{"id":230,"date":"2023-02-20T17:13:46","date_gmt":"2023-02-20T17:13:46","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/scatterplots-learn-it-1\/"},"modified":"2025-05-11T23:09:10","modified_gmt":"2025-05-11T23:09:10","slug":"scatterplots-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/scatterplots-learn-it-1\/","title":{"raw":"Scatterplots &amp; Correlation Coefficients: Learn It 1","rendered":"Scatterplots &amp; Correlation Coefficients: Learn It 1"},"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<h3><strong>Greenhouse Gases<\/strong><\/h3>\r\n<p>Carbon dioxide is a greenhouse gas. This means it absorbs and radiates heat. Warmed by sunlight, Earth\u2019s land and ocean surfaces continuously radiate thermal infrared energy (heat). Unlike oxygen or nitrogen (which make up most of our atmosphere), greenhouse gases absorb that heat and release it gradually over time, like bricks in a fireplace after the fire goes out. Without this natural greenhouse effect, Earth\u2019s average annual temperature would be below freezing instead of close to [latex]60[\/latex]\u00b0F. But increases in greenhouse gases have tipped the Earth's energy budget out of balance, trapping additional heat and raising the Earth's average temperature.[footnote]Lindsey, R. (2020, August 14). <em>Climate change: Atmospheric carbon dioxide<\/em>. NOAA Climate.gov. <a href=\"https:\/\/www.climate.gov\/news-features\/understanding-climate\/climate-change-atmospheric-carbon-dioxide\">https:\/\/www.climate.gov\/news-features\/understanding-climate\/climate-change-atmospheric-carbon-dioxide<\/a>[\/footnote]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2977[\/ohm2_question]<\/section>\r\n<h2>Scatterplots<\/h2>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>scatterplot<\/h3>\r\n<p><strong>Scatterplots<\/strong> are used to illustrate the relationship between two quantitative variables. Such data from two quantitative variables (usually two related\u00a0data) are called <strong>bivariate data.<\/strong><\/p>\r\n<p>When investigating relationships between two quantitative variables, scatterplots are a simple way to visually represent the spread, direction, strength of relationship, and potential outliers of the data.<\/p>\r\n<\/section>\r\n<p>With larger data sets, a scatterplot can more succinctly display the overall pattern than when the data is presented as a table. This visualization can also hint at the general shape of the relationship. (For example: increasing linear, decreasing linear, or non-linear curves.) This also helps us identify any deviations from that pattern.<\/p>\r\n<p>When working with a bivariate data set, there are two variables to consider:<\/p>\r\n<ul>\r\n\t<li>The <strong>explanatory variable<\/strong> ([latex]x[\/latex]) is the variable that is thought to explain or predict the response variable of a study.<\/li>\r\n\t<li>The <strong>response variable<\/strong> ([latex]y[\/latex]) measures the outcome of interest in the study. This variable is thought to <em>depend <\/em>in some way on the explanatory variable. It is often referred to as the \u201cvariable of interest\u201d for the researcher. (And in previous math courses, this variable may have been referred to as the <strong>dependent variable<\/strong>.)<\/li>\r\n<\/ul>\r\n<p>Sometimes the variables do not have a clear explanatory\/response relationship. In this case, there is no rule to follow. You may plot the variables on either axis.<\/p>\r\n<section class=\"textbox example\"><strong>Carbon Footprint<br \/>\r\n<\/strong><br \/>\r\nA carbon footprint is the total amount of greenhouse gas (GHG) emissions caused directly and indirectly by an individual, organization, event, or product. It is calculated by summing the emissions resulting from every stage of a product or service\u2019s lifetime (material production, manufacturing, use, and end of life). A typical U.S. household has a carbon footprint of [latex]48[\/latex] metric tons of carbon dioxide equivalent per year (CO2e\/yr).[footnote]Center for Sustainable Systems, University of Michigan. (2020). Carbon footprint factsheet. http:\/\/css.umich.edu\/factsheets\/carbon-footprint-factsheet[\/footnote]The food you eat has a carbon footprint. Energy is involved in producing the food, transporting the food, preparing the food, eating the food, and disposing of any waste from the food. We can analyze the energy content and carbon footprint of your food using a scatterplot. Because the purpose of this study is to explore the effect of energy content on the carbon footprint of your food:\r\n\r\n<ul>\r\n\t<li>The <em>explanatory variable<\/em> is energy content, and<\/li>\r\n\t<li>The <em>response variable<\/em> is the carbon footprint of your food.<\/li>\r\n<\/ul>\r\n<p>Both variables are quantitative.