{"id":234585,"date":"2025-06-14T09:52:11","date_gmt":"2025-06-14T09:52:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234585"},"modified":"2025-06-14T09:52:13","modified_gmt":"2025-06-14T09:52:13","slug":"a-sports-statistician-investigated-the-relationship-between-a-professional-basketball-players-salary-in-hundreds-of-thousands-of-dollars-and-the-percentage-of-shots-in-decimal-form-that-she-made","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/a-sports-statistician-investigated-the-relationship-between-a-professional-basketball-players-salary-in-hundreds-of-thousands-of-dollars-and-the-percentage-of-shots-in-decimal-form-that-she-made\/","title":{"rendered":"A sports statistician investigated the relationship between a professional basketball player&#8217;s salary, in hundreds of thousands of dollars, and the percentage of shots, in decimal form, that she made."},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">A sports statistician investigated the relationship between a professional basketball player's salary, in hundreds of thousands of dollars, and the percentage of shots, in decimal form, that she made. The statistician performed a linear regression on the data with a graphing calculator. The results are shown. LinReg y = ax+b a = .2769230769 b = .3884615385 r2&nbsp;= .8613966678 r = .9281145769 What conclusion can be made from the data? Select from the drop-down menus to correctly complete the sentence. Rounded to the nearest hundredth, the correlation coefficient is Choose... so there Choose... a strong correlation between salary and percentage of shots made.<\/pre>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><br>Rounded to the nearest hundredth, the correlation coefficient is <strong>0.93<\/strong>, so there <strong>is<\/strong> a strong correlation between salary and percentage of shots made.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation (300 words):<\/strong><\/p>\n\n\n\n<p>The correlation coefficient, often represented as <strong>r<\/strong>, measures the strength and direction of the linear relationship between two variables. Its value ranges from -1 to 1. A value close to 1 indicates a strong positive linear relationship, a value close to -1 indicates a strong negative linear relationship, and a value near 0 suggests no linear relationship.<\/p>\n\n\n\n<p>In this case, the statistician obtained <strong>r = 0.9281145769<\/strong>, which rounds to <strong>0.93<\/strong> when taken to the nearest hundredth. This value lies very close to 1, which indicates a strong positive correlation.<\/p>\n\n\n\n<p>A strong positive correlation means that as one variable increases, the other tends to increase as well. Here, the two variables being compared are a basketball player&#8217;s <strong>salary (in hundreds of thousands of dollars)<\/strong> and the <strong>percentage of shots made (in decimal form)<\/strong>. A high correlation coefficient like 0.93 implies that players who make a higher percentage of their shots tend to earn higher salaries. Conversely, those with lower shooting percentages tend to earn less.<\/p>\n\n\n\n<p>The linear regression equation provided, <strong>y = 0.2769230769x + 0.3884615385<\/strong>, further supports this interpretation. The positive slope (<strong>a = 0.2769<\/strong>) suggests that for each unit increase in shooting percentage (measured in decimal form), the predicted salary increases.<\/p>\n\n\n\n<p>Therefore, the data shows a clear trend: better shooting accuracy is associated with higher salaries in professional basketball. The strength of the correlation suggests that shooting performance is a significant factor in determining pay, although other factors like experience, defensive skill, and teamwork may also influence salary but are not included in this analysis.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-445.jpeg\" alt=\"\" class=\"wp-image-234586\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A sports statistician investigated the relationship between a professional basketball player&#8217;s salary, in hundreds of thousands of dollars, and the percentage of shots, in decimal form, that she made. The statistician performed a linear regression on the data with a graphing calculator. The results are shown. LinReg y = ax+b a = .2769230769 b = [&hellip;]<\/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-234585","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234585","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=234585"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234585\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234585"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234585"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}