{"id":239,"date":"2023-02-20T17:13:52","date_gmt":"2023-02-20T17:13:52","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/scatterplots-background-youll-need-2\/"},"modified":"2025-05-11T23:12:17","modified_gmt":"2025-05-11T23:12:17","slug":"scatterplots-fresh-take","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/scatterplots-fresh-take\/","title":{"raw":"Scatterplots &amp; Correlation Coefficients: Fresh Take","rendered":"Scatterplots &amp; Correlation Coefficients: Fresh Take"},"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<section>\r\n<h2>Scatterplots<\/h2>\r\n<p><strong>Scatterplots<\/strong> are used to illustrate the relationship between two quantitative variables.<\/p>\r\n<\/section>\r\n<section class=\"textbox example\">The table of data presented below includes information collected from 18 grocery stores in San Antonio, Texas. The average household income (in thousands of dollars)[footnote]Income by Zip Code. (2021). https:\/\/www.incomebyzipcode.com\/[\/footnote] and the number of organic vegetables offered were collected in 2021 to explore this relationship.[footnote]HEB. (2021). Shop by Department. https:\/\/www.heb.com[\/footnote]\r\n\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Store Location<\/strong><\/td>\r\n<td><strong>Average Household Income ($1000s)<\/strong><\/td>\r\n<td><strong>Number of Organic Vegetables Offered<\/strong><\/td>\r\n<td>&nbsp;<\/td>\r\n<td><strong>Store Location<\/strong><\/td>\r\n<td>\r\n<p><strong>Average Household Income<\/strong><\/p>\r\n<p><strong>($1000s)<\/strong><\/p>\r\n<\/td>\r\n<td><strong>Number of Organic Vegetables Offered<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>S. Flores<\/td>\r\n<td>71<\/td>\r\n<td>36<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>Marbach Rd.<\/td>\r\n<td>49<\/td>\r\n<td>38<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>N. Rosillo St.<\/td>\r\n<td>34<\/td>\r\n<td>4<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>Babcock Rd.<\/td>\r\n<td>66<\/td>\r\n<td>84<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Nogalitos St.<\/td>\r\n<td>71<\/td>\r\n<td>28<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>Wurzbach Rd.<\/td>\r\n<td>87<\/td>\r\n<td>61<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Fredericksburg Rd.<\/td>\r\n<td>49<\/td>\r\n<td>31<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>W. Loop 1604 N.<\/td>\r\n<td>78<\/td>\r\n<td>56<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Olmos<\/td>\r\n<td>78<\/td>\r\n<td>78<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>Bandera Rd.<\/td>\r\n<td>59<\/td>\r\n<td>62<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>N. New Braunfels Ave.<\/td>\r\n<td>41<\/td>\r\n<td>14<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>S. New Braunfels<\/td>\r\n<td>50<\/td>\r\n<td>44<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Castroville<\/td>\r\n<td>38<\/td>\r\n<td>12<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>S.W. Military<\/td>\r\n<td>48<\/td>\r\n<td>26<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Culebra Rd.<\/td>\r\n<td>50<\/td>\r\n<td>18<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>S. Zarzamora<\/td>\r\n<td>56<\/td>\r\n<td>29<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>S.E. Military Dr.<\/td>\r\n<td>50<\/td>\r\n<td>65<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>E. Basse Rd.<\/td>\r\n<td>125<\/td>\r\n<td>95<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>Let's enter the data into our statistical tool to create a scatterplot.<\/p>\r\n<\/div>\r\n<div class=\"textbox\">\r\n<p><strong>Step 1:<\/strong> Locate the drop-down menu under <strong>Enter Data<\/strong> and select <strong>Your Own<\/strong>.<\/p>\r\n<p><strong>Step 2:<\/strong> Select the box titled <strong>Use ID Variable<\/strong> and name the ID Variable and the X and Y-Variables appropriately given the three columns in the data table.