{"id":1487,"date":"2023-06-22T02:36:53","date_gmt":"2023-06-22T02:36:53","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/multiple-linear-regression-fresh-take\/"},"modified":"2025-05-17T02:43:46","modified_gmt":"2025-05-17T02:43:46","slug":"multiple-linear-regression-fresh-take","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/multiple-linear-regression-fresh-take\/","title":{"raw":"Multiple Linear Regression - Fresh Take","rendered":"Multiple Linear Regression &#8211; Fresh Take"},"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>Multiple Linear Regression<\/h2>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>Multiple Linear Regression<\/h3>\r\n<p>Multiple linear regression is a statistical modeling technique used to understand the relationship between a dependent variable and two or more independent variables.<\/p>\r\n<\/section>\r\n<p>It extends the concept of simple linear regression, which examines the relationship between a dependent variable and a single independent variable, therefore, it is called \"simple\".<\/p>\r\n<p>In <em>multiple<\/em> linear regression, the goal is to create a linear equation that best fits the data and can be used to predict the value of the dependent variable based on the values of <em>multiple<\/em> independent variables.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>Multiple Linear Regression Equation<\/h3>\r\n<p>The equation takes the form:<\/p>\r\n<p style=\"text-align: center;\">[latex]y = \u03b2_0 + \u03b2_1 x_1 + \u03b2_2 x_2 + ... + \u03b2_p x_p[\/latex]<\/p>\r\n<p>where:<\/p>\r\n<ul>\r\n\t<li>[latex]y[\/latex] is the dependent variable (the variable to be predicted or explained)<\/li>\r\n\t<li>[latex]x_1, x_2, ..., x_p[\/latex] are the independent variables (also known as predictor variables or features)<\/li>\r\n\t<li>[latex]\u03b2_0, \u03b2_1, \u03b2_2, ..., \u03b2_p[\/latex] are the regression coefficients (the estimated coefficients that represent the relationship between each independent variable and the dependent variable.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>The multiple linear regression model estimates the regression coefficients ([latex]\u03b2_0, \u03b2_1, \u03b2_2, ..., \u03b2_p[\/latex]) that minimize the sum of squared residuals (the difference between the predicted values and the actual values of the dependent variable). The coefficients provide information about the magnitude and direction of the relationship between each independent variable and the dependent variable, while taking into account the influence of other independent variables in the model.<\/p>\r\n<p>Multiple linear regression analysis is widely used in various fields, including social sciences, economics, finance, and data analysis, to understand and predict the relationship between multiple variables. It allows for the examination of complex relationships and provides insights into how changes in one or more independent variables impact the dependent variable.<\/p>\r\n<section class=\"textbox linkToLearning\"><a href=\"https:\/\/www.youtube.com\/watch?v=dQNpSa-bq4M\">A video explanation of Multiple Linear Regression<\/a><\/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>Multiple Linear Regression<\/h2>\n<section class=\"textbox keyTakeaway\">\n<h3>Multiple Linear Regression<\/h3>\n<p>Multiple linear regression is a statistical modeling technique used to understand the relationship between a dependent variable and two or more independent variables.<\/p>\n<\/section>\n<p>It extends the concept of simple linear regression, which examines the relationship between a dependent variable and a single independent variable, therefore, it is called &#8220;simple&#8221;.<\/p>\n<p>In <em>multiple<\/em> linear regression, the goal is to create a linear equation that best fits the data and can be used to predict the value of the dependent variable based on the values of <em>multiple<\/em> independent variables.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>Multiple Linear Regression Equation<\/h3>\n<p>The equation takes the form:<\/p>\n<p style=\"text-align: center;\">[latex]y = \u03b2_0 + \u03b2_1 x_1 + \u03b2_2 x_2 + ... + \u03b2_p x_p[\/latex]<\/p>\n<p>where:<\/p>\n<ul>\n<li>[latex]y[\/latex] is the dependent variable (the variable to be predicted or explained)<\/li>\n<li>[latex]x_1, x_2, ..., x_p[\/latex] are the independent variables (also known as predictor variables or features)<\/li>\n<li>[latex]\u03b2_0, \u03b2_1, \u03b2_2, ..., \u03b2_p[\/latex] are the regression coefficients (the estimated coefficients that represent the relationship between each independent variable and the dependent variable.<\/li>\n<\/ul>\n<\/section>\n<p>The multiple linear regression model estimates the regression coefficients ([latex]\u03b2_0, \u03b2_1, \u03b2_2, ..., \u03b2_p[\/latex]) that minimize the sum of squared residuals (the difference between the predicted values and the actual values of the dependent variable). The coefficients provide information about the magnitude and direction of the relationship between each independent variable and the dependent variable, while taking into account the influence of other independent variables in the model.<\/p>\n<p>Multiple linear regression analysis is widely used in various fields, including social sciences, economics, finance, and data analysis, to understand and predict the relationship between multiple variables. It allows for the examination of complex relationships and provides insights into how changes in one or more independent variables impact the dependent variable.<\/p>\n<section class=\"textbox linkToLearning\"><a href=\"https:\/\/www.youtube.com\/watch?v=dQNpSa-bq4M\">A video explanation of Multiple Linear Regression<\/a><\/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":1473,"module-header":"fresh_take","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\/1487"}],"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\/1487\/revisions"}],"predecessor-version":[{"id":6909,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1487\/revisions\/6909"}],"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\/1487\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1487"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1487"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1487"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1487"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}