{"id":15517,"date":"2022-04-17T18:42:48","date_gmt":"2022-04-17T17:42:48","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=15517"},"modified":"2024-02-13T13:47:43","modified_gmt":"2024-02-13T12:47:43","slug":"correlation-et-regressions","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/correlation-and-regressions\/","title":{"rendered":"Correlation and Regressions 101"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"15517\" class=\"elementor elementor-15517\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d513d53 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d513d53\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-a15c6d4\" data-id=\"a15c6d4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b787c43 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"b787c43\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/2020\/04\/03\/theories-and-algorithms-2\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Theories<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b51b278\" data-id=\"b51b278\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7dcaf85 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"7dcaf85\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Home page<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-9feebf1\" data-id=\"9feebf1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-669f080 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"669f080\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/en.wikipedia.org\/wiki\/Correlation\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5460056 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5460056\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9161868\" data-id=\"9161868\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8222948 elementor-widget elementor-widget-toggle\" data-id=\"8222948\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1361\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1361\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">I. Correlation<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1361\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1361\"><ul><li><a class=\"mw-redirect\" title=\"Pearson product-moment correlation coefficient\" href=\"https:\/\/en.wikipedia.org\/wiki\/Pearson_product-moment_correlation_coefficient\" target=\"_blank\" rel=\"noopener\">Pearson product moment<\/a><\/li><li><a title=\"Partial correlation\" href=\"https:\/\/en.wikipedia.org\/wiki\/Partial_correlation\" target=\"_blank\" rel=\"noopener\">Partial correlation<\/a><\/li><li><a title=\"Confounding\" href=\"https:\/\/en.wikipedia.org\/wiki\/Confounding\" target=\"_blank\" rel=\"noopener\">Confounding variable<\/a><\/li><li><a title=\"Coefficient of determination\" href=\"https:\/\/en.wikipedia.org\/wiki\/Coefficient_of_determination\" target=\"_blank\" rel=\"noopener\">Coefficient of determination<\/a><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1362\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-1362\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">II. Regression analysis<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1362\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-1362\"><ul><li><a class=\"mw-redirect\" title=\"Errors and residuals in statistics\" href=\"https:\/\/en.wikipedia.org\/wiki\/Errors_and_residuals_in_statistics\" target=\"_blank\" rel=\"noopener\">Errors and residuals<\/a><\/li><li><a title=\"Regression validation\" href=\"https:\/\/en.wikipedia.org\/wiki\/Regression_validation\" target=\"_blank\" rel=\"noopener\">Regression validation<\/a><\/li><li><a title=\"mixed-model\" href=\"https:\/\/en.wikipedia.org\/wiki\/Mixed_model\" target=\"_blank\" rel=\"noopener\">Mixed effects models<\/a><\/li><li><a title=\"Simultaneous equations model\" href=\"https:\/\/en.wikipedia.org\/wiki\/Simultaneous_equations_model\" target=\"_blank\" rel=\"noopener\">Simultaneous equations models<\/a><\/li><li><a class=\"mw-redirect\" title=\"Multivariate adaptive regression splines\" href=\"https:\/\/en.wikipedia.org\/wiki\/Multivariate_adaptive_regression_splines\" target=\"_blank\" rel=\"noopener\">Multivariate adaptive regression splines (MARS)<\/a><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1363\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-1363\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">III. Linear regression<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1363\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-1363\"><ul><li><a title=\"Simple linear regression\" href=\"https:\/\/en.wikipedia.org\/wiki\/Simple_linear_regression\" target=\"_blank\" rel=\"noopener\">Simple linear regression<\/a><\/li><li><a title=\"Ordinary least squares\" href=\"https:\/\/en.wikipedia.org\/wiki\/Ordinary_least_squares\" target=\"_blank\" rel=\"noopener\">Ordinary