[reveal-answer q=\"600169\"]Note[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"600169\"]If the <strong>Use ID Variable<\/strong> option not clicked, then only the x and y variables will appear in the table. [\/hidden-answer]<\/p>\r\n<p><strong>Step 3:<\/strong> Complete the data table appropriately. Then select <strong>Submit Data<\/strong>\u00a0(you may need to scroll down to see it) to create the scatterplot.<\/p>\r\n<\/div>\r\n<p>[reveal-answer q=\"631362\"]Note[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"631362\"]You may hover over a dot or a point to obtain more detailed information about such dot\/point.[\/hidden-answer]<\/p>\r\n<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/association_quantitative\/\" width=\"100%\" height=\"850\"><\/iframe> [<a href=\"https:\/\/lumen-learning.shinyapps.io\/association_quantitative\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question height=\"550\" hide_question_numbers=1]1118[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question height=\"550\" hide_question_numbers=1]1120[\/ohm2_question]<\/section>\r\n<div align=\"center\">\r\n<h2 style=\"text-align: left;\">Increasing and Decreasing Trends<\/h2>\r\n<\/div>\r\n<section class=\"textbox tryIt\">[ohm2_question height=\"350\"]1121[\/ohm2_question]<\/section>\r\n<p>A\u00a0<strong>positive (or increasing) relationship<\/strong>\u00a0means that an increase in one of the variables is associated with an increase in the other. A\u00a0<strong>negative (or decreasing) relationship<\/strong>\u00a0means that an increase in one of the variables is associated with a decrease in the other.\u00a0 Note that not all relationships can be classified as either positive or negative.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question height=\"325\"]1123[\/ohm2_question]<\/section>\r\n<p>The direction of the relationship can be positive, negative, or neither:<\/p>\r\n\r\n[caption id=\"attachment_6492\" align=\"aligncenter\" width=\"265\"]<img class=\"wp-image-6492 size-medium\" style=\"font-size: 14pt;\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/02\/20171350\/5.1.D.positive-relationship.png\" alt=\"Scatterplot showing positive relationship. Dots on scatterplot are making an upwards trajectory.\" width=\"265\" height=\"300\" \/> Figure 1. A positive relationship is one where as values of X increase, values of Y also increase.[\/caption] [caption id=\"attachment_6491\" align=\"aligncenter\" width=\"265\"]<img class=\"wp-image-6491 size-medium\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/02\/20171351\/5.1.D.negative-relationship.png\" alt=\"Scatterplot showing a negative relationship. Dots on scatterplot are making an downwards trajectory.\" width=\"265\" height=\"300\" \/> Figure 2. A negative relationship is one where as values of X increase, values of Y decrease.[\/caption] [caption id=\"attachment_6490\" align=\"aligncenter\" width=\"265\"]<img class=\"wp-image-6490 size-medium\" style=\"font-size: 14pt;\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/02\/20171351\/5.1..D.Neither.png\" alt=\"Scatterplot showing neither positive nor negative relationship. Dots on the scatterplot form a U shape.\" width=\"265\" height=\"300\" \/> Figure 3. Some relationships may show neither a clear positive nor negative pattern.[\/caption]","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<section>\n<h2>Scatterplots<\/h2>\n<p><strong>Scatterplots<\/strong> are used to illustrate the relationship between two quantitative variables.<\/p>\n<\/section>\n<section class=\"textbox example\">The table of data presented below includes information collected from 18 grocery stores in San Antonio, Texas. The average household income (in thousands of dollars)<a class=\"footnote\" title=\"Income by Zip Code. (2021). https:\/\/www.incomebyzipcode.com\/\" id=\"return-footnote-239-1\" href=\"#footnote-239-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> and the number of organic vegetables offered were collected in 2021 to explore this relationship.