{"id":15553,"date":"2024-01-13T21:58:18","date_gmt":"2024-01-13T18:28:18","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-%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8\/"},"modified":"2024-01-13T21:58:18","modified_gmt":"2024-01-13T18:28:18","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-%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8","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-%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8\/","title":{"rendered":"\u0645\u062d\u0627\u0633\u0628\u0647 \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 \u0628\u0627 Numpy"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">\u0633\u0631\u0641\u0635\u0644\u0647\u0627\u06cc \u0645\u0637\u0644\u0628<\/p>\n<\/div><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" 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-%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8\/#%d9%85%d8%b9%d8%b1%d9%81%db%8c\" >\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-%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8\/#%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86_%da%86%db%8c%d8%b3%d8%aa%d8%9f\" >\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\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-%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8\/#%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86_%da%86%da%af%d9%88%d9%86%d9%87_%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87_%d9%85%db%8c_%d8%b4%d9%88%d8%af%d8%9f\" >\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0686\u06af\u0648\u0646\u0647 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u0634\u0648\u062f\u061f<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><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-%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8\/#%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86_%d8%af%d8%b1_%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86_numpy\" >\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u062f\u0631 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u067e\u0627\u06cc\u062a\u0648\u0646 NumPy<\/a><ul class='ez-toc-list-level-3' ><li class='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-%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8\/#%d9%85%d8%ab%d8%a7%d9%84_%d9%87%d8%a7%db%8c_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d9%85%d8%ab%d8%a8%d8%aa_%d9%88_%d9%85%d9%86%d9%81%db%8c\" >\u0645\u062b\u0627\u0644 \u0647\u0627\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062b\u0628\u062a \u0648 \u0645\u0646\u0641\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><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-%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8\/#%d8%af%d8%b1%da%a9_%d8%aa%d8%ba%db%8c%db%8c%d8%b1%d8%a7%d8%aa_%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86\" >\u062f\u0631\u06a9 \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><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-%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8\/#%db%8c%da%a9_%d8%af%d8%a7%d9%85_%d8%b1%d8%a7%db%8c%d8%ac_%d8%a7%d8%b1%d8%aa%d8%a8%d8%a7%d8%b7_%d8%a8%d8%af%d9%88%d9%86_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c\" >\u06cc\u06a9 \u062f\u0627\u0645 \u0631\u0627\u06cc\u062c: \u0627\u0631\u062a\u0628\u0627\u0637 \u0628\u062f\u0648\u0646 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc<\/a><\/li><\/ul><\/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-%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%a8\/#%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\"> 5<\/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 \u0645\u0642\u0627\u0644\u0647 \u0645\u0642\u062f\u0645\u0647 \u0627\u06cc \u0627\u0633\u062a \u0628\u0631\u0627\u06cc <em>\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646<\/em>\u060c \u0645\u062d\u0627\u0633\u0628\u0647 \u062f\u0633\u062a\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>numpy<\/code> \u0645\u062f\u0648\u0644.<\/p>\n<p>\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0645\u06cc \u0634\u0648\u062f <strong>\u0627\u0631\u062a\u0628\u0627\u0637 \u062e\u0637\u06cc<\/strong> \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627  \u0645\u0642\u062f\u0627\u0631 \u0622\u0646 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u06cc\u0646\u06af\u0648\u0646\u0647 \u062a\u0641\u0633\u06cc\u0631 \u06a9\u0631\u062f:<\/p>\n<ul>\n<li><strong>+1<\/strong> &#8211; \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062b\u0628\u062a \u06a9\u0627\u0645\u0644<\/li>\n<li><strong>+0.8<\/strong> &#8211; \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062b\u0628\u062a \u0642\u0648\u06cc<\/li>\n<li><strong>+0.6<\/strong> &#8211; \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062b\u0628\u062a \u0645\u062a\u0648\u0633\u0637<\/li>\n<li><strong>0<\/strong> &#8211; \u0647\u06cc\u0686 \u0627\u0631\u062a\u0628\u0627\u0637\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f<\/li>\n<li><strong>-0.6<\/strong> &#8211; \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u0646\u0641\u06cc \u0645\u062a\u0648\u0633\u0637<\/li>\n<li><strong>-0.8<\/strong> &#8211; \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u0646\u0641\u06cc \u0642\u0648\u06cc<\/li>\n<li><strong>-1<\/strong> &#8211; \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u0646\u0641\u06cc \u06a9\u0627\u0645\u0644<\/li>\n<\/ul>\n<p>\u0645\u0627 \u0646\u0634\u0627\u0646 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u062f \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0628\u0627 \u0627\u0646\u0648\u0627\u0639 \u0645\u062e\u062a\u0644\u0641 \u0627\u0631\u062a\u0628\u0627\u0637 \u0645\u062a\u0641\u0627\u0648\u062a \u0627\u0633\u062a.  \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647\u060c \u0645\u0627 \u0622\u0646 \u0631\u0627 \u0646\u06cc\u0632 \u0646\u0634\u0627\u0646 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u062f <em>\u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0635\u0641\u0631<\/em> \u0647\u0645\u06cc\u0634\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0646\u06cc\u0633\u062a <em>\u0647\u06cc\u0686 \u0627\u0631\u062a\u0628\u0627\u0637\u06cc<\/em>.  \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u063a\u06cc\u0631 \u062e\u0637\u06cc \u0645\u0631\u062a\u0628\u0637 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0636\u0631\u0627\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647 \u0635\u0641\u0631 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f.<\/p>\n<h2 id=\"whatisthepearsoncorrelationcoefficient\"><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_%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86_%da%86%db%8c%d8%b3%d8%aa%d8%9f\"><\/span>\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0686\u06cc\u0633\u062a\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0646\u06cc\u0632 \u0628\u0647 \u0646\u0627\u0645 <em>\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062d\u0635\u0648\u0644-\u0644\u062d\u0638\u0647 \u067e\u06cc\u0631\u0633\u0648\u0646<\/em>.  \u0627\u06cc\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 \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u0633\u062a &#8211; <strong>\u0627\u06cc\u06a9\u0633<\/strong> \u0648 <strong>Y<\/strong>.  \u0627\u0632 \u0646\u0638\u0631 \u0631\u06cc\u0627\u0636\u06cc \u0627\u06af\u0631 (<strong>\u03c3XY<\/strong>) \u06a9\u0648\u0648\u0627\u0631\u06cc\u0627\u0646\u0633 \u0628\u06cc\u0646 \u0627\u0633\u062a <strong>\u0627\u06cc\u06a9\u0633<\/strong> \u0648 <strong>Y<\/strong>\u060c \u0648 (<strong>\u03c3X<\/strong>) \u0627\u0646\u062d\u0631\u0627\u0641 \u0645\u0639\u06cc\u0627\u0631 \u0627\u0633\u062a <strong>\u0627\u06cc\u06a9\u0633<\/strong>\u060c \u0633\u067e\u0633 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646  <strong>\u03c1<\/strong> \u0627\u0632 \u0631\u0627\u0628\u0637\u0647 \u0632\u06cc\u0631 \u0628\u062f\u0633\u062a \u0645\u06cc \u0622\u06cc\u062f:<\/p>\n<p>$$<br \/>\\rho_{X,Y} = \\frac{\\sigma_{XY}}{\\sigma_X \\sigma_Y}<br \/>$$<\/p>\n<p>\u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u06a9\u0648\u0648\u0627\u0631\u06cc\u0627\u0646\u0633 \u0647\u0645\u06cc\u0634\u0647 \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0627\u0632 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0627\u0646\u062d\u0631\u0627\u0641\u0627\u062a \u0627\u0633\u062a\u0627\u0646\u062f\u0627\u0631\u062f \u0641\u0631\u062f\u06cc \u0627\u0633\u062a\u060c \u0645\u0642\u062f\u0627\u0631 <strong>\u03c1<\/strong> \u0628\u06cc\u0646 <em>-1<\/em> \u0648 <em>+1<\/em>.  \u0627\u0632 \u0645\u0648\u0627\u0631\u062f \u0628\u0627\u0644\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646 \u062f\u0631\u06cc\u0627\u0641\u062a \u06a9\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u0628\u0627 \u062e\u0648\u062f\u0634 \u06cc\u06a9 \u0627\u0633\u062a:<\/p>\n<p>$$<br \/>\\rho_{X,X} = \\frac{\\sigma_{XX}}{\\sigma_X \\sigma_X} = 1<br \/>$$<br \/>\u0642\u0628\u0644 \u0627\u0632 \u0634\u0631\u0648\u0639 \u06a9\u062f\u0646\u0648\u06cc\u0633\u06cc\u060c \u06cc\u06a9 \u0645\u062b\u0627\u0644 \u06a9\u0648\u062a\u0627\u0647 \u0645\u06cc \u0632\u0646\u06cc\u0645 \u062a\u0627 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u0627\u06cc\u0646 \u0636\u0631\u06cc\u0628 \u0686\u06af\u0648\u0646\u0647 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<h3 id=\"howisthepearsoncorrelationcoefficientcomputed\"><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_%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86_%da%86%da%af%d9%88%d9%86%d9%87_%d9%85%d8%ad%d8%a7%d8%b3%d8%a8%d9%87_%d9%85%db%8c_%d8%b4%d9%88%d8%af%d8%9f\"><\/span>\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0686\u06af\u0648\u0646\u0647 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u0634\u0648\u062f\u061f<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 \u0628\u0647 \u0645\u0627 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a <strong>\u0627\u06cc\u06a9\u0633<\/strong> \u0648 <strong>Y<\/strong>.  \u0627\u06af\u0631 \u0642\u0635\u062f \u062f\u0627\u0631\u06cc\u062f \u0647\u0645\u0647 \u0686\u06cc\u0632 \u0631\u0627 \u0627\u0632 \u0627\u0628\u062a\u062f\u0627 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u06a9\u0646\u06cc\u062f \u06cc\u0627 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u062f\u0633\u062a\u06cc \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u062f\u060c \u062f\u0631 \u0635\u0648\u0631\u062a \u0627\u0631\u0627\u0626\u0647 \u0628\u0647 \u0645\u0648\u0627\u0631\u062f \u0632\u06cc\u0631 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u062f <strong>\u0627\u06cc\u06a9\u0633<\/strong> \u0648 <strong>Y<\/strong>:<\/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        <msup>\n          <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n          <mn>2<\/mn>\n        <\/msup>\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>0<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>1<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>4<\/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        <msup>\n          <mi>Y<\/mi>\n          <mn>2<\/mn>\n        <\/msup>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo stretchy=\"false\">(<\/mo>\n      <\/mtd>\n      <mtd>\n        <mn>16<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>1<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>9<\/mn>\n      <\/mtd>\n      <mtd>\n        <mn>4<\/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        <mi>\u0627\u06cc\u06a9\u0633<\/mi>\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        <mo>&#8211;<\/mo>\n        <mn>8<\/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>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  <\/mtable>\n<\/math><\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u0632 \u0645\u0648\u0627\u0631\u062f \u0628\u0627\u0644\u0627 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645.  \u0645\u0627 \u0627\u0632 \u062a\u062e\u0645\u06cc\u0646 \u0633\u0648\u06af\u06cc\u0631\u06cc \u06a9\u0648\u0648\u0627\u0631\u06cc\u0627\u0646\u0633 \u0648 \u0627\u0646\u062d\u0631\u0627\u0641\u0627\u062a \u0627\u0633\u062a\u0627\u0646\u062f\u0627\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.  \u0627\u06cc\u0646 \u0627\u0645\u0631 \u0628\u0631 \u0645\u0642\u062f\u0627\u0631 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u06a9\u0647 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u0634\u0648\u062f \u062a\u0623\u062b\u06cc\u0631 \u0646\u0645\u06cc \u06af\u0630\u0627\u0631\u062f \u0632\u06cc\u0631\u0627 \u062a\u0639\u062f\u0627\u062f \u0645\u0634\u0627\u0647\u062f\u0627\u062a \u062f\u0631 \u0635\u0648\u0631\u062a \u0648 \u0645\u062e\u0631\u062c \u0644\u063a\u0648 \u0645\u06cc \u0634\u0648\u062f:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mtable columnalign=\"right center center left left\" rowspacing=\"4pt\" columnspacing=\"1em\">\n    <mtr>\n      <mtd>\n        <msub>\n          <mi>\u03c3<\/mi>\n          <mrow class=\"MJX-TeXAtom-ORD\">\n            <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n            <mi>Y<\/mi>\n          <\/mrow>\n        <\/msub>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <mi>E<\/mi>\n        <mo stretchy=\"false\">(<\/mo>\n        <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n        <mi>Y<\/mi>\n        <mo stretchy=\"false\">)<\/mo>\n        <mo>&#8211;<\/mo>\n        <mi>E<\/mi>\n        <mo stretchy=\"false\">(<\/mo>\n        <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n        <mo stretchy=\"false\">)<\/mo>\n        <mi>E<\/mi>\n        <mo stretchy=\"false\">(<\/mo>\n        <mi>Y<\/mi>\n        <mo stretchy=\"false\">)<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n        <mo>&#8211;<\/mo>\n        <mn>7<\/mn>\n        <mrow class=\"MJX-TeXAtom-ORD\">\n          <mo>\/<\/mo>\n        <\/mrow>\n        <mn>5<\/mn>\n        <mo>&#8211;<\/mo>\n        <mo stretchy=\"false\">(<\/mo>\n        <mn>0<\/mn>\n        <mo stretchy=\"false\">)<\/mo>\n        <mo stretchy=\"false\">(<\/mo>\n        <mn>2<\/mn>\n        <mo stretchy=\"false\">)<\/mo>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n        <mo>&#8211;<\/mo>\n        <mn>7<\/mn>\n        <mrow class=\"MJX-TeXAtom-ORD\">\n          <mo>\/<\/mo>\n        <\/mrow>\n        <mn>5<\/mn>\n      <\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd>\n        <msub>\n          <mi>\u03c3<\/mi>\n          <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n        <\/msub>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <msqrt>\n          <mi>E<\/mi>\n          <mo stretchy=\"false\">(<\/mo>\n          <msup>\n            <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n            <mn>2<\/mn>\n          <\/msup>\n          <mo stretchy=\"false\">)<\/mo>\n          <mo>&#8211;<\/mo>\n          <mo stretchy=\"false\">(<\/mo>\n          <mi>E<\/mi>\n          <mo stretchy=\"false\">(<\/mo>\n          <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n          <mo stretchy=\"false\">)<\/mo>\n          <msup>\n            <mo stretchy=\"false\">)<\/mo>\n            <mn>2<\/mn>\n          <\/msup>\n        <\/msqrt>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n        <msqrt>\n          <mn>10<\/mn>\n          <mrow class=\"MJX-TeXAtom-ORD\">\n            <mo>\/<\/mo>\n          <\/mrow>\n          <mn>5<\/mn>\n          <mo>&#8211;<\/mo>\n          <mo stretchy=\"false\">(<\/mo>\n          <mn>0<\/mn>\n          <msup>\n            <mo stretchy=\"false\">)<\/mo>\n            <mn>2<\/mn>\n          <\/msup>\n        <\/msqrt>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n        <msqrt>\n          <mn>2<\/mn>\n        <\/msqrt>\n      <\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd>\n        <msub>\n          <mi>\u03c3<\/mi>\n          <mi>Y<\/mi>\n        <\/msub>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <msqrt>\n          <mi>E<\/mi>\n          <mo stretchy=\"false\">(<\/mo>\n          <msup>\n            <mi>Y<\/mi>\n            <mn>2<\/mn>\n          <\/msup>\n          <mo stretchy=\"false\">)<\/mo>\n          <mo>&#8211;<\/mo>\n          <mo stretchy=\"false\">(<\/mo>\n          <mi>E<\/mi>\n          <mo stretchy=\"false\">(<\/mo>\n          <mi>Y<\/mi>\n          <mo stretchy=\"false\">)<\/mo>\n          <msup>\n            <mo stretchy=\"false\">)<\/mo>\n            <mn>2<\/mn>\n          <\/msup>\n        <\/msqrt>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n        <msqrt>\n          <mn>30<\/mn>\n          <mrow class=\"MJX-TeXAtom-ORD\">\n            <mo>\/<\/mo>\n          <\/mrow>\n          <mn>5<\/mn>\n          <mo>&#8211;<\/mo>\n          <mo stretchy=\"false\">(<\/mo>\n          <mn>10<\/mn>\n          <mrow class=\"MJX-TeXAtom-ORD\">\n            <mo>\/<\/mo>\n          <\/mrow>\n          <mn>5<\/mn>\n          <msup>\n            <mo stretchy=\"false\">)<\/mo>\n            <mn>2<\/mn>\n          <\/msup>\n        <\/msqrt>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n        <msqrt>\n          <mn>2<\/mn>\n        <\/msqrt>\n      <\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd>\n        <msub>\n          <mi>\u03c1<\/mi>\n          <mrow class=\"MJX-TeXAtom-ORD\">\n            <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n            <mi>Y<\/mi>\n          <\/mrow>\n        <\/msub>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n      <\/mtd>\n      <mtd>\n        <mfrac>\n          <mfrac>\n            <mrow>\n              <mo>&#8211;<\/mo>\n              <mn>7<\/mn>\n            <\/mrow>\n            <mn>5<\/mn>\n          <\/mfrac>\n          <mrow>\n            <msqrt>\n              <mn>2<\/mn>\n            <\/msqrt>\n            <msqrt>\n              <mn>2<\/mn>\n            <\/msqrt>\n          <\/mrow>\n        <\/mfrac>\n      <\/mtd>\n      <mtd>\n        <mo>=<\/mo>\n        <mo>&#8211;<\/mo>\n        <mn>7<\/mn>\n        <mrow class=\"MJX-TeXAtom-ORD\">\n          <mo>\/<\/mo>\n        <\/mrow>\n        <mn>10<\/mn>\n      <\/mtd>\n    <\/mtr>\n  <\/mtable>\n<\/math><\/p>\n<h2 id=\"pearsoncorrelationcoefficientinpythonusingnumpy\"><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_%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86_%d8%af%d8%b1_%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86_numpy\"><\/span>\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u062f\u0631 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u067e\u0627\u06cc\u062a\u0648\u0646 <em>NumPy<\/em><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <code>corrcoef()<\/code> \u0631\u0648\u0634 \u0627\u0632 NumPy.<\/p>\n<p>\u0648\u0631\u0648\u062f\u06cc \u0627\u06cc\u0646 \u062a\u0627\u0628\u0639 \u0645\u0639\u0645\u0648\u0644\u0627\u064b \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0627\u0633\u062a\u060c \u0645\u062b\u0644\u0627\u064b \u0627\u0646\u062f\u0627\u0632\u0647 <code>mxn<\/code>\u060c \u062c\u0627\u06cc\u06cc \u06a9\u0647:<\/p>\n<ul>\n<li>\u0647\u0631 \u0633\u062a\u0648\u0646 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u0633\u062a<\/li>\n<li>\u0647\u0631 \u0631\u062f\u06cc\u0641 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u06cc\u06a9 \u0646\u0645\u0648\u0646\u0647 \u0648\u0627\u062d\u062f \u0627\u0632 <code>n<\/code> \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc<\/li>\n<li><code>n<\/code>  \u062a\u0639\u062f\u0627\u062f \u06a9\u0644 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0645\u062e\u062a\u0644\u0641 \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f<\/li>\n<li><code>m<\/code>  \u062a\u0639\u062f\u0627\u062f \u06a9\u0644 \u0646\u0645\u0648\u0646\u0647 \u0647\u0627 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0645\u062a\u063a\u06cc\u0631 \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f<\/li>\n<\/ul>\n<p>\u0628\u0631\u0627\u06cc <code>n<\/code> \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc\u060c an \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>M<\/code>\u060c \u0628\u0627 <code>M(i,j)<\/code> \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \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 \u06cc\u06a9 \u0647\u0633\u062a\u0646\u062f.<\/p>\n<p>\u0628\u0647 \u0627\u062e\u062a\u0635\u0627\u0631:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mi>\u0645<\/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>\u03c1<\/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 \u0631\u0627 \u0628\u0628\u06cc\u0646\u06cc\u0645 <code>corrcoef()<\/code> \u0628\u0627 <code>numpy<\/code>.<\/p>\n<p>\u0627\u0648\u0644\u060c \u0627\u062c\u0627\u0632\u0647 \u062f\u0647\u06cc\u062f import \u0631\u0627 <code>numpy<\/code> \u0645\u0627\u0698\u0648\u0644\u060c \u062f\u0631 \u06a9\u0646\u0627\u0631 <code>pyplot<\/code> \u0645\u0627\u0698\u0648\u0644 \u0627\u0632 Matplotlib.  \u0628\u0639\u062f\u0627\u064b \u0627\u0632 Matplotlib \u0628\u0631\u0627\u06cc \u062a\u062c\u0633\u0645 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f \u0631\u0648\u06cc:<\/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> matplotlib.pyplot <span class=\"hljs-keyword\">as<\/span> plt\n<\/code><\/pre>\n<p>\u0645\u0627 \u0627\u0632 \u0647\u0645\u0627\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062b\u0627\u0644 \u062f\u0633\u062a\u06cc \u0642\u0628\u0644\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0622\u0646 \u0631\u0627 \u062f\u0631 \u0622\u0646 \u0630\u062e\u06cc\u0631\u0647 \u06a9\u0646\u06cc\u0645 <code>x_simple<\/code> \u0648 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u062f:<\/p>\n<pre><code class=\"hljs\">x_simple = np.array((-<span class=\"hljs-number\">2<\/span>, -<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>))\ny_simple = np.array((<span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">0<\/span>))\nmy_rho = np.corrcoef(x_simple, y_simple)\n\n<span class=\"hljs-built_in\">print<\/span>(my_rho)\n<\/code><\/pre>\n<p>\u062f\u0631 \u0632\u06cc\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u062e\u0631\u0648\u062c\u06cc \u0622\u0645\u062f\u0647 \u0627\u0633\u062a.  \u0628\u0647 \u0622\u0646\u0647\u0627 \u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \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 \u06cc\u06a9 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">(( 1.  -0.7)\n(-0.7  1. ))\n<\/code><\/pre>\n<h3 id=\"positiveandnegativecorrelationexamples\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%ab%d8%a7%d9%84_%d9%87%d8%a7%db%8c_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d9%85%d8%ab%d8%a8%d8%aa_%d9%88_%d9%85%d9%86%d9%81%db%8c\"><\/span>\u0645\u062b\u0627\u0644 \u0647\u0627\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062b\u0628\u062a \u0648 \u0645\u0646\u0641\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0636\u0631\u0627\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u0686\u0646\u062f \u0631\u0627\u0628\u0637\u0647 \u0645\u062c\u0633\u0645 \u06a9\u0646\u06cc\u0645.  \u0627\u0648\u0644\u060c \u0645\u0627 \u06cc\u06a9 <em>\u0645\u062b\u0628\u062a \u06a9\u0627\u0645\u0644<\/em> (+1) \u0648 <em>\u0645\u0646\u0641\u06cc \u06a9\u0627\u0645\u0644<\/em> (-1) \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631.  \u0633\u067e\u0633\u060c \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u062a\u0635\u0627\u062f\u0641\u06cc \u062a\u0648\u0644\u06cc\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0628\u0627\u06cc\u062f \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647 \u0635\u0641\u0631 \u0628\u0627\u0634\u062f\u060c \u0645\u06af\u0631 \u0627\u06cc\u0646\u06a9\u0647 \u062a\u0635\u0627\u062f\u0641\u06cc \u0628\u0648\u062f\u0646 \u062a\u0635\u0627\u062f\u0641\u06cc \u062f\u0627\u0631\u0627\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0628\u0627\u0634\u062f\u060c \u06a9\u0647 \u0628\u0633\u06cc\u0627\u0631 \u0628\u0639\u06cc\u062f \u0627\u0633\u062a.<\/p>\n<p>\u0645\u0627 \u0627\u0632 a \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f <code>seed<\/code> \u0628\u0647 \u0637\u0648\u0631\u06cc \u06a9\u0647 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u062f\u0631 \u0647\u0646\u06af\u0627\u0645 \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u0642\u0627\u0628\u0644 \u062a\u06a9\u0631\u0627\u0631 \u0628\u0627\u0634\u062f <code>RandomState<\/code> \u0627\u0632 NumPy:<\/p>\n<pre><code class=\"hljs\">seed = <span class=\"hljs-number\">13<\/span>\nrand = np.random.RandomState(seed)\n\nx = rand.uniform(<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">100<\/span>)\nx = np.vstack((x,x*<span class=\"hljs-number\">2<\/span>+<span class=\"hljs-number\">1<\/span>))\nx = np.vstack((x,-x(<span class=\"hljs-number\">0<\/span>,)*<span class=\"hljs-number\">2<\/span>+<span class=\"hljs-number\">1<\/span>))\nx = np.vstack((x,rand.normal(<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">3<\/span>,<span class=\"hljs-number\">100<\/span>)))\n<\/code><\/pre>\n<p>\u0627\u0648\u0644\u06cc\u0646 <code>rand.uniform()<\/code> \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u06cc\u06a9 \u062a\u0648\u0632\u06cc\u0639 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u062f:<\/p>\n<pre><code class=\"hljs\">(7.77702411e-01 2.37541220e-01 8.24278533e-01 9.65749198e-01\n 9.72601114e-01 4.53449247e-01 6.09042463e-01 7.75526515e-01\n 6.41613345e-01 7.22018230e-01 3.50365241e-02 2.98449471e-01\n 5.85124919e-02 8.57060943e-01 3.72854028e-01 6.79847952e-01\n 2.56279949e-01 3.47581215e-01 9.41277008e-03 3.58333783e-01\n 9.49094182e-01 2.17899009e-01 3.19391366e-01 9.17772386e-01\n 3.19036664e-02 6.50845370e-02 6.29828999e-01 8.73813443e-01\n 8.71573230e-03 7.46577237e-01 8.12841171e-01 7.57174462e-02\n 6.56455335e-01 5.09262200e-01 4.79883391e-01 9.55574145e-01\n 1.20335695e-05 2.46978701e-01 7.12232678e-01 3.24582050e-01\n 2.76996356e-01 6.95445453e-01 9.18551748e-01 2.44475702e-01\n 4.58085817e-01 2.52992683e-01 3.79333291e-01 6.04538829e-01\n 7.72378760e-01 6.79174968e-02 6.86085079e-01 5.48260097e-01\n 1.37986053e-01 9.87532192e-02 2.45559105e-01 1.51786663e-01\n 9.25994479e-01 6.80105016e-01 2.37658922e-01 5.68885253e-01\n 5.56632051e-01 7.27372109e-02 8.39708510e-01 4.05319493e-01\n 1.44870989e-01 1.90920059e-01 4.90640137e-01 7.11403374e-01\n 9.84938458e-01 8.74786502e-01 4.99041684e-01 1.06779994e-01\n 9.13212807e-01 3.64915961e-01 2.26587877e-01 8.72431862e-01\n 1.36358352e-01 2.36380160e-01 5.95399245e-01 5.63922609e-01\n 9.58934732e-01 4.53239333e-01 1.28958075e-01 7.60567677e-01\n 2.01634075e-01 1.75729863e-01 4.37118013e-01 3.40260803e-01\n 9.67253109e-01 1.43026077e-01 8.44558533e-01 6.69406140e-01\n 1.09304908e-01 8.82535400e-02 9.66462041e-01 1.94297485e-01\n 8.19000600e-02 2.69384695e-01 6.50130518e-01 5.46777245e-01)\n<\/code><\/pre>\n<p>\u0633\u067e\u0633\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u062a\u0645\u0627\u0633 \u0628\u06af\u06cc\u0631\u06cc\u0645 <code>vstack()<\/code> \u062a\u0627 \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0639\u0645\u0648\u062f\u06cc \u0631\u0648\u06cc \u0622\u0646 \u0642\u0631\u0627\u0631 \u062f\u0647\u06cc\u062f.  \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628\u060c \u0645\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u062f\u0633\u062a\u0647\u200c\u0627\u06cc \u0627\u0632 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0631\u0627 \u0645\u0627\u0646\u0646\u062f \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0628\u0627\u0644\u0627 \u062f\u0631 \u0647\u0645\u0627\u0646 \u062f\u0633\u062a\u0647 \u0642\u0631\u0627\u0631 \u062f\u0647\u06cc\u0645 <code>x<\/code> \u0628\u0647 \u0622\u0646\u0647\u0627 \u0645\u0631\u0627\u062c\u0639\u0647 \u06a9\u0631\u062f\u0647 \u0648 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0628\u0647 \u0622\u0646\u0647\u0627 \u062f\u0633\u062a\u0631\u0633\u06cc \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f.