{"id":656,"date":"2017-04-15T05:36:36","date_gmt":"2017-04-15T05:36:36","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/conceptstest1\/?post_type=chapter&#038;p=656"},"modified":"2019-06-28T12:08:21","modified_gmt":"2019-06-28T12:08:21","slug":"introduction-linear-relationships","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/chapter\/introduction-linear-relationships\/","title":{"raw":"Introduction to Linear Relationships","rendered":"Introduction to Linear Relationships"},"content":{"raw":"<h2>What you'll learn to do: Use a correlation coefficient to describe the direction and strength of a linear relationship. Recognize its limitations as a measure of the relationship between two quantitative variables.<\/h2>\r\n<img class=\"size-medium wp-image-2008 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1768\/2017\/04\/28120656\/990px-Anscombes_quartet_3.svg_-300x218.png\" alt=\"There are 4 scatter plot graphs that shows a line of best fit for each one.  Each graph has a different array of points, but the same line of fit.\" width=\"300\" height=\"218\" \/>Scatterplots are an excellent way to visually inspect the data, but to further investigate the relationship, it would help to quantify some metrics about the relationship. In particular, we are interested in:\r\n<ul>\r\n \t<li style=\"font-weight: 400;\">Direction: Does the response variable increase with the dependent variable? Or does the response variable decrease with the dependent variable?<\/li>\r\n \t<li style=\"font-weight: 400;\">Strength: Does the scatterplot cluster tightly around a line?<\/li>\r\n \t<li style=\"font-weight: 400;\">Form: Is the scatterplot evenly clustered around the line or are there regions where the scatter is more spread out? Does the shape of the scatterplot seem linear or curvilinear?<\/li>\r\n<\/ul>\r\n<h2>Contribute!<\/h2><div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div><a href=\"https:\/\/docs.google.com\/document\/d\/1AzfusbToa0NaMCrhUg-h0yb_ZkaySaHuWIW-VEzemOA\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a>","rendered":"<h2>What you&#8217;ll learn to do: Use a correlation coefficient to describe the direction and strength of a linear relationship. Recognize its limitations as a measure of the relationship between two quantitative variables.<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-2008 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1768\/2017\/04\/28120656\/990px-Anscombes_quartet_3.svg_-300x218.png\" alt=\"There are 4 scatter plot graphs that shows a line of best fit for each one.  Each graph has a different array of points, but the same line of fit.\" width=\"300\" height=\"218\" \/>Scatterplots are an excellent way to visually inspect the data, but to further investigate the relationship, it would help to quantify some metrics about the relationship. In particular, we are interested in:<\/p>\n<ul>\n<li style=\"font-weight: 400;\">Direction: Does the response variable increase with the dependent variable? Or does the response variable decrease with the dependent variable?<\/li>\n<li style=\"font-weight: 400;\">Strength: Does the scatterplot cluster tightly around a line?<\/li>\n<li style=\"font-weight: 400;\">Form: Is the scatterplot evenly clustered around the line or are there regions where the scatter is more spread out? Does the shape of the scatterplot seem linear or curvilinear?<\/li>\n<\/ul>\n<h2>Contribute!<\/h2>\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\n<p><a href=\"https:\/\/docs.google.com\/document\/d\/1AzfusbToa0NaMCrhUg-h0yb_ZkaySaHuWIW-VEzemOA\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-656\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Concepts in Statistics. <strong>Provided by<\/strong>: Open Learning Initiative. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/oli.cmu.edu\">http:\/\/oli.cmu.edu<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":163,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Concepts in Statistics\",\"author\":\"\",\"organization\":\"Open Learning Initiative\",\"url\":\"http:\/\/oli.cmu.edu\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"98b8f828-521a-424b-805d-26fbb06b4bba","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-656","chapter","type-chapter","status-publish","hentry"],"part":140,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/656","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/users\/163"}],"version-history":[{"count":9,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/656\/revisions"}],"predecessor-version":[{"id":2009,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/656\/revisions\/2009"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/parts\/140"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/656\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/media?parent=656"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapter-type?post=656"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/contributor?post=656"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/license?post=656"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}