\u0631\u0628 \u0647\u0627\u060c \u06cc\u06a9 \u0646\u0645\u0648\u062f\u0627\u0631 \u067e\u0631\u0627\u06a9\u0646\u062f\u06af\u06cc \u0627\u0632 \u0647\u0645\u0647 \u062c\u0641\u062a \u0647\u0627\u06cc \u0645\u062a\u063a\u06cc\u0631 \u0645\u06cc \u0633\u0627\u0632\u06cc\u0645.  \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062a\u0642\u0627\u0631\u0646 \u0627\u0633\u062a\u060c \u0645\u0627 \u0628\u0647 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u0628\u0627\u0644\u0627\u06cc \u0642\u0637\u0631\u0647\u0627 \u0646\u06cc\u0627\u0632\u06cc \u0646\u062f\u0627\u0631\u06cc\u0645.<\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0631\u0627 \u0646\u06cc\u0632 \u0628\u0631\u0627\u06cc \u0645\u0642\u0627\u06cc\u0633\u0647 \u0646\u0645\u0627\u06cc\u0634 \u062f\u0647\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">display_corr_pairs<\/span>(<span class=\"hljs-params\">df,color=<span class=\"hljs-string\">\"cyan\"<\/span><\/span>):<\/span>\n    s = set_title = np.vectorize(<span class=\"hljs-keyword\">lambda<\/span> ax,r,rho: ax.title.set_text(<span class=\"hljs-string\">\"r = \"<\/span> + \n                                        <span class=\"hljs-string\">\"{:.2f}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(r) + \n                                        <span class=\"hljs-string\">'\\n $\\\\rho$ = '<\/span> + \n                                        <span class=\"hljs-string\">\"{:.2f}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(rho)) <span class=\"hljs-keyword\">if<\/span> ax!=<span class=\"hljs-literal\">None<\/span> <span class=\"hljs-keyword\">else<\/span> <span class=\"hljs-literal\">None<\/span>\n                            )      \n\n    r = display_correlation(df)\n    rho = df.corr(method=<span class=\"hljs-string\">\"pearson\"<\/span>)\n    g = sns.PairGrid(df,corner=<span class=\"hljs-literal\">True<\/span>)\n    g.map_diag(plt.hist,color=<span class=\"hljs-string\">\"yellow\"<\/span>)\n    g.map_lower(sns.scatterplot,color=<span class=\"hljs-string\">\"magenta\"<\/span>)\n    set_title(g.axes,r,rho)\n    plt.subplots_adjust(hspace = <span class=\"hljs-number\">0.6<\/span>)\n    plt.show()    \n<\/code><\/pre>\n<p>\u0645\u0627 \u06cc\u06a9 DataFrame \u063a\u06cc\u0631 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u0627\u06cc\u062c\u0627\u062f \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f\u060c <code>x_non<\/code>\u060c \u0628\u0627 \u0627\u06cc\u0646 \u062a\u0648\u0627\u0628\u0639 \u0627\u0632 <code>X<\/code>:<\/p>\n<ul>\n<li>\n<p>\u0633\u0647\u0645\u06cc: \\( (X-5)^2 \\)<\/p>\n<\/li>\n<li>\n<p>Sin: \\( \\sin (\\frac{X}{10}2\\pi) \\)<\/p>\n<\/li>\n<li>\n<p>Frac: \\( \\frac{X-5}{(X-5)^2+1} \\)<\/p>\n<\/li>\n<li>\n<p>\u0631\u0646\u062f: \u0627\u0639\u062f\u0627\u062f \u062a\u0635\u0627\u062f\u0641\u06cc \u062f\u0631 \u0645\u062d\u062f\u0648\u062f\u0647 (-1\u060c1)<\/p>\n<\/li>\n<\/ul>\n<p>\u062f\u0631 \u0632\u06cc\u0631 4 \u062e\u0637 \u0627\u0648\u0644 \u0627\u0632 <code>x_non<\/code>:<\/p>\n<pre><code class=\"hljs\">x_non = pd.DataFrame({<span class=\"hljs-string\">\"X\"<\/span>:rand.uniform(<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">10<\/span>,<span class=\"hljs-number\">100<\/span>)})\nx_non(<span class=\"hljs-string\">\"Parabola\"<\/span>) = (x_non.X-<span class=\"hljs-number\">5<\/span>)**<span class=\"hljs-number\">2<\/span>\nx_non(<span class=\"hljs-string\">\"Sin\"<\/span>) = np.sin(x_non.X\/<span class=\"hljs-number\">10<\/span>*<span class=\"hljs-number\">2<\/span>*np.pi)\nx_non(<span class=\"hljs-string\">\"Frac\"<\/span>) = (x_non.X-<span class=\"hljs-number\">5<\/span>)\/((x_non.X-<span class=\"hljs-number\">5<\/span>)**<span class=\"hljs-number\">2<\/span>+<span class=\"hljs-number\">1<\/span>)\nx_non(<span