{"id":211316,"date":"2025-05-03T16:41:13","date_gmt":"2025-05-03T16:41:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=211316"},"modified":"2025-05-03T16:41:15","modified_gmt":"2025-05-03T16:41:15","slug":"if-a-data-set-has-a-relationship-that-is-best-described-by-a-linear-model","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/03\/if-a-data-set-has-a-relationship-that-is-best-described-by-a-linear-model\/","title":{"rendered":"If a data set has a relationship that is best described by a linear model"},"content":{"rendered":"\n

If a data set has a relationship that is best described by a linear model, then the residual plot will<\/p>\n\n\n\n

A) also have a linear pattern with a similar correlation. <\/p>\n\n\n\n

B) have no pattern with a correlation near 0. <\/p>\n\n\n\n

C) have a curved pattern, like a parabola. <\/p>\n\n\n\n

D) be an unknown shape. <\/p>\n\n\n\n

E) none of these<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

The correct answer is B) have no pattern with a correlation near 0.<\/strong><\/p>\n\n\n\n

In regression analysis, when a data set follows a linear relationship, it means that the data points align closely to a straight line, and the model used to describe this relationship fits the data well. A residual plot is a graphical representation of the differences between the observed values and the predicted values (i.e., the residuals). To understand the expected pattern of the residual plot, it\u2019s important to know what residuals indicate.<\/p>\n\n\n\n

Residuals and Their Role<\/h3>\n\n\n\n

Residuals are the vertical distances between the data points and the line predicted by the model. If the model is appropriate, these residuals should be randomly scattered around the horizontal axis, meaning that there should be no systematic pattern in the residuals.<\/p>\n\n\n\n

Why Option B is Correct<\/h3>\n\n\n\n

When a linear model fits the data well, the residual plot should show no obvious pattern. This means the residuals will appear randomly scattered around the horizontal axis, suggesting that there is no correlation between the residuals and the predicted values. Additionally, the correlation between the residuals and the predicted values should be near 0, indicating that the residuals do not provide further information about the relationship between the variables.<\/p>\n\n\n\n

Why the Other Options are Incorrect<\/h3>\n\n\n\n
    \n
  • A) also have a linear pattern with a similar correlation:<\/strong> If the residual plot shows a linear pattern, this suggests that the model is not appropriate and that a non-linear relationship exists between the variables.<\/li>\n\n\n\n
  • C) have a curved pattern, like a parabola:<\/strong> A curved pattern indicates that the relationship between the variables is not linear, and the model needs to be adjusted to better fit the data.<\/li>\n\n\n\n
  • D) be an unknown shape:<\/strong> Residual plots for well-fitted linear models have a specific expected shape (random scatter), not an unknown or irregular shape.<\/li>\n\n\n\n
  • E) none of these provide the correct answer:<\/strong> Since B is the correct answer, this option is incorrect.<\/li>\n<\/ul>\n\n\n\n

    Conclusion<\/h3>\n\n\n\n

    A well-fitted linear model should result in residuals that are randomly scattered with no discernible pattern. This randomness indicates that the model has accounted for all the linear trends in the data, and there are no additional patterns or structures left unexplained by the model. Therefore, option B is the correct choice.<\/p>\n","protected":false},"excerpt":{"rendered":"

    If a data set has a relationship that is best described by a linear model, then the residual plot will A) also have a linear pattern with a similar correlation. B) have no pattern with a correlation near 0. C) have a curved pattern, like a parabola. D) be an unknown shape. E) none of […]<\/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-211316","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211316","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=211316"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211316\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=211316"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=211316"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=211316"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}