File "linear-correlation.html"
Path: /StudyIB/mathsanalysis/page/1926/linear-correlationhtml
File size: 65.45 KB
MIME-type: text/html
Charset: utf-8
<!DOCTYPE html><html lang="EN"><head> <script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer','GTM-PZBWZ8J');</script> <title>Linear Correlation</title><!-- Removed by WebCopy --><!--<base href="/">--><!-- Removed by WebCopy --><meta http-equiv="x-ua-compatible" content="IE=Edge"><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1"><link href="../../../css/bootstrap.flatly.min.css" rel="stylesheet" media="screen"><link rel="stylesheet" href="../../../fonts/awesome/css/font-awesome.min.css"><link href="../../../js/jquery-fancybox/jquery.fancybox.min.css" type="text/css" rel="stylesheet"><link rel="stylesheet" href="../../../css/style.min.css?v=202301301645"><meta name="robots" content="index, follow"><meta name="googlebot" content="noarchive"><meta prefix="og: http://ogp.me/ns#" property="og:title" name="og:title" content="StudyIB Maths: Analysis & Approaches: Linear Correlation"> <meta prefix="og: http://ogp.me/ns#" property="og:image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta prefix="og: http://ogp.me/ns#" property="og:description" name="og:description" content="This page is all about looking for correlations in bivariate data (to see if there is a relationship between x and y variables). You will learn how to calculate r, Pearson’s product-moment correlation coefficient and how to interpret it...."> <meta prefix="og: http://ogp.me/ns#" property="og:url" name="og:url" content="https://studyib.net/mathsanalysis/page/1926/linear-correlation"> <meta prefix="og: http://ogp.me/ns#" property="og:site_name" name="og:site_name" content="StudyIB - Your IB learning companion"> <meta prefix="og: http://ogp.me/ns#" property="og:locale" name="og:locale" content="en"> <meta prefix="og: http://ogp.me/ns#" property="og:type" name="og:type" content="website"> <meta name="description" content="This page is all about looking for correlations in bivariate data (to see if there is a relationship between x and y variables). You will learn how to calculate r, Pearson’s product-moment correlation coefficient and how to interpret it...."> <meta name="image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="keywords" content="Regression, Best fit, R, Pearson, Product moment correlation coefficient, Pmcc, Scatter graphs, Y on x, X on y, IB, IBDP, InThinking, International Baccalaureate, Revision, Revision websites, Student Sites, Students, Learning, Guidance, Exam"> <meta itemprop="name" content="StudyIB Maths: Analysis & Approaches: Linear Correlation"> <meta itemprop="description" content="This page is all about looking for correlations in bivariate data (to see if there is a relationship between x and y variables). You will learn how to calculate r, Pearson’s product-moment correlation coefficient and how to interpret it...."> <meta itemprop="image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="twitter:card" content="summary_large_image"> <meta name="twitter:title" content="StudyIB Maths: Analysis & Approaches: Linear Correlation"> <meta name="twitter:description" content="This page is all about looking for correlations in bivariate data (to see if there is a relationship between x and y variables). You will learn how to calculate r, Pearson’s product-moment correlation coefficient and how to interpret it...."> <meta name="twitter:image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="twitter:creator" content="@inthinker"><link rel="stylesheet" href="../../../css/snippets.min.css?v=202209111300"><link rel="stylesheet" href="../../../css/article.min.css?v=202211221000"><link rel="stylesheet" type="text/css" href="../../../js/slick-carousel/slick.min.css"><link rel="stylesheet" type="text/css" href="../../../js/slick-carousel/slick-theme.min.css"><style type="text/css">.filter-sl-only { display: none; }</style><script src="../../../ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script><script src="../../../js/ifvisible.min.js"></script><script>ifvisible.setIdleDuration(300);</script><link rel="apple-touch-icon-precomposed" sizes="57x57" href="../../../img/favicon/apple-touch-icon-57x57.png"> <link