{"id":1454,"date":"2023-06-22T02:28:47","date_gmt":"2023-06-22T02:28:47","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/anova-for-regression-learn-it-1\/"},"modified":"2025-05-17T02:34:53","modified_gmt":"2025-05-17T02:34:53","slug":"anova-for-regression-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/anova-for-regression-learn-it-1\/","title":{"raw":"ANOVA for Regression - Learn It 1","rendered":"ANOVA for Regression &#8211; Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Understand what is measured by SSRegression, SSResiduals, and SSTotal in a regression context&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Understand what is measured by SSRegression, SSResiduals, and SSTotal in a regression context<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Discuss the factors that affect the value of F-statistics in a regression context&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Discuss the factors that affect the value of F-statistics in a regression context<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<section>Previously, you learned how to conduct a one-way ANOVA for scenarios that involve comparing more than two groups. Now, let's extend what you learned about ANOVA to a regression context.\u00a0<\/section>\r\n<section class=\"textbox recall\"><b><b><b><b><b>ANOVA Table<\/b><\/b><\/b><\/b><\/b>\u00a0\r\n\r\n<p>In an ANOVA table, the calculation illustrating the total variation <em>within<\/em> the groups of interest is known as the <strong>error sum of squares (SSError)<\/strong>. The calculation illustrating the total variation <em>between<\/em> the groups is known as the <strong>group sum of squares (SSGroup)<\/strong>.<br \/>\r\n[reveal-answer q=\"646836\"]ANOVA Table[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"646836\"]<\/p>\r\n<table style=\"height: 850px;\">\r\n<tbody>\r\n<tr style=\"height: 66px;\">\r\n<td style=\"width: 51.25px; height: 66px;\"><strong>Source<\/strong><\/td>\r\n<td style=\"width: 156.345px; height: 66px;\"><strong>Degrees of Freedom (df)<\/strong><\/td>\r\n<td style=\"width: 62.1875px; height: 66px;\"><strong>Sum of Squares<\/strong><\/td>\r\n<td style=\"width: 189.08px; height: 66px;\"><strong>Mean Square<\/strong><\/td>\r\n<td style=\"width: 191.589px; height: 66px;\"><strong>F-Statistic<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 219px;\">\r\n<td style=\"width: 51.25px; height: 219px;\">Group<\/td>\r\n<td style=\"width: 156.345px; height: 219px;\">\r\n<p>[latex]k-1[\/latex]<\/p>\r\n<p>(The number of groups minus 1)<\/p>\r\n<\/td>\r\n<td style=\"width: 62.1875px; height: 219px;\">SSGroup<\/td>\r\n<td style=\"width: 189.08px; height: 219px;\">[latex]\\dfrac{\\text{SSGroup}}{k-1}[\/latex]<\/td>\r\n<td style=\"width: 191.589px; height: 219px;\">[latex]\\dfrac{\\text{MSGroup}}{\\text{MSError}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 321px;\">\r\n<td style=\"width: 51.25px; height: 321px;\">Error<\/td>\r\n<td style=\"width: 156.345px; height: 321px;\">\r\n<p>[latex]N-k[\/latex]<\/p>\r\n<p>(The total number of data points minus the number of groups)<\/p>\r\n<\/td>\r\n<td style=\"width: 62.1875px; height: 321px;\">SSError<\/td>\r\n<td style=\"width: 189.08px; height: 321px;\">[latex]\\dfrac{\\text{SSError}}{N-k}[\/latex]<\/td>\r\n<td style=\"width: 191.589px; height: 321px;\">\u00a0<\/td>\r\n<\/tr>\r\n<tr style=\"height: 244px;\">\r\n<td style=\"width: 51.25px; height: 244px;\">Total<\/td>\r\n<td style=\"width: 156.345px; height: 244px;\">\r\n<p>\u00a0[latex]N-1[\/latex]<\/p>\r\n<p>(The total number of data points minus 1)<\/p>\r\n<\/td>\r\n<td style=\"width: 62.1875px; height: 244px;\">SSGroup + SSError<\/td>\r\n<td style=\"width: 189.08px; height: 244px;\">\u00a0<\/td>\r\n<td style=\"width: 191.589px; height: 244px;\">\u00a0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3149[\/ohm2_question]<\/section>\r\n<section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3058[\/ohm2_question]<\/section>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3150[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3151[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3152[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3153[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Understand what is measured by SSRegression, SSResiduals, and SSTotal in a regression context&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Understand what is measured by SSRegression, SSResiduals, and SSTotal in a regression context<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Discuss the factors that affect the value of F-statistics in a regression context&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Discuss the factors that affect the value of F-statistics in a regression context<\/span><\/li>\n<\/ul>\n<\/section>\n<section>Previously, you learned how to conduct a one-way ANOVA for scenarios that involve comparing more than two groups. Now, let&#8217;s extend what you learned about ANOVA to a regression context.