{"id":1155,"date":"2023-07-27T11:31:28","date_gmt":"2023-07-27T11:31:28","guid":{"rendered":"https:\/\/statorials.org\/my\/logistic-regression-python\/"},"modified":"2023-07-27T11:31:28","modified_gmt":"2023-07-27T11:31:28","slug":"logistic-regression-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/logistic-regression-python\/","title":{"rendered":"Python \u1010\u103d\u1004\u103a logistic regression \u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038 (\u1010\u1005\u103a\u1006\u1004\u1037\u103a\u1015\u103c\u102e\u1038\u1010\u1005\u103a\u1006\u1004\u1037\u103a)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/my\/\u1011\u1031\u102c\u1000\u103a\u1015\u1036\u1037\u1015\u102d\u102f\u1037\u1006\u1031\u102c\u1004\u103a\u101b\u1031\u1038-\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f-\u1041\/\" target=\"_blank\" rel=\"noopener noreferrer\">Logistic regression<\/a> \u101e\u100a\u103a <a href=\"https:\/\/statorials.org\/my\/\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c-\u101b\u103e\u1004\u103a\u1038\u101c\u1004\u103a\u1038\u1001\u103b\u1000\u103a-\u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\/\" target=\"_blank\" rel=\"noopener noreferrer\">response variable<\/a> binary \u1016\u103c\u1005\u103a\u101e\u1031\u102c\u1021\u1001\u102b regression model \u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u101b\u1014\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u102f\u1036\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c method \u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">Logistic regression \u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1015\u102f\u1036\u1005\u1036\u104f \u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a <em>\u1021\u1019\u103b\u102c\u1038\u1006\u102f\u1036\u1038\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031 \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a<\/em> \u101f\u102f \u101c\u1030\u101e\u102d\u1019\u103b\u102c\u1038\u101e\u1031\u102c \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>log[p(X) \/ ( <sub>1<\/sub> -p(X))] = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> X <sub>1<\/sub> + \u03b2 <sub>2<\/sub> X <sub>2<\/sub> + \u2026 + \u03b2 <sub>p<\/sub><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u103d\u103e\u1031-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>X <sub>j<\/sub><\/strong> : j <sup>th<\/sup> \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03b2 <sub>j<\/sub><\/strong> : j <sup>th<\/sup> \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u1010\u103d\u1000\u103a \u1000\u102d\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u1000\u102d\u102f \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103c\u1004\u103a\u1038\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u104f \u100a\u102c\u1018\u1000\u103a\u101b\u103e\u102d \u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u101e\u100a\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u101e\u100a\u103a \u1010\u1014\u103a\u1016\u102d\u102f\u1038 1 \u1000\u102d\u102f \u101a\u1030\u101e\u100a\u1037\u103a <strong>\u1019\u103e\u1010\u103a\u1010\u1019\u103a\u1038\u1021\u1015\u1031\u102b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f<\/strong> \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1015\u1031\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a logistic regression model \u1000\u102d\u102f \u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c observation \u101e\u100a\u103a value 1 \u1000\u102d\u102f\u101a\u1030\u101e\u100a\u1037\u103a\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">p(X) = e <sup>\u03b2 <sub>0<\/sub> + <sub>\u03b2<\/sub> <sub>1<\/sub> <sub>X<\/sub> <sub>1<\/sub> <sub>+<\/sub> <sub>\u03b2<\/sub><\/sup> <sup><sub>2<\/sub> <sub>X<\/sub> <sub>2<\/sub> <sub>+<\/sub> <sub>\u2026<\/sub> <sub>+<\/sub> <sub>\u03b2<\/sub><\/sup> p<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a \u101b\u103e\u102f\u1019\u103c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f 1 \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a 0 \u1021\u1016\u103c\u1005\u103a \u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u1001\u103d\u1032\u1001\u103c\u102c\u1038\u101b\u1014\u103a \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1021\u1006\u1004\u1037\u103a\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a 0.5 \u1011\u1000\u103a\u1000\u103c\u102e\u1038\u101e\u1031\u102c \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101b\u103e\u102d\u101e\u1031\u102c \u101c\u1031\u1037\u101c\u102c\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f &#8220; 1&#8221;  \u1021\u1016\u103c\u1005\u103a \u1001\u103d\u1032\u1001\u103c\u102c\u1038\u1015\u103c\u102e\u1038 \u1021\u1001\u103c\u102c\u1038\u101c\u1031\u1037\u101c\u102c\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1001\u103b\u1000\u103a\u1021\u102c\u1038\u101c\u102f\u1036\u1038\u1000\u102d\u102f &#8220; 0&#8221;  \u1021\u1016\u103c\u1005\u103a \u1001\u103d\u1032\u1001\u103c\u102c\u1038\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1019\u100a\u103a\u101f\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1015\u103c\u1031\u102c\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u101e\u100a\u103a R \u1010\u103d\u1004\u103a \u1011\u1031\u102c\u1000\u103a\u1015\u1036\u1037\u1015\u102d\u102f\u1037\u1006\u1031\u102c\u1004\u103a\u101b\u1031\u1038\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102f\u1036\u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a\u1000\u102d\u102f \u1025\u1015\u1019\u102c\u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 1- \u101c\u102d\u102f\u1021\u1015\u103a\u101e\u1031\u102c \u1015\u1000\u103a\u1000\u1031\u1037\u1001\u103a\u103b\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u1004\u103a\u101e\u103d\u1004\u103a\u1038\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1015\u1011\u1019\u1026\u1038\u1005\u103d\u102c\u104a Python \u1010\u103d\u1004\u103a \u1011\u1031\u102c\u1000\u103a\u1015\u1036\u1037\u1015\u102d\u102f\u1037\u1006\u1031\u102c\u1004\u103a\u101b\u1031\u1038\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u101e\u1031\u102c \u1015\u1000\u103a\u1000\u1031\u1037\u1002\u103b\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u1004\u103a\u101e\u103d\u1004\u103a\u1038\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd\n<span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<span style=\"color: #008000;\">from<\/span> sklearn. <span style=\"color: #3366ff;\">model_selection<\/span> <span style=\"color: #008000;\">import<\/span> train_test_split\n<span style=\"color: #008000;\">from<\/span> sklearn. <span style=\"color: #3366ff;\">linear_model<\/span> <span style=\"color: #008000;\">import<\/span> LogisticRegression\n<span style=\"color: #008000;\">from<\/span> sklearn <span style=\"color: #008000;\">import<\/span> metrics\n<span style=\"color: #008000;\">import<\/span> matplotlib. <span style=\"color: #3366ff;\">pyplot<\/span> <span style=\"color: #008000;\">as<\/span> plt\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 2: \u1012\u1031\u1010\u102c\u1000\u102d\u102f \u1010\u1004\u103a\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1024\u1025\u1015\u1019\u102c\u1021\u1010\u103d\u1000\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a <a href=\"https:\/\/www.ime.unicamp.br\/~dias\/Intoduction%20to%20Statistical%20Learning.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">\u1005\u102c\u1021\u102f\u1015\u103a\u1014\u102d\u1012\u102b\u1014\u103a\u1038\u1019\u103e \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u101e\u1004\u103a\u101a\u1030\u1001\u103c\u1004\u103a\u1038\u1019\u103e<\/a> <strong>\u1019\u1030\u101b\u1004\u103a\u1038<\/strong> \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u1019\u100a\u103a\u104b \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u104f \u1021\u1000\u103b\u1009\u103a\u1038\u1001\u103b\u102f\u1015\u103a\u1000\u102d\u102f \u1010\u1004\u103a\u101b\u1014\u103a\u1014\u103e\u1004\u1037\u103a \u1015\u103c\u101e\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#import dataset from CSV file on Github\n<span style=\"color: #000000;\">url = \"https:\/\/raw.githubusercontent.com\/Statorials\/Python-Guides\/main\/default.csv\"\ndata = pd. <span style=\"color: #3366ff;\">read_csv<\/span> (url)\n<\/span><\/span>\n<span style=\"color: #008080;\">#view first six rows of dataset\n<\/span>data[0:6]\n\n        default student balance income\n0 0 0 729.526495 44361.625074\n1 0 1 817.180407 12106.134700\n2 0 0 1073.549164 31767.138947\n3 0 0 529.250605 35704.493935\n4 0 0 785.655883 38463.495879\n5 0 1 919.588530 7491.558572  \n\n<span style=\"color: #008080;\">#find total observations in dataset<\/span>\nlen( <span style=\"color: #3366ff;\">data.index<\/span> )\n\n10000\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1024\u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u103d\u1004\u103a \u101c\u1030 10,000 \u1026\u1038\u1021\u1010\u103d\u1000\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1001\u103b\u1000\u103a\u1021\u101c\u1000\u103a\u1019\u103b\u102c\u1038\u1015\u102b\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u1015\u102f\u1036\u101e\u1031-<\/strong> \u1010\u1005\u103a\u1026\u1038\u1010\u1005\u103a\u101a\u1031\u102c\u1000\u103a\u101e\u100a\u103a \u1015\u102f\u1036\u101e\u1031\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u1001\u103c\u1004\u103a\u1038 \u101b\u103e\u102d\u104a \u1019\u101b\u103e\u102d\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038-<\/strong> \u1010\u1005\u103a\u1026\u1038\u1010\u1005\u103a\u101a\u1031\u102c\u1000\u103a\u101e\u100a\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u101f\u102f\u1010\u103a\u1019\u101f\u102f\u1010\u103a \u100a\u103d\u103e\u1014\u103a\u1015\u103c\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u101c\u1000\u103a\u1000\u103b\u1014\u103a-<\/strong> \u1010\u1005\u103a\u1026\u1038\u1001\u103b\u1004\u103a\u1038\u1005\u102e\u1019\u103e \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u101c\u1000\u103a\u1000\u103b\u1014\u103a\u1004\u103d\u1031\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u101d\u1004\u103a\u1004\u103d\u1031-<\/strong> \u1010\u1005\u103a\u1026\u1038\u1001\u103b\u1004\u103a\u1038\u104f \u1040\u1004\u103a\u1004\u103d\u1031\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1021\u1001\u103c\u1031\u1021\u1014\u1031\u104a \u1018\u100f\u103a\u101c\u1000\u103a\u1000\u103b\u1014\u103a\u1014\u103e\u1004\u1037\u103a \u101d\u1004\u103a\u1004\u103d\u1031\u1010\u102d\u102f\u1037\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u103c\u102e\u1038 \u1011\u1031\u102c\u1000\u103a\u1015\u1036\u1037\u1015\u102d\u102f\u1037\u1006\u1031\u102c\u1004\u103a\u1015\u1031\u1038\u101e\u1030\u1010\u1005\u103a\u1026\u1038\u101e\u100a\u103a \u1015\u102f\u1036\u101e\u1031\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1000\u102d\u102f \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1015\u1031\u1038\u101e\u100a\u1037\u103a \u1011\u1031\u102c\u1000\u103a\u1015\u1036\u1037\u1015\u102d\u102f\u1037\u1006\u1031\u102c\u1004\u103a\u101b\u1031\u1038\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1000\u102d\u102f \u1010\u100a\u103a\u1006\u1031\u102c\u1000\u103a\u1019\u100a\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 3- \u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u101b\u1031\u1038\u1014\u103e\u1004\u1037\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1014\u1019\u1030\u1014\u102c\u1019\u103b\u102c\u1038 \u1016\u1014\u103a\u1010\u102e\u1038\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a dataset \u1021\u102c\u1038 \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1021\u102c\u1038 <em>\u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a<\/em> \u101b\u1014\u103a \u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u101b\u1031\u1038 \u1021\u1005\u102f\u1036\u1014\u103e\u1004\u1037\u103a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1000\u102d\u102f <em>\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a<\/em> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1021\u1016\u103c\u1005\u103a \u1001\u103d\u1032\u101e\u103d\u102c\u1038\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define the predictor variables and the response variable\n<\/span>X = data[[' <span style=\"color: #008000;\">student<\/span> ',' <span