{"id":4797,"date":"2026-09-18T04:22:25","date_gmt":"2026-09-18T04:22:25","guid":{"rendered":"https:\/\/otus.ru\/journal\/?p=4797"},"modified":"2026-09-25T15:46:33","modified_gmt":"2026-09-25T15:46:33","slug":"linejnaya-regressiya","status":"publish","type":"post","link":"https:\/\/otus.ru\/journal\/linejnaya-regressiya\/","title":{"rendered":"\u041b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f: \u043c\u043e\u0434\u0435\u043b\u044c, \u041c\u041d\u041a \u0438 \u043c\u0435\u0442\u0440\u0438\u043a\u0438 \u043d\u0430 Python"},"content":{"rendered":"<p><strong>\u041b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f<\/strong> &#8212; \u044d\u0442\u043e \u043c\u043e\u0434\u0435\u043b\u044c, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0447\u0438\u0441\u043b\u043e\u0432\u043e\u0439 \u0446\u0435\u043b\u0435\u0432\u043e\u0439 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 y \u043e\u0442 \u043e\u0434\u043d\u043e\u0433\u043e \u0438\u043b\u0438 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u0438\u0445 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u043e\u0432 x \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439: y = a + b*x. \u041c\u043e\u0434\u0435\u043b\u044c \u043e\u0431\u0443\u0447\u0430\u044e\u0442 \u043d\u0430 \u0434\u0430\u043d\u043d\u044b\u0445, \u043f\u043e\u0434\u0431\u0438\u0440\u0430\u044f \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b a \u0438 b \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043d\u0438\u044f \u0431\u044b\u043b\u0438 \u043a\u0430\u043a \u043c\u043e\u0436\u043d\u043e \u0431\u043b\u0438\u0436\u0435 \u043a \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c. \u041d\u0438\u0436\u0435 &#8212; \u043a\u0430\u043a \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u043f\u043e\u0434\u0431\u043e\u0440 (\u043c\u0435\u0442\u043e\u0434 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432), \u043a\u0430\u043a \u043e\u0446\u0435\u043d\u0438\u0432\u0430\u0442\u044c \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u043e (R2 \u0438 MSE), \u043a\u0430\u043a\u0438\u0435 \u0443 \u043c\u043e\u0434\u0435\u043b\u0438 \u0434\u043e\u043f\u0443\u0449\u0435\u043d\u0438\u044f, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0435\u0440\u0435\u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0438 \u0447\u0435\u043c \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442\u0441\u044f \u043e\u0442 \u043b\u043e\u0433\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439. \u0412\u0435\u0441\u044c \u043a\u043e\u0434 \u043d\u0430 Python (numpy \u0438 scikit-learn), \u0432\u044b\u0432\u043e\u0434\u044b \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u044b \u043f\u0440\u043e\u0433\u043e\u043d\u043e\u043c \u0441 \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u043c seed \u0438 \u0432\u043e\u0441\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u044f\u0442\u0441\u044f.<\/p>\n<div class=\"oj-toc\" style=\"background:#f6f6f6;border-radius:8px;padding:14px 20px;margin:20px 0\">\n<p><strong>\u0421\u043e\u0434\u0435\u0440\u0436\u0430\u043d\u0438\u0435<\/strong><\/p>\n<ol>\n<li><a href=\"#s1\">\u041a\u0430\u043a \u0443\u0441\u0442\u0440\u043e\u0435\u043d\u0430 \u043c\u043e\u0434\u0435\u043b\u044c<\/a><\/li>\n<li><a href=\"#s2\">\u041c\u0435\u0442\u043e\u0434 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 (\u041c\u041d\u041a)<\/a><\/li>\n<li><a href=\"#s3\">\u041c\u0435\u0442\u0440\u0438\u043a\u0438 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0430: R2 \u0438 MSE<\/a><\/li>\n<li><a href=\"#s4\">\u041c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f<\/a><\/li>\n<li><a href=\"#s5\">\u0414\u043e\u043f\u0443\u0449\u0435\u043d\u0438\u044f \u043c\u043e\u0434\u0435\u043b\u0438<\/a><\/li>\n<li><a href=\"#s6\">\u041f\u0435\u0440\u0435\u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435<\/a><\/li>\n<li><a href=\"#s7\">\u041e\u0442\u043b\u0438\u0447\u0438\u0435 \u043e\u0442 \u043b\u043e\u0433\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438<\/a><\/li>\n<li><a href=\"#s8\">\u0412\u044b\u0432\u043e\u0434\u044b<\/a><\/li>\n<li><a href=\"#s9\">\u0413\u0434\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \/ \u0441\u0432\u044f\u0437\u044c \u0441 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0439<\/a><\/li>\n<li><a href=\"#s10\">FAQ<\/a><\/li>\n<\/ol>\n<\/div>\n<p>\u0427\u0442\u043e\u0431\u044b \u043d\u0435 \u043f\u0443\u0442\u0430\u0442\u044c \u0431\u043b\u0438\u0437\u043a\u0438\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f, \u0434\u043e\u0433\u043e\u0432\u043e\u0440\u0438\u043c\u0441\u044f \u043e \u0441\u043b\u043e\u0432\u0430\u0440\u0435 \u0441\u0440\u0430\u0437\u0443:<\/p>\n<ul>\n<li><strong>\u041f\u0440\u043e\u0441\u0442\u0430\u044f (\u043f\u0430\u0440\u043d\u0430\u044f) \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f<\/strong> &#8212; \u043e\u0434\u0438\u043d \u043f\u0440\u0438\u0437\u043d\u0430\u043a x, \u043c\u043e\u0434\u0435\u043b\u044c y = a + b*x.<\/li>\n<li><strong>\u041c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f<\/strong> &#8212; \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u043e\u0432, \u043c\u043e\u0434\u0435\u043b\u044c y = a + b1<em>x1 + &#8230; + bk<\/em>xk.<\/li>\n<li><strong>\u0420\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f<\/strong> \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u0447\u0438\u0441\u043b\u043e (\u0446\u0435\u043d\u0443, \u0442\u0435\u043c\u043f\u0435\u0440\u0430\u0442\u0443\u0440\u0443), <strong>\u043a\u043b\u0430\u0441\u0441\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u044f<\/strong> &#8212; \u043c\u0435\u0442\u043a\u0443 \u043a\u043b\u0430\u0441\u0441\u0430. \u041b\u043e\u0433\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f, \u043d\u0435\u0441\u043c\u043e\u0442\u0440\u044f \u043d\u0430 \u0441\u043b\u043e\u0432\u043e \u00ab\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f\u00bb, \u0440\u0435\u0448\u0430\u0435\u0442 \u0437\u0430\u0434\u0430\u0447\u0443 \u043a\u043b\u0430\u0441\u0441\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u0438.<\/li>\n<li><strong>\u041e\u0441\u0442\u0430\u0442\u043e\u043a<\/strong> &#8212; \u0440\u0430\u0437\u043d\u0438\u0446\u0430 \u043c\u0435\u0436\u0434\u0443 \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u043c y \u0438 \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043d\u043d\u044b\u043c y \u0434\u043b\u044f \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438. \u041d\u0435 \u043f\u0443\u0442\u0430\u0442\u044c \u0441\u043e \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0439 \u043e\u0448\u0438\u0431\u043a\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438: \u043e\u0441\u0442\u0430\u0442\u043e\u043a &#8212; \u044d\u0442\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0430\u0435\u043c\u0430\u044f \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430, \u043f\u043e\u0441\u0447\u0438\u0442\u0430\u043d\u043d\u0430\u044f \u043f\u043e\u0441\u043b\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f.