{"id":4808,"date":"2021-07-07T06:34:58","date_gmt":"2021-07-07T06:34:58","guid":{"rendered":"https:\/\/www.aiproblog.com\/index.php\/2021\/07\/07\/an-overview-of-logistic-regression-analysis\/"},"modified":"2021-07-07T06:34:58","modified_gmt":"2021-07-07T06:34:58","slug":"an-overview-of-logistic-regression-analysis","status":"publish","type":"post","link":"https:\/\/www.aiproblog.com\/index.php\/2021\/07\/07\/an-overview-of-logistic-regression-analysis\/","title":{"rendered":"An Overview of Logistic Regression Analysis"},"content":{"rendered":"<p>Author: Muhammad Touhidul Islam<\/p>\n<div>\n<p class=\"has-medium-font-size\">\n<div class=\"wp-block-image\">\n<img decoding=\"async\" src=\"https:\/\/www.statisticalaid.com\/wp-content\/uploads\/2021\/05\/tempsnip2.png\" alt=\"An Intuitive study of Logistic Regression Analysis\"><\/p>\n<div class=\"code-block code-block-10\" style=\"text-align: center;\">Image Source: <a href=\"https:\/\/www.statisticalaid.com\/an-intuitive-study-of-logistic-regression-analysis\/\" target=\"_blank\" rel=\"noopener\">Statistical Aid<\/a>\n<\/div>\n<div class=\"code-block code-block-10\"><\/div>\n<div class=\"code-block code-block-10\">Logistic regression is a statistical technique to find the association between the categorical dependent (response)<span>\u00a0<\/span><a href=\"https:\/\/www.statisticalaid.com\/random-variable-and-its-types-with-properties\/\" target=\"_blank\" rel=\"noopener\">variable<\/a><span>\u00a0<\/span>and one or more categorical or continuous independent (explanatory) variable.<\/div>\n<div class=\"code-block code-block-10\"><\/div>\n<div class=\"code-block code-block-10\"><span>We can define the regression model as,<\/span><\/div>\n<div class=\"code-block code-block-10\">\n<p class=\"has-medium-font-size\">G(probability of event)=\u03b2<sub>0<\/sub>+\u03b2<sub>1<\/sub>x<sub>1<\/sub>+\u03b2<sub>2<\/sub>x<sub>2<\/sub>+\u2026+\u03b2<sub>k<\/sub>x<sub>k<\/sub><\/p>\n<p class=\"has-medium-font-size\">We determine G using link function as following,<\/p>\n<p class=\"has-medium-font-size\">Y={1 ; \u03b2<sub>0<\/sub>+\u03b2<sub>1<\/sub>x<sub>1<\/sub>+\u03f5&gt;0<\/p>\n<p class=\"has-medium-font-size\">{0 ; else<\/p>\n<p class=\"has-medium-font-size\">There are three types of link fuction. They are,<\/p>\n<ul class=\"has-medium-font-size\">\n<li>Logit<\/li>\n<li>Normit (probit)<\/li>\n<li>Gombit<\/li>\n<\/ul>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n<div class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.statisticalaid.com\/wp-content\/uploads\/2021\/05\/tempsnip.png\" alt=\"An Intuitive study of Logistic Regression Analysis\"><\/div>\n<h2 style=\"text-align: center;\"><span style=\"font-size: 10pt;\">Image Source: <a href=\"https:\/\/www.statisticalaid.com\/\" target=\"_blank\" rel=\"noopener\">Statistical Aid<\/a><\/span><\/h2>\n<\/p>\n<h2>Why we use logistic regression?<\/h2>\n<p class=\"has-medium-font-size\">We use it when there exists,<\/p>\n<ul class=\"has-medium-font-size\">\n<li>One Categorical response variable<\/li>\n<li>One or more explanatory variable.<\/li>\n<li>No linear relationship between dependent and independent variables.<\/li>\n<\/ul>\n<h2>Assumptions of Logistic Regression<\/h2>\n<ul class=\"has-medium-font-size\">\n<li>The dependent variable should be categorical (binary,<span>\u00a0<\/span><a href=\"https:\/\/www.statisticalaid.com\/levels-of-measurement-nominal-ordinal-interval-ratio-in-statistics\/\" target=\"_blank\" rel=\"noopener\">ordinal, nominal<\/a><span>\u00a0<\/span>or count occurrences).<\/li>\n<li>The predictor or independent variable should be continuous or categorical.<\/li>\n<li>The correlation among the predictors or independent variable (multi-collinearity) should not be severe but there exists linearity of independent variables and log odds.<\/li>\n<li>The data should be the representative part of population and record the data in the order its collected.<\/li>\n<li>The model should provide a good fit of the data.