{"id":256201,"date":"2025-07-14T05:41:38","date_gmt":"2025-07-14T05:41:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=256201"},"modified":"2025-07-14T05:41:42","modified_gmt":"2025-07-14T05:41:42","slug":"you-are-given-the-following-information-about-y-and-dependent-variable-independent-variable-in-addition-the-least-squares-method-yielded-the-following-equation","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/14\/you-are-given-the-following-information-about-y-and-dependent-variable-independent-variable-in-addition-the-least-squares-method-yielded-the-following-equation\/","title":{"rendered":"You are given the following information about y and Dependent Variable Independent Variable In addition, the least squares method yielded the following equation"},"content":{"rendered":"\n

You are given the following information about y and Dependent Variable Independent Variable In addition, the least squares method yielded the following equation: y = 12.06 + 0.12x Calculate the value of SSE; round your answer to three decimal places.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To calculate the value of the Sum of Squared Errors (SSE)<\/strong>, we need more information than just the equation of the regression line. Specifically, we need the observed values of y<\/strong> and the corresponding predicted values of y<\/strong> based on the regression equation. However, I will outline the process for calculating the SSE using the regression equation.<\/p>\n\n\n\n

The regression equation is:
y=12.06+0.12xy = 12.06 + 0.12xy=12.06+0.12x<\/p>\n\n\n\n

Steps to Calculate SSE:<\/h3>\n\n\n\n
    \n
  1. Obtain the Observed Values of y<\/strong>:\n
      \n
    • These are the actual values of the dependent variable y<\/strong> that you have collected in your dataset.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Calculate the Predicted Values of y (\u0177)<\/strong>:
      • For each value of x<\/strong>, substitute it into the regression equation to calculate the predicted value of y<\/strong> (denoted as \u0177<\/strong>).<\/li><\/ul>y^=12.06+0.12x\u0177 = 12.06 + 0.12xy^\u200b=12.06+0.12x Example:
        If x = 5<\/strong>, then:
        y^=12.06+0.12(5)=12.06+0.60=12.66\u0177 = 12.06 + 0.12(5) = 12.06 + 0.60 = 12.66y^\u200b=12.06+0.12(5)=12.06+0.60=12.66<\/li>\n\n\n\n
      • Calculate the Errors (Residuals)<\/strong>:
        • The error (or residual) for each observation is the difference between the observed value y<\/strong> and the predicted value \u0177<\/strong>.<\/li><\/ul>e=y\u2212y^e = y – \u0177e=y\u2212y^\u200b Example:
          If the observed value is y = 14<\/strong>, and the predicted value \u0177 = 12.66<\/strong>, then:
          e=14\u221212.66=1.34e = 14 – 12.66 = 1.34e=14\u221212.66=1.34<\/li>\n\n\n\n
        • Square the Errors<\/strong>:
          • For each observation, square the error (residual).<\/li><\/ul>e2=(y\u2212y^)2e^2 = (y – \u0177)^2e2=(y\u2212y^\u200b)2<\/li>\n\n\n\n
          • Sum the Squared Errors<\/strong>:
            • Sum all the squared errors to obtain the Sum of Squared Errors (SSE)<\/strong>.<\/li><\/ul>SSE=\u2211(y\u2212y^)2SSE = \\sum (y – \u0177)^2SSE=\u2211(y\u2212y^\u200b)2 This step gives the total squared deviation of the observed values from the predicted values, which is the SSE.<\/li>\n<\/ol>\n\n\n\n

              Formula Recap:<\/h3>\n\n\n\n

              SSE=\u2211(y\u2212(12.06+0.12x))2SSE = \\sum (y – (12.06 + 0.12x))^2SSE=\u2211(y\u2212(12.06+0.12x))2<\/p>\n\n\n\n

              Once you have all the values of y<\/strong> and x<\/strong>, you can compute SSE<\/strong> by following the outlined steps.<\/p>\n\n\n\n

              \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

              You are given the following information about y and Dependent Variable Independent Variable In addition, the least squares method yielded the following equation: y = 12.06 + 0.12x Calculate the value of SSE; round your answer to three decimal places. The Correct Answer and Explanation is: To calculate the value of the Sum of Squared […]<\/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-256201","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256201","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=256201"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256201\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=256201"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=256201"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=256201"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}