<\/li>\n<\/ul>\n<h2 id=\"s1\">\u041a\u0430\u043a \u0443\u0441\u0442\u0440\u043e\u0435\u043d\u0430 \u043c\u043e\u0434\u0435\u043b\u044c<\/h2>\n<p>\u0412 \u043f\u0430\u0440\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0434\u0432\u0430 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0430: a &#8212; \u0441\u0432\u043e\u0431\u043e\u0434\u043d\u044b\u0439 \u0447\u043b\u0435\u043d (\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 y \u043f\u0440\u0438 x = 0), b &#8212; \u0443\u0433\u043b\u043e\u0432\u043e\u0439 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 (\u043d\u0430 \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0432 \u0441\u0440\u0435\u0434\u043d\u0435\u043c \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f y \u043f\u0440\u0438 \u0440\u043e\u0441\u0442\u0435 x \u043d\u0430 \u0435\u0434\u0438\u043d\u0438\u0446\u0443). \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438 \u043c\u043e\u0434\u0435\u043b\u044c &#8212; \u043f\u0440\u044f\u043c\u0430\u044f, \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u043d\u0430\u044f \u0441\u043a\u0432\u043e\u0437\u044c \u043e\u0431\u043b\u0430\u043a\u043e \u0442\u043e\u0447\u0435\u043a \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u0442\u043e\u0447\u043a\u0438 \u043b\u0435\u0436\u0430\u043b\u0438 \u043a \u043d\u0435\u0439 \u043a\u0430\u043a \u043c\u043e\u0436\u043d\u043e \u0431\u043b\u0438\u0436\u0435.<\/p>\n<p>\u0412 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u043a\u0430\u0436\u0434\u044b\u0439 \u043f\u0440\u0438\u0437\u043d\u0430\u043a \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442 \u0441\u0432\u043e\u0439 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 b_i &#8212; \u0432\u043a\u043b\u0430\u0434 \u044d\u0442\u043e\u0433\u043e \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u0430 \u043f\u0440\u0438 \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0445. \u041c\u043e\u0434\u0435\u043b\u044c \u043f\u0435\u0440\u0435\u0441\u0442\u0430\u0435\u0442 \u0431\u044b\u0442\u044c \u043f\u0440\u044f\u043c\u043e\u0439 \u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u0433\u0438\u043f\u0435\u0440\u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e, \u043d\u043e \u043f\u0440\u0438\u043d\u0446\u0438\u043f \u0442\u043e\u0442 \u0436\u0435: \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u043e\u0432 \u043f\u043b\u044e\u0441 \u0441\u0432\u043e\u0431\u043e\u0434\u043d\u044b\u0439 \u0447\u043b\u0435\u043d.<\/p>\n<h2 id=\"s2\">\u041c\u0435\u0442\u043e\u0434 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 (\u041c\u041d\u041a)<\/h2>\n<p>\u041a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u043f\u043e\u0434\u0431\u0438\u0440\u0430\u044e\u0442 \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b <strong>\u0441\u0443\u043c\u043c\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 \u043e\u0441\u0442\u0430\u0442\u043a\u043e\u0432<\/strong> \u0431\u044b\u043b\u0430 \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0439. \u042d\u0442\u043e \u0438 \u0435\u0441\u0442\u044c \u043c\u0435\u0442\u043e\u0434 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 (\u041c\u041d\u041a, \u0430\u043d\u0433\u043b. OLS). \u041a\u0432\u0430\u0434\u0440\u0430\u0442\u044b \u0431\u0435\u0440\u0443\u0442, \u0447\u0442\u043e\u0431\u044b \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u044f \u0432\u0432\u0435\u0440\u0445 \u0438 \u0432\u043d\u0438\u0437 \u043d\u0435 \u0433\u0430\u0441\u0438\u043b\u0438 \u0434\u0440\u0443\u0433 \u0434\u0440\u0443\u0433\u0430 \u0438 \u0447\u0442\u043e\u0431\u044b \u043a\u0440\u0443\u043f\u043d\u044b\u0435 \u043f\u0440\u043e\u043c\u0430\u0445\u0438 \u0448\u0442\u0440\u0430\u0444\u043e\u0432\u0430\u043b\u0438\u0441\u044c \u0441\u0438\u043b\u044c\u043d\u0435\u0435.<\/p>\n<p>\u041d\u0430\u0447\u043d\u0435\u043c \u0441 \u043f\u043e\u043b\u043d\u043e\u0433\u043e \u0440\u0430\u0431\u043e\u0447\u0435\u0433\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u0430: \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u0435\u043c \u0434\u0430\u043d\u043d\u044b\u0435 \u0441 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0439 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c\u044e y = 2.5*x + 4 \u043f\u043b\u044e\u0441 \u0448\u0443\u043c \u0438 \u043e\u0431\u0443\u0447\u0438\u043c \u043c\u043e\u0434\u0435\u043b\u044c \u0447\u0435\u0440\u0435\u0437 scikit-learn.<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">import<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">numpy<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #C678DD\">as<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">np<\/span>\n<span style=\"color: #C678DD\">from<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">sklearn.linear_model<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #C678DD\">import<\/span> <span style=\"color: #E06C75\">LinearRegression<\/span>\n<span style=\"color: #C678DD\">from<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">sklearn.metrics<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #C678DD\">import<\/span> <span style=\"color: #E06C75\">mean_squared_error<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">r2_score<\/span>\n\n<span style=\"color: #E06C75\">rng<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">random<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">default_rng<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">42<\/span><span style=\"color: #ABB2BF\">)<\/span>          <span style=\"color: #7F848E\"># \u0444\u0438\u043a\u0441\u0438\u0440\u0443\u0435\u043c seed - \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u0432\u043e\u0441\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u0438\u043c<\/span>\n<span style=\"color: #E06C75\">n<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">50<\/span>\n<span style=\"color: #E06C75\">x<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">linspace<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">10<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">n<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E06C75\">y<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">2.5<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">x<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">4.0<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">rng<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">normal<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">2.0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">n<\/span><span style=\"color: #ABB2BF\">)<\/span>  <span style=\"color: #7F848E\"># \u0438\u0441\u0442\u0438\u043d\u043d\u044b\u0435 a=4.0, b=2.5, \u0448\u0443\u043c sd=2<\/span>\n\n<span style=\"color: #E06C75\">X<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">x<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">reshape<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #56B6C2\">-<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">)<\/span>                      <span style=\"color: #7F848E\"># sklearn \u0436\u0434\u0435\u0442 2D-\u043c\u0430\u0441\u0441\u0438\u0432 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u043e\u0432<\/span>\n<span style=\"color: #E06C75\">model<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">LinearRegression<\/span><span style=\"color: #ABB2BF\">()<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">fit<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">X<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">y<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E06C75\">y_pred<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">model<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">predict<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">X<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">f\"a = {<\/span><span style=\"color: #E06C75\">model<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">intercept_<\/span><span style=\"color: #98C379\">:.4f}\"<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">f\"b = {<\/span><span style=\"color: #E06C75\">model<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">coef_<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">]<\/span><span style=\"color: #98C379\">:.4f}\"<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">f\"MSE = {<\/span><span style=\"color: #E06C75\">mean_squared_error<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">y<\/span><span style=\"color: #ABB2BF\">, <\/span><span style=\"color: #E06C75\">y_pred<\/span><span style=\"color: #ABB2BF\">)<\/span><span style=\"color: #98C379\">:.4f}\"<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">f\"R2  = {<\/span><span style=\"color: #E06C75\">r2_score<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">y<\/span><span style=\"color: #ABB2BF\">, <\/span><span style=\"color: #E06C75\">y_pred<\/span><span style=\"color: #ABB2BF\">)<\/span><span style=\"color: #98C379\">:.4f}\"<\/span><span style=\"color: #ABB2BF\">)<\/span><\/code><\/pre>\n<p>\u0424\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0432\u044b\u0432\u043e\u0434:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">a = 3.7301\nb = 2.5905\nMSE = 2.2428\nR2  = 0.9629\n<\/code><\/pre>\n<p>\u041c\u043e\u0434\u0435\u043b\u044c \u0432\u043e\u0441\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u043b\u0430 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0431\u043b\u0438\u0437\u043a\u043e \u043a \u0438\u0441\u0442\u0438\u043d\u043d\u044b\u043c (a \u043e\u043a\u043e\u043b\u043e 4, b \u043e\u043a\u043e\u043b\u043e 2.5) &#8212; \u0442\u043e\u0447\u043d\u043e\u0433\u043e \u0441\u043e\u0432\u043f\u0430\u0434\u0435\u043d\u0438\u044f \u043d\u0435\u0442, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u0432 \u0434\u0430\u043d\u043d\u044b\u0435 \u0434\u043e\u0431\u0430\u0432\u043b\u0435\u043d \u0448\u0443\u043c. \u0420\u0430\u0437\u0431\u043e\u0440 \u043f\u043e \u0441\u0442\u0440\u043e\u043a\u0430\u043c: <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">reshape(-1, 1)<\/code> \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0430\u0435\u0442 \u0432\u0435\u043a\u0442\u043e\u0440 \u0432 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u043e\u0432 (\u0441\u0442\u043e\u043b\u0431\u0435\u0446), <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">fit<\/code> \u043f\u043e\u0434\u0431\u0438\u0440\u0430\u0435\u0442 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u043f\u043e \u041c\u041d\u041a, <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">predict<\/code> \u0441\u0447\u0438\u0442\u0430\u0435\u0442 \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043d\u0438\u044f, <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">intercept_<\/code> \u0438 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">coef_<\/code> &#8212; \u044d\u0442\u043e a \u0438 b.<\/p>\n<p>\u0414\u043b\u044f \u043f\u0430\u0440\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0442\u0435 \u0436\u0435 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u041c\u041d\u041a \u0432\u0440\u0443\u0447\u043d\u0443\u044e, \u0431\u0435\u0437 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #E06C75\">x_mean<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">y_mean<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">x<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">mean<\/span><span style=\"color: #ABB2BF\">(),<\/span> <span style=\"color: #E06C75\">y<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">mean<\/span><span style=\"color: #ABB2BF\">()<\/span>\n<span style=\"color: #E06C75\">b<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">sum<\/span><span style=\"color: #ABB2BF\">((<\/span><span style=\"color: #E06C75\">x<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #E06C75\">x_mean<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">y<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #E06C75\">y_mean<\/span><span style=\"color: #ABB2BF\">))<\/span> <span style=\"color: #56B6C2\">\/<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">sum<\/span><span style=\"color: #ABB2BF\">((<\/span><span style=\"color: #E06C75\">x<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #E06C75\">x_mean<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">**<\/span> <span style=\"color: #D19A66\">2<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E06C75\">a<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">y_mean<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #E06C75\">b<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">x_mean<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">f\"a = {<\/span><span style=\"color: #E06C75\">a<\/span><span style=\"color: #98C379\">:.4f}, b = {<\/span><span style=\"color: #E06C75\">b<\/span><span style=\"color: #98C379\">:.4f}\"<\/span><span style=\"color: #ABB2BF\">)<\/span>   <span style=\"color: #7F848E\"># a = 3.7301, b = 2.5905<\/span><\/code><\/pre>\n<p>\u0427\u0438\u0441\u043b\u0430 \u0441\u043e\u0432\u043f\u0430\u043b\u0438 \u0441 \u0432\u044b\u0432\u043e\u0434\u043e\u043c scikit-learn &#8212; \u044d\u0442\u043e \u043f\u043e\u0434\u0442\u0432\u0435\u0440\u0436\u0434\u0430\u0435\u0442, \u0447\u0442\u043e <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">LinearRegression<\/code> \u043f\u043e\u0434 \u043a\u0430\u043f\u043e\u0442\u043e\u043c \u0440\u0435\u0448\u0430\u0435\u0442 \u0442\u0443 \u0436\u0435 \u0437\u0430\u0434\u0430\u0447\u0443 \u043c\u0438\u043d\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0441\u0443\u043c\u043c\u044b \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432.<\/p>\n<h2 id=\"s3\">\u041c\u0435\u0442\u0440\u0438\u043a\u0438 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0430: R2 \u0438 MSE<\/h2>\n<p>\u0414\u0432\u0435 \u0431\u0430\u0437\u043e\u0432\u044b\u0435 \u043c\u0435\u0442\u0440\u0438\u043a\u0438 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0438\u0437\u043c\u0435\u0440\u044f\u044e\u0442 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u043e \u043f\u043e-\u0440\u0430\u0437\u043d\u043e\u043c\u0443, \u0443 \u043a\u0430\u0436\u0434\u043e\u0439 \u0441\u0432\u043e\u044f \u0433\u0440\u0430\u043d\u0438\u0446\u0430 \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c\u043e\u0441\u0442\u0438.<\/p>\n<table>\n<thead>\n<tr>\n<th>\u041c\u0435\u0442\u0440\u0438\u043a\u0430<\/th>\n<th>\u0427\u0442\u043e \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442<\/th>\n<th>\u0415\u0434\u0438\u043d\u0438\u0446\u044b<\/th>\n<th>\u0414\u0438\u0430\u043f\u0430\u0437\u043e\u043d<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>MSE<\/td>\n<td>\u0441\u0440\u0435\u0434\u043d\u0438\u0439 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u043e\u0441\u0442\u0430\u0442\u043a\u0430<\/td>\n<td>\u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0435\u0434\u0438\u043d\u0438\u0446 y<\/td>\n<td>\u043e\u0442 0 (\u0438\u0434\u0435\u0430\u043b) \u0438 \u0432\u044b\u0448\u0435<\/td>\n<\/tr>\n<tr>\n<td>R2<\/td>\n<td>\u0434\u043e\u043b\u044e \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0438\u0438 y, \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u043d\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c\u044e<\/td>\n<td>\u0431\u0435\u0437\u0440\u0430\u0437\u043c\u0435\u0440\u043d\u0430\u044f<\/td>\n<td>\u0434\u043e 1; \u043d\u0430 \u043d\u043e\u0432\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445 \u0431\u044b\u0432\u0430\u0435\u0442 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>MSE<\/strong> (mean squared error) &#8212; \u0441\u0440\u0435\u0434\u043d\u0438\u0439 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u043e\u0448\u0438\u0431\u043a\u0438; \u0447\u0435\u043c \u043c\u0435\u043d\u044c\u0448\u0435, \u0442\u0435\u043c \u043b\u0443\u0447\u0448\u0435. \u041e\u043d\u0430 \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435 \u0435\u0434\u0438\u043d\u0438\u0446 \u0446\u0435\u043b\u0435\u0432\u043e\u0439 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0447\u0430\u0441\u0442\u043e \u0431\u0435\u0440\u0443\u0442 \u043a\u043e\u0440\u0435\u043d\u044c (RMSE), \u0447\u0442\u043e\u0431\u044b \u0432\u0435\u0440\u043d\u0443\u0442\u044c\u0441\u044f \u043a \u0438\u0441\u0445\u043e\u0434\u043d\u044b\u043c \u0435\u0434\u0438\u043d\u0438\u0446\u0430\u043c. \u0421\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0442\u044c MSE \u043c\u0435\u0436\u0434\u0443 \u0440\u0430\u0437\u043d\u044b\u043c\u0438 \u0437\u0430\u0434\u0430\u0447\u0430\u043c\u0438 \u043d\u0435\u043b\u044c\u0437\u044f &#8212; \u043c\u0430\u0441\u0448\u0442\u0430\u0431 y \u0443 \u043d\u0438\u0445 \u0440\u0430\u0437\u043d\u044b\u0439.