style=\"color: #008000;\">balance<\/span> ',' <span style=\"color: #008000;\">income<\/span> ']]\ny = data[' <span style=\"color: #008000;\">default<\/span> ']\n\n<span style=\"color: #008080;\">#split the dataset into training (70%) and testing (30%) sets\n<\/span>X_train,X_test,y_train,y_test = <span style=\"color: #3366ff;\">train_test_split<\/span> (X,y,test_size=0.3,random_state=0)<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 4- \u1011\u1031\u102c\u1000\u103a\u1015\u1036\u1037\u1015\u102d\u102f\u1037\u1006\u1031\u102c\u1004\u103a\u101b\u1031\u1038 \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1000\u102d\u102f \u1021\u1036\u1000\u102d\u102f\u1000\u103a\u101c\u102f\u1015\u103a\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1012\u1031\u1010\u102c\u1021\u1005\u102f\u1036\u1014\u103e\u1004\u1037\u103a \u1011\u1031\u102c\u1000\u103a\u1015\u1036\u1037\u1015\u102d\u102f\u1037\u1006\u1031\u102c\u1004\u103a\u101b\u1031\u1038 \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1000\u102d\u102f \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1005\u1031\u101b\u1014\u103a <b>LogisticRegression()<\/b> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#instantiate the model\n<\/span>log_regression = LogisticRegression()\n\n<span style=\"color: #008080;\">#fit the model using the training data\n<\/span>log_regression. <span style=\"color: #3366ff;\">fit<\/span> (X_train,y_train)\n\n<span style=\"color: #008080;\">#use model to make predictions on test data\n<\/span>y_pred = log_regression. <span style=\"color: #3366ff;\">predict<\/span> (X_test)\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 5- \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101b\u1031\u102c\u1002\u102b\u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1031\u1038<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1000\u102d\u102f \u1010\u1015\u103a\u1006\u1004\u103a\u1015\u103c\u102e\u1038\u101e\u100a\u103a\u1014\u103e\u1004\u1037\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u103d\u1004\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u104f\u1005\u103d\u1019\u103a\u1038\u1006\u1031\u102c\u1004\u103a\u101b\u100a\u103a\u1000\u102d\u102f \u1015\u102d\u102f\u1004\u103a\u1038\u1001\u103c\u102c\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> \u1015\u1011\u1019\u1026\u1038\u1005\u103d\u102c\u104a <span style=\"color: #000000;\">\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1021\u1010\u103d\u1000\u103a<\/span> <span style=\"color: #000000;\">\u101b\u103e\u102f\u1015\u103a\u1011\u103d\u1031\u1038\u1019\u103e\u102f matrix \u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u1015\u102b\u1019\u100a\u103a<\/span> \u104b<\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong>cnf_matrix = metrics. <span style=\"color: #3366ff;\">confusion_matrix<\/span> (y_test, y_pred)\ncnf_matrix\n\narray([[2886, 1],\n       [113,0]])\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">\u101b\u103e\u102f\u1015\u103a\u1011\u103d\u1031\u1038\u101e\u1031\u102c matrix \u1019\u103e \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1019\u103c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">#\u1019\u103e\u1014\u103a\u1000\u1014\u103a\u101e\u1031\u102c \u1021\u1015\u103c\u102f\u101e\u1018\u1031\u102c\u1006\u1031\u102c\u1004\u103a\u101e\u1031\u102c \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038- 2886<\/span><\/li>\n<li> <span style=\"color: #000000;\">#\u1019\u103e\u1014\u103a\u1000\u1014\u103a\u101e\u1031\u102c \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c\u101f\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u1019\u103b\u102c\u1038- 0<\/span><\/li>\n<li> <span style=\"color: #000000;\">#\u1019\u103e\u102c\u1038\u101a\u103d\u1004\u103a\u1038\u101e\u1031\u102c \u1021\u1015\u103c\u102f\u101e\u1018\u1031\u102c\u1006\u1031\u102c\u1004\u103a\u101e\u1031\u102c \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038- \u1041\u1041\u1043<\/span><\/li>\n<li> <span style=\"color: #000000;\">#\u1019\u103e\u102c\u1038\u101a\u103d\u1004\u103a\u1038\u101e\u1031\u102c \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c\u101f\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u1019\u103b\u102c\u1038 \u1041<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1019\u103e \u1015\u103c\u102f\u101c\u102f\u1015\u103a\u101e\u1031\u102c \u1021\u1019\u103e\u102c\u1038\u1015\u103c\u1004\u103a\u1006\u1004\u103a\u1019\u103e\u102f \u101b\u102c\u1001\u102d\u102f\u1004\u103a\u1014\u103e\u102f\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u103c\u1031\u102c\u1015\u103c\u101e\u100a\u1037\u103a \u1010\u102d\u1000\u103b\u1019\u103e\u102f \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1000\u102d\u102f\u101c\u100a\u103a\u1038 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u101b\u101b\u103e\u102d\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>print(\" <span style=\"color: #008000;\">Accuracy:<\/span> \", <span style=\"color: #3366ff;\">metrics.accuracy_score<\/span> (y_test, y_pred))l\n\nAccuracy: 0.962\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101e\u100a\u103a \u1021\u1001\u103b\u102d\u1014\u103a\u104f <strong>96.2% \u1000\u102d\u102f<\/strong> \u1015\u102f\u1036\u101e\u1031\u1016\u103c\u1005\u103a\u1005\u1031\u1019\u100a\u103a\u104a<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1014\u1031\u102c\u1000\u103a\u1006\u102f\u1036\u1038\u1010\u103d\u1004\u103a\u104a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1021\u1006\u1004\u1037\u103a\u1000\u102d\u102f 1 \u1019\u103e 0 \u1019\u103e 0 \u1019\u103e \u101c\u103b\u103e\u1031\u102c\u1037\u1001\u103b\u101e\u100a\u1037\u103a\u1021\u1001\u102b \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1000 \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1011\u102c\u1038\u101e\u1031\u102c \u1005\u1005\u103a\u1019\u103e\u1014\u103a\u101e\u1031\u102c positive \u101b\u102c\u1001\u102d\u102f\u1004\u103a\u1014\u103e\u102f\u1014\u103a\u1038\u1000\u102d\u102f \u1015\u103c\u101e\u101e\u100a\u1037\u103a Receiver Operating Characteristic (ROC) \u1019\u103b\u1009\u103a\u1038\u1000\u103d\u1031\u1038\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1000\u103c\u1036\u1005\u100a\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">AUC (\u1019\u103b\u1009\u103a\u1038\u1000\u103d\u1031\u1038\u1021\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a \u1027\u101b\u102d\u101a\u102c) \u1019\u103c\u1004\u1037\u103a\u1019\u102c\u1038\u101c\u1031\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101e\u100a\u103a \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u102d\u102f\u1019\u102d\u102f\u1010\u102d\u1000\u103b\u1005\u103d\u102c \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101c\u1031\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#define metrics<\/span>\ny_pred_proba = log_regression. <span style=\"color: #3366ff;\">predict_proba<\/span> (X_test)[::,1]\nfpr, tpr, _ = metrics. <span style=\"color: #3366ff;\">roc_curve<\/span> (y_test, y_pred_proba)\nauc = metrics. <span style=\"color: #3366ff;\">roc_auc_score<\/span> (y_test, y_pred_proba)\n\n<span style=\"color: #008080;\">#create ROC curve\n<\/span>plt. <span style=\"color: #3366ff;\">plot<\/span> (fpr,tpr,label=\" <span style=\"color: #008000;\">AUC=<\/span> \"+str(auc))\nplt. <span style=\"color: #3366ff;\">legend<\/span> (loc=4)\nplt. <span style=\"color: #3366ff;\">show<\/span> ()\n<\/strong><\/span><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11591 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/auc1.png\" alt=\"Python \u101b\u103e\u102d ROC \u1019\u103b\u1009\u103a\u1038\u1000\u103d\u1031\u1038\" width=\"389\" height=\"262\" srcset=\"\" sizes=\"\"><\/p>\n<div class=\"entry-content entry-content-single\" data-content-ads-inserted=\"true\">\n<p> <em><span style=\"color: #000000;\">\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1011\u102c\u1038\u101e\u1031\u102c Python \u1000\u102f\u1012\u103a\u1021\u1015\u103c\u100a\u1037\u103a\u1021\u1005\u102f\u1036\u1000\u102d\u102f <a href=\"https:\/\/github.com\/Statorials\/Python-Guides\/blob\/main\/logistic_regression.py\" target=\"_blank\" rel=\"noopener