{"id":232,"date":"2023-02-20T17:13:47","date_gmt":"2023-02-20T17:13:47","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/scatterplots-learn-it-3\/"},"modified":"2025-05-11T23:09:52","modified_gmt":"2025-05-11T23:09:52","slug":"scatterplots-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/scatterplots-learn-it-3\/","title":{"raw":"Scatterplots &amp; Correlation Coefficients: Learn It 3","rendered":"Scatterplots &amp; Correlation Coefficients: Learn It 3"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Create scatterplots for bivariate data and answer questions from the graph.<\/li>\r\n\t<li>Describe the trend of bivariate data.<\/li>\r\n\t<li>Calculate the correlation coefficient and explain what it means.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Relationship of Bivariate Data<\/h2>\r\n<p>Scatterplots can be used to identify shapes and patterns.<\/p>\r\n<h3>Linear<\/h3>\r\n<p>The relationship between two variables is said to be <strong>linear<\/strong> when the points on the scatterplot resemble a straight line. The following scatterplot could be described as being linear.<\/p>\r\n\r\n[caption id=\"attachment_990\" align=\"aligncenter\" width=\"624\"]<img class=\"wp-image-990 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5826\/2022\/09\/17002151\/Picture15.png\" alt=\"A linear scatter plot showing vote totals for a reform party candidate. An outlier is circled.\" width=\"624\" height=\"272\" \/> Figure 1. A scatterplot showing a mostly linear relationship between Perot votes in 1996 and Buchanan votes in 2000 across Florida counties, with one clear outlier circled.[\/caption]\r\n\r\n<p>The circled point in the upper right-hand corner of the scatterplot represents an outlier (Palm Beach). <strong>Outliers<\/strong> appear as departures from the general trend. Scatterplots can be used to identify outliers or extreme observations in the bivariate data.<\/p>\r\n<h3>Non-linear<\/h3>\r\n<p>Scatterplots are also useful for identifying <strong>non-linear<\/strong> relationships. The data points can appear scattered about a smooth curve or have no patterns at all. The following scatterplot could be described as being non-linear.<\/p>\r\n\r\n[caption id=\"attachment_991\" align=\"aligncenter\" width=\"936\"]<img class=\"wp-image-991 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5826\/2022\/09\/17002401\/Picture16.png\" alt=\"A non-linear scatterplot of fuel efficiency vs steady driving speed. \" width=\"936\" height=\"406\" \/> Figure 2. A scatterplot showing a non-linear relationship between driving speed and fuel efficiency, where fuel efficiency increases up to a point and then decreases, forming a curved pattern.[\/caption]\r\n\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1139[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Create scatterplots for bivariate data and answer questions from the graph.<\/li>\n<li>Describe the trend of bivariate data.<\/li>\n<li>Calculate the correlation coefficient and explain what it means.<\/li>\n<\/ul>\n<\/section>\n<h2>Relationship of Bivariate Data<\/h2>\n<p>Scatterplots can be used to identify shapes and patterns.<\/p>\n<h3>Linear<\/h3>\n<p>The relationship between two variables is said to be <strong>linear<\/strong> when the points on the scatterplot resemble a straight line. The following scatterplot could be described as being linear.<\/p>\n<figure id=\"attachment_990\" aria-describedby=\"caption-attachment-990\" style=\"width: 624px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-990 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5826\/2022\/09\/17002151\/Picture15.png\" alt=\"A linear scatter plot showing vote totals for a reform party candidate. An outlier is circled.\" width=\"624\" height=\"272\" \/><figcaption id=\"caption-attachment-990\" class=\"wp-caption-text\">Figure 1. A scatterplot showing a mostly linear relationship between Perot votes in 1996 and Buchanan votes in 2000 across Florida counties, with one clear outlier circled.<\/figcaption><\/figure>\n<p>The circled point in the upper right-hand corner of the scatterplot represents an outlier (Palm Beach). <strong>Outliers<\/strong> appear as departures from the general trend. Scatterplots can be used to identify outliers or extreme observations in the bivariate data.<\/p>\n<h3>Non-linear<\/h3>\n<p>Scatterplots are also useful for identifying <strong>non-linear<\/strong> relationships. The data points can appear scattered about a smooth curve or have no patterns at all. The following scatterplot could be described as being non-linear.<\/p>\n<figure id=\"attachment_991\" aria-describedby=\"caption-attachment-991\" style=\"width: 936px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-991 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5826\/2022\/09\/17002401\/Picture16.png\" alt=\"A non-linear scatterplot of fuel efficiency vs steady driving speed.\" width=\"936\" height=\"406\" \/><figcaption id=\"caption-attachment-991\" class=\"wp-caption-text\">Figure 2. A scatterplot showing a non-linear relationship between driving speed and fuel efficiency, where fuel efficiency increases up to a point and then decreases, forming a curved pattern.<\/figcaption><\/figure>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1139\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1139&theme=lumen&iframe_resize_id=ohm1139&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":12,"menu_order":8,"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\/232"}],"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":11,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/232\/revisions"}],"predecessor-version":[{"id":6648,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/232\/revisions\/6648"}],"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\/232\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=232"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=232"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=232"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=232"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}