<\/p>\n<p><strong>R2<\/strong> (\u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u0434\u0435\u0442\u0435\u0440\u043c\u0438\u043d\u0430\u0446\u0438\u0438) = 1 &#8212; (\u0441\u0443\u043c\u043c\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 \u043e\u0441\u0442\u0430\u0442\u043a\u043e\u0432) \/ (\u0441\u0443\u043c\u043c\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0439 y \u043e\u0442 \u0441\u0440\u0435\u0434\u043d\u0435\u0433\u043e). \u041d\u0430 \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0435\u0439 \u0432\u044b\u0431\u043e\u0440\u043a\u0435 \u0443 \u041c\u041d\u041a R2 \u043b\u0435\u0436\u0438\u0442 \u0432 \u0434\u0438\u0430\u043f\u0430\u0437\u043e\u043d\u0435 \u043e\u0442 0 \u0434\u043e 1, \u0433\u0434\u0435 1 &#8212; \u0438\u0434\u0435\u0430\u043b\u044c\u043d\u0430\u044f \u043f\u043e\u0434\u0433\u043e\u043d\u043a\u0430. \u041d\u043e \u043d\u0430 \u043d\u043e\u0432\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445 R2 \u043c\u043e\u0436\u0435\u0442 \u0441\u0442\u0430\u0442\u044c \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439: \u044d\u0442\u043e \u0437\u043d\u0430\u0447\u0438\u0442, \u0447\u0442\u043e \u043c\u043e\u0434\u0435\u043b\u044c \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u0445\u0443\u0436\u0435, \u0447\u0435\u043c \u043f\u0440\u043e\u0441\u0442\u043e\u0435 \u0441\u0440\u0435\u0434\u043d\u0435\u0435. \u0412 \u043f\u0430\u0440\u043d\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 R2 \u0440\u0430\u0432\u0435\u043d \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0443 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0430 \u043a\u043e\u0440\u0440\u0435\u043b\u044f\u0446\u0438\u0438 \u041f\u0438\u0440\u0441\u043e\u043d\u0430 (r2), \u0432 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 &#8212; \u0443\u0436\u0435 \u043d\u0435\u0442.<\/p>\n<h2 id=\"s4\">\u041c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f<\/h2>\n<p>\u0414\u043e\u0431\u0430\u0432\u0438\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u043e\u0432. \u0421\u043c\u043e\u0434\u0435\u043b\u0438\u0440\u0443\u0435\u043c \u0446\u0435\u043d\u0443 \u0436\u0438\u043b\u044c\u044f \u043f\u043e \u043f\u043b\u043e\u0449\u0430\u0434\u0438, \u0447\u0438\u0441\u043b\u0443 \u043a\u043e\u043c\u043d\u0430\u0442 \u0438 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044e \u0434\u043e \u0446\u0435\u043d\u0442\u0440\u0430:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #E06C75\">rng2<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">random<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">default_rng<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E06C75\">m<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">200<\/span>\n<span style=\"color: #E06C75\">area<\/span>  <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">rng2<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">uniform<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">30<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">100<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">m<\/span><span style=\"color: #ABB2BF\">)<\/span>     <span style=\"color: #7F848E\"># \u043f\u043b\u043e\u0449\u0430\u0434\u044c, \u043a\u0432.\u043c<\/span>\n<span style=\"color: #E06C75\">rooms<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">rng2<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">integers<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">5<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">m<\/span><span style=\"color: #ABB2BF\">)<\/span>       <span style=\"color: #7F848E\"># \u0447\u0438\u0441\u043b\u043e \u043a\u043e\u043c\u043d\u0430\u0442<\/span>\n<span style=\"color: #E06C75\">dist<\/span>  <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">rng2<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">uniform<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">20<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">m<\/span><span style=\"color: #ABB2BF\">)<\/span>       <span style=\"color: #7F848E\"># \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u0434\u043e \u0446\u0435\u043d\u0442\u0440\u0430, \u043a\u043c<\/span>\n<span style=\"color: #E06C75\">price<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">50<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">3.0<\/span><span style=\"color: #56B6C2\">*<\/span><span style=\"color: #E06C75\">area<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">20<\/span><span style=\"color: #56B6C2\">*<\/span><span style=\"color: #E06C75\">rooms<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #D19A66\">4.0<\/span><span style=\"color: #56B6C2\">*<\/span><span style=\"color: #E06C75\">dist<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">rng2<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">normal<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">15<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">m<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n<span style=\"color: #E06C75\">X<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">column_stack<\/span><span style=\"color: #ABB2BF\">([<\/span><span style=\"color: #E06C75\">area<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">rooms<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">dist<\/span><span style=\"color: #ABB2BF\">])<\/span>\n<span style=\"color: #E06C75\">model<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">LinearRegression<\/span><span style=\"color: #ABB2BF\">()<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">fit<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">X<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">price<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"intercept =\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">round<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E5C07B\">float<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">model<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">intercept_<\/span><span style=\"color: #ABB2BF\">),<\/span> <span style=\"color: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">))<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"coefs [area, rooms, dist] =\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">round<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">model<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">coef_<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">)<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">tolist<\/span><span style=\"color: #ABB2BF\">())<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">f\"R2 = {<\/span><span style=\"color: #E06C75\">r2_score<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">price<\/span><span style=\"color: #ABB2BF\">, <\/span><span style=\"color: #E06C75\">model<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">predict<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">X<\/span><span style=\"color: #ABB2BF\">))<\/span><span style=\"color: #98C379\">:.4f}\"<\/span><span style=\"color: #ABB2BF\">)<\/span><\/code><\/pre>\n<p>\u0424\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0432\u044b\u0432\u043e\u0434:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">intercept = 49.841\ncoefs [area, rooms, dist] = [3.066, 19.202, -4.209]\nR2 = 0.9642\n<\/code><\/pre>\n<p>\u0417\u043d\u0430\u043a\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 \u0447\u0438\u0442\u0430\u044e\u0442\u0441\u044f \u0441\u043e\u0434\u0435\u0440\u0436\u0430\u0442\u0435\u043b\u044c\u043d\u043e: \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0438 \u0447\u0438\u0441\u043b\u043e \u043a\u043e\u043c\u043d\u0430\u0442 \u043f\u043e\u0434\u043d\u0438\u043c\u0430\u044e\u0442 \u0446\u0435\u043d\u0443 (\u043f\u043b\u044e\u0441), \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u0434\u043e \u0446\u0435\u043d\u0442\u0440\u0430 \u0441\u043d\u0438\u0436\u0430\u0435\u0442 (\u043c\u0438\u043d\u0443\u0441). \u0412\u0435\u043b\u0438\u0447\u0438\u043d\u0430 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0430 &#8212; \u0432\u043a\u043b\u0430\u0434 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u0430 \u043f\u0440\u0438 \u043f\u0440\u043e\u0447\u0438\u0445 \u0440\u0430\u0432\u043d\u044b\u0445, \u043d\u043e \u0441\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0442\u044c \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u043c\u0435\u0436\u0434\u0443 \u0441\u043e\u0431\u043e\u0439 \u043d\u0430\u043f\u0440\u044f\u043c\u0443\u044e \u043c\u043e\u0436\u043d\u043e \u0442\u043e\u043b\u044c\u043a\u043e \u0435\u0441\u043b\u0438 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u0438 \u0432 \u0441\u043e\u043f\u043e\u0441\u0442\u0430\u0432\u0438\u043c\u044b\u0445 \u043c\u0430\u0441\u0448\u0442\u0430\u0431\u0430\u0445 (\u0438\u043d\u0430\u0447\u0435 \u0438\u0445 \u043f\u0440\u0435\u0434\u0432\u0430\u0440\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u0438\u0437\u0438\u0440\u0443\u044e\u0442).<\/p>\n<h2 id=\"s5\">\u0414\u043e\u043f\u0443\u0449\u0435\u043d\u0438\u044f \u043c\u043e\u0434\u0435\u043b\u0438<\/h2>\n<p>\u041a\u043b\u0430\u0441\u0441\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u0434\u0430\u0435\u0442 \u043d\u0430\u0434\u0435\u0436\u043d\u044b\u0435 \u043e\u0446\u0435\u043d\u043a\u0438 \u043f\u0440\u0438 \u0440\u044f\u0434\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u0439. \u042d\u0442\u043e \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u043d\u0430\u044f \u0440\u0430\u043c\u043a\u0430: \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u0434\u043e\u043f\u0443\u0449\u0435\u043d\u0438\u044f \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u044e\u0442\u0441\u044f \u0447\u0430\u0441\u0442\u0438\u0447\u043d\u043e, \u0438 \u0438\u0445 \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u044e\u0442 \u043f\u043e \u043e\u0441\u0442\u0430\u0442\u043a\u0430\u043c.<\/p>\n<ul>\n<li><strong>\u041b\u0438\u043d\u0435\u0439\u043d\u043e\u0441\u0442\u044c.<\/strong> \u0421\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u0430\u043c\u0438 \u0438 y \u0431\u043b\u0438\u0437\u043a\u0430 \u043a \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439. \u0415\u0441\u043b\u0438 \u043d\u0435\u0442 &#8212; \u043f\u043e\u043c\u043e\u0433\u0430\u0435\u0442 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u043e\u0432 (\u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c) \u0438\u043b\u0438 \u0434\u0440\u0443\u0433\u0430\u044f \u043c\u043e\u0434\u0435\u043b\u044c.<\/li>\n<li><strong>\u041d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u043e\u0441\u0442\u0430\u0442\u043a\u043e\u0432.<\/strong> \u041e\u0441\u0442\u0430\u0442\u043a\u0438 \u043d\u0435 \u0441\u0432\u044f\u0437\u0430\u043d\u044b \u043c\u0435\u0436\u0434\u0443 \u0441\u043e\u0431\u043e\u0439 (\u043d\u0430\u0440\u0443\u0448\u0430\u0435\u0442\u0441\u044f, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0432\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0440\u044f\u0434\u0430\u0445).<\/li>\n<li><strong>\u041f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u0430\u044f \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0438\u044f \u043e\u0441\u0442\u0430\u0442\u043a\u043e\u0432<\/strong> (\u0433\u043e\u043c\u043e\u0441\u043a\u0435\u0434\u0430\u0441\u0442\u0438\u0447\u043d\u043e\u0441\u0442\u044c). \u0420\u0430\u0437\u0431\u0440\u043e\u0441 \u043e\u0441\u0442\u0430\u0442\u043a\u043e\u0432 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432 \u043f\u043e \u0432\u0441\u0435\u043c\u0443 \u0434\u0438\u0430\u043f\u0430\u0437\u043e\u043d\u0443 \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043d\u0438\u0439.<\/li>\n<li><strong>\u041e\u0442\u0441\u0443\u0442\u0441\u0442\u0432\u0438\u0435 \u0441\u0438\u043b\u044c\u043d\u043e\u0439 \u043c\u0443\u043b\u044c\u0442\u0438\u043a\u043e\u043b\u043b\u0438\u043d\u0435\u0430\u0440\u043d\u043e\u0441\u0442\u0438.<\/strong> \u041f\u0440\u0438\u0437\u043d\u0430\u043a\u0438 \u043d\u0435 \u0434\u043e\u043b\u0436\u043d\u044b \u0431\u044b\u0442\u044c \u043f\u043e\u0447\u0442\u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b \u0434\u0440\u0443\u0433 \u043e\u0442 \u0434\u0440\u0443\u0433\u0430, \u0438\u043d\u0430\u0447\u0435 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0441\u0442\u0430\u043d\u043e\u0432\u044f\u0442\u0441\u044f \u043d\u0435\u0443\u0441\u0442\u043e\u0439\u0447\u0438\u0432\u044b\u043c\u0438.<\/li>\n<\/ul>\n<p>\u041d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0441\u0442\u044c \u043e\u0441\u0442\u0430\u0442\u043a\u043e\u0432 \u043d\u0443\u0436\u043d\u0430 \u043d\u0435 \u0434\u043b\u044f \u0441\u0430\u043c\u0438\u0445 \u043e\u0446\u0435\u043d\u043e\u043a \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432, \u0430 \u0434\u043b\u044f \u043a\u043e\u0440\u0440\u0435\u043a\u0442\u043d\u044b\u0445 \u0434\u043e\u0432\u0435\u0440\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u043e\u0432 \u0438 \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u0438 \u0437\u043d\u0430\u0447\u0438\u043c\u043e\u0441\u0442\u0438. \u041d\u0430\u0440\u0443\u0448\u0435\u043d\u0438\u0435 \u0434\u043e\u043f\u0443\u0449\u0435\u043d\u0438\u044f &#8212; \u043d\u0435 \u0432\u0441\u0435\u0433\u0434\u0430 \u043f\u0440\u0438\u0433\u043e\u0432\u043e\u0440 \u043c\u043e\u0434\u0435\u043b\u0438, \u043d\u043e \u043f\u043e\u0432\u043e\u0434 \u043e\u0441\u0442\u043e\u0440\u043e\u0436\u043d\u0435\u0435 \u0442\u0440\u0430\u043a\u0442\u043e\u0432\u0430\u0442\u044c \u0432\u044b\u0432\u043e\u0434\u044b.