[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-572078-105":53,"doc-detail-572078-en":127},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":120,"head_meta":122,"extra_data":124,"updated_unix":126},105,"en","ap-statistics-unit-2-cheat-sheet","AP Statistics Unit 2 Cheat Sheet","","AP Statistics Unit 2 cheat sheet summarizing key regression and correlation concepts for analyzing the relationship between two numerical variables. It defines terms such as scatterplots, explanatory and response variables, residuals, outliers, influential points, lurking variables, and extrapolation. The sheet explains correlation strength via the value range of r, interpretation of the least-squares regression line (LSRL), the slope, correlation coefficient r, and coefficient of determination r^2, including residual plots, model appropriateness, common error guidance, and non-linear transformations.",{"@graph":63,"@context":119},[64,80,102],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/ap-statistics-unit-2-cheat-sheet/572078/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/ap-statistics-unit-2-cheat-sheet/572078.png","ImageObject",442,249,{"name":88,"@type":89},"kopisore","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-21","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",7,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"What do explanatory and response variables mean in linear regression?","Question",{"text":109,"@type":110},"The explanatory variable (x) explains the other variable, and it causes the response variable to change. The response variable (y) is the outcome being modeled as it responds to x.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"How do you interpret the least-squares regression line (LSRL) slope, correlation coefficient r, and r²?",{"text":114,"@type":110},"The slope describes the predicted change in y for a one-unit increase in x. The correlation coefficient r indicates the strength, direction, and linear relationship. The coefficient of determination r² gives the percent of variation in y explained by the approximate linear relationship.",{"name":116,"@type":107,"acceptedAnswer":117},"How should you use residual plots to judge whether a linear model is appropriate?",{"text":118,"@type":110},"Residual plots help check model appropriateness by looking for patterns. Random, pattern-free residuals suggest the model is appropriate, while visible structure indicates the model may not fit and the data may need transformation.","https://schema.org",{"og:url":78,"og:type":121,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":123,"canonical":78},"index,follow",{"doc_id":125,"site_id":56},572078,1792033486,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":73,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":9},962090880963,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","AP Statistics Unit 2 Cheat Sheet  \nby kayheartsuu (kayheartsuu) [via](via cheatography.com/162660/cs/34375/)[ cheatography.com/162660/cs/34375/](via cheatography.com/162660/cs/34375/)  \nTerms to Know  \nscatterplot display the relationship between two numerical variables  \ncorrelation  \ncoefficient \"‐  \n\"r  \nthe strength , direction , and linear relationship between the x-variable and y-variable  \nleast square regression line  \nline of best fit for the scatterplot; minimizes the sum of the square of the deviations from a line  \nexplanatory variable  \nexplains the other variable; causes the response variable to change  \nresponse variable  \nresponse to the other variable; dependant  \nextrap‐ olation  \nnot right; using LSRL to predict values outside of the range of the original data set  \noutliers points that are far away from the LSRL relative to  \nother points  \ninfluential  \npoints  \npoints that significantly impacts the slope of the LSRL  \nlurking variable  \ndifferent outside variables that causes both x and y to change  \nresidual y- ŷ  \ncoefficient of determ‐ ination \"‐ r^2\"  \nr^2% of the variation in y-variable can be explained by the approximate linear relationship between xvariable and y-variable  \nStrength of \"r\" (Correlation Coefficient)  \n| legitimate values | [-1 , 1] |\n| --- | --- |\n| none | 0 |\n| weak | (-0 .5 ,0) U (0 , 0.5) |\n| moderate | (-0 .8 , -0.5) U (0 .5 , 0.8) |\n| strong | [-1 , -0.8) U 90.8 , 1] |\n\nLSRL Example  \nDesiree is interested to see if students who consume more caffeine tend to study more as well. She randomly selects 202020 students at her school and records their caffeine intake (mg) and the number of hours spent studying. A scatterplot of the data showed a linear relati‐ onship.  \nThis is computer output from a least-squares regression analysis on the data.  \nLSRL Example Interpretations  \nfind the LSRL  \nŷ = 2.544 + 0. 164x  \n\n| identify the variables | x = amount of caffeine intake (mg); y = number hours spent studying |\n| --- | --- |\n| interpret the slope | when the amount of caffeine intake increases by one , the number of hours spent studying increase by 0.164 |\n| identify the coefficient of\u003Cbr>determination | r^2 = 60.032 |\n| interpret the coefficient of determination | 60.032% of the variation in the amount of hours spent studying can be explained by the approximate linear relationship with caffeine intake |\n| find the correlation\u003Cbr>coefficient | r = 0.7748 |\n| interpret the correlation\u003Cbr>coefficient | there is a moderately strong , positive , linear relati‐ onship between the intake of caffeine and the amount of time spent studying |\n\n By kayheartsuu (kayheartsuu)  \n[cheatography.com/kayheartsuu/](cheatography.com/kayheartsuu/)  \nPublished 28th February , 2024. Last updated 3rd November, 2022. Page 1 of 2.  \nSponsored by Readable.com Measure your website readability!  \n[https://readable.com](https://readable.com)  \nAP Statistics Unit 2 Cheat Sheet  \nby kayheartsuu (kayheartsuu) [via](via cheatography.com/162660/cs/34375/)[ cheatography.com/162660/cs/34375/](via cheatography.com/162660/cs/34375/)  \nInterpretations  \n| slope of LSRL | for each increase in the \"x-variable\" of one \"x-unit\" , there is a predicted \"increase/decrease\" in the \"y-vari‐ able\" of \"b constant\" \"y-units\" |\n| --- | --- |\n| correl‐ ation coeffi‐\u003Cbr>cient | there is a \"strength\" , \"direction\" , linear relationship between \"x-variable\" and \"y-variable\" |\n| correl‐ ation of determ‐ ination | \"r^2\"% of the variation in the \"y-variable\" can be explained by the approximate linear relationship between \"x-variable\" and \"y-variable\" |\n| residual | the actual \"y-variable\" is \"residual\" \"y-unit\" \"above/bel‐ ow\" the predicted \"y-variable\" |\n\nResiduals and Residual Plots  \nthe sum of the residual is always zero  \nerror = observed-predicted  \nresidual plots show if the model is appropriate or not between two variables  \nif there is no pattern between the points on the residual plot , the model is appropriate  \nif there is a patte","cbCaialtCUfeFkJI","https://ap.wps.com/l/cbCaialtCUfeFkJI","pdf",204356,"English","# Terms to Know\n# LSRL Example and Interpretations\n# Strength of r (Correlation Coefficient)\n# Interpretations of Slope, r, and r^2\n# Residuals and Residual Plots\n# Non-Linear Transform Data\n# Correlation Doesn't Imply Causation","[{\"question\":\"What do explanatory and response variables mean in linear regression?\",\"answer\":\"The explanatory variable (x) explains the other variable, and it causes the response variable to change. The response variable (y) is the outcome being modeled as it responds to x.\"},{\"question\":\"How do you interpret the least-squares regression line (LSRL) slope, correlation coefficient r, and r²?\",\"answer\":\"The slope describes the predicted change in y for a one-unit increase in x. The correlation coefficient r indicates the strength, direction, and linear relationship. The coefficient of determination r² gives the percent of variation in y explained by the approximate linear relationship.\"},{\"question\":\"How should you use residual plots to judge whether a linear model is appropriate?\",\"answer\":\"Residual plots help check model appropriateness by looking for patterns. Random, pattern-free residuals suggest the model is appropriate, while visible structure indicates the model may not fit and the data may need transformation.\"}]","AP Statistics Unit 2 Cheat Sheet | PDF",1791925350]