{"id":19335,"date":"2025-06-13T16:06:38","date_gmt":"2025-06-13T16:06:38","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=19335"},"modified":"2025-06-13T16:06:39","modified_gmt":"2025-06-13T16:06:39","slug":"if-the-coefficient-of-determination-r-squared-1-00","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/if-the-coefficient-of-determination-r-squared-1-00\/","title":{"rendered":"If the coefficient of determination R-squared = 1.00"},"content":{"rendered":"\n<p>If the coefficient of determination R-squared = 1.00, then A. the explained variation equals the unexplained variation B. there is no unexplained variation C. the Y-intercept (B0) must equal 0 D. there is no explained variation<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p><strong>Correct Answer: B. there is no unexplained variation<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300 words)<\/strong><\/h3>\n\n\n\n<p>The coefficient of determination, <strong>R-squared (R\u00b2)<\/strong>, is a statistical measure that represents the proportion of the variance in the dependent variable (<strong>Y<\/strong>) that is predictable or explained by the independent variable(s) (<strong>X<\/strong>) in a regression model.<\/p>\n\n\n\n<p>R-squared values range from <strong>0 to 1<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>An R\u00b2 of <strong>0<\/strong> means that the model explains none of the variation in the response variable.<\/li>\n\n\n\n<li>An R\u00b2 of <strong>1.00<\/strong> means that the model explains <strong>100%<\/strong> of the variation in the response variable.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Why Option B is Correct<\/strong><\/h3>\n\n\n\n<p>If <strong>R\u00b2 = 1.00<\/strong>, it implies <strong>perfect prediction<\/strong> by the regression model. This means:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Every data point lies exactly on the regression line.<\/li>\n\n\n\n<li><strong>There is no error (or residual)<\/strong> between the observed Y values and the predicted Y values.<\/li>\n\n\n\n<li>As a result, the <strong>unexplained variation (residual sum of squares)<\/strong> is <strong>zero<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Thus, <strong>all variation<\/strong> in Y is <strong>explained by X<\/strong>, and <strong>there is no unexplained variation<\/strong>, making <strong>option B<\/strong> the correct choice.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Why the Other Options Are Incorrect<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A. &#8220;The explained variation equals the unexplained variation&#8221;<\/strong><br>Incorrect. This would be true if R\u00b2 = 0.5, not 1.0. If R\u00b2 = 1.00, all variation is explained, and unexplained variation is zero.<\/li>\n\n\n\n<li><strong>C. &#8220;The Y-intercept (B\u2080) must equal 0&#8221;<\/strong><br>Incorrect. R\u00b2 = 1.00 does not require the intercept to be 0. A model can perfectly fit the data and still have a non-zero intercept.<\/li>\n\n\n\n<li><strong>D. &#8220;There is no explained variation&#8221;<\/strong><br>Incorrect. The opposite is true. When R\u00b2 = 1.00, <strong>all<\/strong> variation is explained.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Conclusion<\/strong><\/h3>\n\n\n\n<p>A perfect R-squared value of 1.00 signifies a flawless fit of the regression model to the data, meaning <strong>there is no unexplained variation<\/strong>, making <strong>option B<\/strong> the correct answer.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>If the coefficient of determination R-squared = 1.00, then A. the explained variation equals the unexplained variation B. there is no unexplained variation C. the Y-intercept (B0) must equal 0 D. there is no explained variation The correct answer and explanation is: Correct Answer: B. there is no unexplained variation Explanation (300 words) The coefficient [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-19335","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19335","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=19335"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19335\/revisions"}],"predecessor-version":[{"id":19336,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19335\/revisions\/19336"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=19335"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=19335"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=19335"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}