<a class=\"footnote\" title=\"HEB. (2021). Shop by Department. https:\/\/www.heb.com\" id=\"return-footnote-239-2\" href=\"#footnote-239-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/p>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>Store Location<\/strong><\/td>\n<td><strong>Average Household Income ($1000s)<\/strong><\/td>\n<td><strong>Number of Organic Vegetables Offered<\/strong><\/td>\n<td>&nbsp;<\/td>\n<td><strong>Store Location<\/strong><\/td>\n<td>\n<p><strong>Average Household Income<\/strong><\/p>\n<p><strong>($1000s)<\/strong><\/p>\n<\/td>\n<td><strong>Number of Organic Vegetables Offered<\/strong><\/td>\n<\/tr>\n<tr>\n<td>S. Flores<\/td>\n<td>71<\/td>\n<td>36<\/td>\n<td>&nbsp;<\/td>\n<td>Marbach Rd.<\/td>\n<td>49<\/td>\n<td>38<\/td>\n<\/tr>\n<tr>\n<td>N. Rosillo St.<\/td>\n<td>34<\/td>\n<td>4<\/td>\n<td>&nbsp;<\/td>\n<td>Babcock Rd.<\/td>\n<td>66<\/td>\n<td>84<\/td>\n<\/tr>\n<tr>\n<td>Nogalitos St.<\/td>\n<td>71<\/td>\n<td>28<\/td>\n<td>&nbsp;<\/td>\n<td>Wurzbach Rd.<\/td>\n<td>87<\/td>\n<td>61<\/td>\n<\/tr>\n<tr>\n<td>Fredericksburg Rd.<\/td>\n<td>49<\/td>\n<td>31<\/td>\n<td>&nbsp;<\/td>\n<td>W. Loop 1604 N.<\/td>\n<td>78<\/td>\n<td>56<\/td>\n<\/tr>\n<tr>\n<td>Olmos<\/td>\n<td>78<\/td>\n<td>78<\/td>\n<td>&nbsp;<\/td>\n<td>Bandera Rd.<\/td>\n<td>59<\/td>\n<td>62<\/td>\n<\/tr>\n<tr>\n<td>N. New Braunfels Ave.<\/td>\n<td>41<\/td>\n<td>14<\/td>\n<td>&nbsp;<\/td>\n<td>S. New Braunfels<\/td>\n<td>50<\/td>\n<td>44<\/td>\n<\/tr>\n<tr>\n<td>Castroville<\/td>\n<td>38<\/td>\n<td>12<\/td>\n<td>&nbsp;<\/td>\n<td>S.W. Military<\/td>\n<td>48<\/td>\n<td>26<\/td>\n<\/tr>\n<tr>\n<td>Culebra Rd.<\/td>\n<td>50<\/td>\n<td>18<\/td>\n<td>&nbsp;<\/td>\n<td>S. Zarzamora<\/td>\n<td>56<\/td>\n<td>29<\/td>\n<\/tr>\n<tr>\n<td>S.E. Military Dr.<\/td>\n<td>50<\/td>\n<td>65<\/td>\n<td>&nbsp;<\/td>\n<td>E. Basse Rd.<\/td>\n<td>125<\/td>\n<td>95<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Let&#8217;s enter the data into our statistical tool to create a scatterplot.<\/p>\n<\/div>\n<div class=\"textbox\">\n<p><strong>Step 1:<\/strong> Locate the drop-down menu under <strong>Enter Data<\/strong> and select <strong>Your Own<\/strong>.<\/p>\n<p><strong>Step 2:<\/strong> Select the box titled <strong>Use ID Variable<\/strong> and name the ID Variable and the X and Y-Variables appropriately given the three columns in the data table.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q600169\">Note<\/button><\/p>\n<div id=\"q600169\" class=\"hidden-answer\" style=\"display: none\">If the <strong>Use ID Variable<\/strong> option not clicked, then only the x and y variables will appear in the table. <\/div>\n<\/div>\n<p><strong>Step 3:<\/strong> Complete the data table appropriately. Then select <strong>Submit Data<\/strong>\u00a0(you may need to scroll down to see it) to create the scatterplot.<\/p>\n<\/div>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q631362\">Note<\/button><\/p>\n<div id=\"q631362\" class=\"hidden-answer\" style=\"display: none\">You may hover over a dot or a point to obtain more detailed information about such dot\/point.<\/div>\n<\/div>\n<\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/association_quantitative\/\" width=\"100%\" height=\"850\"><\/iframe> [<a href=\"https:\/\/lumen-learning.shinyapps.io\/association_quantitative\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1118\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1118&theme=lumen&iframe_resize_id=ohm1118&source=tnh\" width=\"100%\" height=\"550\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1120\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1120&theme=lumen&iframe_resize_id=ohm1120&source=tnh\" width=\"100%\" height=\"550\"><\/iframe><\/section>\n<div style=\"margin: auto;\">\n<h2 