<\/p>\r\n<p>Here is what the raw bivariate data look like:<\/p>\r\n<table style=\"border-collapse: collapse; width: 78.5048%; height: 96px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 14.9206%; height: 16px;\"><strong>Sandwich<\/strong><\/td>\r\n<td style=\"width: 28.3966%; height: 16px;\"><strong>Energy Content (kCal)<\/strong><\/td>\r\n<td style=\"width: 39.6227%; height: 16px;\"><strong>Carbon Footprint (g CO2)<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 14.9206%; height: 16px;\">Chicken salad<\/td>\r\n<td style=\"width: 28.3966%; height: 16px;\">[latex]351[\/latex]<\/td>\r\n<td style=\"width: 39.6227%; height: 16px;\">[latex]963[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 14.9206%; height: 16px;\">Prawn, mayo<\/td>\r\n<td style=\"width: 28.3966%; height: 16px;\">[latex]339[\/latex]<\/td>\r\n<td style=\"width: 39.6227%; height: 16px;\">[latex]1255[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 14.9206%; height: 16px;\">Egg, mayo, cress<\/td>\r\n<td style=\"width: 28.3966%; height: 16px;\">[latex]319[\/latex]<\/td>\r\n<td style=\"width: 39.6227%; height: 16px;\">[latex]739[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 14.9206%; height: 16px;\">...<\/td>\r\n<td style=\"width: 28.3966%; height: 16px;\">...<\/td>\r\n<td style=\"width: 39.6227%; height: 16px;\">...<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 14.9206%; height: 16px;\">Egg, rocket<\/td>\r\n<td style=\"width: 28.3966%; height: 16px;\">[latex]363[\/latex]<\/td>\r\n<td style=\"width: 39.6227%; height: 16px;\">[latex]854[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>Note that for each sandwich, we have two values: Energy content and carbon footprint.<\/p>\r\n<p>To explore the relationship between the two quantitative variables, we create a graph called a <strong>scatterplot<\/strong>. To create a scatterplot, we use an ordered pair [latex](x,y)[\/latex] to represent the data for each sandwich. The [latex]x[\/latex]-coordinate is the explanatory variable, energy content. The [latex]y[\/latex]-coordinate is the response variable, carbon footprint.<\/p>\r\n<p>For example, the point [latex](351,963)[\/latex] represents chicken salad.<\/p>\r\n<p>Let's use the statistical tool below to plot the scatterplot! Select \"<strong>Carbon Footprint<\/strong>\" data set from the drop-down menu under \"<strong>Choose Dataset<\/strong>.\"<\/p>\r\n<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/association_quantitative\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\r\n<p><br \/>\r\n[<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 hide_question_numbers=1]1134[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1135[\/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<h3><strong>Greenhouse Gases<\/strong><\/h3>\n<p>Carbon dioxide is a greenhouse gas. This means it absorbs and radiates heat. Warmed by sunlight, Earth\u2019s land and ocean surfaces continuously radiate thermal infrared energy (heat). Unlike oxygen or nitrogen (which make up most of our atmosphere), greenhouse gases absorb that heat and release it gradually over time, like bricks in a fireplace after the fire goes out. Without this natural greenhouse effect, Earth\u2019s average annual temperature would be below freezing instead of close to [latex]60[\/latex]\u00b0F. But increases in greenhouse gases have tipped the Earth&#8217;s energy budget out of balance, trapping additional heat and raising the Earth&#8217;s average temperature.<a class=\"footnote\" title=\"Lindsey, R. (2020, August 14). Climate change: Atmospheric carbon dioxide. NOAA Climate.gov. https:\/\/www.climate.gov\/news-features\/understanding-climate\/climate-change-atmospheric-carbon-dioxide\" id=\"return-footnote-230-1\" href=\"#footnote-230-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2977\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2977&theme=lumen&iframe_resize_id=ohm2977&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h2>Scatterplots<\/h2>\n<section class=\"textbox keyTakeaway\">\n<h3>scatterplot<\/h3>\n<p><strong>Scatterplots<\/strong> are used to illustrate the relationship between two quantitative variables. Such data from two quantitative variables (usually two related\u00a0data) are called <strong>bivariate data.<\/strong><\/p>\n<p>When investigating relationships between two quantitative variables, scatterplots are a simple way to visually represent the spread, direction, strength of relationship, and potential outliers of the data.<\/p>\n<\/section>\n<p>With larger data sets, a scatterplot can more succinctly display the overall pattern than when the data is presented as a table. This visualization can also hint at the general shape of the relationship. (For example: increasing linear, decreasing linear, or non-linear curves.) This also helps us identify any deviations from that pattern.<\/p>\n<p>When working with a bivariate data set, there are two variables to consider:<\/p>\n<ul>\n<li>The <strong>explanatory variable<\/strong> ([latex]x[\/latex]) is the variable that is thought to explain or predict the response variable of a study.<\/li>\n<li>The <strong>response variable<\/strong> ([latex]y[\/latex]) measures the outcome of interest in the study. This variable is thought to <em>depend <\/em>in some way on the explanatory variable. It is often referred to as the \u201cvariable of interest\u201d for the researcher. (And in previous math courses, this variable may have been referred to as the <strong>dependent variable<\/strong>.)<\/li>\n<\/ul>\n<p>Sometimes the variables do not have a clear explanatory\/response relationship. In this case, there is no rule to follow. You may plot the variables on either axis.