{"id":461,"date":"2016-04-21T22:43:38","date_gmt":"2016-04-21T22:43:38","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstats1xmaster\/?post_type=chapter&#038;p=461"},"modified":"2019-01-01T18:08:57","modified_gmt":"2019-01-01T18:08:57","slug":"introduction-linear-regression-and-correlation","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/chapter\/introduction-linear-regression-and-correlation\/","title":{"raw":"Introduction: Linear Regression and Correlation","rendered":"Introduction: Linear Regression and Correlation"},"content":{"raw":"<div class=\"media-body\">\r\n<figure id=\"fs-idm37352640\" class=\"splash ui-has-child-figcaption\"><span id=\"fs-idm47477408\"><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21214810\/CNX_Stats_C12_CO.jpg\" alt=\"This is a photo of a car mechanic\u2019s shop. There are three United States Postal Services trucks being serviced, and one not being serviced.\" width=\"380\" \/><\/span><figcaption>Linear regression and correlation can help you determine if an auto mechanic\u2019s salary is related to his work experience. (credit: Joshua Rothhaas)<\/figcaption><\/figure>\r\n<div id=\"fs-idm16563264\" class=\"note chapter-objectives ui-has-child-title\"><header>\r\n<div class=\"title\">\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<section>By the end of this chapter, the student should be able to:\r\n<ul>\r\n \t<li>Discuss basic ideas of linear regression and correlation.<\/li>\r\n \t<li>Create and interpret a line of best fit.<\/li>\r\n \t<li>Calculate and interpret the correlation coefficient.<\/li>\r\n \t<li>Calculate and interpret outliers.<\/li>\r\n<\/ul>\r\n<\/section><\/div>\r\nProfessionals often want to know how two or more numeric variables are related. For example, is there a relationship between the grade on the second math exam a student takes and the grade on the final exam? If there is a relationship, what is the relationship and how strong is it?\r\n\r\n<\/div>\r\n<\/header><\/div>\r\nIn another example, your income may be determined by your education, your profession, your years of experience, and your ability. The amount you pay a repair person for labor is often determined by an initial amount plus an hourly fee.\r\n\r\nThe type of data described in the examples is <span>bivariate<\/span> data \u2014 \"bi\" for two variables. In reality, statisticians use <span>multivariate<\/span> data, meaning many variables.\r\n<p id=\"element-601\">In this chapter, you will be studying the simplest form of regression, \"linear regression\" with one independent variable (<em>x<\/em>). This involves data that fits a line in two dimensions. You will also study correlation which measures how strong the relationship is.<\/p>\r\n\r\n<\/div>","rendered":"<div class=\"media-body\">\n<figure id=\"fs-idm37352640\" class=\"splash ui-has-child-figcaption\"><span id=\"fs-idm47477408\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21214810\/CNX_Stats_C12_CO.jpg\" alt=\"This is a photo of a car mechanic\u2019s shop. There are three United States Postal Services trucks being serviced, and one not being serviced.\" width=\"380\" \/><\/span><figcaption>Linear regression and correlation can help you determine if an auto mechanic\u2019s salary is related to his work experience. (credit: Joshua Rothhaas)<\/figcaption><\/figure>\n<div id=\"fs-idm16563264\" class=\"note chapter-objectives ui-has-child-title\">\n<header>\n<div class=\"title\">\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<section>By the end of this chapter, the student should be able to:<\/p>\n<ul>\n<li>Discuss basic ideas of linear regression and correlation.<\/li>\n<li>Create and interpret a line of best fit.<\/li>\n<li>Calculate and interpret the correlation coefficient.<\/li>\n<li>Calculate and interpret outliers.<\/li>\n<\/ul>\n<\/section>\n<\/div>\n<p>Professionals often want to know how two or more numeric variables are related. For example, is there a relationship between the grade on the second math exam a student takes and the grade on the final exam? If there is a relationship, what is the relationship and how strong is it?<\/p>\n<\/div>\n<\/header>\n<\/div>\n<p>In another example, your income may be determined by your education, your profession, your years of experience, and your ability. The amount you pay a repair person for labor is often determined by an initial amount plus an hourly fee.<\/p>\n<p>The type of data described in the examples is <span>bivariate<\/span> data \u2014 &#8220;bi&#8221; for two variables. In reality, statisticians use <span>multivariate<\/span> data, meaning many variables.<\/p>\n<p id=\"element-601\">In this chapter, you will be studying the simplest form of regression, &#8220;linear regression&#8221; with one independent variable (<em>x<\/em>). This involves data that fits a line in two dimensions. You will also study correlation which measures how strong the relationship is.<\/p>\n<\/div>\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-461\">\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>Introductory Statistics . <strong>Authored by<\/strong>: Barbara Illowski, Susan Dean. <strong>Provided by<\/strong>: Open Stax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\">http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44<\/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":21,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Introductory Statistics \",\"author\":\"Barbara Illowski, Susan Dean\",\"organization\":\"Open Stax\",\"url\":\"http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-461","chapter","type-chapter","status-publish","hentry"],"part":457,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/461","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/461\/revisions"}],"predecessor-version":[{"id":1711,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/461\/revisions\/1711"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/pressbooks\/v2\/parts\/457"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/461\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/wp\/v2\/media?parent=461"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/pressbooks\/v2\/chapter-type?post=461"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/wp\/v2\/contributor?post=461"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/wp-json\/wp\/v2\/license?post=461"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}