{"id":2908,"date":"2023-08-15T16:52:12","date_gmt":"2023-08-15T16:52:12","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/?post_type=chapter&#038;p=2908"},"modified":"2025-05-11T23:07:13","modified_gmt":"2025-05-11T23:07:13","slug":"module-5-background-youll-need-1-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/module-5-background-youll-need-1-2\/","title":{"raw":"Module 5: Background You'll Need 1","rendered":"Module 5: Background You&#8217;ll Need 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Identify the two quantitative variables as an explanatory variable and a response variable.<\/li>\r\n<\/ul>\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<p>When investigating relationships between two quantitative variables, scatterplots are a simple way to visually represent the <strong>spread<\/strong>, <strong>direction<\/strong>, <strong>strength of relationship<\/strong>, and potential <strong>outliers<\/strong> of the data. 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) while also helping us identify any deviations from that pattern.<\/p>\r\n<p>Note:\u00a0The explanatory variable is typically placed on the horizontal x-axis. The response variable is on the vertical y-axis. Sometimes the variables do not have a clear explanatory\u2013response relationship. In this case, there is no rule to follow. Plot the variables on either axis.<\/p>\r\n<section class=\"textbox example\">\r\n<h3>Highway Signs<\/h3>\r\n<p>A research firm conducts a study to explore the relationship between a driver\u2019s age and the driver\u2019s ability to read highway signs. The subjects are a random sample of 30 drivers between the ages of 18 and 82. <cite>(Source: Jessica M. Utts and Robert F. Heckard, <em>Mind on Statistics<\/em> [Brooks\/Cole, 2002]. Original source: Data collected by The Last Resource, Inc., Bellfonte, PA.)<\/cite><\/p>\r\n<p>Because the purpose of this study is to explore the effect of age on the driver\u2019s ability to read highway signs,<\/p>\r\n<ul>\r\n\t<li>the explanatory variable is age, and<\/li>\r\n\t<li>the response variable is the maximum distance at which the driver can read a highway sign, or maximum reading distance.<\/li>\r\n<\/ul>\r\n<p>Both variables are quantitative.<\/p>\r\n<p>Here is what the raw data look like:<\/p>\r\n\r\n[caption id=\"\" align=\"alignnone\" width=\"280\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031748\/m3_examining_relationships_topic_3_1_scatter_linear_corr_scatterplot2.gif\" alt=\"Raw data: Drivers\u2019 ages (explanatory variables) and distance (response variables) at which they can see highway sign\" width=\"280\" height=\"238\" \/> Figure 1. A data table showing driver age as the explanatory variable and stopping distance as the response variable.[\/caption]\r\n\r\n<p>In this data set, the individuals are the 30 drivers. For each driver, we have two values: age and maximum reading distance.<\/p>\r\n<p>To explore the relationship between age and distance, we create a graph called a <strong>scatterplot<\/strong>. To create a scatterplot, we use an ordered pair (<em>x<\/em>, <em>y<\/em>) to represent the data for each driver. The <strong><em>x<\/em>-coordinate<\/strong> is the explanatory variable: driver\u2019s age. The <strong><em>y<\/em>-coordinate<\/strong> is the response variable: maximum reading distance.<\/p>\r\n<p>Here is the completed scatterplot:<\/p>\r\n\r\n[caption id=\"\" align=\"alignnone\" width=\"400\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031756\/m3_examining_relationships_topic_3_1_scatter_linear_corr_scatterplot4a.gif\" alt=\"Completed scatterplot, where each dot represents a driver's age and maximum distance at which they can read a road sign\" width=\"400\" height=\"301\" \/> Figure 2. A scatterplot showing a negative association between driver age and the maximum distance at which a sign can be read\u2014older drivers tend to read signs from shorter distances.[\/caption]\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1117[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Identify the two quantitative variables as an explanatory variable and a response variable.<\/li>\n<\/ul>\n<\/section>\n<h2>Scatterplots<\/h2>\n<p><strong>Scatterplots<\/strong> are used to illustrate the relationship between two quantitative variables.<\/p>\n<p>When investigating relationships between two quantitative variables, scatterplots are a simple way to visually represent the <strong>spread<\/strong>, <strong>direction<\/strong>, <strong>strength of relationship<\/strong>, and potential <strong>outliers<\/strong> of the data. 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) while also helping us identify any deviations from that pattern.<\/p>\n<p>Note:\u00a0The explanatory variable is typically placed on the horizontal x-axis. The response variable is on the vertical y-axis. Sometimes the variables do not have a clear explanatory\u2013response relationship. In this case, there is no rule to follow. Plot the variables on either axis.<\/p>\n<section class=\"textbox example\">\n<h3>Highway Signs<\/h3>\n<p>A research firm conducts a study to explore the relationship between a driver\u2019s age and the driver\u2019s ability to read highway signs. The subjects are a random sample of 30 drivers between the ages of 18 and 82. <cite>(Source: Jessica M. Utts and Robert F. Heckard, <em>Mind on Statistics<\/em> [Brooks\/Cole, 2002]. Original source: Data collected by The Last Resource, Inc., Bellfonte, PA.)<\/cite><\/p>\n<p>Because the purpose of this study is to explore the effect of age on the driver\u2019s ability to read highway signs,<\/p>\n<ul>\n<li>the explanatory variable is age, and<\/li>\n<li>the response variable is the maximum distance at which the driver can read a highway sign, or maximum reading distance.<\/li>\n<\/ul>\n<p>Both variables are quantitative.<\/p>\n<p>Here is what the raw data look like:<\/p>\n<figure style=\"width: 280px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031748\/m3_examining_relationships_topic_3_1_scatter_linear_corr_scatterplot2.gif\" alt=\"Raw data: Drivers\u2019 ages (explanatory variables) and distance (response variables) at which they can see highway sign\" width=\"280\" height=\"238\" \/><figcaption class=\"wp-caption-text\">Figure 1. A data table showing driver age as the explanatory variable and stopping distance as the response variable.<\/figcaption><\/figure>\n<p>In this data set, the individuals are the 30 drivers. For each driver, we have two values: age and maximum reading distance.<\/p>\n<p>To explore the relationship between age and distance, we create a graph called a <strong>scatterplot<\/strong>. To create a scatterplot, we use an ordered pair (<em>x<\/em>, <em>y<\/em>) to represent the data for each driver. The <strong><em>x<\/em>-coordinate<\/strong> is the explanatory variable: driver\u2019s age. The <strong><em>y<\/em>-coordinate<\/strong> is the response variable: maximum reading distance.<\/p>\n<p>Here is the completed scatterplot:<\/p>\n<figure style=\"width: 400px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031756\/m3_examining_relationships_topic_3_1_scatter_linear_corr_scatterplot4a.gif\" alt=\"Completed scatterplot, where each dot represents a driver's age and maximum distance at which they can read a road sign\" width=\"400\" height=\"301\" \/><figcaption class=\"wp-caption-text\">Figure 2. A scatterplot showing a negative association between driver age and the maximum distance at which a sign can be read\u2014older drivers tend to read signs from shorter distances.<\/figcaption><\/figure>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1117\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1117&theme=lumen&iframe_resize_id=ohm1117&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":13,"menu_order":2,"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":"background_you_need","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\/2908"}],"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\/13"}],"version-history":[{"count":8,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/2908\/revisions"}],"predecessor-version":[{"id":7134,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/2908\/revisions\/7134"}],"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\/2908\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=2908"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=2908"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=2908"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=2908"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}