{"id":2488,"date":"2021-10-15T11:37:16","date_gmt":"2021-10-15T11:37:16","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2488"},"modified":"2022-04-23T00:34:12","modified_gmt":"2022-04-23T00:34:12","slug":"introduction-to-testing-the-significance-of-the-correlation-coefficient","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/introduction-to-testing-the-significance-of-the-correlation-coefficient\/","title":{"raw":"Introduction to Testing the Significance of the Correlation Coefficient","rendered":"Introduction to Testing the Significance of the Correlation Coefficient"},"content":{"raw":"<h2>What you\u2019ll learn to do: Use a linear regression <em>t<\/em>-test with <em>p<\/em>-values and critical values<\/h2>\r\n<img class=\"size-medium wp-image-2489 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/10\/15113617\/pexels-maria-orlova-4916023-300x200.jpg\" alt=\"A picture of a hand holding a ice cream cone.\" width=\"300\" height=\"200\" \/>It appears from a scatterplot that there is a positive linear relationship between temperature and ice cream sales. Should we use the least-squares regression line to make a prediction about ice cream sales from temperature? How strong does the correlation coefficient need to be to say that the correlation is statistically significant? We will be addressing these questions by using a test of significance for the population correlation coefficient.","rendered":"<h2>What you\u2019ll learn to do: Use a linear regression <em>t<\/em>-test with <em>p<\/em>-values and critical values<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-2489 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/10\/15113617\/pexels-maria-orlova-4916023-300x200.jpg\" alt=\"A picture of a hand holding a ice cream cone.\" width=\"300\" height=\"200\" \/>It appears from a scatterplot that there is a positive linear relationship between temperature and ice cream sales. Should we use the least-squares regression line to make a prediction about ice cream sales from temperature? How strong does the correlation coefficient need to be to say that the correlation is statistically significant? We will be addressing these questions by using a test of significance for the population correlation coefficient.<\/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-2488\">\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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Crop person showing delicious ice cream cone on street. <strong>Authored by<\/strong>: Maria Orlova. <strong>Provided by<\/strong>: Pexels. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.pexels.com\/photo\/crop-person-showing-delicious-ice-cream-cone-on-street-4916023\/\">https:\/\/www.pexels.com\/photo\/crop-person-showing-delicious-ice-cream-cone-on-street-4916023\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/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":18,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Crop person showing delicious ice cream cone on street\",\"author\":\"Maria Orlova\",\"organization\":\"Pexels\",\"url\":\"https:\/\/www.pexels.com\/photo\/crop-person-showing-delicious-ice-cream-cone-on-street-4916023\/\",\"project\":\"\",\"license\":\"pd\",\"license_terms\":\"\"},{\"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-2488","chapter","type-chapter","status-publish","hentry"],"part":303,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2488","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":5,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2488\/revisions"}],"predecessor-version":[{"id":3981,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2488\/revisions\/3981"}],"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\/2488\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=2488"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=2488"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=2488"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=2488"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}