{"id":1484,"date":"2023-06-22T02:36:52","date_gmt":"2023-06-22T02:36:52","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/multiple-linear-regression-learn-it-4\/"},"modified":"2025-05-17T02:43:14","modified_gmt":"2025-05-17T02:43:14","slug":"multiple-linear-regression-learn-it-4","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/multiple-linear-regression-learn-it-4\/","title":{"raw":"Multiple Linear Regression - Learn It 4","rendered":"Multiple Linear Regression &#8211; Learn It 4"},"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;Write and describe a multiple linear regression model equation&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;}\">Write and describe a multiple linear regression model equation<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate and describe the unadjusted coefficient of determination&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;}\">Calculate and describe the unadjusted coefficient of determination<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Assess the model assumptions with a residual or a predicted values plot&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;}\">Assess the model assumptions with a residual or a predicted values plot<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Residuals<\/h2>\r\n<p>We can assess whether or not it is reasonable to fit a linear regression model using residual plots, similar to simple linear regression. In multiple linear regression, the [latex]y[\/latex]-axis has the residual values, and the [latex]x[\/latex]-axis has the explanatory variables and\/or the fitted values. For a multiple linear regression model, you create a residual plot for each continuous explanatory variable, as well as the fitted value.<\/p>\r\n<section class=\"textbox proTip\">We would expect to see the residual values appear randomly scattered across the [latex]x[\/latex]-values with no clear patterns (e.g., residual plots that display a curvature violate the linearity condition). Residual plots that increase or decrease in magnitude (distance from zero) violate the constant variance condition.<\/section>\r\n<p>The residual plot of the residuals vs. predicted values accounts for all the variables in the model. Residual plots of the residuals vs. individual exploratory variables allow us to identify a potential source of a violation. The normality condition is beyond the scope of this course.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3236[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write and describe a multiple linear regression model equation&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;}\">Write and describe a multiple linear regression model equation<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate and describe the unadjusted coefficient of determination&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;}\">Calculate and describe the unadjusted coefficient of determination<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Assess the model assumptions with a residual or a predicted values plot&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;}\">Assess the model assumptions with a residual or a predicted values plot<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Residuals<\/h2>\n<p>We can assess whether or not it is reasonable to fit a linear regression model using residual plots, similar to simple linear regression. In multiple linear regression, the [latex]y[\/latex]-axis has the residual values, and the [latex]x[\/latex]-axis has the explanatory variables and\/or the fitted values. For a multiple linear regression model, you create a residual plot for each continuous explanatory variable, as well as the fitted value.<\/p>\n<section class=\"textbox proTip\">We would expect to see the residual values appear randomly scattered across the [latex]x[\/latex]-values with no clear patterns (e.g., residual plots that display a curvature violate the linearity condition). Residual plots that increase or decrease in magnitude (distance from zero) violate the constant variance condition.<\/section>\n<p>The residual plot of the residuals vs. predicted values accounts for all the variables in the model. Residual plots of the residuals vs. individual exploratory variables allow us to identify a potential source of a violation. The normality condition is beyond the scope of this course.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3236\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3236&theme=lumen&iframe_resize_id=ohm3236&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":11,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1473,"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\/1484"}],"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":6,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1484\/revisions"}],"predecessor-version":[{"id":6908,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1484\/revisions\/6908"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1473"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1484\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1484"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1484"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1484"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1484"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}