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The content explains how to model Old Faithful eruptions, including interpreting positive correlation between eruption duration and interval, matching an appropriate regression line to the graph, assessing model quality, and comparing model fit through sums of squared differences, including least-squares and alternative linear or quadratic models.",{"@graph":69,"@context":122},[70,84,105],{"@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":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/answer-key-lab-manuals-for-calculus/444346/",{"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/answer-key-lab-manuals-for-calculus/444346.png","ImageObject",300,407,{"name":92,"@type":93},"Finn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-17","2026-09-29",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What relationship should the model reflect for Old Faithful eruptions?","Question",{"text":112,"@type":113},"The acceptable answer states a positive correlation between eruption duration x and interval y: longer eruptions correspond to longer intervals, and shorter eruptions correspond to shorter intervals.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How should students choose and justify a regression line for the data?",{"text":117,"@type":113},"A best-fitting hand-drawn line should be reasonably similar to the provided graph, and the equation should match the graph shown (for the example shown: y = 11.824x + 35.301). Justifications should discuss how well the model fits graphically and numerically.",{"name":119,"@type":110,"acceptedAnswer":120},"Why is the least-squares model expected to be the best fit?",{"text":121,"@type":113},"The least-squares model minimizes the differences between model results and the data by using the sum of squared differences; squaring prevents negative differences from canceling out and makes the total discrepancy reflect overall fit quality.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},444346,1791473309,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"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":144,"read_time":145},34359740700684,"https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487","# AnswerKeyTO ACCOMPANY LAB MANUALS FORCALCULUS\n\n5%  \nM A P L E  \nM A T H E M A T IC A  \nM A T H C A D  \nD E R I V E  \nTI-92  \n# CalculusSERIES\n\nLarson     Hostetler        Edwards  \n# ANSWER KEY TO ACCOMPANY\n\nLab Manuals forCALCULUS  \nMaple·Mathematica·Mathcad·Derive·TI-92  \nDetailed suggested solutions are given where appropriate.For some open-ended questionsguidelines on judging a wide variety of possible student answers are given instead.Theseguidelines focus on checking the reasonableness of student responses.  \nLarson/Hostetler/EdwardsCalculus Series  \nHoughton Mifflin Company Boston New York  \nEditor in Chief,Mathematics:Charles Hartford  \nManaging Editor:Cathy Cantin  \nSenior Associate Editor:Maureen Brooks  \nAssociate Editor:Michael Richards  \nAssistant Editor:Carolyn Johnson  \nSupervising Editor:Karen Carter  \nArt Supervisor:Gary Crespo  \nMarketing Manager:Sara Whittern  \nAssociate Marketing Manager:Ros Kane  \nMarketing Assistant:Carrie Lipscomb  \nDesign:Henry Rachlin  \nComposition and Art:Meridian Creative Group  \nTrademark Acknowledgments:Maple is a registered trademark of the University of Waterloo,Mathcad is a registeredtrademark of MathSoft,Inc,Mathematica is a registered trademark of Wolfram Research,Inc.,Derive is a registered trademark of Soft Warehouse,Inc.,TI-92 is a registered trade-mark of Texas Instruments,Inc.  \n\n|  |  |  | CONTENTS   |  |\n| --- | --- | --- | --- | --- |\n| LAB    | P.1    | .....................1   | LAB 8.1 .   | ...................16   |\n| LAB    | 1.1    | .....................2   | LAB 8.2 .   | ...................17   |\n| LAB    | 2.1    | .....................3   | LAB 9.1 .   | ...................18   |\n| LAB    | 2.2    | .....................4   | LAB 10.1.   | ...................20   |\n| LAB   |  3.1    | .....................6   | LAB 11.1 .   | ...................22   |\n| LAB    | 4.1    | .....................8   | LAB 11.2 .   | ...................23   |\n| LAB    | 5.1    | .....................9   | LAB 12.1 .   | ...................25   |\n| LAB   |  6.1    | ....................11   | LAB 13.1 .   | ...................26   |\n| LAB   |  6.2    | ....................13   | LAB 14.1 .   | ...................28   |\n| LAB    | 7.1    | ....................14   | LAB 15.1 .   | ...................29   |\n\nCopyright ◎1998 by Houghton Mifflin Company.All rights reserved.  \nNo part of this work may be reproduced or transmitted in any form or by anymeans,electronic or mechanical,including photocopying and recording,or by anyinformation storage or retrieval system without the prior written permission ofHoughton Mifflin Company unless such copying is expressly permitted by federalcopyright law.Address inquiries to College Permissions,Houghton MifflinCompany,222 Berkeley Street,Boston,MA02116-3764.  \nPrinted in the U.S.A.  \nISBN:0-395-89551-0  \n123456789-PO-0100999897  \nANSWER KEY FOR LAB MANUALS  \n## LAB P.1 MODELING OLD FAITHFUL's ERUPTIONSModeling Data\n\n1.An acceptable answer should state that the duration x and interval y have a positive correlation.This means thestudent should understand that as the duration of an eruption increases,the interval between eruptions increases.Likewise,as the duration of an eruption decreases,the interval between eruptions decreases.A reasonableexplanation of why x and y are related in this manner is that after an eruption,water seeps into the geyser'splumbing system to replace the water that was forced out by the eruption.For a long eruption,more water is forcedout than a short eruption and it will take longer for the plumbing system to refill with water.Also,it will takelonger for the water to be heated to produce the next eruption.  \n2.A best-fitting line drawn by hand should be reasonably similar to the one shown in the graph below.  \nOld Faithful Eruptions  \ny  \nInterval (in minutes)  \nDuration (in minutes)  \nThe equation given should match the graph.For the graph shown above,the equation is  \ny=11.824x+35.301.  \n3.A conclusion about how good a ","cbCaijz0kqAB1K1o","https://ap.wps.com/l/cbCaijz0kqAB1K1o","pdf",2990260,36,"English","# LAB P.1 Model Old Faithful's Eruptions - Modeling Data\n## Modeling Data - Suggested Answers and Guidelines","[{\"question\":\"What relationship should the model reflect for Old Faithful eruptions?\",\"answer\":\"The acceptable answer states a positive correlation between eruption duration x and interval y: longer eruptions correspond to longer intervals, and shorter eruptions correspond to shorter intervals.\"},{\"question\":\"How should students choose and justify a regression line for the data?\",\"answer\":\"A best-fitting hand-drawn line should be reasonably similar to the provided graph, and the equation should match the graph shown (for the example shown: y = 11.824x + 35.301). Justifications should discuss how well the model fits graphically and numerically.\"},{\"question\":\"Why is the least-squares model expected to be the best fit?\",\"answer\":\"The least-squares model minimizes the differences between model results and the data by using the sum of squared differences; squaring prevents negative differences from canceling out and makes the total discrepancy reflect overall fit quality.\"}]","ANSWER KEY - Lab Manuals for CALCULUS | PDF",1790707668,91]