{"id":205,"date":"2017-04-15T03:19:17","date_gmt":"2017-04-15T03:19:17","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/conceptstest1\/chapter\/wrap-up-fitting-a-line\/"},"modified":"2019-06-28T13:32:12","modified_gmt":"2019-06-28T13:32:12","slug":"introduction-assessing-the-fit-of-a-line","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/chapter\/introduction-assessing-the-fit-of-a-line\/","title":{"raw":"Introduction to Assessing the Fit of a Line","rendered":"Introduction to Assessing the Fit of a Line"},"content":{"raw":"<h2>What you'll learn to do: Use residuals, standard error, and r<sup>2<\/sup> to assess the fit of a linear model.<\/h2>\r\n<img class=\"size-medium wp-image-2015 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1768\/2017\/04\/28133124\/regression-residuals-300x256.png\" alt=\"This graph shows a sample relationship between height and weight of people as a residual plot.\" width=\"300\" height=\"256\" \/>Graphing the regression line with the scatterplot gives a visual depiction of how well the regression line fits the data.\u00a0 To further hone in on assessing the fit of our regression line to the data, in this section we present:\r\n<ul>\r\n \t<li style=\"font-weight: 400;\">Residual plots.<\/li>\r\n \t<li style=\"font-weight: 400;\">The correlation coefficient r gives us a numerical way to measure this fit.<\/li>\r\n \t<li style=\"font-weight: 400;\">Interpreting the square of the correlation coefficient r<sup>2<\/sup>\u00a0.<\/li>\r\n \t<li style=\"font-weight: 400;\">Interpreting the standard error\u00a0s<sub>e<\/sub>.<\/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\/11TEKc0p0kSoGxh-Z8J8Y4PWN_5UJr0cs1Wi3CZ8Xrlo\" 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 residuals, standard error, and r<sup>2<\/sup> to assess the fit of a linear model.<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-2015 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1768\/2017\/04\/28133124\/regression-residuals-300x256.png\" alt=\"This graph shows a sample relationship between height and weight of people as a residual plot.\" width=\"300\" height=\"256\" \/>Graphing the regression line with the scatterplot gives a visual depiction of how well the regression line fits the data.\u00a0 To further hone in on assessing the fit of our regression line to the data, in this section we present:<\/p>\n<ul>\n<li style=\"font-weight: 400;\">Residual plots.<\/li>\n<li style=\"font-weight: 400;\">The correlation coefficient r gives us a numerical way to measure this fit.<\/li>\n<li style=\"font-weight: 400;\">Interpreting the square of the correlation coefficient r<sup>2<\/sup>\u00a0.<\/li>\n<li style=\"font-weight: 400;\">Interpreting the standard error\u00a0s<sub>e<\/sub>.<\/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\/11TEKc0p0kSoGxh-Z8J8Y4PWN_5UJr0cs1Wi3CZ8Xrlo\" 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-205\">\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":21,"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":"1bbe606f-ad84-4a6e-ad4e-3bef550b5ba7","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-205","chapter","type-chapter","status-publish","hentry"],"part":140,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/205","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\/205\/revisions"}],"predecessor-version":[{"id":2016,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/205\/revisions\/2016"}],"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\/205\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/media?parent=205"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapter-type?post=205"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/contributor?post=205"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/license?post=205"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}