least squares<\/a><\/li><li><a title=\"General linear model\" href=\"https:\/\/en.wikipedia.org\/wiki\/General_linear_model\" target=\"_blank\" rel=\"noopener\">General linear model<\/a><\/li><li><a title=\"Bayesian linear regression\" href=\"https:\/\/en.wikipedia.org\/wiki\/Bayesian_linear_regression\" target=\"_blank\" rel=\"noopener\">Bayesian regression<\/a><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1364\" class=\"elementor-tab-title\" data-tab=\"4\" role=\"button\" aria-controls=\"elementor-tab-content-1364\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">IV. Nonlinear regression<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1364\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"4\" role=\"region\" aria-labelledby=\"elementor-tab-title-1364\"><ul><li><a title=\"Nonlinear regression\" href=\"https:\/\/en.wikipedia.org\/wiki\/Nonlinear_regression\" target=\"_blank\" rel=\"noopener\">Nonlinear regression<\/a><\/li><li><a title=\"Nonparametric regression\" href=\"https:\/\/en.wikipedia.org\/wiki\/Nonparametric_regression\" target=\"_blank\" rel=\"noopener\">Nonparametric<\/a><\/li><li><a title=\"Semiparametric regression\" href=\"https:\/\/en.wikipedia.org\/wiki\/Semiparametric_regression\" target=\"_blank\" rel=\"noopener\">Semiparametric<\/a><\/li><li><a title=\"Isotonic regression\" href=\"https:\/\/en.wikipedia.org\/wiki\/Isotonic_regression\" target=\"_blank\" rel=\"noopener\">Isotonic<\/a><\/li><li><a title=\"Robust regression\" href=\"https:\/\/en.wikipedia.org\/wiki\/Robust_regression\" target=\"_blank\" rel=\"noopener\">Robust<\/a><\/li><li><a title=\"Heteroscedasticity\" href=\"https:\/\/en.wikipedia.org\/wiki\/Heteroscedasticity\" target=\"_blank\" rel=\"noopener\">Heteroscedasticity<\/a><\/li><li><a title=\"Homoscedasticity\" href=\"https:\/\/en.wikipedia.org\/wiki\/Homoscedasticity\" target=\"_blank\" rel=\"noopener\">Homoscedasticity<\/a><\/li><\/ul><p><a href=\"https:\/\/complex-systems-ai.com\/en\/correlation-and-regressions\/data-transformation-and-regression\/\">Regression<\/a> generalized:<\/p><ul><li><a title=\"exponential family\" href=\"https:\/\/en.wikipedia.org\/wiki\/Exponential_family\" target=\"_blank\" rel=\"noopener\">exponential families<\/a><\/li><li><a title=\"Logistic regression\" href=\"https:\/\/en.wikipedia.org\/wiki\/Logistic_regression\" target=\"_blank\" rel=\"noopener\">Logistics (Bernoulli)<\/a>\u00a0\/\u00a0<a title=\"Binomial regression\" href=\"https:\/\/en.wikipedia.org\/wiki\/Binomial_regression\" target=\"_blank\" rel=\"noopener\">Binomial<\/a>\u00a0\/\u00a0<a title=\"regression fish\" href=\"https:\/\/en.wikipedia.org\/wiki\/Poisson_regression\" target=\"_blank\" rel=\"noopener\">Fish regressions<\/a><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1365\" class=\"elementor-tab-title\" data-tab=\"5\" role=\"button\" aria-controls=\"elementor-tab-content-1365\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">V. Tutorials<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1365\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"5\" role=\"region\" aria-labelledby=\"elementor-tab-title-1365\"><ul><li><a href=\"https:\/\/vigneshmadanan.medium.com\/linear-regression-basics-and-regularization-methods-b40359b0aea5\" target=\"_blank\" rel=\"noopener\">How to find the right regression?<\/a><\/li><li><a href=\"https:\/\/complex-systems-ai.com\/en\/correlation-and-regressions\/data-transformation-and-regression\/\">From data normalization to regression<\/a><\/li><li><a href=\"https:\/\/complex-systems-ai.com\/en\/data-analysis\/how-to-handle-missing-data\/\">How to handle missing data<\/a><\/li><li><a href=\"https:\/\/complex-systems-ai.com\/en\/data-analysis\/selection-of-columns\/\">Selection of columns<\/a><\/li><li><a href=\"https:\/\/complex-systems-ai.com\/en\/descriptive-analysis\/good-practices-for-exploratory-data-analysis\/\">Tutorial on best practices in exploratory data analysis<\/a><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2b970d0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2b970d0\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7b1a5dd\" data-id=\"7b1a5dd\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1bb8089 elementor-widget elementor-widget-heading\" data-id=\"1bb8089\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/en\/correlation-and-regressions\/#Correlation-et-Regressions\" >Correlation and Regressions<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Correlation-et-Regressions\"><\/span>Correlation and Regressions<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6c33bf4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6c33bf4\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-76957d9\" data-id=\"76957d9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-eacb0be elementor-widget elementor-widget-text-editor\" data-id=\"eacb0be\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In statistics, correlation or dependence is any statistical relationship, causal or not, between two random variables or bivariate data. Although in the broadest sense &quot;correlation&quot; can indicate any type of association, in statistics it normally refers to the degree to which a pair of variables is linearly related. Familiar examples of dependent phenomena include the correlation between the size of parents and their offspring, and the correlation between the price of a good and the quantity that consumers are willing to buy, as represented in the so-called curve of request.