class=\"hljs-string\">\"Rand\"<\/span>) = rand.uniform(-<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">100<\/span>)\n\n<span class=\"hljs-built_in\">print<\/span>(x_non.head())\n<\/code><\/pre>\n<table class=\"table table-striped\">\n<thead>\n<tr>\n<th><\/th>\n<th>\u0627\u06cc\u06a9\u0633<\/th>\n<th>\u0633\u0647\u0645\u06cc<\/th>\n<th>\u06af\u0646\u0627\u0647<\/th>\n<th>\u0641\u0631\u0627\u06a9<\/th>\n<th>\u0631\u0646\u062f<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>0<\/th>\n<td>0.654466<\/td>\n<td>18.883667<\/td>\n<td>0.399722<\/td>\n<td>-0.218548<\/td>\n<td>0.072827<\/td>\n<\/tr>\n<tr>\n<th>1<\/th>\n<td>5.746559<\/td>\n<td>0.557351<\/td>\n<td>-0.452063<\/td>\n<td>0.479378<\/td>\n<td>-0.818150<\/td>\n<\/tr>\n<tr>\n<th>2<\/th>\n<td>6.879362<\/td>\n<td>3.532003<\/td>\n<td>-0.924925<\/td>\n<td>0.414687<\/td>\n<td>-0.868501<\/td>\n<\/tr>\n<tr>\n<th>3<\/th>\n<td>5.683058<\/td>\n<td>0.466569<\/td>\n<td>-0.416124<\/td>\n<td>0.465753<\/td>\n<td>0.337066<\/td>\n<\/tr>\n<tr>\n<th>4<\/th>\n<td>6.037265<\/td>\n<td>1.075920<\/td>\n<td>-0.606565<\/td>\n<td>0.499666<\/td>\n<td>0.583229<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0628\u06cc\u0646 \u062c\u0641\u062a \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">display_corr_pairs(x_non)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/calculating-spearmans-rank-correlation-coefficient-in-python-with-pandas-6.png\" alt=\"\u0646\u0642\u0634\u0647 \u062d\u0631\u0627\u0631\u062a\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/calculating-spearmans-rank-correlation-coefficient-in-python-with-pandas-7.png\" alt=\"\u062a\u0648\u0627\u0628\u0639 \u063a\u06cc\u0631 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a\" title=\"\"><\/p>\n<p>\u0627\u06cc\u0646 \u0645\u062b\u0627\u0644\u200c\u0647\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u0646\u062f \u06a9\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0628\u0631\u0627\u06cc \u0686\u0647 \u0646\u0648\u0639 \u062f\u0627\u062f\u0647\u200c\u0627\u06cc \u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647 \u0635\u0641\u0631 \u0627\u0633\u062a \u0648 \u062f\u0631 \u06a9\u062c\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u06cc\u0627\u0646\u06cc \u062f\u0627\u0631\u062f.  \u0646\u06a9\u062a\u0647 \u062f\u06cc\u06af\u0631\u06cc \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0628\u0647 \u0622\u0646 \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0648 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0647\u0645\u06cc\u0634\u0647 \u0628\u0627 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0647\u0645\u062e\u0648\u0627\u0646\u06cc \u0646\u062f\u0627\u0631\u0646\u062f\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0641\u0642\u062f\u0627\u0646 \u06cc\u06a9\u06cc \u0628\u0647 \u0645\u0639\u0646\u0627\u06cc \u0641\u0642\u062f\u0627\u0646 \u062f\u06cc\u06af\u0631\u06cc \u0646\u06cc\u0633\u062a.<\/p>\n<p>\u0622\u0646\u0647\u0627 \u0628\u0631\u0627\u06cc \u0622\u0632\u0645\u0627\u06cc\u0634 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0628\u0631\u0627\u06cc \u062c\u0646\u0628\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062f\u0627\u062f\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u0646\u062f \u0648 \u0646\u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u0628\u0647 \u062c\u0627\u06cc \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u0648\u0646\u062f.  \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0622\u0646\u0647\u0627 \u062f\u0631 \u0628\u0631\u062e\u06cc \u0645\u0648\u0627\u0631\u062f \u0645\u0648\u0627\u0641\u0642 \u0647\u0633\u062a\u0646\u062f\u060c \u0627\u0645\u0627 \u0647\u0645\u06cc\u0634\u0647 \u0627\u06cc\u0646\u0637\u0648\u0631 \u0646\u06cc\u0633\u062a\u0646\u062f.