{"id":53999,"date":"2024-04-16T00:02:43","date_gmt":"2024-04-16T00:02:43","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=53999"},"modified":"2024-04-16T00:02:43","modified_gmt":"2024-04-16T00:02:43","slug":"a-measure-of-goodness-of-fit-for-the-estimated-regression-equation-is-the","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-measure-of-goodness-of-fit-for-the-estimated-regression-equation-is-the\/","title":{"rendered":"A measure of goodness of fit for the estimated regression equation is the"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;multiple coefficient of determination&#8221; option2=&#8221;mean square due to error&#8221; option3=&#8221;mean square due to regression&#8221; option4=&#8221;none of the above&#8221; correct=&#8221;option1&#8243;]<!--more--><\/p>\n<p>The correct answer is A. multiple coefficient of determination.<\/p>\n<p>The multiple coefficient of determination, denoted by $R^2$, is a measure of how well the data fit the estimated regression equation. It is calculated by taking the sum of squares of the residuals (SSR) and dividing it by the total sum of squares (SST). The closer $R^2$ is to 1, the better the fit of the data to the estimated regression equation.<\/p>\n<p>The mean square due to error (MSE) is a measure of the variability of the residuals. It is calculated by taking the sum of squares of the residuals (SSR) and dividing it by the number of degrees of freedom. The MSE is used to calculate the standard error of the estimate, which is a measure of the precision of the estimated regression equation.<\/p>\n<p>The mean square due to regression (MSR) is a measure of the variability of the predicted values. It is calculated by taking the sum of squares of the regression (SSR) and dividing it by the number of degrees of freedom. The MSR is used to calculate the F statistic, which is used to test the significance of the regression model.<\/p>\n<p>Therefore, the multiple coefficient of determination is the best measure of goodness of fit for the estimated regression equation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;multiple coefficient of determination&#8221; option2=&#8221;mean square due to error&#8221; option3=&#8221;mean square due to regression&#8221; option4=&#8221;none of the above&#8221; correct=&#8221;option1&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[729],"tags":[],"class_list":["post-53999","post","type-post","status-publish","format-standard","hentry","category-machine-learning","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A measure of goodness of fit for the estimated regression equation is the<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-measure-of-goodness-of-fit-for-the-estimated-regression-equation-is-the\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A measure of goodness of fit for the estimated regression equation is the\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=&#8221;multiple coefficient of determination&#8221; 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