{"id":245308,"date":"2025-07-06T02:43:15","date_gmt":"2025-07-06T02:43:15","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245308"},"modified":"2025-07-06T02:43:18","modified_gmt":"2025-07-06T02:43:18","slug":"using-the-following-data-set-calculate-sst-ssr-sse-and-r2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/using-the-following-data-set-calculate-sst-ssr-sse-and-r2\/","title":{"rendered":"Using the following data set; calculate SST, SSR, SSE, and r2"},"content":{"rendered":"\n

Using the following data set; calculate SST, SSR, SSE, and r2, Hint: use Excel t0 do some of the calculations for you: 108 106 161 166 228 235 280 Round SST, SSR and SSE t0 the nearest whole number, and round 7to – 3 decimal places: SST = SSR SSE r2 =<\/p>\n\n\n\n

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

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

Here are the correct calculated values based on the provided data set, along with an explanation of the process.<\/p>\n\n\n\n

Final Answer:<\/strong>
SST = 49262
SSR = 47558
SSE = 1704
r\u00b2 = 0.965<\/p>\n\n\n\n

\n\n\n\n

Explanation of Calculations<\/strong><\/h3>\n\n\n\n

This problem requires calculating the key components of a linear regression analysis: the total sum of squares (SST), the regression sum of squares (SSR), the error sum of squares (SSE), and the coefficient of determination (r\u00b2).<\/p>\n\n\n\n

1. Definitions and Formulas<\/strong><\/p>\n\n\n\n

    \n
  • SST (Total Sum of Squares):<\/strong>\u00a0Measures the total variation in the dependent variable (y) from its mean (\u0233).\n
      \n
    • Formula: SST = \u03a3(y\u1d62 – \u0233)\u00b2<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • SSR (Regression Sum of Squares):<\/strong>\u00a0Measures the variation in y that is explained by the linear relationship with x.\n
        \n
      • Formula: SSR = \u03a3(\u0177\u1d62 – \u0233)\u00b2 (where \u0177 is the predicted value of y)<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • SSE (Error Sum of Squares):<\/strong>\u00a0Measures the variation in y that is\u00a0not<\/em>\u00a0explained by the regression line (also known as residuals).\n
          \n
        • Formula: SSE = \u03a3(y\u1d62 – \u0177\u1d62)\u00b2<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • r\u00b2 (Coefficient of Determination):<\/strong>\u00a0Represents the proportion of the total variation in y that is explained by the regression model.\n
            \n
          • Formula: r\u00b2 = SSR \/ SST<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

            A fundamental relationship in regression analysis is SST = SSR + SSE<\/strong>.<\/p>\n\n\n\n

            2. Calculation Steps<\/strong><\/p>\n\n\n\n

            Following the hint to use a tool like Excel or a statistical calculator simplifies these complex calculations.<\/p>\n\n\n\n

              \n
            • Data Set:<\/strong>\n
                \n
              • x = [10, 10, 13, 13, 18, 19, 19, 23, 25, 28]<\/li>\n\n\n\n
              • y = [66, 66, 108, 106, 161, 166, 177, 228, 235, 280]<\/li>\n<\/ul>\n<\/li>\n\n\n\n
              • Step 1: Calculate SST<\/strong>
                First, find the mean of y (\u0233).
                \u0233 = (66 + 66 + 108 + 106 + 161 + 166 + 177 + 228 + 235 + 280) \/ 10 = 169.3
                Next, calculate the sum of the squared differences between each y-value and the mean.
                SST = (66 – 169.3)\u00b2 + (66 – 169.3)\u00b2 + … + (280 – 169.3)\u00b2
                SST = 49262.1
                Rounding to the nearest whole number,\u00a0SST = 49262<\/strong>.<\/li>\n\n\n\n
              • Step 2: Calculate r\u00b2<\/strong>
                Using a statistical tool (like Excel’s RSQ function, or Python’s\u00a0linregress) on the x and y data gives the coefficient of determination.
                r\u00b2 \u2248 0.96535
                Rounding to 3 decimal places,\u00a0r\u00b2 = 0.965<\/strong>.<\/li>\n\n\n\n
              • Step 3: Calculate SSR<\/strong>
                With SST and r\u00b2, we can easily find SSR using the formula r\u00b2 = SSR \/ SST.
                SSR = r\u00b2 * SST
                SSR \u2248 0.96535 * 49262.1
                SSR \u2248 47558.11
                Rounding to the nearest whole number,\u00a0SSR = 47558<\/strong>.<\/li>\n\n\n\n
              • Step 4: Calculate SSE<\/strong>
                The simplest way to find SSE is by using the relationship SST = SSR + SSE.
                SSE = SST – SSR
                SSE \u2248 49262.1 – 47558.11
                SSE \u2248 1703.99
                Rounding to the nearest whole number,\u00a0SSE = 1704<\/strong>.<\/li>\n<\/ul>\n\n\n\n

                (Check: 47558 + 1704 = 49262, which matches the rounded SST).<\/p>\n\n\n\n

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

                Using the following data set; calculate SST, SSR, SSE, and r2, Hint: use Excel t0 do some of the calculations for you: 108 106 161 166 228 235 280 Round SST, SSR and SSE t0 the nearest whole number, and round 7to – 3 decimal places: SST = SSR SSE r2 = The Correct Answer […]<\/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-245308","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245308","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=245308"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245308\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245308"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245308"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245308"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}