<\/p>\n<h2 id=\"spearmancorrelationcoefficientonlinneruddataset\"><span class=\"ez-toc-section\" id=\"%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d8%a7%d8%b3%d9%be%db%8c%d8%b1%d9%85%d9%86_%d8%b1%d9%88%db%8c_%d9%84%db%8c%d9%86%d8%b1%d9%88%d8%af_%d9%85%d8%ac%d9%85%d9%88%d8%b9%d9%87_%d8%af%d8%a7%d8%af%d9%87\"><\/span>\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0631\u0648\u06cc <em>\u0644\u06cc\u0646\u0631\u0648\u062f<\/em> \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u0631\u0627 \u0627\u0639\u0645\u0627\u0644 \u06a9\u0646\u06cc\u0645 \u0631\u0648\u06cc \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0648\u0627\u0642\u0639\u06cc  \u0645\u0627 \u0633\u0627\u062f\u0647 \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/scikit-learn.org\/stable\/modules\/generated\/sklearn.datasets.load_linnerud.html#sklearn.datasets.load_linnerud\">\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062a\u0645\u0631\u06cc\u0646\u0627\u062a \u0628\u062f\u0646\u06cc<\/a> \u062a\u0645\u0627\u0633 \u06af\u0631\u0641\u062a <code>linnerud<\/code> \u0627\u0632 <code>sklearn.datasets<\/code> \u0628\u0633\u062a\u0647 \u0628\u0631\u0627\u06cc \u0646\u0645\u0627\u06cc\u0634:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> sklearn.datasets.load_linnerud\n<\/code><\/pre>\n<p>\u06a9\u062f \u0632\u06cc\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0631\u0627 \u0628\u0627\u0631\u06af\u06cc\u0631\u06cc \u0645\u06cc \u06a9\u0646\u062f \u0648 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0648 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0647\u062f\u0641 \u0631\u0627 \u062f\u0631 \u06cc\u06a9 \u0645\u06cc \u067e\u06cc\u0648\u0646\u062f\u062f <code>DataFrame<\/code>.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0647 4 \u0631\u062f\u06cc\u0641 \u0627\u0648\u0644 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645 <code>linnerud<\/code> \u062f\u0627\u062f\u0647 \u0647\u0627:<\/p>\n<pre><code class=\"hljs\">d=load_linnerud()\n\ndat = pd.DataFrame(d.data,columns=d.feature_names)\nalldat=dat.join(pd.DataFrame(d.target,columns=d.target_names) )\nalldat.head()\n<\/code><\/pre>\n<table class=\"table table-striped\">\n<thead>\n<tr style=\"text-align:right\">\n<th><\/th>\n<th>\u0686\u0627\u0646\u0647<\/th>\n<th>\u0633\u06cc\u062a\u0648\u067e \u0647\u0627<\/th>\n<th>\u0645\u06cc \u067e\u0631\u062f<\/th>\n<th>\u0648\u0632\u0646<\/th>\n<th>\u06a9\u0645\u0631<\/th>\n<th>\u0646\u0628\u0636<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>0<\/th>\n<td>5.0<\/td>\n<td>162.0<\/td>\n<td>60.0<\/td>\n<td>191.0<\/td>\n<td>36.0<\/td>\n<td>50.0<\/td>\n<\/tr>\n<tr>\n<th>1<\/th>\n<td>2.0<\/td>\n<td>110.0<\/td>\n<td>60.0<\/td>\n<td>189.0<\/td>\n<td>37.0<\/td>\n<td>52.0<\/td>\n<\/tr>\n<tr>\n<th>2<\/th>\n<td>12.0<\/td>\n<td>101.0<\/td>\n<td>101.0<\/td>\n<td>193.0<\/td>\n<td>38.0<\/td>\n<td>58.0<\/td>\n<\/tr>\n<tr>\n<th>3<\/th>\n<td>12.0<\/td>\n<td>105.0<\/td>\n<td>37.0<\/td>\n<td>162.0<\/td>\n<td>35.0<\/td>\n<td>62.0<\/td>\n<\/tr>\n<tr>\n<th>4<\/th>\n<td>13.0<\/td>\n<td>155.0<\/td>\n<td>58.0<\/td>\n<td>189.0<\/td>\n<td>35.0<\/td>\n<td>46.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u062d\u0627\u0644\u0627 \u0628\u06cc\u0627\u06cc\u06cc\u062f \u062c\u0641\u062a \u0647\u0627\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u0627 \u0646\u0645\u0627\u06cc\u0634 \u062f\u0647\u06cc\u0645 <code>display_corr_pairs()<\/code> \u062a\u0627\u0628\u0639:<\/p>\n<pre><code class=\"hljs\">display_corr_pairs(alldat)\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/calculating-spearmans-rank-correlation-coefficient-in-python-with-pandas-8.png\" alt=\"\u0646\u0642\u0634\u0647 \u062d\u0631\u0627\u0631\u062a\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/calculating-spearmans-rank-correlation-coefficient-in-python-with-pandas-9.png\" alt=\"\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062a\u0645\u0631\u06cc\u0646 \u0628\u062f\u0646\u06cc\" title=\"\"><\/p>\n<p>\u0628\u0627 \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0646\u062a\u0627\u06cc\u062c \u062c\u0627\u0644\u0628\u06cc \u0627\u0632 \u0642\u0628\u06cc\u0644:<\/p>\n<ul>\n<li>\u0645\u0642\u0627\u062f\u06cc\u0631 \u0628\u0627\u0644\u0627\u062a\u0631 \u062f\u0648\u0631 \u06a9\u0645\u0631 \u0628\u0647 \u0645\u0639\u0646\u06cc \u0627\u0641\u0632\u0627\u06cc\u0634 \u0627\u0631\u0632\u0634 \u0648\u0632\u0646 (\u0627\u0632 <strong>r = 0.81<\/strong>)<\/li>\n<li>\u0646\u0634\u0633\u062a\u0646 \u0647\u0627\u06cc \u0628\u06cc\u0634\u062a\u0631 \u062f\u0627\u0631\u0627\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u06a9\u0645\u062a\u0631\u06cc \u0627\u0632 \u06a9\u0645\u0631 \u0647\u0633\u062a\u0646\u062f (\u0627\u0632 <strong>r = -0.72<\/strong>)<\/li>\n<li>\u0628\u0647 \u0646\u0638\u0631 \u0646\u0645\u06cc \u0631\u0633\u062f \u0686\u0627\u0646\u0647 \u0647\u0627\u060c \u0646\u0634\u0633\u062a\u0646 \u0647\u0627 \u0648 \u067e\u0631\u0634 \u0647\u0627 \u0631\u0627\u0628\u0637\u0647 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a\u06cc \u0628\u0627 \u0646\u0628\u0636 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f\u060c \u0632\u06cc\u0631\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631 r \u0645\u0631\u0628\u0648\u0637\u0647 \u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647 \u0635\u0641\u0631 \u0647\u0633\u062a\u0646\u062f.<\/li>\n<\/ul>\n<h2 id=\"conclusions\"><span class=\"ez-toc-section\" id=\"%d9%86%d8%aa%db%8c%d8%ac%d9%87_%da%af%db%8c%d8%b1%db%8c\"><\/span>\u0646\u062a\u06cc\u062c\u0647 \u06af\u06cc\u0631\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0631\u0627\u0647\u0646\u0645\u0627\u060c \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646\u060c \u0628\u06cc\u0627\u0646 \u0631\u06cc\u0627\u0636\u06cc \u0622\u0646\u060c \u0648 \u0645\u062d\u0627\u0633\u0628\u0647 \u0622\u0646 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0631\u0627 \u0645\u0648\u0631\u062f \u0628\u062d\u062b \u0642\u0631\u0627\u0631 \u062f\u0627\u062f\u06cc\u0645. <code>pandas<\/code> \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647<\/p>\n<p>\u0645\u0627 \u0627\u06cc\u0646 \u0636\u0631\u06cc\u0628 \u0631\u0627 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u06cc\u0645 \u0631\u0648\u06cc \u0646\u0645\u0648\u0646\u0647 \u0647\u0627\u06cc \u0645\u0635\u0646\u0648\u0639\u06cc \u0645\u062e\u062a\u0644\u0641 \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0631\u0648\u06cc \u0631\u0627 <code>Linnerrud<\/code> \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647  \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc Spearman \u06cc\u06a9 \u0627\u0642\u062f\u0627\u0645 \u0627\u06cc\u062f\u0647 \u0622\u0644 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a\u06cc \u0631\u0627\u0628\u0637\u0647 \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0627\u0633\u062a.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644 \u060c \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 \u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647 \u0635\u0641\u0631 \u0644\u0632\u0648\u0645\u0627\u064b \u0646\u0634\u0627\u0646 \u0646\u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0647\u06cc\u0686 \u0627\u0631\u062a\u0628\u0627\u0637\u06cc \u0628\u06cc\u0646 \u0622\u0646\u0647\u0627 \u0646\u062f\u0627\u0631\u0646\u062f.<\/p>\n<\/div>\n<p><script>\n                        !function(f,b,e,v,n,t,s)\n                        {if(f.fbq)return;n=f.fbq=function(){n.callMethod?