{"id":1773,"date":"2024-06-06T18:15:41","date_gmt":"2024-06-06T18:15:41","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=1773"},"modified":"2025-08-14T00:16:26","modified_gmt":"2025-08-14T00:16:26","slug":"fitting-linear-models-to-data-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/fitting-linear-models-to-data-apply-it-1\/","title":{"raw":"Fitting Linear Models to Data: Apply It 1","rendered":"Fitting Linear Models to Data: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Use linear functions to model and draw conclusions from real-world problems<\/li>\r\n \t<li>Sketch scatter plots to see patterns and tell apart straight-line relationships from curves<\/li>\r\n \t<li>Find the best straight line that goes through a set of data points<\/li>\r\n \t<li><span data-sheets-root=\"1\">Identify the differences between linear and nonlinear relations <\/span><\/li>\r\n<\/ul>\r\n<\/section><section><section><strong>Scatterplots<\/strong> are used to illustrate the relationship between two variables in a data set.<\/section>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\r\n\r\nOne 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.\r\n\r\nThe 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.\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;\"><strong>Midterm Score<\/strong>\r\n\r\n<strong>(out of [latex]50[\/latex] points)<\/strong><\/td>\r\n<td style=\"height: 116px; width: 190.055px;\"><strong>Final Exam Score<\/strong>\r\n\r\n<strong>(out of [latex]100[\/latex] points)<\/strong><\/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;\">[latex]42[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]64[\/latex]<\/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;\">[latex]52[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]94[\/latex]<\/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;\">[latex]44[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]87[\/latex]<\/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;\">[latex]25[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]46[\/latex]<\/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;\">[latex]41[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]73[\/latex]<\/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;\">[latex]39[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]73[\/latex]<\/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;\">[latex]33[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]53[\/latex]<\/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;\">[latex]40[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]77[\/latex]<\/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;\">[latex]35[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]60[\/latex]<\/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;\">[latex]31[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]62[\/latex]<\/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;\">[latex]37[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]71[\/latex]<\/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;\">[latex]49[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]95[\/latex]<\/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;\">[latex]38[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]70[\/latex]<\/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;\">[latex]45[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]80[\/latex]<\/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;\">[latex]49[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]80[\/latex]<\/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;\">[latex]48[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]82[\/latex]<\/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;\">[latex]50[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 190.055px;\">[latex]81[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div><section class=\"textbox interact\">Steps to create the scatterplot and the linear regression line:\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]\r\n[hidden-answer a=\"276079\"]<\/p>\r\n\r\n<table>\r\n<tbody>\r\n<tr style=\"height: 116px;\">\r\n<td style=\"height: 116px; width: 184.531px;\"><strong>Midterm Score<\/strong>\r\n\r\n<strong>(out of [latex]50[\/latex] points)<\/strong><\/td>\r\n<td style=\"height: 116px; width: 190.055px;\"><strong>Final Exam Score<\/strong>\r\n\r\n<strong>(out of [latex]100[\/latex] points)<\/strong><\/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\r\n<\/section><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" width=\"100%\" height=\"950\"><\/iframe>\r\n\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]\r\n\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1148[\/ohm2_question]<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1149[\/ohm2_question]<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1150[\/ohm2_question]<\/section><\/div>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Use linear functions to model and draw conclusions from real-world problems<\/li>\n<li>Sketch scatter plots to see patterns and tell apart straight-line relationships from curves<\/li>\n<li>Find the best straight line that goes through a set of data points<\/li>\n<li><span data-sheets-root=\"1\">Identify the differences between linear and nonlinear relations <\/span><\/li>\n<\/ul>\n<\/section>\n<section>\n<section><strong>Scatterplots<\/strong> are used to illustrate the relationship between two variables in a data set.<\/section>\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;\"><strong>Midterm Score<\/strong><\/p>\n<p><strong>(out of [latex]50[\/latex] points)<\/strong><\/td>\n<td style=\"height: 116px; width: 190.055px;\"><strong>Final Exam Score<\/strong><\/p>\n<p><strong>(out of [latex]100[\/latex] points)<\/strong><\/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;\">[latex]42[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]64[\/latex]<\/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;\">[latex]52[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]94[\/latex]<\/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;\">[latex]44[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]87[\/latex]<\/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;\">[latex]25[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]46[\/latex]<\/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;\">[latex]41[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]73[\/latex]<\/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;\">[latex]39[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]73[\/latex]<\/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;\">[latex]33[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]53[\/latex]<\/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;\">[latex]40[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]77[\/latex]<\/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;\">[latex]35[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]60[\/latex]<\/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;\">[latex]31[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]62[\/latex]<\/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;\">[latex]37[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]71[\/latex]<\/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;\">[latex]49[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]95[\/latex]<\/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;\">[latex]38[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]70[\/latex]<\/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;\">[latex]45[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]80[\/latex]<\/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;\">[latex]49[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]80[\/latex]<\/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;\">[latex]48[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]82[\/latex]<\/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;\">[latex]50[\/latex]<\/td>\n<td style=\"height: 18px; width: 190.055px;\">[latex]81[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div>\n<section class=\"textbox interact\">Steps to create the scatterplot and the linear regression line:<\/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;\"><strong>Midterm Score<\/strong><\/p>\n<p><strong>(out of [latex]50[\/latex] points)<\/strong><\/td>\n<td style=\"height: 116px; width: 190.055px;\"><strong>Final Exam Score<\/strong><\/p>\n<p><strong>(out of [latex]100[\/latex] points)<\/strong><\/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=\"950\"><\/iframe><\/p>\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? 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