<\/p>\n<p>\u067e\u0633 \u0627\u0632 \u0627\u0648\u0644\u06cc\u0646 \u062a\u0648\u0632\u06cc\u0639 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a\u060c \u0645\u0627 \u0686\u0646\u062f \u0645\u062c\u0645\u0648\u0639\u0647 \u0645\u062a\u063a\u06cc\u0631 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0639\u0645\u0648\u062f\u06cc \u0631\u0648\u06cc \u0647\u0645 \u0686\u06cc\u062f\u0647 \u0627\u06cc\u0645 &#8211; \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0648\u0645 \u062f\u0627\u0631\u0627\u06cc \u0631\u0627\u0628\u0637\u0647 \u0645\u062b\u0628\u062a \u06a9\u0627\u0645\u0644 \u0628\u0627 \u0627\u0648\u0644\u06cc\u060c \u0633\u0648\u0645\u06cc \u062f\u0627\u0631\u0627\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u0646\u0641\u06cc \u06a9\u0627\u0645\u0644 \u0628\u0627 \u0627\u0648\u0644\u06cc\u0646\u060c \u0648 \u0686\u0647\u0627\u0631\u0645\u06cc \u06a9\u0627\u0645\u0644\u0627 \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u0633\u062a. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0628\u0627\u06cc\u062f \u0647\u0645\u0628\u0633\u062a\u06af\u06cc ~0 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f.<\/p>\n<p>\u0648\u0642\u062a\u06cc \u0645\u062c\u0631\u062f \u062f\u0627\u0631\u06cc\u0645 <code>x<\/code> \u0645\u0631\u062c\u0639\u06cc \u0645\u0627\u0646\u0646\u062f \u0627\u06cc\u0646\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0639\u0646\u0627\u0635\u0631 \u062f\u0631 \u067e\u0634\u062a\u0647 \u0639\u0645\u0648\u062f\u06cc \u0628\u0627 \u0627\u0631\u0633\u0627\u0644 \u0622\u0646 \u0628\u0647 \u062a\u0646\u0647\u0627\u06cc\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u0645 <code>np.corrcoef()<\/code>:<\/p>\n<pre><code class=\"hljs\">rho = np.corrcoef(x)\n\nfig, ax = plt.subplots(nrows=<span class=\"hljs-number\">1<\/span>, ncols=<span class=\"hljs-number\">3<\/span>, figsize=(<span class=\"hljs-number\">12<\/span>, <span class=\"hljs-number\">3<\/span>))\n<span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> (<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">2<\/span>):\n    ax(i).scatter(x(<span class=\"hljs-number\">0<\/span>,),x(<span class=\"hljs-number\">1<\/span>+i,))\n    ax(i).title.set_text(<span class=\"hljs-string\">'Correlation = '<\/span> + <span class=\"hljs-string\">\"{:.2f}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(rho(<span class=\"hljs-number\">0<\/span>,i+<span class=\"hljs-number\">1<\/span>)))\n    ax(i).<span class=\"hljs-built_in\">set<\/span>(xlabel=<span class=\"hljs-string\">'x'<\/span>,ylabel=<span class=\"hljs-string\">'y'<\/span>)\nfig.subplots_adjust(wspace=<span class=\"hljs-number\">.4<\/span>)    \nplt.show()\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/stackabuse.s3.amazonaws.com\/media\/calculating-pearson-correlation-coefficient-in-python-with-numpy-1.png\" alt=\"\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646\" title=\"\"><\/p>\n<h3 id=\"understandingpearsonscorrelationcoefficientchanges\"><span class=\"ez-toc-section\" id=\"%d8%af%d8%b1%da%a9_%d8%aa%d8%ba%db%8c%db%8c%d8%b1%d8%a7%d8%aa_%d8%b6%d8%b1%db%8c%d8%a8_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86\"><\/span>\u062f\u0631\u06a9 \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0641\u0642\u0637 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0628\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0631 \u0631\u0627\u0628\u0637\u0647 \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0686\u06af\u0648\u0646\u0647 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc \u06a9\u0646\u062f\u060c \u0627\u062c\u0627\u0632\u0647 \u062f\u0647\u06cc\u062f \u0645\u0642\u062f\u0627\u0631\u06cc \u0646\u0648\u06cc\u0632 \u062a\u0635\u0627\u062f\u0641\u06cc \u0628\u0647 \u0622\u0646 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u0645. <code>x<\/code> \u0645\u0627\u062a\u0631\u06cc\u0633 \u062f\u0631 \u0628\u062e\u0634 \u0642\u0628\u0644 \u0627\u06cc\u062c\u0627\u062f \u0634\u062f\u0647 \u0648 \u06a9\u062f \u0631\u0627 \u062f\u0648\u0628\u0627\u0631\u0647 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u062f.<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644\u060c \u0645\u0627 \u0628\u0647 \u0622\u0631\u0627\u0645\u06cc \u062f\u0631\u062c\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u06cc \u0627\u0632 \u0646\u0648\u06cc\u0632 \u0631\u0627 \u0628\u0647 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0636\u0631\u0627\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645. \u0631\u0648\u06cc \u0647\u0631 \u0645\u0631\u062d\u0644\u0647:<\/p>\n<pre><code class=\"hljs\">fig, ax = plt.subplots(nrows=<span class=\"hljs-number\">2<\/span>, ncols=<span class=\"hljs-number\">4<\/span>, figsize=(<span class=\"hljs-number\">15<\/span>, <span class=\"hljs-number\">8<\/span>))\n\n<span class=\"hljs-keyword\">for<\/span> noise, i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">zip<\/span>((<span class=\"hljs-number\">0.05<\/span>,<span class=\"hljs-number\">0.2<\/span>,<span class=\"hljs-number\">0.8<\/span>,<span class=\"hljs-number\">2<\/span>),(<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">2<\/span>,<span class=\"hljs-number\">3<\/span>)):\n    \n    x_with_noise = x+rand.normal(<span class=\"hljs-number\">0<\/span>,noise,x.shape)\n    \n    \n    rho_noise = np.corrcoef(x_with_noise)\n    \n    \n    ax(<span class=\"hljs-number\">0<\/span>,i).scatter(x_with_noise(<span class=\"hljs-number\">0<\/span>,),x_with_noise(<span class=\"hljs-number\">1<\/span>,),color=<span