\u00a0<\/section>\n<section class=\"textbox recall\"><b><b><b><b><b>ANOVA Table<\/b><\/b><\/b><\/b><\/b>\u00a0<\/p>\n<p>In an ANOVA table, the calculation illustrating the total variation <em>within<\/em> the groups of interest is known as the <strong>error sum of squares (SSError)<\/strong>. The calculation illustrating the total variation <em>between<\/em> the groups is known as the <strong>group sum of squares (SSGroup)<\/strong>.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q646836\">ANOVA Table<\/button><\/p>\n<div id=\"q646836\" class=\"hidden-answer\" style=\"display: none\">\n<table style=\"height: 850px;\">\n<tbody>\n<tr style=\"height: 66px;\">\n<td style=\"width: 51.25px; height: 66px;\"><strong>Source<\/strong><\/td>\n<td style=\"width: 156.345px; height: 66px;\"><strong>Degrees of Freedom (df)<\/strong><\/td>\n<td style=\"width: 62.1875px; height: 66px;\"><strong>Sum of Squares<\/strong><\/td>\n<td style=\"width: 189.08px; height: 66px;\"><strong>Mean Square<\/strong><\/td>\n<td style=\"width: 191.589px; height: 66px;\"><strong>F-Statistic<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 219px;\">\n<td style=\"width: 51.25px; height: 219px;\">Group<\/td>\n<td style=\"width: 156.345px; height: 219px;\">\n[latex]k-1[\/latex]<\/p>\n<p>(The number of groups minus 1)<\/p>\n<\/td>\n<td style=\"width: 62.1875px; height: 219px;\">SSGroup<\/td>\n<td style=\"width: 189.08px; height: 219px;\">[latex]\\dfrac{\\text{SSGroup}}{k-1}[\/latex]<\/td>\n<td style=\"width: 191.589px; height: 219px;\">[latex]\\dfrac{\\text{MSGroup}}{\\text{MSError}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 321px;\">\n<td style=\"width: 51.25px; height: 321px;\">Error<\/td>\n<td style=\"width: 156.345px; height: 321px;\">\n[latex]N-k[\/latex]<\/p>\n<p>(The total number of data points minus the number of groups)<\/p>\n<\/td>\n<td style=\"width: 62.1875px; height: 321px;\">SSError<\/td>\n<td style=\"width: 189.08px; height: 321px;\">[latex]\\dfrac{\\text{SSError}}{N-k}[\/latex]<\/td>\n<td style=\"width: 191.589px; height: 321px;\">\u00a0<\/td>\n<\/tr>\n<tr style=\"height: 244px;\">\n<td style=\"width: 51.25px; height: 244px;\">Total<\/td>\n<td style=\"width: 156.345px; height: 244px;\">\n[latex]N-1[\/latex]<\/p>\n<p>(The total number of data points minus 1)<\/p>\n<\/td>\n<td style=\"width: 62.1875px; height: 244px;\">SSGroup + SSError<\/td>\n<td style=\"width: 189.08px; height: 244px;\">\u00a0<\/td>\n<td style=\"width: 191.589px; height: 244px;\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3149\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3149&theme=lumen&iframe_resize_id=ohm3149&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3058\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3058&theme=lumen&iframe_resize_id=ohm3058&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3150\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3150&theme=lumen&iframe_resize_id=ohm3150&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3151\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3151&theme=lumen&iframe_resize_id=ohm3151&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3152\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3152&theme=lumen&iframe_resize_id=ohm3152&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3153\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3153&theme=lumen&iframe_resize_id=ohm3153&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":14,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1438,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1454"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":7,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1454\/revisions"}],"predecessor-version":[{"id":5837,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1454\/revisions\/5837"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1438"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1454\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1454"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1454"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1454"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1454"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}