{"id":467,"date":"2023-02-24T23:40:35","date_gmt":"2023-02-24T23:40:35","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/?post_type=chapter&#038;p=467"},"modified":"2025-05-11T23:14:55","modified_gmt":"2025-05-11T23:14:55","slug":"line-of-best-fit-learn-it-5","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/line-of-best-fit-learn-it-5\/","title":{"raw":"Line of Best Fit: Learn It 5","rendered":"Line of Best Fit: Learn It 5"},"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<h3>Prediction and extrapolation<\/h3>\r\n<p>We can use the line of best fit to make predictions about the response variable. However, when calculating predicted values using a line of best fit, we should use it to calculate the predicted response for values of the explanatory variable within the range of values that are in the data set.<\/p>\r\n<p>Caution: Prediction for values of the explanatory variable that fall outside the range of the data is called <strong>extrapolation<\/strong>. These predictions are unreliable because we do not know if the pattern observed in the data continues outside the range of the data. Avoid making predictions outside the range of the data.<\/p>\r\n<p>Extrapolation was originally introduced when determining if it was reasonable to interpret the estimated [latex]y[\/latex]-intercept. We should avoid extrapolation in practice, since it is unreliable to assume the same line will best describe the relationship between the explanatory and response variables outside the range of our data.<\/p>\r\n<p>Let's look at the data set about the striped ground cricket chirps and temperature!<\/p>\r\n<p>[reveal-answer q=\"958723\"]Dataset[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"958723\"]<\/p>\r\n<table style=\"margin-left: 40px;\">\r\n<tbody style=\"padding-left: 40px;\">\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\"><strong>Chirps per second<\/strong><\/td>\r\n<td style=\"padding-left: 40px;\"><strong>Temperature in degrees Fahrenheit<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">20<\/td>\r\n<td style=\"padding-left: 40px;\">88.6<\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">16<\/td>\r\n<td style=\"padding-left: 40px;\">71.6<\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">19.8<\/td>\r\n<td style=\"padding-left: 40px;\">93.3<\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">18.4<\/td>\r\n<td style=\"padding-left: 40px;\">84.3<\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">17.1<\/td>\r\n<td style=\"padding-left: 40px;\">80.6<\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">15.5<\/td>\r\n<td style=\"padding-left: 40px;\">75.2<\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">14.7<\/td>\r\n<td style=\"padding-left: 40px;\">69.7<\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">17.1<\/td>\r\n<td style=\"padding-left: 40px;\">82<\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">15.4<\/td>\r\n<td style=\"padding-left: 40px;\">69.4<\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">16.2<\/td>\r\n<td style=\"padding-left: 40px;\">83.3<\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">15<\/td>\r\n<td style=\"padding-left: 40px;\">79.6<\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">17.2<\/td>\r\n<td style=\"padding-left: 40px;\">82.6<\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">16<\/td>\r\n<td style=\"padding-left: 40px;\">80.6<\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">17<\/td>\r\n<td style=\"padding-left: 40px;\">83.5<\/td>\r\n<\/tr>\r\n<tr style=\"padding-left: 40px;\">\r\n<td style=\"padding-left: 40px;\">14.4<\/td>\r\n<td style=\"padding-left: 40px;\">76.3<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p style=\"padding-left: 40px;\">[\/hidden-answer]<\/p>\r\n<section><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" width=\"100%\" height=\"850\"><\/iframe>\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>]\u00a0<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2980[\/ohm2_question]<\/section>\r\n<section class=\"textbox example\">[reveal-answer q=\"1002855\"]See the example question[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"1002855\"][ohm2_question hide_question_numbers=1]1180[\/ohm2_question][\/hidden-answer]<br \/>\r\n[videopicker divId=\"tnh-video-picker\" title=\"Predictions Using the Line of Best Fit\" label=\"Select Instructor\"]<br \/>\r\n[videooption displayName=\"Dr. Pamela E. Harris\" value=\"https:\/\/www.youtube.com\/watch?v=Gspr9nq-_pY\"][videooption displayName=\"Dr. Aris Winger\" value=\"https:\/\/www.youtube.com\/watch?v=hbdy1jKNWT0\"] [videooption displayName=\"Dr. Lane Fisher\" value=\"https:\/\/www.youtube.com\/watch?v=qKjfSBw8HRw\"]<br \/>\r\n[\/videopicker]<\/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<h3>Prediction and extrapolation<\/h3>\n<p>We can use the line of best fit to make predictions about the response variable. However, when calculating predicted values using a line of best fit, we should use it to calculate the predicted response for values of the explanatory variable within the range of values that are in the data set.