class=\"hljs-string\">'magenta'<\/span>)\n    ax(<span class=\"hljs-number\">1<\/span>,i).scatter(x_with_noise(<span class=\"hljs-number\">0<\/span>,),x_with_noise(<span class=\"hljs-number\">2<\/span>,),color=<span class=\"hljs-string\">'green'<\/span>)\n    ax(<span class=\"hljs-number\">0<\/span>,i).title.set_text(<span class=\"hljs-string\">'Correlation = '<\/span> + <span class=\"hljs-string\">\"{:.2f}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(rho_noise(<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">1<\/span>))\n                        + <span class=\"hljs-string\">'\\n Noise = '<\/span> + <span class=\"hljs-string\">\"{:.2f}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(noise) )\n    ax(<span class=\"hljs-number\">1<\/span>,i).title.set_text(<span class=\"hljs-string\">'Correlation = '<\/span> + <span class=\"hljs-string\">\"{:.2f}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(rho_noise(<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">2<\/span>))\n                        + <span class=\"hljs-string\">'\\n Noise = '<\/span> + <span class=\"hljs-string\">\"{:.2f}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(noise))\n    ax(<span class=\"hljs-number\">0<\/span>,i).<span class=\"hljs-built_in\">set<\/span>(xlabel=<span class=\"hljs-string\">'x'<\/span>,ylabel=<span class=\"hljs-string\">'y'<\/span>)    \n    ax(<span class=\"hljs-number\">1<\/span>,i).<span class=\"hljs-built_in\">set<\/span>(xlabel=<span class=\"hljs-string\">'x'<\/span>,ylabel=<span class=\"hljs-string\">'y'<\/span>)\n    \nfig.subplots_adjust(wspace=<span class=\"hljs-number\">0.3<\/span>,hspace=<span class=\"hljs-number\">0.4<\/span>)    \nplt.show()\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/calculating-pearson-correlation-coefficient-in-python-with-numpy-2.png\" alt=\"\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0628\u0627 \u0646\u0648\u06cc\u0632\" title=\"\"><\/p>\n<h3 id=\"acommonpitfallassociationswithnocorrelation\"><span class=\"ez-toc-section\" id=\"%db%8c%da%a9_%d8%af%d8%a7%d9%85_%d8%b1%d8%a7%db%8c%d8%ac_%d8%a7%d8%b1%d8%aa%d8%a8%d8%a7%d8%b7_%d8%a8%d8%af%d9%88%d9%86_%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c\"><\/span>\u06cc\u06a9 \u062f\u0627\u0645 \u0631\u0627\u06cc\u062c: \u0627\u0631\u062a\u0628\u0627\u0637 \u0628\u062f\u0648\u0646 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u06cc\u06a9 \u062a\u0635\u0648\u0631 \u063a\u0644\u0637 \u0631\u0627\u06cc\u062c \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0635\u0641\u0631 \u0628\u0647 \u0645\u0639\u0646\u0627\u06cc \u0639\u062f\u0645 \u0627\u0631\u062a\u0628\u0627\u0637 \u0627\u0633\u062a.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0631\u0648\u0634\u0646 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u062f\u0642\u06cc\u0642\u0627\u064b \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0645\u06cc \u06a9\u0646\u062f <em>\u0631\u0627\u0628\u0637\u0647 \u062e\u0637\u06cc<\/em> \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631<\/p>\n<p>\u0645\u062b\u0627\u0644 \u0647\u0627\u06cc \u0632\u06cc\u0631 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc\u06cc \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0628\u0647 \u0635\u0648\u0631\u062a \u063a\u06cc\u0631 \u062e\u0637\u06cc \u0628\u0627 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0645\u0631\u062a\u0628\u0637 \u0647\u0633\u062a\u0646\u062f \u0627\u0645\u0627 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0635\u0641\u0631 \u062f\u0627\u0631\u0646\u062f.<\/p>\n<p>\u0622\u062e\u0631\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0627\u0632 (y=e<sup>\u0627\u06cc\u06a9\u0633<\/sup>) \u062f\u0627\u0631\u0627\u06cc \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u062d\u062f\u0648\u062f 0.52 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0627\u0632\u062a\u0627\u0628\u06cc \u0627\u0632 \u0627\u0631\u062a\u0628\u0627\u0637 \u0648\u0627\u0642\u0639\u06cc \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0646\u06cc\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">\nx_nonlinear = np.linspace(-<span class=\"hljs-number\">10<\/span>,<span class=\"hljs-number\">10<\/span>,<span class=\"hljs-number\">100<\/span>)\nx_nonlinear = np.vstack((x_nonlinear,x_nonlinear*x_nonlinear))\nx_nonlinear = np.vstack((x_nonlinear,-x_nonlinear(<span class=\"hljs-number\">0<\/span>,)**<span class=\"hljs-number\">2<\/span>))\nx_nonlinear = np.vstack((x_nonlinear,x_nonlinear(<span class=\"hljs-number\">0<\/span>,)**<span class=\"hljs-number\">4<\/span>))\nx_nonlinear = np.vstack((x_nonlinear,np.log(x_nonlinear(<span class=\"hljs-number\">0<\/span>,)**<span class=\"hljs-number\">2<\/span>+<span class=\"hljs-number\">1<\/span>)))\nx_nonlinear = np.vstack((x_nonlinear,np.exp(x_nonlinear(<span class=\"hljs-number\">0<\/span>,))))\n\n\nrho_nonlinear = np.corrcoef(x_nonlinear)\n\n\nfig, ax = plt.subplots(nrows=<span class=\"hljs-number\">1<\/span>, ncols=<span class=\"hljs-number\">5<\/span>, figsize=(<span class=\"hljs-number\">16<\/span>, <span class=\"hljs-number\">3<\/span>))\ntitle = (<span class=\"hljs-string\">'$y=x^2$'<\/span>,<span class=\"hljs-string\">'$y=-x^2$'<\/span>,<span class=\"hljs-string\">'$y=x^4$'<\/span>,<span class=\"hljs-string\">'$y=\\log(x^2+1)$'<\/span>,<span class=\"hljs-string\">'$y=\\exp(x)$'<\/span>)\n<span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> (<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">1<\/span>,<span class=\"hljs-number\">2<\/span>,<span class=\"hljs-number\">3<\/span>,<span class=\"hljs-number\">4<\/span>):\n    ax(i).scatter(x_nonlinear(<span class=\"hljs-number\">0<\/span>,),x_nonlinear(<span class=\"hljs-number\">1<\/span>+i,),color=<span class=\"hljs-string\">'cyan'<\/span>)\n    ax(i).title.set_text(title(i) + <span class=\"hljs-string\">'\\n'<\/span> + \n                         <span class=\"hljs-string\">'Correlation = '<\/span> + <span class=\"hljs-string\">\"{:.2f}\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(rho_nonlinear(<span class=\"hljs-number\">0<\/span>,i+<span class=\"hljs-number\">1<\/span>)))\n    ax(i).