rel="apple-touch-icon-precomposed" sizes="114x114" href="../../../img/favicon/apple-touch-icon-114x114.png"> <link rel="apple-touch-icon-precomposed" sizes="72x72" href="../../../img/favicon/apple-touch-icon-72x72.png"> <link rel="apple-touch-icon-precomposed" sizes="144x144" href="../../../img/favicon/apple-touch-icon-144x144.png"> <link rel="apple-touch-icon-precomposed" sizes="60x60" href="../../../img/favicon/apple-touch-icon-60x60.png"> <link rel="apple-touch-icon-precomposed" sizes="120x120" href="../../../img/favicon/apple-touch-icon-120x120.png"> <link rel="apple-touch-icon-precomposed" sizes="76x76" href="../../../img/favicon/apple-touch-icon-76x76.png"> <link rel="apple-touch-icon-precomposed" sizes="152x152" href="../../../img/favicon/apple-touch-icon-152x152.png"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-196x196.png" sizes="196x196"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-96x96.png" sizes="96x96"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-32x32.png" sizes="32x32"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-16x16.png" sizes="16x16"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-128.png" sizes="128x128"> <meta name="application-name" content="StudyIB: Your IB Learning Companion"> <meta name="msapplication-TileColor" content="#A5BED5"> <meta name="msapplication-TileImage" content="/img/favicon/mstile-144x144.png"> <meta name="msapplication-square70x70logo" content="/img/favicon/mstile-70x70.png"> <meta name="msapplication-square150x150logo" content="/img/favicon/mstile-150x150.png"> <meta name="msapplication-wide310x150logo" content="/img/favicon/mstile-310x150.png"> <meta name="msapplication-square310x310logo" content="/img/favicon/mstile-310x310.png"><script>var stdHash = "6da675cbcb3d25f050b05557349abc79", stdTicket = "082b9c9c4ae3624d";</script><script src="../../../js/user/local-stats.min.js?v=202205311700"></script><link href="../../../css/subjects-frontpage.min.css?v=202302031000" rel="stylesheet"></head><body class="public mathsanalysis"> <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PZBWZ8J" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript> <div id="top-header"> <div class="wmap general hidden-sm hidden-xs subjects"> <div class="layout-wrapper"> <div class="container-fluid"> <a href=""> <img class="header-thinker" src="../../../img/header-thinker.svg"> </a> <h1> <a href="../../../mathsanalysis.html"> <span style="font-family: 'Helvetica Narrow','Arial Narrow',Tahoma,Arial,Helvetica,sans-serif;font-stretch: condensed;letter-spacing: -1px">IBDP Maths: Analysis & Approaches</span> </a> <a href="https://inthinking.net" title="inthinking.net" class="inthinking-logo pull-right"> <img src="../../../img/header-logo.svg" style="height: 80px; width: auto;"> </a> </h1> <p class="slogan">InThinking Revision Sites for students</p> <p class="author">Website by <strong>Richard Wade</strong></p> <p class="updated">Updated 3 February 2023</p> </div> </div> </div> <nav id="public-topnav" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <a class="navbar-brand hidden-md hidden-lg" href="../../../index.htm"> <img class="header-xs-thinker" src="../../../img/header-thinker.svg"> </a> <button type="button" class="collapsed navbar-toggle" data-toggle="collapse" data-target="#subject-navbar-collapse" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <i class="fa fa-fw fa-2x fa-user"></i> </button> <div class="brand hidden-lg hidden-md hidden-sm"> <a class="brand-xs" href="../../../mathsanalysis.html"> <strong class="title" style="white-space: nowrap;font-size: 18px;">Maths: A&A</strong> </a> </div> </div> <div class="collapse navbar-collapse" id="subject-navbar-collapse"> <ul class="nav navbar-bar navbar-userbox hidden-md hidden-lg"><li class="dropdown"><a href="#" class="dropdown-toggle" data-toggle="dropdown"><i class="fa fa-fw fa-lg fa-user-circle" style="margin-right: 5px;"></i><span style="font-size: 16px;"></span></a><ul class="dropdown-menu"><li class="dropdown-submenu"><a class="dropdown-toggle" href="#" data-toggle="dropdown"><i class="fa fa-fw fa-globe"></i> Subjects</a><ul class="dropdown-menu"><li></li><li class=""><a href="../../../biology.html">DP Biology</a></li><li class=""><a href="../../../chemistry.html">DP Chemistry</a></li><li class=""><a