{"id":1446,"date":"2023-06-22T02:28:40","date_gmt":"2023-06-22T02:28:40","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/test-for-significance-of-slope-learn-it-1\/"},"modified":"2025-05-17T02:32:01","modified_gmt":"2025-05-17T02:32:01","slug":"test-for-significance-of-slope-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/test-for-significance-of-slope-learn-it-1\/","title":{"raw":"Test for Significance of Slope - Learn It 1","rendered":"Test for Significance of Slope &#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;Perform a test for significance of slope and interpret the results&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:6913,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;}\">Perform a test for significance of slope and interpret the results<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Check the conditions that are necessary to perform a test for significance of slope&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:6913,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;}\">Check the conditions that are necessary to perform a test for significance of slope<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Previously, we used scatterplots to visualize the relationship between two quantitative variables and the correlation coefficient, [latex]r[\/latex], to describe the strength and direction of the linear relationship between the bivariate variables. We also modeled that relationship using a line of best fit given by [latex]\\hat{y}=a+bx[\/latex].<\/p>\r\n<p>Let's review them before conducting a hypothesis test to find out whether or not two quantitative variables have a significant linear relationship.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3048[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3049[\/ohm2_question]<\/section>\r\n<section><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" width=\"100%\" height=\"1050\" 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\/linear_regression\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3050[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Perform a test for significance of slope and interpret the results&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:6913,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;}\">Perform a test for significance of slope and interpret the results<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Check the conditions that are necessary to perform a test for significance of slope&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:6913,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;}\">Check the conditions that are necessary to perform a test for significance of slope<\/span><\/li>\n<\/ul>\n<\/section>\n<p>Previously, we used scatterplots to visualize the relationship between two quantitative variables and the correlation coefficient, [latex]r[\/latex], to describe the strength and direction of the linear relationship between the bivariate variables. We also modeled that relationship using a line of best fit given by [latex]\\hat{y}=a+bx[\/latex].<\/p>\n<p>Let&#8217;s review them before conducting a hypothesis test to find out whether or not two quantitative variables have a significant linear relationship.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3048\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3048&theme=lumen&iframe_resize_id=ohm3048&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3049\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3049&theme=lumen&iframe_resize_id=ohm3049&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" width=\"100%\" height=\"1050\" 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\/linear_regression\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3050\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3050&theme=lumen&iframe_resize_id=ohm3050&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":8,"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\/1446"}],"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":4,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1446\/revisions"}],"predecessor-version":[{"id":6890,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1446\/revisions\/6890"}],"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\/1446\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1446"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1446"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1446"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}