{"id":304,"date":"2021-07-14T15:59:10","date_gmt":"2021-07-14T15:59:10","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/introduction-linear-regression-and-correlation\/"},"modified":"2022-04-22T23:54:39","modified_gmt":"2022-04-22T23:54:39","slug":"why-it-matters-linear-regression-and-correlation","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/why-it-matters-linear-regression-and-correlation\/","title":{"raw":"Why It Matters: Linear Regression and Correlation","rendered":"Why It Matters: Linear Regression and Correlation"},"content":{"raw":"<h2>Why learn how to analyze data by examining the relationships between quantitative data?<\/h2>\r\nOften multiple pieces of data are gathered on a single subject or data from two different data sets can be paired together. When the variables involved are quantitative variables, we want to know if there is a relationship between the two variables. For example, is there a relationship between the third exam score for students in a math class and their final exam score? And if there is a relationship, how can we predict a particular student\u2019s final exam score from their third exam score? Scatterplots and lines of best fit can be used to answer these questions. The scatterplot below shows a positive linear relationship between the third exam score and the final exam score for the data.\r\n\r\n<img class=\"aligncenter wp-image-2660 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/07\/11204729\/Picture14.png\" alt=\"A scatterplot with the x-axis labeled \u2018Third Exam Score\u2019 and the y-axis labeled \u2018Final Exam Score\u2019. There are 11 points on the plot and the points begin on the bottom left and end in the upper right. A line with a positive slope goes through the points from bottom left to upper right.\" width=\"505\" height=\"338\" \/>","rendered":"<h2>Why learn how to analyze data by examining the relationships between quantitative data?<\/h2>\n<p>Often multiple pieces of data are gathered on a single subject or data from two different data sets can be paired together. When the variables involved are quantitative variables, we want to know if there is a relationship between the two variables. For example, is there a relationship between the third exam score for students in a math class and their final exam score? And if there is a relationship, how can we predict a particular student\u2019s final exam score from their third exam score? Scatterplots and lines of best fit can be used to answer these questions. The scatterplot below shows a positive linear relationship between the third exam score and the final exam score for the data.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2660 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/07\/11204729\/Picture14.png\" alt=\"A scatterplot with the x-axis labeled \u2018Third Exam Score\u2019 and the y-axis labeled \u2018Final Exam Score\u2019. There are 11 points on the plot and the points begin on the bottom left and end in the upper right. A line with a positive slope goes through the points from bottom left to upper right.\" width=\"505\" height=\"338\" \/><\/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-304\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <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":169134,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-304","chapter","type-chapter","status-publish","hentry"],"part":303,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/304","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":8,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/304\/revisions"}],"predecessor-version":[{"id":3957,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/304\/revisions\/3957"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/303"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/304\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=304"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=304"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=304"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}