{"id":1474,"date":"2023-06-22T02:36:48","date_gmt":"2023-06-22T02:36:48","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/module-17-cheat-sheets\/"},"modified":"2025-02-11T04:27:12","modified_gmt":"2025-02-11T04:27:12","slug":"module-17-cheat-sheets","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/module-17-cheat-sheets\/","title":{"raw":"Module 16: Cheat Sheet","rendered":"Module 16: Cheat Sheet"},"content":{"raw":"<h4 style=\"text-align: right;\"><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Statistics+Exemplar\/Cheat+Sheets\/Module+16_+Cheat+Sheet.pdf\" target=\"_blank\" rel=\"noopener\">Download a pdf of this page here.<\/a><\/h4>\r\n<h2>Essential Concepts<\/h2>\r\n<ul>\r\n\t<li>A linear regression model with two or more explanatory variables is called a multiple linear regression model. Since there is more than one explanatory variable, the model is no longer a line. In fact, we can include [latex]p[\/latex] explanatory variables in our model. The equation for the estimated model that uses [latex]p[\/latex] variables is[latex]\\hat{y} = a + b_1 \\cdot x_1 + b_2 \\cdot x_2 + ... + b_p \\cdot x_p[\/latex]where [latex]b_1, b_2, ... ,b_p[\/latex] are the regression coefficients for explanatory variables [latex]x_1, x_2, ... ,x_p[\/latex], respectively. In multiple linear regression, [latex]b_1, b_2, ... , b_p[\/latex] are called partial slopes.<\/li>\r\n\t<li>The coefficient of determination, [latex]R^2[\/latex], is used to determine the percentage of variability in the response variable that is accounted for by the explanatory variables.<\/li>\r\n\t<li>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.<\/li>\r\n\t<li>An indicator variable is a binary variable with only two values: [latex]0[\/latex] and [latex]1[\/latex]. When creating an indicator variable, we assign the value of [latex]1[\/latex] for a certain category, and the value of [latex]0[\/latex] is used for all other categories.<\/li>\r\n\t<li>A reference group is the value of the categorical variable that is not represented explicitly by the indicator variable (which is why we only require [latex]k-1[\/latex]\u00a0indicator variables to define our regression model).<\/li>\r\n\t<li>An interaction occurs when an explanatory variable has a different effect on the response variable, depending on the values of another explanatory variable. An interaction term is a variable that represents an interaction between two variables.<\/li>\r\n<\/ul>\r\n<h2>Key Equations<\/h2>\r\n<p><strong>multiple linear regression model<\/strong><\/p>\r\n<p>[latex]\\hat{y} = a + b_1 \\cdot x_1 + b_2 \\cdot x_2 + ... + b_p \\cdot x_p[\/latex]<\/p>\r\n<p><strong>partial slopes<\/strong><\/p>\r\n<p>[latex]b_1, b_2, ... , b_p[\/latex]<\/p>\r\n<h2>Glossary<\/h2>\r\n<p><strong>indicator variable<\/strong><\/p>\r\n<p>a binary variable with only two values: [latex]0[\/latex] and [latex]1[\/latex]<\/p>\r\n<p><strong>interaction<\/strong><\/p>\r\n<p>an explanatory variable that has a different effect on the response variable, depending on the values of another explanatory variable<\/p>\r\n<p><strong>interaction term<\/strong><\/p>\r\n<p>a variable that represents an interaction between two variables<\/p>\r\n<p><strong>multiple linear regression model<\/strong><\/p>\r\n<p>a linear regression model with two or more explanatory variables<\/p>\r\n<p>&nbsp;<\/p>","rendered":"<h4 style=\"text-align: right;\"><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Statistics+Exemplar\/Cheat+Sheets\/Module+16_+Cheat+Sheet.pdf\" target=\"_blank\" rel=\"noopener\">Download a pdf of this page here.<\/a><\/h4>\n<h2>Essential Concepts<\/h2>\n<ul>\n<li>A linear regression model with two or more explanatory variables is called a multiple linear regression model. Since there is more than one explanatory variable, the model is no longer a line. In fact, we can include [latex]p[\/latex] explanatory variables in our model. The equation for the estimated model that uses [latex]p[\/latex] variables is[latex]\\hat{y} = a + b_1 \\cdot x_1 + b_2 \\cdot x_2 + ... + b_p \\cdot x_p[\/latex]where [latex]b_1, b_2, ... ,b_p[\/latex] are the regression coefficients for explanatory variables [latex]x_1, x_2, ... ,x_p[\/latex], respectively. In multiple linear regression, [latex]b_1, b_2, ... , b_p[\/latex] are called partial slopes.<\/li>\n<li>The coefficient of determination, [latex]R^2[\/latex], is used to determine the percentage of variability in the response variable that is accounted for by the explanatory variables.<\/li>\n<li>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.<\/li>\n<li>An indicator variable is a binary variable with only two values: [latex]0[\/latex] and [latex]1[\/latex]. When creating an indicator variable, we assign the value of [latex]1[\/latex] for a certain category, and the value of [latex]0[\/latex] is used for all other categories.<\/li>\n<li>A reference group is the value of the categorical variable that is not represented explicitly by the indicator variable (which is why we only require [latex]k-1[\/latex]\u00a0indicator variables to define our regression model).<\/li>\n<li>An interaction occurs when an explanatory variable has a different effect on the response variable, depending on the values of another explanatory variable. An interaction term is a variable that represents an interaction between two variables.<\/li>\n<\/ul>\n<h2>Key Equations<\/h2>\n<p><strong>multiple linear regression model<\/strong><\/p>\n<p>[latex]\\hat{y} = a + b_1 \\cdot x_1 + b_2 \\cdot x_2 + ... + b_p \\cdot x_p[\/latex]<\/p>\n<p><strong>partial slopes<\/strong><\/p>\n<p>[latex]b_1, b_2, ... , b_p[\/latex]<\/p>\n<h2>Glossary<\/h2>\n<p><strong>indicator variable<\/strong><\/p>\n<p>a binary variable with only two values: [latex]0[\/latex] and [latex]1[\/latex]<\/p>\n<p><strong>interaction<\/strong><\/p>\n<p>an explanatory variable that has a different effect on the response variable, depending on the values of another explanatory variable<\/p>\n<p><strong>interaction term<\/strong><\/p>\n<p>a variable that represents an interaction between two variables<\/p>\n<p><strong>multiple linear regression model<\/strong><\/p>\n<p>a linear regression model with two or more explanatory variables<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"author":8,"menu_order":1,"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":"cheat_sheet","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\/1474"}],"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\/1474\/revisions"}],"predecessor-version":[{"id":6269,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1474\/revisions\/6269"}],"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\/1474\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1474"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1474"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1474"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1474"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}