{"id":170736,"date":"2024-11-19T22:51:20","date_gmt":"2024-11-19T22:51:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=170736"},"modified":"2024-11-19T22:51:22","modified_gmt":"2024-11-19T22:51:22","slug":"which-of-the-following-statements-about-correlation-is-true","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/19\/which-of-the-following-statements-about-correlation-is-true\/","title":{"rendered":"Which of the following statements about correlation is \u200btrue"},"content":{"rendered":"\n<p>Which of the following statements about correlation is\u200b true? Choose the correct answer below.<br>A. We say that there is a positive correlation between x and y if there is no distinct pattern in the scatterplot.<br>B. We say that there is a positive correlation between x and y if the\u200b x-values increase as the corresponding\u200b y-values increase.<br>C. We say that there is a negative correlation between x and y if the\u200b x-values increase as the corresponding\u200b y-values increase.<br>D. We say that there is a positive correlation between x and y if the\u200b x-values increase as the corresponding\u200b y-values decreas<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is <strong>B. We say that there is a positive correlation between x and y if the x-values increase as the corresponding y-values increase.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>Correlation refers to the relationship between two variables, typically represented as <strong>x<\/strong> and <strong>y<\/strong>, and how changes in one variable relate to changes in the other. The correlation can be positive, negative, or there can be no correlation at all. Understanding the different types of correlation helps in interpreting the relationship between the variables. Let\u2019s break down each of the choices:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A. &#8220;We say that there is a positive correlation between x and y if there is no distinct pattern in the scatterplot.&#8221;<\/strong><\/li>\n\n\n\n<li>This statement is <strong>incorrect<\/strong>. If there is no distinct pattern in the scatterplot, it indicates <strong>no correlation<\/strong> or a very weak correlation between the variables. A positive correlation implies that as <strong>x<\/strong> increases, <strong>y<\/strong> also increases, and this would be visible in the scatterplot as a clear upward trend.<\/li>\n\n\n\n<li><strong>B. &#8220;We say that there is a positive correlation between x and y if the x-values increase as the corresponding y-values increase.&#8221;<\/strong><\/li>\n\n\n\n<li>This statement is <strong>correct<\/strong>. A <strong>positive correlation<\/strong> means that as the <strong>x-values<\/strong> increase, the corresponding <strong>y-values<\/strong> also increase. In a scatterplot, this would be represented by points that tend to form an upward trend. A real-world example could be the relationship between hours studied and test scores: generally, as study time (x) increases, test scores (y) also tend to increase, indicating a positive correlation.<\/li>\n\n\n\n<li><strong>C. &#8220;We say that there is a negative correlation between x and y if the x-values increase as the corresponding y-values increase.&#8221;<\/strong><\/li>\n\n\n\n<li>This statement is <strong>incorrect<\/strong>. A <strong>negative correlation<\/strong> means that as <strong>x<\/strong> increases, <strong>y<\/strong> decreases. If the <strong>x-values<\/strong> increase and the corresponding <strong>y-values<\/strong> increase, it is a positive correlation, not negative. For a negative correlation, you would expect the scatterplot to show a downward trend.<\/li>\n\n\n\n<li><strong>D. &#8220;We say that there is a positive correlation between x and y if the x-values increase as the corresponding y-values decrease.&#8221;<\/strong><\/li>\n\n\n\n<li>This statement is <strong>incorrect<\/strong>. If <strong>x-values<\/strong> increase and <strong>y-values<\/strong> decrease, this indicates a <strong>negative correlation<\/strong>, not a positive one. The scatterplot for this would show a downward trend, meaning as <strong>x<\/strong> increases, <strong>y<\/strong> decreases.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<p>A <strong>positive correlation<\/strong> is observed when both variables move in the same direction, i.e., as <strong>x<\/strong> increases, <strong>y<\/strong> also increases. This is visually represented in a scatterplot where the data points generally rise from left to right. Conversely, a <strong>negative correlation<\/strong> occurs when one variable increases while the other decreases. Thus, option <strong>B<\/strong> is the correct answer, as it accurately describes a positive correlation between <strong>x<\/strong> and <strong>y<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which of the following statements about correlation is\u200b true? Choose the correct answer below.A. We say that there is a positive correlation between x and y if there is no distinct pattern in the scatterplot.B. We say that there is a positive correlation between x and y if the\u200b x-values increase as the corresponding\u200b y-values [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-170736","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170736","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=170736"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170736\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=170736"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=170736"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=170736"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}