{"id":249,"date":"2023-02-20T17:14:01","date_gmt":"2023-02-20T17:14:01","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/lines-of-best-fit-apply-it-1\/"},"modified":"2025-05-10T03:21:27","modified_gmt":"2025-05-10T03:21:27","slug":"lines-of-best-fit-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/lines-of-best-fit-apply-it-1\/","title":{"raw":"Line of Best Fit: Apply It 1","rendered":"Line of Best Fit: Apply 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>Midterm vs. Final Exam Score<\/h2>\r\n\r\n[caption id=\"attachment_1188\" align=\"aligncenter\" width=\"651\"]<img class=\"wp-image-1188\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/02\/20171359\/pexels-thirdman-5257576.jpg\" alt=\"Colleagues talking and pointing to a whiteboard with drawings of figures\" width=\"651\" height=\"434\" \/> Figure 1. After his midterm, George asks, \u201cWhat can I expect on the final?\u201d Here, he and his instructor look at past data to find the answer.[\/caption]\r\n\r\n<p>George, a current student, got a [latex]36[\/latex] out of [latex]50[\/latex] on the first midterm (C-). He asked his instructor, \u201cIf I don\u2019t change my study approach, how do you predict I will do on the final exam?\u201d<\/p>\r\n<p>One way to answer this question is to look at the bivariate data of student scores from a previous class. In this case, we choose a random sample of past students who did not seek out additional tutoring and\/or support between the midterm and the final.<\/p>\r\n<p>The following is a data set from a random sample of past students who did not seek out advice on study skills or additional tutoring between the midterm and the final exam. To protect their anonymity, only first names are shown.<\/p>\r\n<table style=\"height: 422px;\">\r\n<tbody>\r\n<tr style=\"height: 116px;\">\r\n<td style=\"height: 116px; width: 122.414px;\"><strong>Student First Name<\/strong><\/td>\r\n<td style=\"height: 116px; width: 184.531px;\">\r\n<p><strong>Midterm Score<\/strong><\/p>\r\n<p><strong>(out of [latex]50[\/latex] points)<\/strong><\/p>\r\n<\/td>\r\n<td style=\"height: 116px; width: 190.055px;\">\r\n<p><strong>Final Exam Score<\/strong><\/p>\r\n<p><strong>(out of [latex]100[\/latex] points)<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Joe<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">42<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">64<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Barak<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">52<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">94<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Hillary<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">44<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">87<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Donald<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">25<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">46<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Cher<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">41<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">73<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Katy<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">39<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">73<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Taylor<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">33<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">53<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Miley<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">40<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">77<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Justin<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">35<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">60<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Snoop<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">31<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">62<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Bruno<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">37<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">71<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Kanye<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">49<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">95<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Leonardo<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">38<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">70<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Rosie<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">45<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">80<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Maya<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">49<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">80<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Tyra<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">48<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">82<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 122.414px;\">Selena<\/td>\r\n<td style=\"height: 18px; width: 184.531px;\">50<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">81<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1147[\/ohm2_question]<\/section>\r\n<\/div>\r\n<section class=\"textbox interact\">Steps to create the LSR:\r\n\r\n<p style=\"padding-left: 40px;\"><strong>Step 1: <\/strong>Under <strong>Enter Data<\/strong>, select <strong>Enter Own<\/strong>.<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 2: <\/strong>Name the X (explanatory) and Y (response) variables appropriately.<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 3: <\/strong>Copy and paste the data set.