<\/p>\n<p>Caution: Prediction for values of the explanatory variable that fall outside the range of the data is called <strong>extrapolation<\/strong>. These predictions are unreliable because we do not know if the pattern observed in the data continues outside the range of the data. Avoid making predictions outside the range of the data.<\/p>\n<p>Extrapolation was originally introduced when determining if it was reasonable to interpret the estimated [latex]y[\/latex]-intercept. We should avoid extrapolation in practice, since it is unreliable to assume the same line will best describe the relationship between the explanatory and response variables outside the range of our data.<\/p>\n<p>Let&#8217;s look at the data set about the striped ground cricket chirps and temperature!<\/p>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q958723\">Dataset<\/button><\/p>\n<div id=\"q958723\" class=\"hidden-answer\" style=\"display: none\">\n<table style=\"margin-left: 40px;\">\n<tbody style=\"padding-left: 40px;\">\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\"><strong>Chirps per second<\/strong><\/td>\n<td style=\"padding-left: 40px;\"><strong>Temperature in degrees Fahrenheit<\/strong><\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">20<\/td>\n<td style=\"padding-left: 40px;\">88.6<\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">16<\/td>\n<td style=\"padding-left: 40px;\">71.6<\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">19.8<\/td>\n<td style=\"padding-left: 40px;\">93.3<\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">18.4<\/td>\n<td style=\"padding-left: 40px;\">84.3<\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">17.1<\/td>\n<td style=\"padding-left: 40px;\">80.6<\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">15.5<\/td>\n<td style=\"padding-left: 40px;\">75.2<\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">14.7<\/td>\n<td style=\"padding-left: 40px;\">69.7<\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">17.1<\/td>\n<td style=\"padding-left: 40px;\">82<\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">15.4<\/td>\n<td style=\"padding-left: 40px;\">69.4<\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">16.2<\/td>\n<td style=\"padding-left: 40px;\">83.3<\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">15<\/td>\n<td style=\"padding-left: 40px;\">79.6<\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">17.2<\/td>\n<td style=\"padding-left: 40px;\">82.6<\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">16<\/td>\n<td style=\"padding-left: 40px;\">80.6<\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">17<\/td>\n<td style=\"padding-left: 40px;\">83.5<\/td>\n<\/tr>\n<tr style=\"padding-left: 40px;\">\n<td style=\"padding-left: 40px;\">14.4<\/td>\n<td style=\"padding-left: 40px;\">76.3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"padding-left: 40px;\"><\/div>\n<\/div>\n<section><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? Click to open in a new tab.<\/a>]\u00a0<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2980\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2980&theme=lumen&iframe_resize_id=ohm2980&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox example\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q1002855\">See the example question<\/button><\/p>\n<div id=\"q1002855\" class=\"hidden-answer\" style=\"display: none\"><iframe loading=\"lazy\" id=\"ohm1180\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1180&theme=lumen&iframe_resize_id=ohm1180&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/div>\n<\/div>\n<div class=\"wp-nocaption \"><\/div>\n<div id=\"tnh-video-picker\" class=\"videoPicker\">\n<h3>Predictions Using the Line of Best Fit<\/h3>\n<form><label>Select Instructor:<\/label><select name=\"video\"><option value=\"https:\/\/www.youtube.com\/embed\/Gspr9nq-_pY\">Dr. Pamela E. Harris<\/option><option value=\"https:\/\/www.youtube.com\/embed\/hbdy1jKNWT0\">Dr. Aris Winger<\/option><option value=\"https:\/\/www.youtube.com\/embed\/qKjfSBw8HRw\">Dr. Lane Fisher<\/option><\/select><\/form>\n<div class=\"videoContainer\"><iframe src=\"https:\/\/www.youtube.com\/embed\/Gspr9nq-_pY\" allowfullscreen><\/iframe><\/div>\n<\/section>\n","protected":false},"author":12,"menu_order":16,"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":[{"divId":"tnh-video-picker","title":"Predictions Using the Line of Best Fit","label":"Select Instructor","video_collection":[{"displayName":"Dr. Pamela E. 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