{"id":198543,"date":"2025-03-10T06:41:16","date_gmt":"2025-03-10T06:41:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=198543"},"modified":"2025-03-10T06:41:18","modified_gmt":"2025-03-10T06:41:18","slug":"which-of-the-following-statements-is-true-about-the-correlation-coefficient","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/10\/which-of-the-following-statements-is-true-about-the-correlation-coefficient\/","title":{"rendered":"Which of the following statements is true about the correlation coefficient"},"content":{"rendered":"\n

Which of the following statements is true about the correlation coefficient?
Multiple Choice<\/p>\n\n\n\n

A. A negative correlation coefficient indicates a direct relationship between two quantitative variables.
B. A positive correlation coefficient indicates an indirect relationship between two quantitative variables.
C. A correlation coefficient of zero means that two quantitative variables are not linearly related to each other.
D. The correlation coefficient ranges in value from -3 to +3.<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

Correct Answer:<\/strong><\/h3>\n\n\n\n

C. A correlation coefficient of zero means that two quantitative variables are not linearly related to each other.<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/strong><\/h3>\n\n\n\n

The correlation coefficient, commonly denoted as r<\/strong>, measures the strength and direction of the linear relationship between two quantitative variables. It takes values between -1 and +1<\/strong>.<\/p>\n\n\n\n

    \n
  • A correlation coefficient of +1<\/strong> indicates a perfect positive linear relationship<\/strong>, meaning that as one variable increases, the other increases proportionally.<\/li>\n\n\n\n
  • A correlation coefficient of -1<\/strong> indicates a perfect negative linear relationship<\/strong>, meaning that as one variable increases, the other decreases proportionally.<\/li>\n\n\n\n
  • A correlation coefficient of 0<\/strong> suggests no linear relationship<\/strong> between the two variables, though there may still be a non-linear relationship.<\/li>\n<\/ul>\n\n\n\n

    Let\u2019s analyze the given answer choices:<\/p>\n\n\n\n

      \n
    1. Option A (Incorrect)<\/strong>: A negative correlation coefficient<\/strong> does not indicate a direct relationship<\/strong>. Instead, it shows an inverse relationship<\/strong>, where one variable increases while the other decreases.<\/li>\n\n\n\n
    2. Option B (Incorrect)<\/strong>: A positive correlation coefficient<\/strong> does not indicate an indirect relationship<\/strong>. Instead, it shows a direct relationship<\/strong>, where both variables increase or decrease together.<\/li>\n\n\n\n
    3. Option C (Correct)<\/strong>: A correlation coefficient of zero<\/strong> means that there is no linear relationship<\/strong> between the two variables, making this the correct answer.<\/li>\n\n\n\n
    4. Option D (Incorrect)<\/strong>: The correlation coefficient ranges from -1 to +1<\/strong>, not from -3 to +3<\/strong>.<\/li>\n<\/ol>\n\n\n\n

      Thus, the correct answer is C<\/strong>, as a correlation coefficient of zero means no linear relationship exists between the two variables.<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      The image above visually represents different types of correlation:<\/p>\n\n\n\n

        \n
      1. Positive Correlation (Left Plot, Blue):<\/strong> As one variable increases, the other also increases, indicating a direct relationship.<\/li>\n\n\n\n
      2. Negative Correlation (Middle Plot, Red):<\/strong> As one variable increases, the other decreases, showing an inverse relationship.<\/li>\n\n\n\n
      3. No Correlation (Right Plot, Green):<\/strong> The points are scattered randomly, indicating no linear relationship.<\/li>\n<\/ol>\n\n\n\n

        This visualization supports the explanation that a correlation coefficient of zero means no linear relationship, making option C<\/strong> the correct answer.<\/p>\n","protected":false},"excerpt":{"rendered":"

        Which of the following statements is true about the correlation coefficient?Multiple Choice A. A negative correlation coefficient indicates a direct relationship between two quantitative variables.B. A positive correlation coefficient indicates an indirect relationship between two quantitative variables.C. A correlation coefficient of zero means that two quantitative variables are not linearly related to each other.D. The […]<\/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-198543","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/198543","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=198543"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/198543\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=198543"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=198543"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=198543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}