[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-267587-105":59,"doc-detail-267587-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","outlier-lies-an-illustrative-example-of-identifying-outliers-and-applying-robust-models","Outlier Lies - An Illustrative Example of Identifying Outliers and Applying Robust Models","","Outlier Lies illustrates how a small typographical error can cause a standard OLS regression to misestimate parameters and distort model fit when outliers are present. The study uses survey data from metropolitan colleges and universities, relating institutions’ average SAT scores for new freshmen to six-year graduation rates. Two extreme cases from 48 observations reduce explained variation to 15%, while removing them increases explained variation to 48%. Robust techniques are proposed to remain insensitive to extreme cases and yield improved predictions.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/outlier-lies-an-illustrative-example-of-identifying-outliers-and-applying-robust-models/267587/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/outlier-lies-an-illustrative-example-of-identifying-outliers-and-applying-robust-models/267587.png","ImageObject",300,407,{"name":92,"@type":93},"Pentious","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do outliers affect r and R2 in the example dataset?","Question",{"text":113,"@type":114},"Including two outliers in 48 observations reduces the explained variation to R2 = 0.15 (r = 0.39). Removing the two outliers increases explained variation to R2 = 0.48 (r = 0.69).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What variables are used to model the relationship in the article?",{"text":118,"@type":114},"The independent variable is each institution’s average SAT score for new freshmen, and the dependent variable is the institution’s six-year graduation rate.",{"name":120,"@type":111,"acceptedAnswer":121},"Which statistical tools are recommended for identifying regression outliers beyond visual inspection?",{"text":122,"@type":114},"The article highlights Mahalanobis distance and Cook’s distance as influence measures that help detect outlying cases.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},267587,1789422318,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":24,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":105,"preview_page_count":4},1374404730887,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Ho & Naugher  \nOutlier Lies: An Illustrative Example of Identifying Outliers and Applying Robust Models  \n\n| Karl Ho, University of North Texas\u003Cbr>Jimmie R. Naugher, University of North Texas |\n| --- |\n| The presence of outliers can contribute to serious deviance in findings of statistical models. In this study, we illustrate how a minor, typographical error in the data could make a standard OLS model “lie” in the estimates and model fit. We propose robust techniques that are insensitive to extreme, outlying cases and provide better predictions. With implementation examples, we demonstrate how robust technique improves estimations over conventional models based on normality and outlier-free assumptions. |\n\nT he possibility of outliers is an important  \nconsideration when applying regression statistics such as R2 and the Pearson product moment  \ncorrelation coefficient (Huber 1981, Hempel et al 1986) . We provide an example in this article that illustrates how dramatic the influence of only a tiny portion of the data can have on the model estimate and goodness of fit statistics. In the following analysis, we demonstrate that with two outliers included in a data set of 48 observations, only 15% of the variation in the dependent variable is accounted for by the differences on the independent variable (r = .39 and r2 = . 15, N=48) . However, when the two outliers are removed, 48% of the variation is accounted for (r = .69 and r2 = .48, N=46) .  \nThe data are from a survey of metropolitan colleges and universities conducted by the Office of University Planning at the University of North Texas. The institutions ranged from some with essentially open admissions to those with selective admissions criteria. The independent variable is the institution’s average SAT score for new freshmen and the dependent variable is the institution’s six-year graduation rate. As expected, there was a strong linear relationship between the average SAT score for new freshmen and the graduation rates. However, only two outliers can hide this fact in terms of rand r2 analysis. There are three purposes to this article:  \n• To illustrate how only two outliers can have a dramatic influence on r and r2 values.  \n• To demonstrate that outliers can be identified by visual inspection of the scattergram, provided the difference is extreme enough.  \n• To point to statistical tools that provide more reliable statistical means to identify outliers than visual inspection alone.  \nThe reported SAT averages ranged from 464 to 1152. The reported graduation rates ranged from 12.0% to 74.4% . The outliers reported the two lowest average SAT scores with relatively high graduation rates, i.e., an SAT of 464 with a graduation rate of 44.1%(near the middle) and an SAT of 598 with a graduation rate of 72.0%(near the top) . Institutions were requested to use the total SAT for averages, for which 400 is the lowest possible value. An average SAT of 464 or 598 is not believable. (Probably a clerk recorded either the math SAT or verbal SAT instead of the total SAT. Doubling the two reported SAT values of 464 and 598 yields values that fit well with the graduation rates.)  \nFigure 1 is based on the 48 cases that include the two outliers. The SAT values and graduation rates are plotted as a graph and the resulting regression line is plotted. Note how the paired values of SAT=464 and graduation rate=44.1 and SAT=598 and graduation rate=72.0 are isolated in the top left corner of the graph. The two points“lie outside” the general pattern formed by the other cases. The R2 is 0.1523.  \nFigure 2 is based on 46 cases, with the two outliers excluded. The SAT values and graduation rates as shown in Table 1 are plotted as a graph with the regression line. Note how much better the fit of the regression line with the two outlying cases discarded (R2 =0 .4735) .  \nIdentifying and Dealing with Outliers  \nApart from visual methods, statistical tools for identifying regression outliers abound. The m","cbCaijBwFjiLshrO","https://ap.wps.com/l/cbCaijBwFjiLshrO","pdf",158231,"English","# Identifying Outliers and the Limits of Visual Inspection\n## Influence of Outliers on r and R2\n## Data Source and Variables (SAT and Graduation Rate)\n## Mahalanobis Distance and Cook’s Distance\n## Dealing with Outliers Without Losing Information","[{\"question\":\"How do outliers affect r and R2 in the example dataset?\",\"answer\":\"Including two outliers in 48 observations reduces the explained variation to R2 = 0.15 (r = 0.39). Removing the two outliers increases explained variation to R2 = 0.48 (r = 0.69).\"},{\"question\":\"What variables are used to model the relationship in the article?\",\"answer\":\"The independent variable is each institution’s average SAT score for new freshmen, and the dependent variable is the institution’s six-year graduation rate.\"},{\"question\":\"Which statistical tools are recommended for identifying regression outliers beyond visual inspection?\",\"answer\":\"The article highlights Mahalanobis distance and Cook’s distance as influence measures that help detect outlying cases.\"}]","Outlier Lies - An Illustrative Example of Identifying Outliers and Applying Robust Models | PDF"]