<span class=\"hljs-built_in\">set<\/span>(xlabel=<span class=\"hljs-string\">'x'<\/span>,ylabel=<span class=\"hljs-string\">'y'<\/span>)\nfig.subplots_adjust(wspace=<span class=\"hljs-number\">.4<\/span>)    \nplt.show()\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/1705170498_991_calculating-pearson-correlation-coefficient-in-python-with-numpy-3.png\" alt=\"\u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u062f\u0631 \u0645\u0642\u0627\u0628\u0644 \u0627\u0631\u062a\u0628\u0627\u0637 \u0645\u062a\u063a\u06cc\u0631\" title=\"\"><\/p>\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 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u067e\u0631\u062f\u0627\u062e\u062a\u06cc\u0645.  \u0645\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f\u06cc\u0645 <code>corrcoef()<\/code> \u0631\u0648\u0634 \u0627\u0632 \u067e\u0627\u06cc\u062a\u0648\u0646 <code>numpy<\/code> \u0645\u0627\u0698\u0648\u0644 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u0642\u062f\u0627\u0631 \u0622\u0646<\/p>\n<p>\u0627\u06af\u0631 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u062f\u0627\u0631\u0627\u06cc \u0627\u0631\u062a\u0628\u0627\u0637 \u062e\u0637\u06cc \u0628\u0627\u0644\u0627\u06cc\u06cc \u0628\u0627\u0634\u0646\u062f\u060c \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0622\u0646\u0647\u0627 \u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647 1+ \u06cc\u0627 1- \u0627\u0633\u062a.  \u0627\u0632 \u0633\u0648\u06cc \u062f\u06cc\u06af\u0631\u060c \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0645\u0633\u062a\u0642\u0644 \u0622\u0645\u0627\u0631\u06cc \u062f\u0627\u0631\u0627\u06cc \u0636\u0631\u0627\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647 \u0635\u0641\u0631 \u0647\u0633\u062a\u0646\u062f.<\/p>\n<p>\u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u06cc\u0645 \u06a9\u0647 \u0627\u0646\u062c\u0645\u0646\u200c\u0647\u0627\u06cc \u063a\u06cc\u0631\u062e\u0637\u06cc \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0646\u062f \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0635\u0641\u0631 \u06cc\u0627 \u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647 \u0635\u0641\u0631 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f\u060c \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u06a9\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0627\u0631\u062a\u0628\u0627\u0637 \u0628\u0627\u0644\u0627\u06cc\u06cc \u062f\u0627\u0631\u0646\u062f \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0645\u0642\u062f\u0627\u0631 \u0628\u0627\u0644\u0627\u06cc\u06cc \u0627\u0632 \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0646\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\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 1403-01-13 21:58:04<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;15553&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 \u067e\u06cc\u0631\u0633\u0648\u0646 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0628\u0627 Numpy&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\"> 5<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>\u0645\u0639\u0631\u0641\u06cc \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \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 \u067e\u06cc\u0631\u0633\u0648\u0646\u060c \u0645\u062d\u0627\u0633\u0628\u0647 \u062f\u0633\u062a\u06cc \u0622\u0646 \u0648 \u0645\u062d\u0627\u0633\u0628\u0647 \u0622\u0646 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u067e\u0627\u06cc\u062a\u0648\u0646 numpy \u0645\u062f\u0648\u0644. \u0636\u0631\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0645\u06cc \u0634\u0648\u062f \u0627\u0631\u062a\u0628\u0627\u0637 \u062e\u0637\u06cc \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0645\u0642\u062f\u0627\u0631 \u0622\u0646 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u06cc\u0646\u06af\u0648\u0646\u0647 \u062a\u0641\u0633\u06cc\u0631 \u06a9\u0631\u062f: +1 &#8211; \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062b\u0628\u062a \u06a9\u0627\u0645\u0644 +0.8 &#8211; \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062b\u0628\u062a \u0642\u0648\u06cc +0.6 &#8211; \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062b\u0628\u062a \u0645\u062a\u0648\u0633\u0637 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":15554,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1743,620],"tags":[],"class_list":["post-15553","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\/15553","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=15553"}],"version-history":[{"count":0,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/15553\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media\/15554"}],"wp:attachment":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media?parent=15553"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/categories?post=15553"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/tags?post=15553"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}