<\/li>\n<\/ul>\n<h2>Logistic regression vs Linear regression<\/h2>\n<ul class=\"has-medium-font-size\">\n<li>In the case of\u00a0<a href=\"https:\/\/www.statisticalaid.com\/regression-analysis-with-its-types-objectives-%20and-application\/\" target=\"_blank\" rel=\"noopener\">Linear Regressio<\/a>n,\u00a0the outcome is continuous while in the case of\u00a0logistic regression\u00a0outcome is discrete (not continuous)<\/li>\n<li>To perform\u00a0linear regression,\u00a0we require a linear relationship between the dependent and independent variables. But to perform\u00a0Logit\u00a0we do not require a linear relationship between the dependent and independent variables.<\/li>\n<li>Linear Regression\u00a0is all about fitting a straight line in the data while\u00a0Logit \u00a0is about fitting a curve to the data.<\/li>\n<li>Linear Regression\u00a0is a\u00a0regression\u00a0algorithm for Machine Learning while\u00a0Logit \u00a0is a\u00a0classification\u00a0Algorithm for machine learning.<\/li>\n<li>Linear regression\u00a0assumes Gaussian (or normal) distribution of the dependent variable.\u00a0Logit\u00a0assumes the binomial distribution of the dependent variable.<\/li>\n<\/ul>\n<p class=\"has-medium-font-size\">*Logit=logistic regression<\/p>\n<h2>Types<\/h2>\n<p class=\"has-medium-font-size\">There are four types of logistic regression. They are,<\/p>\n<ul class=\"has-medium-font-size\">\n<li>\n<strong>Binary logistic:<\/strong><span>\u00a0<\/span>When the dependent variable has two categories and the characteristics are at two levels such as yes or no, pass or fail, high or low etc. then the regression is called binary logistic regression.<\/li>\n<li>\n<strong>Ordinal logistic:<\/strong><span>\u00a0<\/span>When the dependent variable has three categories and the characteristics are at natural ordering of the levels such as survey results (disagree, neutral, agree) then the regression is called ordinal logistic regression.<\/li>\n<li>\n<strong>Nominal logistic:<\/strong><span>\u00a0<\/span>When the dependent variable has three or more categories but the characteristics are not at natural ordering of the levels such as colors (red, blue, green) then the regression is called nominal logistic.<\/li>\n<li>\n<strong>Poisson logistic:<\/strong><span>\u00a0<\/span>When the dependent variable has three or more categories but the characteristics are the number of time of an event occurs such as 0, 1, 2, 3, \u2026, etc. \u00a0then the regression is called Poisson logistic regression.<\/li>\n<\/ul>\n<p><a href=\"https:\/\/www.statisticalaid.com\/an-intuitive-study-of-logistic-regression-analysis\/\" target=\"_blank\" rel=\"noopener\">Source&#8230;<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><a href=\"https:\/\/www.datasciencecentral.com\/xn\/detail\/6448529:BlogPost:1056037\">Go to Source<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Author: Muhammad Touhidul Islam Image Source: Statistical Aid Logistic regression is a statistical technique to find the association between the categorical dependent (response)\u00a0variable\u00a0and one or [&hellip;] <span class=\"read-more-link\"><a class=\"read-more\" href=\"https:\/\/www.aiproblog.com\/index.php\/2021\/07\/07\/an-overview-of-logistic-regression-analysis\/\">Read More<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":4809,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[26],"tags":[],"_links":{"self":[{"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/posts\/4808"}],"collection":[{"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/comments?post=4808"}],"version-history":[{"count":0,"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/posts\/4808\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/media\/4809"}],"wp:attachment":[{"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/media?parent=4808"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/categories?post=4808"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/tags?post=4808"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}