<\/p>\n<h2 id=\"s6\">\u041f\u0435\u0440\u0435\u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435<\/h2>\n<p>\u0415\u0441\u043b\u0438 \u0443\u0441\u043b\u043e\u0436\u043d\u044f\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u044c (\u0434\u043e\u0431\u0430\u0432\u043b\u044f\u0442\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u0430), \u043e\u043d\u0430 \u0432\u0441\u0435 \u0442\u043e\u0447\u043d\u0435\u0435 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442 \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0438\u0435 \u0434\u0430\u043d\u043d\u044b\u0435, \u043d\u043e \u0442\u0435\u0440\u044f\u0435\u0442 \u043e\u0431\u043e\u0431\u0449\u0430\u044e\u0449\u0443\u044e \u0441\u043f\u043e\u0441\u043e\u0431\u043d\u043e\u0441\u0442\u044c. \u042d\u0442\u043e <strong>\u043f\u0435\u0440\u0435\u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435<\/strong>: \u043d\u0438\u0437\u043a\u0430\u044f \u043e\u0448\u0438\u0431\u043a\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0438 \u0438 \u0432\u044b\u0441\u043e\u043a\u0430\u044f \u043d\u0430 \u043d\u043e\u0432\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445. \u041f\u0440\u043e\u0432\u0435\u0440\u0438\u043c \u043d\u0430 \u0434\u0430\u043d\u043d\u044b\u0445, \u0433\u0434\u0435 \u0438\u0441\u0442\u0438\u043d\u043d\u0430\u044f \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u0430, \u0441\u0440\u0430\u0432\u043d\u0438\u0432 \u043f\u0440\u044f\u043c\u0443\u044e (\u0441\u0442\u0435\u043f\u0435\u043d\u044c 1) \u0438 \u043f\u043e\u043b\u0438\u043d\u043e\u043c \u0441\u0442\u0435\u043f\u0435\u043d\u0438 15 \u043f\u043e \u043c\u0435\u0442\u0440\u0438\u043a\u0435 \u043d\u0430 \u043e\u0442\u043b\u043e\u0436\u0435\u043d\u043d\u043e\u0439 \u0432\u044b\u0431\u043e\u0440\u043a\u0435:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">from<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">sklearn.preprocessing<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #C678DD\">import<\/span> <span style=\"color: #E06C75\">PolynomialFeatures<\/span>\n<span style=\"color: #C678DD\">from<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">sklearn.pipeline<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #C678DD\">import<\/span> <span style=\"color: #E06C75\">make_pipeline<\/span>\n<span style=\"color: #C678DD\">from<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">sklearn.model_selection<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #C678DD\">import<\/span> <span style=\"color: #E06C75\">train_test_split<\/span>\n\n<span style=\"color: #E06C75\">rng3<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">random<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">default_rng<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E06C75\">xo<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">sort<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">rng3<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">uniform<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #56B6C2\">-<\/span><span style=\"color: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">3<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">40<\/span><span style=\"color: #ABB2BF\">))<\/span>\n<span style=\"color: #E06C75\">yo<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">xo<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">rng3<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">normal<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">1.0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">40<\/span><span style=\"color: #ABB2BF\">)<\/span>          <span style=\"color: #7F848E\"># \u0438\u0441\u0442\u0438\u043d\u043d\u0430\u044f \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u0430<\/span>\n<span style=\"color: #E06C75\">X<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">xo<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">reshape<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #56B6C2\">-<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E06C75\">Xtr<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">Xte<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">ytr<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">yte<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">train_test_split<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">X<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">yo<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">test_size<\/span><span style=\"color: #56B6C2\">=<\/span><span style=\"color: #D19A66\">0.4<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">random_state<\/span><span style=\"color: #56B6C2\">=<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n<span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">deg<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">15<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E06C75\">pipe<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">make_pipeline<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">PolynomialFeatures<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">deg<\/span><span style=\"color: #ABB2BF\">),<\/span> <span style=\"color: #E06C75\">LinearRegression<\/span><span style=\"color: #ABB2BF\">())<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">fit<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">Xtr<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">ytr<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #E06C75\">r2_tr<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">r2_score<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">ytr<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">pipe<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">predict<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">Xtr<\/span><span style=\"color: #ABB2BF\">))<\/span>\n    <span style=\"color: #E06C75\">r2_te<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">r2_score<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">yte<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">pipe<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">predict<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">Xte<\/span><span style=\"color: #ABB2BF\">))<\/span>\n    <span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">f\"degree {<\/span><span style=\"color: #E06C75\">deg<\/span><span style=\"color: #98C379\">:2d}: R2_train={<\/span><span style=\"color: #E06C75\">r2_tr<\/span><span style=\"color: #98C379\">:.3f}  R2_test={<\/span><span style=\"color: #E06C75\">r2_te<\/span><span style=\"color: #98C379\">:.3f}\"<\/span><span style=\"color: #ABB2BF\">)<\/span><\/code><\/pre>\n<p>\u0424\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0432\u044b\u0432\u043e\u0434:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">degree  1: R2_train=0.846  R2_test=0.806\ndegree 15: R2_train=0.943  R2_test=-715379.945\n<\/code><\/pre>\n<p>\u041f\u043e\u043b\u0438\u043d\u043e\u043c \u0441\u0442\u0435\u043f\u0435\u043d\u0438 15 \u043f\u043e\u043a\u0430\u0437\u0430\u043b R2 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0438 \u0432\u044b\u0448\u0435 (0.943 \u043f\u0440\u043e\u0442\u0438\u0432 0.846), \u043d\u043e \u043d\u0430 \u0442\u0435\u0441\u0442\u0435 \u043c\u0435\u0442\u0440\u0438\u043a\u0430 \u0440\u0443\u0445\u043d\u0443\u043b\u0430 \u0432 \u0433\u043b\u0443\u0431\u043e\u043a\u0438\u0439 \u043c\u0438\u043d\u0443\u0441 &#8212; \u043c\u043e\u0434\u0435\u043b\u044c \u043f\u043e\u0434\u0441\u0442\u0440\u043e\u0438\u043b\u0430\u0441\u044c \u043f\u043e\u0434 \u0448\u0443\u043c \u0438 \u043d\u0430 \u043d\u043e\u0432\u044b\u0445 \u0442\u043e\u0447\u043a\u0430\u0445 \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u0430\u0431\u0441\u0443\u0440\u0434\u043d\u043e. \u041f\u0440\u044f\u043c\u0430\u044f \u0441\u043a\u0440\u043e\u043c\u043d\u0435\u0435 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0438, \u0437\u0430\u0442\u043e \u0434\u0435\u0440\u0436\u0438\u0442 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u043e \u043d\u0430 \u0442\u0435\u0441\u0442\u0435. \u041e\u0442\u0441\u044e\u0434\u0430 \u043f\u0440\u0430\u0432\u0438\u043b\u043e: \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u043e \u0441\u0443\u0434\u044f\u0442 \u043f\u043e \u043e\u0442\u043b\u043e\u0436\u0435\u043d\u043d\u043e\u0439 \u0432\u044b\u0431\u043e\u0440\u043a\u0435 \u0438\u043b\u0438 \u043a\u0440\u043e\u0441\u0441-\u0432\u0430\u043b\u0438\u0434\u0430\u0446\u0438\u0438, \u0430 \u043d\u0435 \u043f\u043e \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0435\u0439; \u043b\u0438\u0448\u043d\u044e\u044e \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u0433\u0430\u0441\u044f\u0442 \u0440\u0435\u0433\u0443\u043b\u044f\u0440\u0438\u0437\u0430\u0446\u0438\u0435\u0439 (Ridge, Lasso).