{"id":247,"date":"2023-02-20T17:13:58","date_gmt":"2023-02-20T17:13:58","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/lines-of-best-fit-learn-it-3\/"},"modified":"2025-05-11T23:14:22","modified_gmt":"2025-05-11T23:14:22","slug":"lines-of-best-fit-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/lines-of-best-fit-learn-it-3\/","title":{"raw":"Line of Best Fit: Learn It 3","rendered":"Line of Best Fit: Learn It 3"},"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>Crickets can tell us the outside temperature?!<\/h3>\r\n<p>A famous study was conducted by Dr. Pierce in the 1940s on the relationship between the number of chirps made by a striped ground cricket (measured in number of wing vibrations per second) and the surrounding ground temperature (measured in degrees Fahrenheit)[footnote]Pierce, G. W. (1948). \"The Song of Insects.\" <em>Harvard University Press<\/em>.[\/footnote]. Dr. Pierce wanted to see if it seemed reasonable to predict the temperature based on the number of chirps.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1158[\/ohm2_question]<\/section>\r\n<p>Now, let's use our statistical tool to generate appropriate scatterplots, the line of best fit, and the correlation coefficient.<\/p>\r\n<p>We will use the data the scientist collected[footnote]Pierce, G. W. (1948). \"The Song of Insects.\" <em>Harvard University Press<\/em>.[\/footnote] to help him answer his research question:<\/p>\r\n<p style=\"padding-left: 40px;\">Can ground temperature (measured in degrees Fahrenheit) be predicted by the number of chirps the striped ground cricket makes per second measured in number of wing vibrations per second?<\/p>\r\n<section class=\"textbox interact\">Plot the data using the following steps:\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 [latex]x[\/latex] (explanatory) and [latex]y[\/latex] (response) variables appropriately.<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 3: <\/strong>Copy and paste the data from the table (make sure the explanatory variable is in the first column and the response variable is in the second column).<\/p>\r\n<p style=\"padding-left: 80px;\">[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<p style=\"padding-left: 40px;\"><strong>Step 4: <\/strong>Under <strong>Plot Options<\/strong>, select <strong>Regression Line<\/strong> and <strong>Submit Data<\/strong>.<\/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><br \/>\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>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2664[\/ohm2_question]<\/section>\r\n<p>Let\u2019s quickly summarize the list of our data analysis tools for working with linear relationships between bivariate data:<\/p>\r\n<ul>\r\n\t<li>Use a scatterplot and [latex]r[\/latex] to describe direction and strength of the linear relationship.<\/li>\r\n\t<li>Find the equation of the least-squares regression line, [latex]\\hat{y} = a+bx[\/latex], to summarize the relationship.<\/li>\r\n<\/ul>","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>Crickets can tell us the outside temperature?!<\/h3>\n<p>A famous study was conducted by Dr. Pierce in the 1940s on the relationship between the number of chirps made by a striped ground cricket (measured in number of wing vibrations per second) and the surrounding ground temperature (measured in degrees Fahrenheit)<a class=\"footnote\" title=\"Pierce, G. W. (1948). &quot;The Song of Insects.&quot; Harvard University Press.\" id=\"return-footnote-247-1\" href=\"#footnote-247-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a>. Dr. Pierce wanted to see if it seemed reasonable to predict the temperature based on the number of chirps.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1158\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1158&theme=lumen&iframe_resize_id=ohm1158&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Now, let&#8217;s use our statistical tool to generate appropriate scatterplots, the line of best fit, and the correlation coefficient.<\/p>\n<p>We will use the data the scientist collected<a class=\"footnote\" title=\"Pierce, G. W. (1948). &quot;The Song of Insects.&quot; Harvard University Press.\" id=\"return-footnote-247-2\" href=\"#footnote-247-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a> to help him answer his research question:<\/p>\n<p style=\"padding-left: 40px;\">Can ground temperature (measured in degrees Fahrenheit) be predicted by the number of chirps the striped ground cricket makes per second measured in number of wing vibrations per second?<\/p>\n<section class=\"textbox interact\">Plot the data using the following steps:<\/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 [latex]x[\/latex] (explanatory) and [latex]y[\/latex] (response) variables appropriately.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 3: <\/strong>Copy and paste the data from the table (make sure the explanatory variable is in the first column and the response variable is in the second column).<\/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=\"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<p style=\"padding-left: 40px;\"><strong>Step 4: <\/strong>Under <strong>Plot Options<\/strong>, select <strong>Regression Line<\/strong> and <strong>Submit Data<\/strong>.<\/p>\n<\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2664\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2664&theme=lumen&iframe_resize_id=ohm2664&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Let\u2019s quickly summarize the list of our data analysis tools for working with linear relationships between bivariate data:<\/p>\n<ul>\n<li>Use a scatterplot and [latex]r[\/latex] to describe direction and strength of the linear relationship.<\/li>\n<li>Find the equation of the least-squares regression line, [latex]\\hat{y} = a+bx[\/latex], to summarize the relationship.<\/li>\n<\/ul>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-247-1\">Pierce, G. W. (1948). \"The Song of Insects.\" <em>Harvard University Press<\/em>. <a href=\"#return-footnote-247-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-247-2\">Pierce, G. W. (1948). \"The Song of Insects.\" <em>Harvard University Press<\/em>. <a href=\"#return-footnote-247-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":12,"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":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\/247"}],"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":19,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/247\/revisions"}],"predecessor-version":[{"id":6651,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/247\/revisions\/6651"}],"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\/247\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=247"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=247"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=247"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=247"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}