{"id":1246,"date":"2021-07-01T16:34:24","date_gmt":"2021-07-01T20:34:24","guid":{"rendered":"https:\/\/openbooks.macewan.ca\/rcommander\/?post_type=part&#038;p=1246"},"modified":"2024-02-08T14:45:50","modified_gmt":"2024-02-08T19:45:50","slug":"chapter-13-descriptive-and-inferential-methods-in-simple-linear-regression","status":"publish","type":"part","link":"https:\/\/openbooks.macewan.ca\/introstats\/part\/chapter-13-descriptive-and-inferential-methods-in-simple-linear-regression\/","title":{"raw":"Chapter 13: Descriptive and Inferential Methods in Simple Linear Regression","rendered":"Chapter 13: Descriptive and Inferential Methods in Simple Linear Regression"},"content":{"raw":"<h2><strong>Overview<\/strong><\/h2>\r\nThis chapter introduces simple linear regression, which models the relationship between two quantitative variables using a straight line; we discuss descriptive and inferential methods in simple linear regression.\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nAs a result of completing this chapter, you will be able to do the following:\r\n<ul>\r\n \t<li>Identify situations where simple linear regression should be used.<\/li>\r\n \t<li>Explain the main idea of the method of least squares.<\/li>\r\n \t<li>Calculate the least-squares fitted line.<\/li>\r\n \t<li>Calculate and interpret the correlation coefficient <em>r<\/em>.<\/li>\r\n \t<li>Calculate and interpret the coefficient of determination <em>r<\/em><sup>2<\/sup>.<\/li>\r\n \t<li>Explain the terms in a simple linear regression model.<\/li>\r\n \t<li>Conduct a [latex]t[\/latex] test and obtain a [latex]t[\/latex] confidence interval for the slope parameter [latex]\\beta_1[\/latex].<\/li>\r\n \t<li>Explain the difference between confidence intervals and prediction intervals.<\/li>\r\n \t<li>Obtain a confidence interval for the conditional mean and a prediction interval for a single response.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>","rendered":"<h2><strong>Overview<\/strong><\/h2>\n<p>This chapter introduces simple linear regression, which models the relationship between two quantitative variables using a straight line; we discuss descriptive and inferential methods in simple linear regression.<\/p>\n<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>As a result of completing this chapter, you will be able to do the following:<\/p>\n<ul>\n<li>Identify situations where simple linear regression should be used.<\/li>\n<li>Explain the main idea of the method of least squares.<\/li>\n<li>Calculate the least-squares fitted line.<\/li>\n<li>Calculate and interpret the correlation coefficient <em>r<\/em>.<\/li>\n<li>Calculate and interpret the coefficient of determination <em>r<\/em><sup>2<\/sup>.<\/li>\n<li>Explain the terms in a simple linear regression model.<\/li>\n<li>Conduct a [latex]t[\/latex] test and obtain a [latex]t[\/latex] confidence interval for the slope parameter [latex]\\beta_1[\/latex].<\/li>\n<li>Explain the difference between confidence intervals and prediction intervals.<\/li>\n<li>Obtain a confidence interval for the conditional mean and a prediction interval for a single response.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n","protected":false},"parent":0,"menu_order":13,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-1246","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/1246","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":11,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/1246\/revisions"}],"predecessor-version":[{"id":4916,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/1246\/revisions\/4916"}],"wp:attachment":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/media?parent=1246"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/contributor?post=1246"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/license?post=1246"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}