<\/p>\n<h2 id=\"s7\">\u041e\u0442\u043b\u0438\u0447\u0438\u0435 \u043e\u0442 \u043b\u043e\u0433\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438<\/h2>\n<p>\u041d\u0430\u0437\u0432\u0430\u043d\u0438\u044f \u043f\u043e\u0445\u043e\u0436\u0438, \u0437\u0430\u0434\u0430\u0447\u0438 \u0440\u0430\u0437\u043d\u044b\u0435. \u041a\u043b\u044e\u0447\u0435\u0432\u043e\u0435 \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u0435 &#8212; \u0447\u0442\u043e \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043c\u043e\u0434\u0435\u043b\u044c.<\/p>\n<table>\n<thead>\n<tr>\n<th>\u041f\u0440\u0438\u0437\u043d\u0430\u043a<\/th>\n<th>\u041b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f<\/th>\n<th>\u041b\u043e\u0433\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0417\u0430\u0434\u0430\u0447\u0430<\/td>\n<td>\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f (\u0447\u0438\u0441\u043b\u043e)<\/td>\n<td>\u043a\u043b\u0430\u0441\u0441\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u044f (\u043c\u0435\u0442\u043a\u0430)<\/td>\n<\/tr>\n<tr>\n<td>\u0427\u0442\u043e \u043d\u0430 \u0432\u044b\u0445\u043e\u0434\u0435<\/td>\n<td>\u043b\u044e\u0431\u043e\u0435 \u0447\u0438\u0441\u043b\u043e<\/td>\n<td>\u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043a\u043b\u0430\u0441\u0441\u0430 \u043e\u0442 0 \u0434\u043e 1<\/td>\n<\/tr>\n<tr>\n<td>\u0424\u043e\u0440\u043c\u0430<\/td>\n<td>y = a + b*x<\/td>\n<td>\u0441\u0438\u0433\u043c\u043e\u0438\u0434\u0430 \u043e\u0442 a + b*x<\/td>\n<\/tr>\n<tr>\n<td>\u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u043e\u0442\u0435\u0440\u044c<\/td>\n<td>\u0441\u0443\u043c\u043c\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 (\u041c\u041d\u041a)<\/td>\n<td>\u043b\u043e\u0433\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f (log-loss)<\/td>\n<\/tr>\n<tr>\n<td>\u041c\u0435\u0442\u0440\u0438\u043a\u0438<\/td>\n<td>R2, MSE, MAE<\/td>\n<td>accuracy, precision, recall, ROC-AUC<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u041b\u043e\u0433\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u0441\u0442\u0440\u043e\u0438\u0442 \u0442\u0443 \u0436\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044e \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u043e\u0432, \u043d\u043e \u043f\u0440\u043e\u043f\u0443\u0441\u043a\u0430\u0435\u0442 \u0435\u0435 \u0447\u0435\u0440\u0435\u0437 \u0441\u0438\u0433\u043c\u043e\u0438\u0434\u0443, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c, \u0438 \u043e\u0431\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u043d\u0430 \u0434\u0440\u0443\u0433\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u043e\u0442\u0435\u0440\u044c. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043d\u0438\u044f \u0446\u0435\u043d\u044b \u0431\u0435\u0440\u0443\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044e, \u0430 \u0434\u043b\u044f \u043e\u0442\u0432\u0435\u0442\u0430 \u00ab\u043a\u0443\u043f\u0438\u0442 \u0438\u043b\u0438 \u043d\u0435\u0442\u00bb &#8212; \u043b\u043e\u0433\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e.<\/p>\n<h2 id=\"s8\">\u0412\u044b\u0432\u043e\u0434\u044b<\/h2>\n<ul>\n<li>\u041b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u0447\u0438\u0441\u043b\u043e \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u043e\u0432; \u043f\u0430\u0440\u043d\u0430\u044f &#8212; \u043e\u0434\u0438\u043d \u043f\u0440\u0438\u0437\u043d\u0430\u043a, \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f &#8212; \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e.<\/li>\n<li>\u041a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u043f\u043e\u0434\u0431\u0438\u0440\u0430\u0435\u0442 \u043c\u0435\u0442\u043e\u0434 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432, \u043c\u0438\u043d\u0438\u043c\u0438\u0437\u0438\u0440\u0443\u044f \u0441\u0443\u043c\u043c\u0443 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 \u043e\u0441\u0442\u0430\u0442\u043a\u043e\u0432; \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u041c\u041d\u041a \u0438 scikit-learn \u0434\u0430\u044e\u0442 \u043e\u0434\u0438\u043d \u0438 \u0442\u043e\u0442 \u0436\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442.<\/li>\n<li>MSE \u043c\u0435\u0440\u044f\u0435\u0442 \u043e\u0448\u0438\u0431\u043a\u0443 \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435 \u0435\u0434\u0438\u043d\u0438\u0446 y, R2 &#8212; \u0434\u043e\u043b\u044e \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u043d\u043e\u0439 \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0438\u0438; \u043d\u0430 \u043d\u043e\u0432\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445 R2 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439.<\/li>\n<li>\u041c\u043e\u0434\u0435\u043b\u044c \u043e\u043f\u0438\u0440\u0430\u0435\u0442\u0441\u044f \u043d\u0430 \u0434\u043e\u043f\u0443\u0449\u0435\u043d\u0438\u044f (\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0441\u0442\u044c, \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0438 \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u0430\u044f \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0438\u044f \u043e\u0441\u0442\u0430\u0442\u043a\u043e\u0432, \u043e\u0442\u0441\u0443\u0442\u0441\u0442\u0432\u0438\u0435 \u0441\u0438\u043b\u044c\u043d\u043e\u0439 \u043c\u0443\u043b\u044c\u0442\u0438\u043a\u043e\u043b\u043b\u0438\u043d\u0435\u0430\u0440\u043d\u043e\u0441\u0442\u0438) &#8212; \u0438\u0445 \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u044e\u0442 \u043f\u043e \u043e\u0441\u0442\u0430\u0442\u043a\u0430\u043c.<\/li>\n<li>\u0421\u043b\u0438\u0448\u043a\u043e\u043c \u0441\u043b\u043e\u0436\u043d\u0430\u044f \u043c\u043e\u0434\u0435\u043b\u044c \u043f\u0435\u0440\u0435\u043e\u0431\u0443\u0447\u0430\u0435\u0442\u0441\u044f: \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u043e \u043d\u0430\u0434\u043e \u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u043d\u0430 \u043e\u0442\u043b\u043e\u0436\u0435\u043d\u043d\u043e\u0439 \u0432\u044b\u0431\u043e\u0440\u043a\u0435, \u0430 \u043b\u043e\u0433\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f &#8212; \u044d\u0442\u043e \u0443\u0436\u0435 \u043f\u0440\u043e \u043a\u043b\u0430\u0441\u0441\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u044e, \u043d\u0435 \u043f\u0440\u043e \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043d\u0438\u0435 \u0447\u0438\u0441\u043b\u0430.<\/li>\n<\/ul>\n<h2 id=\"s9\">\u0413\u0434\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \/ \u0441\u0432\u044f\u0437\u044c \u0441 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0439<\/h2>\n<p>\u041b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f &#8212; \u043f\u0435\u0440\u0432\u0430\u044f \u043c\u043e\u0434\u0435\u043b\u044c, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u0440\u0430\u0437\u0431\u0438\u0440\u0430\u044e\u0442 \u0432 \u0430\u043d\u0430\u043b\u0438\u0437\u0435 \u0434\u0430\u043d\u043d\u044b\u0445 \u0438 \u043c\u0430\u0448\u0438\u043d\u043d\u043e\u043c \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0438: \u043d\u0430 \u043d\u0435\u0439 \u043f\u0440\u043e\u0449\u0435 \u0432\u0441\u0435\u0433\u043e \u043f\u043e\u043d\u044f\u0442\u044c \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043f\u043e \u0434\u0430\u043d\u043d\u044b\u043c, \u043c\u0435\u0442\u0440\u0438\u043a\u0438 \u0438 \u043f\u0435\u0440\u0435\u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435, \u0430 \u0443\u0436\u0435 \u043f\u043e\u0442\u043e\u043c \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u0442\u044c \u043a \u0434\u0435\u0440\u0435\u0432\u044c\u044f\u043c, \u0430\u043d\u0441\u0430\u043c\u0431\u043b\u044f\u043c \u0438 \u043d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u044f\u043c. \u041e\u043d\u0430 \u0440\u0435\u0430\u043b\u044c\u043d\u043e \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u0432 \u043e\u0446\u0435\u043d\u043a\u0435 \u043d\u0435\u0434\u0432\u0438\u0436\u0438\u043c\u043e\u0441\u0442\u0438, \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0435 \u0441\u043f\u0440\u043e\u0441\u0430, \u0430\u043d\u0430\u043b\u0438\u0437\u0435 A\/B-\u0442\u0435\u0441\u0442\u043e\u0432 \u0438 \u043a\u0430\u043a \u0431\u044b\u0441\u0442\u0440\u044b\u0439 \u0431\u0435\u0439\u0437\u043b\u0430\u0439\u043d \u0434\u043b\u044f \u0431\u043e\u043b\u0435\u0435 \u0441\u043b\u043e\u0436\u043d\u044b\u0445 \u0437\u0430\u0434\u0430\u0447.