<\/p>\n<section class=\"textbox example\"><strong>Carbon Footprint<br \/>\n<\/strong><br \/>\nA carbon footprint is the total amount of greenhouse gas (GHG) emissions caused directly and indirectly by an individual, organization, event, or product. It is calculated by summing the emissions resulting from every stage of a product or service\u2019s lifetime (material production, manufacturing, use, and end of life). A typical U.S. household has a carbon footprint of [latex]48[\/latex] metric tons of carbon dioxide equivalent per year (CO2e\/yr).<a class=\"footnote\" title=\"Center for Sustainable Systems, University of Michigan. (2020). Carbon footprint factsheet. http:\/\/css.umich.edu\/factsheets\/carbon-footprint-factsheet\" id=\"return-footnote-230-2\" href=\"#footnote-230-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a>The food you eat has a carbon footprint. Energy is involved in producing the food, transporting the food, preparing the food, eating the food, and disposing of any waste from the food. We can analyze the energy content and carbon footprint of your food using a scatterplot. Because the purpose of this study is to explore the effect of energy content on the carbon footprint of your food:<\/p>\n<ul>\n<li>The <em>explanatory variable<\/em> is energy content, and<\/li>\n<li>The <em>response variable<\/em> is the carbon footprint of your food.<\/li>\n<\/ul>\n<p>Both variables are quantitative.<\/p>\n<p>Here is what the raw bivariate data look like:<\/p>\n<table style=\"border-collapse: collapse; width: 78.5048%; height: 96px;\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 14.9206%; height: 16px;\"><strong>Sandwich<\/strong><\/td>\n<td style=\"width: 28.3966%; height: 16px;\"><strong>Energy Content (kCal)<\/strong><\/td>\n<td style=\"width: 39.6227%; height: 16px;\"><strong>Carbon Footprint (g CO2)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 14.9206%; height: 16px;\">Chicken salad<\/td>\n<td style=\"width: 28.3966%; height: 16px;\">[latex]351[\/latex]<\/td>\n<td style=\"width: 39.6227%; height: 16px;\">[latex]963[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 14.9206%; height: 16px;\">Prawn, mayo<\/td>\n<td style=\"width: 28.3966%; height: 16px;\">[latex]339[\/latex]<\/td>\n<td style=\"width: 39.6227%; height: 16px;\">[latex]1255[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 14.9206%; height: 16px;\">Egg, mayo, cress<\/td>\n<td style=\"width: 28.3966%; height: 16px;\">[latex]319[\/latex]<\/td>\n<td style=\"width: 39.6227%; height: 16px;\">[latex]739[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 14.9206%; height: 16px;\">&#8230;<\/td>\n<td style=\"width: 28.3966%; height: 16px;\">&#8230;<\/td>\n<td style=\"width: 39.6227%; height: 16px;\">&#8230;<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 14.9206%; height: 16px;\">Egg, rocket<\/td>\n<td style=\"width: 28.3966%; height: 16px;\">[latex]363[\/latex]<\/td>\n<td style=\"width: 39.6227%; height: 16px;\">[latex]854[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Note that for each sandwich, we have two values: Energy content and carbon footprint.<\/p>\n<p>To explore the relationship between the two quantitative variables, we create a graph called a <strong>scatterplot<\/strong>. To create a scatterplot, we use an ordered pair [latex](x,y)[\/latex] to represent the data for each sandwich. The [latex]x[\/latex]-coordinate is the explanatory variable, energy content. The [latex]y[\/latex]-coordinate is the response variable, carbon footprint.<\/p>\n<p>For example, the point [latex](351,963)[\/latex] represents chicken salad.<\/p>\n<p>Let&#8217;s use the statistical tool below to plot the scatterplot! Select &#8220;<strong>Carbon Footprint<\/strong>&#8221; data set from the drop-down menu under &#8220;<strong>Choose Dataset<\/strong>.&#8221;<\/p>\n<\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/association_quantitative\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>\n[<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=\"ohm1134\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1134&theme=lumen&iframe_resize_id=ohm1134&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1135\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1135&theme=lumen&iframe_resize_id=ohm1135&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-230-1\">Lindsey, R. (2020, August 14). <em>Climate change: Atmospheric carbon dioxide<\/em>. NOAA Climate.gov. <a href=\"https:\/\/www.climate.gov\/news-features\/understanding-climate\/climate-change-atmospheric-carbon-dioxide\">https:\/\/www.climate.gov\/news-features\/understanding-climate\/climate-change-atmospheric-carbon-dioxide<\/a> <a href=\"#return-footnote-230-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-230-2\">Center for Sustainable Systems, University of Michigan. (2020). Carbon footprint factsheet. http:\/\/css.umich.edu\/factsheets\/carbon-footprint-factsheet <a href=\"#return-footnote-230-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":12,"menu_order":6,"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\/230"}],"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":24,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/230\/revisions"}],"predecessor-version":[{"id":6646,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/230\/revisions\/6646"}],"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\/230\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=230"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=230"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=230"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}