<\/p><p>Correlations are useful because they can indicate a predictive relationship that can be used in practice. For example, an electric utility may produce less electricity in mild weather depending on the correlation between electricity demand and weather conditions. In this example, there is a causal relationship, as extreme weather causes people to use more electricity for heating or cooling. However, in general, the presence of a correlation is not sufficient to infer the presence of a causal relationship (i.e. correlation does not imply causation).<\/p><p>In statistical modeling, regression analysis is a set of statistical processes for estimating relationships between a dependent variable (often called an &quot;outcome&quot; or &quot;response&quot; variable) and one or more independent variables (often called &quot;predictors&quot;). , &#039;covariates&#039;, &#039;explanatory variables&#039; or &#039;characteristics&#039;). The most common form of regression analysis is linear regression, in which one finds the line (or more complex linear combination) that best fits the data according to a specific mathematical criterion.\u00a0<\/p><p>For example, the ordinary least squares method calculates the single line (or hyperplane) that minimizes the sum of the squared differences between the true data and that line (or hyperplane). For reasons <a href=\"https:\/\/complex-systems-ai.com\/en\/logic-math-27\/\">math<\/a> (see linear regression), this allows the researcher to estimate the conditional expectation (or population mean value) of the dependent variable when the independent variables take on a given set of values. Less common forms of regression use slightly different procedures to estimate alternative location parameters (e.g., quantile regression or necessary condition analysis) or estimate conditional expectation across a larger collection of nonlinear models ( for example, nonparametric regression).<\/p><p>Regression analysis is primarily used for two conceptually distinct purposes.<\/p><p>First, regression analysis is widely used for prediction and forecasting, where its use significantly overlaps with the field of machine learning.<\/p><p>Second, in some situations, regression analysis can be used to infer causal relationships between independent and dependent variables. It is important to note that regressions by themselves only reveal the relationships between a dependent variable and a set of independent variables in a fixed data set. To use regressions for prediction or to infer causal relationships, respectively, a researcher must carefully justify why existing relationships have predictive power for a new context or why a relationship between two variables has a causal interpretation. The latter is particularly important when researchers hope to estimate causal relationships using observational data.<\/p><p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter wp-image-15519 size-medium\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/corral10-300x170.jpg\" alt=\"correlation and regressions\" width=\"300\" height=\"170\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/corral10-300x170.jpg 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/corral10-18x10.jpg 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/corral10-600x340.jpg 600w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/corral10.jpg 762w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Theories Wiki home page I. Pearson product-moment correlation Partial correlation Confounding variable Coefficient of determination II. Regression analysis Errors and residuals Regression validation Mixed \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-15517","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/15517","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/comments?post=15517"}],"version-history":[{"count":13,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/15517\/revisions"}],"predecessor-version":[{"id":20643,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/15517\/revisions\/20643"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=15517"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}