href="../../../englishalanglit.html">DP English A: Language & Literature</a></li><li class="active"><a href="../../../mathsanalysis.html"><i class="fa fa-caret-right"></i> DP Maths: Analysis & Approaches</a></li><li class=""><a href="../../../mathsapplications.html">DP Maths: Applications & Interpretations SL</a></li><li class=""><a href="../../../physics.html">DP Physics</a></li><li class=""><a href="../../../spanishb.html">DP Spanish B</a></li></ul></li><li class="menu-item"><a href="../../../user.html"><i class="fa fa-fw fa-dashboard"></i> Dashboard</a></li><li class="menu-item"><a href="../../../user/profile.html"><i class="fa fa-fw fa-cog"></i> My profile</a></li><li class="menu-item"><a href="../../../user/messages.html"><i class="fa fa-fw fa-envelope"></i> Messages</a></li><li class="menu-item hidden-md hidden-lg mt-xs-3"><a href="../../../index.htm?logout=1" class="btn btn-primary btn-xs-block"><i class="fa fa-fw fa-lg fa-power-off text-danger"></i>Log out</a></li></ul></li></ul> <ul class="nav navbar-bar"><li class=""><a class="home" href="../../../mathsanalysis.html"><i class="fa fa-fw fa-home"></i> Home</a></li><li class=""><a class="topics" href="#"><i class="fa fa-fw fa-th-large"></i> Topics</a></li><li class=""><a class="favorites" href="../../../mathsanalysis.html"><i class="fa fa-fw fa-star"></i> My favorites</a></li><li class=""><a class="qbank" href="../../test-your-knowledge.html"><i class="fa fa-fw fa-question"></i> Question bank</a></li><li class=""><a class="sitemap" href="../../sitemap.html"><i class="fa fa-fw fa-sitemap"></i> Sitemap</a></li><li class=""><a class="activity" href="../../../mathsanalysis.html"><i class="fa fa-fw fa-calendar-check-o"></i> My activity</a></li></ul> <ul class="nav navbar-bar navbar-right"> <li> <form class="navbar-form hidden-md hidden-lg" role="search" method="get" action="mathsanalysis/search"> <div class="input-group"> <input class="form-control nav-search" name="glob" type="search" placeholder="Search..."> <span class="input-group-btn"> <button type="submit" class="btn bg-blue"> <i class="fa fa-search"> </i> </button> </span> </div> </form> <a href="#" class="toggle-menu-search hidden-sm hidden-xs" data-toggle="dropdown"> <i class="fa fa-lg fa-search"></i> </a> </li></ul> </div> </div></nav><nav id="nav-menu-search" class="shadow-bottom hidden-sm hidden-xs" style="display: none;"> <div class="container-fluid"> <form class="" role="search" method="get" action="mathsanalysis/search"> <input class="form-control nav-search" name="glob" type="search" placeholder="Search Maths: A&A..."> <button class="btn btn-sm btn-primary" type="submit"> Search </button> </form> </div></nav><div class="modal fade" tabindex="-1" role="dialog" id="modal-mini-login"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-body"> <button aria-hidden="true" data-dismiss="modal" class="close hidden-xs login-button-close" type="button">×</button> <form method="post"> <div class="form-group"> <input name="user-email" class="form-control" type="text" placeholder="Email"> </div> <div class="form-group"> <input name="user-password" class="form-control" type="password" placeholder="Password"> <input name="user-fp" class="fp" value="d8c893da5db7501669ffeeac46273ba6" type="hidden"> </div> <div class="form-group"> <a href="../../../reset-password.html" class="reset-password" style="font-weight: normal;"> Forgot your password? </a> </div> <div class="form-group"> <button type="submit" name="submit-login" value="1" class="btn btn-primary btn-block text-center"> <i class="fa fa-user fa-fw"></i> Log in </button> </div> </form> </div> </div> </div></div></div><div class="modal fade" id="show-topics" tabindex="-1" role="dialog"><div id="dialog-topics" class="modal-dialog modal-dialog-topics"><div class="modal-content"><div class="modal-body modal-body-topics"><div id="new-frontpage-toplevels-topics" class="frontpage-box"><div class="row"><div class="col-md-4 col-sm-4"><div class="item"><a href="../3016/free-access-weekend.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Free Access Weekend</h3></div><div class="body"><div class="cropper" style="background-image: url('../../images/free.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../2696/start-here.