\n                        n.callMethod.apply(n,arguments):n.queue.push(arguments)};\n                        if(!f._fbq)f._fbq=n;n.push=n;n.loaded=!0;n.version='2.0';\n                        n.queue=();t=b.createElement(e);t.async=!0;\n                        t.src=v;s=b.getElementsByTagName(e)(0);\n                        s.parentNode.insertBefore(t,s)}(window, document,'script',\n                        'https:\/\/connect.facebook.net\/en_US\/fbevents.js');\n                        fbq('init', '525232124909042');\n                        fbq('track', 'PageView');\n                    <\/script>    (\u0628\u0631\u0686\u0633\u0628\u200c\u0647\u0627 \u0628\u0647 \u062a\u0631\u062c\u0645\u0647)# python<br \/>\n<br \/><br \/>\n<br \/>\u0645\u0646\u062a\u0634\u0631 \u0634\u062f\u0647 \u062f\u0631 1403-01-09 03:22:04<br \/>\n<\/p>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;15149&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;0&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;0&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628&quot;,&quot;legend&quot;:&quot;0\\\/5 (0 \u0631\u0627\u06cc)&quot;,&quot;size&quot;:&quot;30&quot;,&quot;title&quot;:&quot;\u0645\u062d\u0627\u0633\u0628\u0647 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0628\u0627 \u067e\u0627\u0646\u062f\u0627\u0647\u0627&quot;,&quot;width&quot;:&quot;0&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} ({count} \u0631\u0627\u06cc)&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 0px;\">\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 24px;\">\n            <span class=\"kksr-muted\">\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628<\/span>\n    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p><span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 8<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>\u0645\u0639\u0631\u0641\u06cc \u0627\u06cc\u0646 \u0631\u0627\u0647\u0646\u0645\u0627 \u0645\u0642\u062f\u0645\u0647 \u0627\u06cc \u0627\u0633\u062a \u0628\u0631\u0627\u06cc \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u0627\u0633\u067e\u06cc\u0631\u0645\u0646\u060c \u0645\u062d\u0627\u0633\u0628\u0647 \u0631\u06cc\u0627\u0636\u06cc \u0622\u0646 \u0648 \u0645\u062d\u0627\u0633\u0628\u0647 \u0622\u0646 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u067e\u0627\u06cc\u062a\u0648\u0646 pandas \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u0645\u0627 \u0645\u062b\u0627\u0644\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u0645\u06cc\u200c\u0633\u0627\u0632\u06cc\u0645 \u062a\u0627 \u062f\u0631\u06a9 \u0627\u0633\u0627\u0633\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0636\u0631\u06cc\u0628 \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645 \u0648 \u0631\u0648\u0634 \u062a\u062c\u0633\u0645 \u0622\u0646 \u0631\u0627 \u0646\u0634\u0627\u0646 \u062f\u0647\u06cc\u0645 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0632 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[&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":15150,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1743,620],"tags":[],"class_list":["post-15149","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-python","category-programming"],"acf":[],"_links":{"self":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/15149","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/comments?post=15149"}],"version-history":[{"count":0,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/15149\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media\/15150"}],"wp:attachment":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media?parent=15149"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/categories?post=15149"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/tags?post=15149"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}