<\/p>\n<div class=\"oj-cta\" style=\"background:#fbf4e4;border-left:4px solid #c9962b;border-radius:8px;padding:16px 20px;margin:24px 0\">\n<p style=\"margin:0 0 8px\"><strong>\u041e\u0441\u0432\u043e\u0439\u0442\u0435 \u0442\u0435\u043c\u0443 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435<\/strong><\/p>\n<p>\u0420\u0430\u0437\u043e\u0431\u0440\u0430\u0442\u044c \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044e, \u043c\u0435\u0442\u0440\u0438\u043a\u0438 \u0438 \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0443 \u0434\u0430\u043d\u043d\u044b\u0445 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435, \u0441 \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u043d\u0430 \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0445 \u0432\u044b\u0431\u043e\u0440\u043a\u0430\u0445, \u043c\u043e\u0436\u043d\u043e \u043d\u0430 \u043a\u0443\u0440\u0441\u0435 <a href=\"https:\/\/otus.ru\/lessons\/ml-basic\/?int_article=linejnaya-regressiya&amp;int_place=article&amp;int_variant=v1\">Machine Learning. Basic<\/a>. \u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0444\u043e\u0440\u043c\u0430\u0442 \u0438 \u0443\u0440\u043e\u0432\u0435\u043d\u044c \u0434\u043e \u0437\u0430\u043f\u0438\u0441\u0438 \u043f\u043e\u043c\u043e\u0433\u0430\u044e\u0442 <a href=\"https:\/\/otus.ru\/events\/?int_article=linejnaya-regressiya&amp;int_place=article&amp;int_variant=v1\">\u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0435 \u0443\u0440\u043e\u043a\u0438 Otus<\/a> &#8212; \u0442\u0430\u043c \u0440\u0430\u0437\u0431\u0438\u0440\u0430\u044e\u0442 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u044b\u0435 \u0442\u0435\u043c\u044b \u0432 \u043f\u0440\u044f\u043c\u043e\u043c \u044d\u0444\u0438\u0440\u0435 \u0441 \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u0442\u0435\u043b\u0435\u043c.<\/p>\n<\/div>\n<h2 id=\"s10\">FAQ<\/h2>\n<p><strong>\u0427\u0435\u043c R2 \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442\u0441\u044f \u043e\u0442 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0430 \u043a\u043e\u0440\u0440\u0435\u043b\u044f\u0446\u0438\u0438?<\/strong> \u041a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u043a\u043e\u0440\u0440\u0435\u043b\u044f\u0446\u0438\u0438 r \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u0441\u0438\u043b\u0443 \u0438 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0441\u0432\u044f\u0437\u0438 \u0434\u0432\u0443\u0445 \u0432\u0435\u043b\u0438\u0447\u0438\u043d (\u043e\u0442 -1 \u0434\u043e 1). R2 \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u0434\u043e\u043b\u044e \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0438\u0438, \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u043d\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c\u044e. \u0412 \u043f\u0430\u0440\u043d\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 R2 \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e \u0440\u0430\u0432\u0435\u043d r \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435, \u0432 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 &#8212; \u043d\u0435\u0442.<\/p>\n<p><strong>\u041d\u0443\u0436\u043d\u043e \u043b\u0438 \u043c\u0430\u0441\u0448\u0442\u0430\u0431\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u0438 \u0434\u043b\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438?<\/strong> \u0414\u043b\u044f \u0441\u0430\u043c\u0438\u0445 \u043e\u0446\u0435\u043d\u043e\u043a \u041c\u041d\u041a &#8212; \u043d\u0435\u0442, \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u043d\u0435 \u0438\u0437\u043c\u0435\u043d\u0438\u0442\u0441\u044f. \u041c\u0430\u0441\u0448\u0442\u0430\u0431\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u043d\u0443\u0436\u043d\u043e, \u0447\u0442\u043e\u0431\u044b \u0441\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0442\u044c \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u043c\u0435\u0436\u0434\u0443 \u043f\u0440\u0438\u0437\u043d\u0430\u043a\u0430\u043c\u0438, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0434\u043b\u044f \u0440\u0435\u0433\u0443\u043b\u044f\u0440\u0438\u0437\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u0432\u0435\u0440\u0441\u0438\u0439 (Ridge, Lasso), \u0433\u0434\u0435 \u043c\u0430\u0441\u0448\u0442\u0430\u0431 \u0432\u043b\u0438\u044f\u0435\u0442 \u043d\u0430 \u0448\u0442\u0440\u0430\u0444.<\/p>\n<p><strong>\u0427\u0442\u043e \u0434\u0435\u043b\u0430\u0442\u044c \u0441 \u0432\u044b\u0431\u0440\u043e\u0441\u0430\u043c\u0438?<\/strong> \u041d\u0435 \u0443\u0434\u0430\u043b\u044f\u0442\u044c \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438: \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u044b\u044f\u0441\u043d\u0438\u0442\u044c \u043f\u0440\u0438\u0440\u043e\u0434\u0443 (\u043e\u0448\u0438\u0431\u043a\u0430 \u0434\u0430\u043d\u043d\u044b\u0445 \u0438\u043b\u0438 \u0440\u0435\u0434\u043a\u043e\u0435, \u043d\u043e \u0440\u0435\u0430\u043b\u044c\u043d\u043e\u0435 \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u0435). \u041f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c \u0432\u043b\u0438\u044f\u043d\u0438\u0435 \u043c\u043e\u0436\u043d\u043e, \u043e\u0431\u0443\u0447\u0438\u0432 \u043c\u043e\u0434\u0435\u043b\u044c \u0441 \u0432\u044b\u0431\u0440\u043e\u0441\u0430\u043c\u0438 \u0438 \u0431\u0435\u0437 \u0438 \u0441\u0440\u0430\u0432\u043d\u0438\u0432 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b; 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\u043a\u0430\u043a \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u043f\u043e\u0434\u0431\u043e\u0440 (\u043c\u0435\u0442\u043e\u0434 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432), \u043a\u0430\u043a \u043e\u0446\u0435\u043d\u0438\u0432\u0430\u0442\u044c \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u043e [&hellip;]<\/p>\n","protected":false},"author":11,"featured_media":4798,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[44],"class_list":["post-4797","post","type-post","status-publish","format-standard","has-post-thumbnail","","category-polza","tag-matematika"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.2 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f, \u043a\u0430\u043a \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u043c\u0435\u0442\u043e\u0434 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432, \u043a\u0430\u043a \u0441\u0447\u0438\u0442\u0430\u0442\u044c R2 \u0438 MSE, \u0447\u0435\u043c \u043c\u043e\u0434\u0435\u043b\u044c \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442\u0441\u044f \u043e\u0442 \u043b\u043e\u0433\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 - \u0441 \u043a\u043e\u0434\u043e\u043c \u043d\u0430 Python.\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"A. 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