style=\"text-align: left;\">Increasing and Decreasing Trends<\/h2>\n<\/div>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1121\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1121&theme=lumen&iframe_resize_id=ohm1121&source=tnh&show_question_numbers\" width=\"100%\" height=\"350\"><\/iframe><\/section>\n<p>A\u00a0<strong>positive (or increasing) relationship<\/strong>\u00a0means that an increase in one of the variables is associated with an increase in the other. A\u00a0<strong>negative (or decreasing) relationship<\/strong>\u00a0means that an increase in one of the variables is associated with a decrease in the other.\u00a0 Note that not all relationships can be classified as either positive or negative.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1123\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1123&theme=lumen&iframe_resize_id=ohm1123&source=tnh&show_question_numbers\" width=\"100%\" height=\"325\"><\/iframe><\/section>\n<p>The direction of the relationship can be positive, negative, or neither:<\/p>\n<figure id=\"attachment_6492\" aria-describedby=\"caption-attachment-6492\" style=\"width: 265px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6492 size-medium\" style=\"font-size: 14pt;\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/02\/20171350\/5.1.D.positive-relationship.png\" alt=\"Scatterplot showing positive relationship. Dots on scatterplot are making an upwards trajectory.\" width=\"265\" height=\"300\" \/><figcaption id=\"caption-attachment-6492\" class=\"wp-caption-text\">Figure 1. A positive relationship is one where as values of X increase, values of Y also increase.<\/figcaption><\/figure>\n<figure id=\"attachment_6491\" aria-describedby=\"caption-attachment-6491\" style=\"width: 265px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6491 size-medium\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/02\/20171351\/5.1.D.negative-relationship.png\" alt=\"Scatterplot showing a negative relationship. Dots on scatterplot are making an downwards trajectory.\" width=\"265\" height=\"300\" \/><figcaption id=\"caption-attachment-6491\" class=\"wp-caption-text\">Figure 2. A negative relationship is one where as values of X increase, values of Y decrease.<\/figcaption><\/figure>\n<figure id=\"attachment_6490\" aria-describedby=\"caption-attachment-6490\" style=\"width: 265px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6490 size-medium\" style=\"font-size: 14pt;\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/02\/20171351\/5.1..D.Neither.png\" alt=\"Scatterplot showing neither positive nor negative relationship. Dots on the scatterplot form a U shape.\" width=\"265\" height=\"300\" \/><figcaption id=\"caption-attachment-6490\" class=\"wp-caption-text\">Figure 3. Some relationships may show neither a clear positive nor negative pattern.<\/figcaption><\/figure>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-239-1\">Income by Zip Code. (2021). https:\/\/www.incomebyzipcode.com\/ <a href=\"#return-footnote-239-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-239-2\">HEB. (2021). Shop by Department. https:\/\/www.heb.com <a href=\"#return-footnote-239-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":12,"menu_order":11,"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":"fresh_take","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\/239"}],"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\/239\/revisions"}],"predecessor-version":[{"id":6501,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/239\/revisions\/6501"}],"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\/239\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=239"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=239"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=239"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=239"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}