noreferrer\">\u1024\u1014\u1031\u101b\u102c\u1010\u103d\u1004\u103a<\/a> \u1010\u103d\u1031\u1037\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/em><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Logistic regression \u101e\u100a\u103a response variable binary \u1016\u103c\u1005\u103a\u101e\u1031\u102c\u1021\u1001\u102b regression model \u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u101b\u1014\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u102f\u1036\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c method \u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b Logistic regression \u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1015\u102f\u1036\u1005\u1036\u104f \u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a \u1021\u1019\u103b\u102c\u1038\u1006\u102f\u1036\u1038\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031 \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a \u101f\u102f \u101c\u1030\u101e\u102d\u1019\u103b\u102c\u1038\u101e\u1031\u102c \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a- log[p(X) \/ ( 1 -p(X))] = \u03b2 0 + \u03b2 1 X 1 + \u03b2 2 X 2 + \u2026 + \u03b2 p \u101b\u103d\u103e\u1031- X j : j th [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Python \u1010\u103d\u1004\u103a Logistic Regression \u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038 (\u1010\u1005\u103a\u1006\u1004\u1037\u103a\u1015\u103c\u102e\u1038\u1010\u1005\u103a\u1006\u1004\u1037\u103a) - Statology<\/title>\n<meta name=\"description\" content=\"\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a \u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a\u1025\u1015\u1019\u102c\u1010\u1005\u103a\u1001\u102f\u1021\u1015\u102b\u1021\u101d\u1004\u103a Python \u1010\u103d\u1004\u103a 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(\u1010\u1005\u103a\u1006\u1004\u1037\u103a\u1015\u103c\u102e\u1038\u1010\u1005\u103a\u1006\u1004\u1037\u103a) - Statology\" \/>\n<meta property=\"og:description\" content=\"\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a \u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a\u1025\u1015\u1019\u102c\u1010\u1005\u103a\u1001\u102f\u1021\u1015\u102b\u1021\u101d\u1004\u103a Python \u1010\u103d\u1004\u103a \u1011\u1031\u102c\u1000\u103a\u1015\u1036\u1037\u1015\u102d\u102f\u1037\u1006\u1031\u102c\u1004\u103a\u101b\u1031\u1038\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/my\/logistic-regression-python\/\" \/>\n<meta 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\u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038 (\u1010\u1005\u103a\u1006\u1004\u1037\u103a\u1015\u103c\u102e\u1038\u1010\u1005\u103a\u1006\u1004\u1037\u103a) - Statology\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/my\/#website\"},\"datePublished\":\"2023-07-27T11:31:28+00:00\",\"dateModified\":\"2023-07-27T11:31:28+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/my\/#\/schema\/person\/e47470981684a202f7ed4c0cb1e10097\"},\"description\":\"\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a \u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a\u1025\u1015\u1019\u102c\u1010\u1005\u103a\u1001\u102f\u1021\u1015\u102b\u1021\u101d\u1004\u103a Python \u1010\u103d\u1004\u103a \u1011\u1031\u102c\u1000\u103a\u1015\u1036\u1037\u1015\u102d\u102f\u1037\u1006\u1031\u102c\u1004\u103a\u101b\u1031\u1038\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f 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\u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/statorials.org\/my\/logistic-regression-python\/","og_locale":"my_MM","og_type":"article","og_title":"Python \u1010\u103d\u1004\u103a Logistic Regression \u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038 (\u1010\u1005\u103a\u1006\u1004\u1037\u103a\u1015\u103c\u102e\u1038\u1010\u1005\u103a\u1006\u1004\u1037\u103a) - Statology","og_description":"\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a \u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a\u1025\u1015\u1019\u102c\u1010\u1005\u103a\u1001\u102f\u1021\u1015\u102b\u1021\u101d\u1004\u103a Python 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