<\/p>\r\n<p style=\"padding-left: 80px;\">[reveal-answer q=\"276079\"]Dataset (name removed)[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"276079\"]<\/p>\r\n<table>\r\n<tbody>\r\n<tr style=\"height: 116px;\">\r\n<td style=\"height: 116px; width: 184.531px;\">\r\n<p><strong>Midterm Score<\/strong><\/p>\r\n<p><strong>(out of [latex]50[\/latex] points)<\/strong><\/p>\r\n<\/td>\r\n<td style=\"height: 116px; width: 190.055px;\">\r\n<p><strong>Final Exam Score<\/strong><\/p>\r\n<p><strong>(out of [latex]100[\/latex] points)<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">42<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">64<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">52<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">94<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">44<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">87<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">25<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">46<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">41<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">73<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">39<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">73<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">33<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">53<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">40<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">77<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">35<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">60<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">31<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">62<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">37<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">71<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">49<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">95<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">38<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">70<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">45<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">80<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">49<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">80<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">48<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">82<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 184.531px;\">50<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">81<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p style=\"padding-left: 40px;\">[\/hidden-answer]<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 4: <\/strong>Under <strong>Plot Options<\/strong>, select <strong>Regression Line<\/strong>, and click the <strong>Submit Data<\/strong>\u00a0button.<\/p>\r\n<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\r\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1148[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1149[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1150[\/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>Midterm vs. Final Exam Score<\/h2>\n<figure id=\"attachment_1188\" aria-describedby=\"caption-attachment-1188\" style=\"width: 651px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1188\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/02\/20171359\/pexels-thirdman-5257576.jpg\" alt=\"Colleagues talking and pointing to a whiteboard with drawings of figures\" width=\"651\" height=\"434\" \/><figcaption id=\"caption-attachment-1188\" class=\"wp-caption-text\">Figure 1. After his midterm, George asks, \u201cWhat can I expect on the final?\u201d Here, he and his instructor look at past data to find the answer.<\/figcaption><\/figure>\n<p>George, a current student, got a [latex]36[\/latex] out of [latex]50[\/latex] on the first midterm (C-). He asked his instructor, \u201cIf I don\u2019t change my study approach, how do you predict I will do on the final exam?\u201d<\/p>\n<p>One way to answer this question is to look at the bivariate data of student scores from a previous class. In this case, we choose a random sample of past students who did not seek out additional tutoring and\/or support between the midterm and the final.<\/p>\n<p>The following is a data set from a random sample of past students who did not seek out advice on study skills or additional tutoring between the midterm and the final exam. To protect their anonymity, only first names are shown.<\/p>\n<table style=\"height: 422px;\">\n<tbody>\n<tr style=\"height: 116px;\">\n<td style=\"height: 116px; width: 122.414px;\"><strong>Student First Name<\/strong><\/td>\n<td style=\"height: 116px; width: 184.531px;\">\n<p><strong>Midterm Score<\/strong><\/p>\n<p><strong>(out of [latex]50[\/latex] points)<\/strong><\/p>\n<\/td>\n<td style=\"height: 116px; width: 190.055px;\">\n<p><strong>Final Exam Score<\/strong><\/p>\n<p><strong>(out of [latex]100[\/latex] points)<\/strong><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Joe<\/td>\n<td style=\"height: 18px; width: 184.531px;\">42<\/td>\n<td style=\"height: 18px; width: 190.055px;\">64<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Barak<\/td>\n<td style=\"height: 18px; width: 184.531px;\">52<\/td>\n<td style=\"height: 18px; width: 190.055px;\">94<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Hillary<\/td>\n<td style=\"height: 18px; width: 184.531px;\">44<\/td>\n<td style=\"height: 18px; width: 190.055px;\">87<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Donald<\/td>\n<td style=\"height: 18px; width: 184.531px;\">25<\/td>\n<td style=\"height: 18px; width: 190.055px;\">46<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Cher<\/td>\n<td