{"id":3322,"date":"2015-04-11T23:04:31","date_gmt":"2015-04-12T04:04:31","guid":{"rendered":"http:\/\/www.ssc.wisc.edu\/~jfrees\/?page_id=3322"},"modified":"2015-08-21T13:38:23","modified_gmt":"2015-08-21T18:38:23","slug":"2-3-is-the-model-useful-some-basic-summary-measures","status":"publish","type":"page","link":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/regression\/basic-linear-regression\/2-3-is-the-model-useful-some-basic-summary-measures\/","title":{"rendered":"2.3 Is the Model Useful? Some Basic Summary Measures"},"content":{"rendered":"<div class=\"scbb-content-box scbb-content-box-gray\">In this section, you learn how to: \n<ul>\n<li>Visualize the ANOVA decomposition of variability<\/li>\n<li>Calculate and interpret \\(R^2\\)  &#8211; the coefficient of determination<\/li>\n<li>Calculate and interpret \\(s^2\\) &#8211; the mean square error<\/li>\n<li>Explain the components of the ANOVA table<\/li>\n<\/ul>\n<h2 style=\"text-align: center\"><a href=\"http:\/\/flash.bus.wisc.edu\/data\/act_sci\/Frees\/Regression2015\/Chapter2\/Part3\/IsTheModelUseful.html\" target=\"_blank\">Video Overview of the Section <\/a><a href=\"http:\/\/flash.bus.wisc.edu\/data\/act_sci\/Frees\/Regression2015\/Chapter2\/Part3\/IsTheModelUseful.mp4\" target=\"_blank\">(<em>Alternative .mp4 Version &#8211; 10:46  min<\/em>)<\/a><\/h2>\n<p><\/p><\/div>\n<p>Although statistics is the science of summarizing data, it is also the art of arguing with data. This section develops some of the basic tools used to justify the basic linear regression model. A scatter plot may provide strong <em>visual<\/em> evidence that <em>x<\/em> influences <em>y<\/em>; developing <em>numerical<\/em> evidence will enable us to quantify the strength of the relationship. Further, numerical evidence will be useful when we consider other data sets where the graphical evidence is not compelling. <\/p>\n<p><div class=\"alignleft\"><a href=\"https:\/\/users.ssc.wisc.edu\/~ewfrees\/regression\/basic-linear-regression\/2-3-basic-linear-regression-model\/\" title=\"2.2 Basic Linear Regression Model\">&#9668 Previous page<\/a><\/div><div class=\"alignright\"><a href=\"https:\/\/users.ssc.wisc.edu\/~ewfrees\/regression\/basic-linear-regression\/2-3-is-the-model-useful-some-basic-summary-measures\/partitioning-the-variability\/\" title=\"Partitioning the Variability\">Next page &#9658<\/a><\/div><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Although statistics is the science of summarizing data, it is also the art of arguing with data. This section develops some of the basic tools used to justify the basic linear regression model. A scatter &hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":3243,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"jetpack_post_was_ever_published":false},"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/P8cLPd-RA","acf":[],"_links":{"self":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/3322"}],"collection":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/comments?post=3322"}],"version-history":[{"count":9,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/3322\/revisions"}],"predecessor-version":[{"id":5026,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/3322\/revisions\/5026"}],"up":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/3243"}],"wp:attachment":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/media?parent=3322"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}