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Start Here</h3></div><div class="body"><div class="cropper" style="background-image: url('../../images/start-here.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../2902/examination-questions.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Examination Questions</h3></div><div class="body"><div class="cropper" style="background-image: url('../../images/exam.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../2563/question-bank.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Question Bank</h3></div><div class="body"><div class="cropper" style="background-image: url('../../images/questionbank.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../537/algebra.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Algebra</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/mathsanalysis/images/algebra.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../539/functions.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Functions</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/mathsanalysis/images/function_s.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../540/geometry-trigonometry.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Geometry & Trigonometry</h3></div><div class="body"><div class="cropper" style="background-image: url('../../images/photo-by-a-href=httpsunsplash.com@pawel_czerwinskiutm_source=unsplash-utm_medium=referral-utm_content=creditcopytextpawel-czerwinskia-on-a-href=httpsunsplash.comutm_source=unsplash-utm_medium=referral-utm_co.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../549/stats-probability.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Stats & Probability</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/mathsanalysis/images/probability.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../550/calculus.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Calculus</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/mathsanalysis/images/calculus1.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../857/exam-tips.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Exam Tips</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/mathsanalysis/files/exam-tips/exam-tips.jpg'); height: 10vw;"></div></div></a></div></div></div></div></div></div></div></div><div class="container-fluid shadow-ith"><div class="row frontpage"> <div class="col-md-3" id="left-column"> <p class="visible-xs-block"></p><div class="dropdown user-menu hidden-xs" style="margin-bottom: 20px;"> <button type="button" class="btn btn-default dropdown-toggle" data-toggle="dropdown" style="border-radius: 0; padding: 6px 18px;"> <i class="fa fa-fw fa-user-circle"></i> <small><i class="fa fa-caret-down"></i></small> </button> <ul class="dropdown-menu"> <li class="dropdown-submenu"><a href="#"><i class="fa fa-fw fa-globe"></i> Subjects</a><ul id="user-subjects-menu" class="dropdown-menu"><li></li><li class=""><a href="../../../biology.html">DP Biology</a></li><li class=""><a href="../../../chemistry.html">DP Chemistry</a></li><li class=""><a href="../../../englishalanglit.html">DP English A: Language & Literature</a></li><li class="active"><a href="../../../mathsanalysis.html"><i class="fa fa-caret-right"></i> DP Maths: Analysis & Approaches</a></li><li class=""><a href="../../../mathsapplications.html">DP Maths: Applications & Interpretations SL</a></li><li class=""><a href="../../../physics.html">DP Physics</a></li><li class=""><a href="../../../spanishb.html">DP Spanish B</a></li></ul></li><li class="divider"></li><li><a href="../../../user.html"><i class="fa fa-fw fa-dashboard"></i> Dashboard</a></li><li><a href="../../../user/profile.html"><i class="fa fa-fw fa-cog"></i> My profile</a></li><li><a href="../../../user/messages.html"><i class="fa fa-fw fa-envelope"></i> Messages</a></li> <li class="divider"></li> <li> <a href="../../../index.htm?logout=1"> <i class="fa fa-fw fa-power-off"></i> Log out </a> </li> </ul></div> <div id="side-nav"><h4 class="side-nav-title dropdown"><a href="../549/stats-probability.html" class="dropdown-toggle toplevel-dropdown" data-toggle="dropdown"><i class="fa fa-ellipsis-v"></i></a> <a href="../549/stats-probability.html">Stats & Probability</a><ul class="dropdown-menu"><li><a href="../../../mathsanalysis.html" style="padding-left: 