style=\"height: 18px; width: 184.531px;\">41<\/td>\n<td style=\"height: 18px; width: 190.055px;\">73<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Katy<\/td>\n<td style=\"height: 18px; width: 184.531px;\">39<\/td>\n<td style=\"height: 18px; width: 190.055px;\">73<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Taylor<\/td>\n<td style=\"height: 18px; width: 184.531px;\">33<\/td>\n<td style=\"height: 18px; width: 190.055px;\">53<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Miley<\/td>\n<td style=\"height: 18px; width: 184.531px;\">40<\/td>\n<td style=\"height: 18px; width: 190.055px;\">77<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Justin<\/td>\n<td style=\"height: 18px; width: 184.531px;\">35<\/td>\n<td style=\"height: 18px; width: 190.055px;\">60<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Snoop<\/td>\n<td style=\"height: 18px; width: 184.531px;\">31<\/td>\n<td style=\"height: 18px; width: 190.055px;\">62<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Bruno<\/td>\n<td style=\"height: 18px; width: 184.531px;\">37<\/td>\n<td style=\"height: 18px; width: 190.055px;\">71<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Kanye<\/td>\n<td style=\"height: 18px; width: 184.531px;\">49<\/td>\n<td style=\"height: 18px; width: 190.055px;\">95<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Leonardo<\/td>\n<td style=\"height: 18px; width: 184.531px;\">38<\/td>\n<td style=\"height: 18px; width: 190.055px;\">70<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Rosie<\/td>\n<td style=\"height: 18px; width: 184.531px;\">45<\/td>\n<td style=\"height: 18px; width: 190.055px;\">80<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Maya<\/td>\n<td style=\"height: 18px; width: 184.531px;\">49<\/td>\n<td style=\"height: 18px; width: 190.055px;\">80<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Tyra<\/td>\n<td style=\"height: 18px; width: 184.531px;\">48<\/td>\n<td style=\"height: 18px; width: 190.055px;\">82<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 122.414px;\">Selena<\/td>\n<td style=\"height: 18px; width: 184.531px;\">50<\/td>\n<td style=\"height: 18px; width: 190.055px;\">81<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1147\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1147&theme=lumen&iframe_resize_id=ohm1147&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/div>\n<section class=\"textbox interact\">Steps to create the LSR:<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 1: <\/strong>Under <strong>Enter Data<\/strong>, select <strong>Enter Own<\/strong>.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 2: <\/strong>Name the X (explanatory) and Y (response) variables appropriately.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 3: <\/strong>Copy and paste the data set.<\/p>\n<p style=\"padding-left: 80px;\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q276079\">Dataset (name removed)<\/button><\/p>\n<div id=\"q276079\" class=\"hidden-answer\" style=\"display: none\">\n<table>\n<tbody>\n<tr style=\"height: 116px;\">\n<td style=\"height: 116px; width: 184.531px;\">\n<p><strong>Midterm Score<\/strong><\/p>\n<p><strong>(out of [latex]50[\/latex] points)<\/strong><\/p>\n<\/td>\n<td style=\"height: 116px; width: 190.055px;\">\n<p><strong>Final Exam Score<\/strong><\/p>\n<p><strong>(out of [latex]100[\/latex] points)<\/strong><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">42<\/td>\n<td style=\"height: 18px; width: 190.055px;\">64<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">52<\/td>\n<td style=\"height: 18px; width: 190.055px;\">94<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">44<\/td>\n<td style=\"height: 18px; width: 190.055px;\">87<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">25<\/td>\n<td style=\"height: 18px; width: 190.055px;\">46<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">41<\/td>\n<td style=\"height: 18px; width: 190.055px;\">73<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">39<\/td>\n<td style=\"height: 18px; width: 190.055px;\">73<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">33<\/td>\n<td style=\"height: 18px; width: 190.055px;\">53<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">40<\/td>\n<td style=\"height: 18px; width: 190.055px;\">77<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">35<\/td>\n<td style=\"height: 18px; width: 190.055px;\">60<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">31<\/td>\n<td style=\"height: 18px; width: 190.055px;\">62<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">37<\/td>\n<td style=\"height: 18px; width: 190.055px;\">71<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">49<\/td>\n<td style=\"height: 18px; width: 190.055px;\">95<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">38<\/td>\n<td style=\"height: 18px; width: 190.055px;\">70<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">45<\/td>\n<td style=\"height: 18px; width: 190.055px;\">80<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">49<\/td>\n<td style=\"height: 18px; width: 190.055px;\">80<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">48<\/td>\n<td style=\"height: 18px; width: 190.055px;\">82<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 184.531px;\">50<\/td>\n<td style=\"height: 18px; width: 190.055px;\">81<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"padding-left: 40px;\"><\/div>\n<\/div>\n<p style=\"padding-left: 40px;\"><strong>Step 4: <\/strong>Under <strong>Plot Options<\/strong>, select <strong>Regression Line<\/strong>, and click the <strong>Submit Data<\/strong>\u00a0button.<\/p>\n<\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? 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