{"id":1456,"date":"2023-06-22T02:28:48","date_gmt":"2023-06-22T02:28:48","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/anova-for-regression-learn-it-3\/"},"modified":"2024-03-01T20:01:52","modified_gmt":"2024-03-01T20:01:52","slug":"anova-for-regression-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/anova-for-regression-learn-it-3\/","title":{"raw":"ANOVA for Regression - Learn It 3","rendered":"ANOVA for Regression &#8211; Learn It 3"},"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<p>The ANOVA table will also include a P-value, which tells the probability of obtaining an F-statistic as large or larger than the one in the sample if the null hypothesis was true.<\/p>\r\n<p>An ANOVA F-test can be used to test the population slope for simple linear regression, the same scenario where you used a t-test.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3177[\/ohm2_question]<\/section>\r\n<p>To model the values of the F-statistic that would occur if the null hypothesis was true and the assumptions for inference were met, you will use an F Distribution with [latex]df_1 = p[\/latex]\u00a0and [latex]df_2 = n-1-p[\/latex].<\/p>\r\n<section class=\"textbox interact\"><strong>Step 1:\u00a0<\/strong>Select the \"Find Probability\" tab<br \/>\r\n<strong>Step 2:\u00a0<\/strong> Enter the df<sub>1<\/sub> and df<sub>2<\/sub> accordingly<br \/>\r\n<strong>Step 3:<\/strong> For the \"Type of Probability\" select \"Upper Tail\".<br \/>\r\n<strong>Step 4:\u00a0<\/strong>Enter the [latex]F[\/latex] value as the value of [latex]x[\/latex]<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/fdist\" width=\"100%\" height=\"700\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/fdist\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3156[\/ohm2_question]<\/section>\r\n<section>\r\n<p class=\"student12ptnumberlist\" style=\"margin-left: 0in; text-indent: 0in;\">Suppose you had conducted a t-test for the slope instead of an F-test for the slope in this scenario. The value of the t-statistic would have been [latex]7.50[\/latex], the square root of the F-statistic. The P-value for the two-sided t-test would be the same as the P-value for the F-test.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3178[\/ohm2_question]<\/section>\r\n<\/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<p>The ANOVA table will also include a P-value, which tells the probability of obtaining an F-statistic as large or larger than the one in the sample if the null hypothesis was true.<\/p>\n<p>An ANOVA F-test can be used to test the population slope for simple linear regression, the same scenario where you used a t-test.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3177\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3177&theme=lumen&iframe_resize_id=ohm3177&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>To model the values of the F-statistic that would occur if the null hypothesis was true and the assumptions for inference were met, you will use an F Distribution with [latex]df_1 = p[\/latex]\u00a0and [latex]df_2 = n-1-p[\/latex].<\/p>\n<section class=\"textbox interact\"><strong>Step 1:\u00a0<\/strong>Select the &#8220;Find Probability&#8221; tab<br \/>\n<strong>Step 2:\u00a0<\/strong> Enter the df<sub>1<\/sub> and df<sub>2<\/sub> accordingly<br \/>\n<strong>Step 3:<\/strong> For the &#8220;Type of Probability&#8221; select &#8220;Upper Tail&#8221;.<br \/>\n<strong>Step 4:\u00a0<\/strong>Enter the [latex]F[\/latex] value as the value of [latex]x[\/latex]<\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/fdist\" width=\"100%\" height=\"700\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/fdist\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3156\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3156&theme=lumen&iframe_resize_id=ohm3156&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>\n<p class=\"student12ptnumberlist\" style=\"margin-left: 0in; text-indent: 0in;\">Suppose you had conducted a t-test for the slope instead of an F-test for the slope in this scenario. The value of the t-statistic would have been [latex]7.50[\/latex], the square root of the F-statistic. The P-value for the two-sided t-test would be the same as the P-value for the F-test.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3178\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3178&theme=lumen&iframe_resize_id=ohm3178&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n","protected":false},"author":8,"menu_order":16,"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\/1456"}],"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":3,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1456\/revisions"}],"predecessor-version":[{"id":5839,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1456\/revisions\/5839"}],"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\/1456\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1456"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1456"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1456"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1456"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}