{"id":244,"date":"2023-02-20T17:13:55","date_gmt":"2023-02-20T17:13:55","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/lines-of-best-fit-learn-it-1\/"},"modified":"2023-12-27T16:40:15","modified_gmt":"2023-12-27T16:40:15","slug":"lines-of-best-fit-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/lines-of-best-fit-learn-it-1\/","title":{"raw":"Line of Best Fit: Learn It 1","rendered":"Line of Best Fit: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Recognize when a linear regression model will fit a given data set.<\/li>\r\n\t<li>Use technology to create scatterplots, find the line of best fit and find the correlation coefficient.<\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Find the estimated slope and y-intercept for a linear regression model&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;}\">Find the estimated slope and [latex]y[\/latex]-intercept for a linear regression model.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use the line of best fit to predict values&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;}\">Use the line of best fit to predict values.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Explanatory and Response Variables<\/h2>\r\n<section class=\"textbox recall\"><strong>Bivariate data<\/strong> are defined as pairs of data values, where each pair consists of two different measurements that come from the same individual or unit. There are two variables to consider when working with bivariate data sets:\r\n\r\n<ul>\r\n\t<li>The <strong>explanatory variable<\/strong> ([latex]x[\/latex]) is the variable thought to explain or predict the response variable of a study.<\/li>\r\n\t<li>The <strong>response variable<\/strong> ([latex]y[\/latex]) measures the outcome of interest in the study. This variable is thought to <em>depend <\/em>in some way on the explanatory variable. It is often referred to as the \u201cvariable of interest\u201d for the researcher. (And in previous math classes, this variable may have been referred to as the \"dependent variable.\")<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Identifying explanatory and response variables can sometimes be difficult. When trying to identify explanatory and response variables, make sure to carefully read the scenario and keep the following phrases in mind:<\/p>\r\n<p style=\"text-align: center\">The <strong>e<\/strong><strong>xplanatory variable <\/strong>is used to predict\u00a0the<strong> response variable<\/strong><\/p>\r\n<p style=\"text-align: center\">The <strong>explanatory variable <\/strong>is used to calculate the<strong> response variable<\/strong><\/p>\r\n<p style=\"text-align: center\">The <strong>explanatory variable <\/strong>is used to determine the<strong> response variable<\/strong><\/p>\r\n<p>It is good practice to identify both variables and then ask yourself, \u201cWhich one is the main outcome or focus of the study?\u201d This variable will be the response variable and the other variable will be your explanatory variable. It is not up to the researcher(s) to decide the main focus or outcome of a pre-existing study. Instead, researchers need to carefully read the context of the study to identify which variable is being used to explain (the explanatory variable) an outcome or response (the response variable).<\/p>\r\n<section class=\"textbox example\">A teacher wonders if students' number of absences per semester is related to academic performance in her classes. She might look back on her class records from previous semesters and generate a data set by observing both the final overall average grade and total number of missed classes for each student in a random sample of students. This is an example of a bivariate data set.<br \/>\r\nDetermine the explanatory and response variable of this scenario.<br \/>\r\n[reveal-answer q=\"165390\"]Show solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"165390\"]In this example, the outcome the teacher is most interested in is how well her students will do in her class, so the response variable is <strong>o<\/strong><strong>verall average grade<\/strong>. The other variable, <strong>number of absences<\/strong>, is the explanatory variable.[\/hidden-answer]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question]1154[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question]1155[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Recognize when a linear regression model will fit a given data set.<\/li>\n<li>Use technology to create scatterplots, find the line of best fit and find the correlation coefficient.<\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Find the estimated slope and y-intercept for a linear regression model&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;}\">Find the estimated slope and [latex]y[\/latex]-intercept for a linear regression model.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use the line of best fit to predict values&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;}\">Use the line of best fit to predict values.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Explanatory and Response Variables<\/h2>\n<section class=\"textbox recall\"><strong>Bivariate data<\/strong> are defined as pairs of data values, where each pair consists of two different measurements that come from the same individual or unit. There are two variables to consider when working with bivariate data sets:<\/p>\n<ul>\n<li>The <strong>explanatory variable<\/strong> ([latex]x[\/latex]) is the variable thought to explain or predict the response variable of a study.<\/li>\n<li>The <strong>response variable<\/strong> ([latex]y[\/latex]) measures the outcome of interest in the study. This variable is thought to <em>depend <\/em>in some way on the explanatory variable. It is often referred to as the \u201cvariable of interest\u201d for the researcher. (And in previous math classes, this variable may have been referred to as the &#8220;dependent variable.&#8221;)<\/li>\n<\/ul>\n<\/section>\n<p>Identifying explanatory and response variables can sometimes be difficult. When trying to identify explanatory and response variables, make sure to carefully read the scenario and keep the following phrases in mind:<\/p>\n<p style=\"text-align: center\">The <strong>e<\/strong><strong>xplanatory variable <\/strong>is used to predict\u00a0the<strong> response variable<\/strong><\/p>\n<p style=\"text-align: center\">The <strong>explanatory variable <\/strong>is used to calculate the<strong> response variable<\/strong><\/p>\n<p style=\"text-align: center\">The <strong>explanatory variable <\/strong>is used to determine the<strong> response variable<\/strong><\/p>\n<p>It is good practice to identify both variables and then ask yourself, \u201cWhich one is the main outcome or focus of the study?\u201d This variable will be the response variable and the other variable will be your explanatory variable. It is not up to the researcher(s) to decide the main focus or outcome of a pre-existing study. Instead, researchers need to carefully read the context of the study to identify which variable is being used to explain (the explanatory variable) an outcome or response (the response variable).<\/p>\n<section class=\"textbox example\">A teacher wonders if students&#8217; number of absences per semester is related to academic performance in her classes. She might look back on her class records from previous semesters and generate a data set by observing both the final overall average grade and total number of missed classes for each student in a random sample of students. This is an example of a bivariate data set.<br \/>\nDetermine the explanatory and response variable of this scenario.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q165390\">Show solution<\/button><\/p>\n<div id=\"q165390\" class=\"hidden-answer\" style=\"display: none\">In this example, the outcome the teacher is most interested in is how well her students will do in her class, so the response variable is <strong>o<\/strong><strong>verall average grade<\/strong>. The other variable, <strong>number of absences<\/strong>, is the explanatory variable.<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1154\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1154&theme=lumen&iframe_resize_id=ohm1154&source=tnh&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1155\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1155&theme=lumen&iframe_resize_id=ohm1155&source=tnh&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":12,"menu_order":12,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":225,"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\/244"}],"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\/12"}],"version-history":[{"count":8,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/244\/revisions"}],"predecessor-version":[{"id":4649,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/244\/revisions\/4649"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/225"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/244\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=244"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=244"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=244"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}