{"id":233310,"date":"2025-06-13T04:24:16","date_gmt":"2025-06-13T04:24:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233310"},"modified":"2025-06-13T04:24:18","modified_gmt":"2025-06-13T04:24:18","slug":"how-well-do-professional-golfers-putt-from-different-distances","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/how-well-do-professional-golfers-putt-from-different-distances\/","title":{"rendered":"How well do professional golfers putt from different distances"},"content":{"rendered":"\n
How well do professional golfers putt from different distances? Researchers collected data on the percent of putts made for various distances to the hole (in feet). Model: ln(percent made) vs. Distance Predictor Coef SE Coef T P Constant 4.6649 0.0825 56.511 0.0000 Distance -0.1091 0.0067 -16.24 0.0000 S = 0.160 R-sq = 0.939 R-Sq (adj) = 0.936 Calculate and interpret the residual for the point where the golfers made 31% of putts from 14 feet away. Enter all calculations below accurate to at least 2 decimal places.<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Solution and Explanation<\/strong><\/h3>\n\n\n\n
We are given a log-linear regression model<\/strong>:ln\u2061(percent made)=4.6649\u22120.1091\u22c5Distance\\ln(\\text{percent made}) = 4.6649 – 0.1091 \\cdot \\text{Distance}ln(percent made)=4.6649\u22120.1091\u22c5Distance<\/p>\n\n\n\n
We are told that at 14 feet<\/strong>, the actual percent made<\/strong> is 31%<\/strong>, or as a decimal, 0.31.<\/p>\n\n\n\n
We need to calculate the residual<\/strong>, which is defined as:Residual=Actual\u2212Predicted\\text{Residual} = \\text{Actual} – \\text{Predicted}Residual=Actual\u2212Predicted<\/p>\n\n\n\n
But note: since the model uses the natural logarithm<\/strong> of percent made, we must work in the log scale first, and then return to the original percent scale to compute the residual correctly.<\/p>\n\n\n\n\n\n\n\n
Step 1: Calculate the predicted ln(percent made)<\/strong><\/h3>\n\n\n\n
Using a calculator:e3.1375\u224823.04e^{3.1375} \\approx 23.04e3.1375\u224823.04<\/p>\n\n\n\n
So the predicted percent made is approximately 23.04%<\/strong>.<\/p>\n\n\n\n\n\n\n\n
Step 3: Calculate the residual<\/strong><\/h3>\n\n\n\n
The actual percent made is 31%<\/strong>, and the predicted is 23.04%<\/strong>.Residual=Actual\u2212Predicted=31\u221223.04=7.96%\\text{Residual} = \\text{Actual} – \\text{Predicted} = 31 – 23.04 = \\boxed{7.96\\%}Residual=Actual\u2212Predicted=31\u221223.04=7.96%\u200b<\/p>\n\n\n\n\n\n\n\n
Interpretation<\/strong><\/h3>\n\n\n\n
The residual of 7.96%<\/strong> means that professional golfers made 7.96 percentage points more<\/strong> putts from 14 feet than what the model predicted. In other words, at 14 feet, the golfers performed better than expected based on the overall trend.<\/p>\n\n\n\n\n\n\n\n
Summary<\/strong><\/h3>\n\n\n\n
\n
Predicted percent made<\/strong> at 14 feet: 23.04%<\/strong><\/li>\n\n\n\n
Actual percent made<\/strong>: 31%<\/strong><\/li>\n\n\n\n
Residual<\/strong>: 7.96%<\/strong><\/li>\n\n\n\n
The model underestimated<\/strong> golfer performance at this distance.<\/li>\n<\/ul>\n\n\n\n
This type of residual analysis helps evaluate the accuracy of a model<\/strong> and identify distances where performance significantly deviates from the predicted trend.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
How well do professional golfers putt from different distances? Researchers collected data on the percent of putts made for various distances to the hole (in feet). Model: ln(percent made) vs. Distance Predictor Coef SE Coef T P Constant 4.6649 0.0825 56.511 0.0000 Distance -0.1091 0.0067 -16.24 0.0000 S = 0.160 R-sq = 0.939 R-Sq (adj) […]<\/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-233310","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233310","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=233310"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233310\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233310"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233310"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233310"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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