{"id":193340,"date":"2025-02-19T10:26:16","date_gmt":"2025-02-19T10:26:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=193340"},"modified":"2025-02-19T10:26:19","modified_gmt":"2025-02-19T10:26:19","slug":"the-value-of-the-durbin-watson-d-statistic-always-falls-in-the-interval-from-0-to-1","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/19\/the-value-of-the-durbin-watson-d-statistic-always-falls-in-the-interval-from-0-to-1\/","title":{"rendered":"\u00a0The value of the Durbin-Watson d-statistic always falls in the interval from 0 to 1"},"content":{"rendered":"\n

 The value of the Durbin-Watson d-statistic always falls in the interval from 0 to 1.<\/p>\n\n\n\n

A) True<\/p>\n\n\n\n

B) False<\/p>\n\n\n\n

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

The correct answer is B) False<\/strong>.<\/p>\n\n\n\n

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

The Durbin-Watson (DW) statistic is used to test for autocorrelation in the residuals from a regression analysis, particularly in time series data. Autocorrelation refers to the correlation of a time series with its own past values. The DW statistic is valuable for checking whether the residuals from a regression model exhibit patterns over time, which can violate the assumption of independence in linear regression.<\/p>\n\n\n\n

The value of the Durbin-Watson statistic actually ranges between 0 and 4, not 0 to 1. Here\u2019s a breakdown of the interpretation:<\/p>\n\n\n\n

    \n
  • DW = 2<\/strong>: No autocorrelation. This suggests that there is no significant correlation between the residuals.<\/li>\n\n\n\n
  • DW < 2<\/strong>: Positive autocorrelation. This indicates that residuals from earlier periods tend to be similar to residuals from later periods.<\/li>\n\n\n\n
  • DW > 2<\/strong>: Negative autocorrelation. This suggests that residuals from earlier periods tend to be opposite in sign from those of later periods.<\/li>\n<\/ul>\n\n\n\n

    Values closer to 0 indicate strong positive autocorrelation, while values closer to 4 suggest strong negative autocorrelation.<\/p>\n\n\n\n

    The DW statistic is computed using the following formula:<\/p>\n\n\n\n

    [
    DW = \\frac{\\sum_{t=2}^{n} (e_t – e_{t-1})^2}{\\sum_{t=1}^{n} e_t^2}
    ]<\/p>\n\n\n\n

    Where (e_t) represents the residuals at time (t). The statistic measures the squared differences between consecutive residuals, which is why it provides information about autocorrelation.<\/p>\n\n\n\n

    If the statistic is closer to 0, it indicates a higher level of autocorrelation between consecutive residuals. A value close to 4 suggests the residuals are negatively correlated.<\/p>\n\n\n\n

    The Durbin-Watson test is commonly used in regression analysis to determine the validity of the assumption of no autocorrelation. If there is autocorrelation, model adjustments or transformations may be needed.<\/p>\n\n\n\n

    \n\n\n\n

    I will now generate an image to visually explain the range of the Durbin-Watson statistic.<\/p>\n\n\n\n

    Here is the visual representation of the Durbin-Watson statistic range. It shows the values from 0 to 4, where 0 indicates strong positive autocorrelation, 2 indicates no autocorrelation, and 4 indicates strong negative autocorrelation.<\/p>\n\n\n\n

    Let me know if you need further details or clarification!<\/p>\n\n\n\n

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

     The value of the Durbin-Watson d-statistic always falls in the interval from 0 to 1. A) True B) False The Correct Answer and Explanation is : The correct answer is B) False. Explanation: The Durbin-Watson (DW) statistic is used to test for autocorrelation in the residuals from a regression analysis, particularly in time series data. […]<\/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-193340","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193340","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=193340"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193340\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=193340"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=193340"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=193340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}