5px; border-bottom: solid 1px #ddd"><i class="fa fa-fw fa-home"></i> Home</a></li><li><a href="../3016/free-access-weekend.html"><i class="fa fa-fw fa-caret-right"></i> Free Access Weekend</a></li><li><a href="../2696/start-here.html"><i class="fa fa-fw fa-caret-right"></i> Start Here</a></li><li><a href="../2902/examination-questions.html"><i class="fa fa-fw fa-caret-right"></i> Examination Questions</a></li><li><a href="../2563/question-bank.html"><i class="fa fa-fw fa-caret-right"></i> Question Bank</a></li><li><a href="../537/algebra.html"><i class="fa fa-fw fa-caret-right"></i> Algebra</a></li><li><a href="../539/functions.html"><i class="fa fa-fw fa-caret-right"></i> Functions</a></li><li><a href="../540/geometry-trigonometry.html"><i class="fa fa-fw fa-caret-right"></i> Geometry & Trigonometry</a></li><li><a href="../550/calculus.html"><i class="fa fa-fw fa-caret-right"></i> Calculus</a></li><li><a href="../857/exam-tips.html"><i class="fa fa-fw fa-caret-right"></i> Exam Tips</a></li></ul><div class="pull-right"><a class="sidenav-expand" title="Expand all" href="#"><i class="fa fa-plus-circle"></i></a> <a class="sidenav-compress" title="Compress all" href="#"><i class="fa fa-minus-circle"></i></a></div></h4><ul class="side-nav level-0"><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../687/representing-and-measuring-data.html">Representing and Measuring Data</a></label></li><li class="expanded parent selected"><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="linear-correlation.html">Linear Correlation</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../919/probability-calculations.html">Probability Calculations</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../689/conditional-probability.html">Conditional Probability</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../690/discrete-random-variables.html">Discrete Random Variables</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../692/binomial-distribution.html">Binomial Distribution</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../691/continuous-random-variables.html">Continuous Random Variables</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../693/normal-distribution.html">Normal Distribution</a></label></li></ul></div> <div class="hidden-xs hidden-sm"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> Linear Correlation <a href="#" class="mark-page-favorite pull-right" data-pid="1926" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../mathsanalysis.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../549/stats-probability.html">Stats & Probability</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Linear Correlation</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 30 minutes"><i class="fa fa-clock-o"></i> 30'</span> </ol> <article id="main-article"> <p><img alt="" src="../../files/data-handling/bivariate-data/main-1.png" style="float: left; width: 100px; height: 100px;">This page is all about looking for correlations in bivariate data (to see if there is a relationship between x and y variables). You will learn how to calculate <strong><em>r</em></strong>, Pearson’s product-moment correlation coefficient and how to interpret it. We will look at y on x regression as well as x on y regression using them to consider interpolation and extrapolation.</p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div> <p>On this page, you should learn about</p> <ul> <li>linear correlation of bi-variate data</li> <li>scatter diagrams</li> <li>y on x regression line</li> <li>x on y regression line</li> <li>interpolation and extrapolation</li> <li>Pearson' product-moment correlation coefficient, <span class="math-tex">\(r\)</span></li> </ul> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-violet"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Summary</p> </div> </div> <div class="panel-body"> <div> <p><iframe align="middle" frameborder="1" height="480" scrolling="yes" src="../../files/data-handling/bivariate-data/revision-notes_bivariate_data.pdf" width="640"></iframe></p> <p>Print from <a href="../../files/data-handling/bivariate-data/revision-notes_bivariate_data.pdf" target="_blank">here</a></p> </div> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p>Here is a quiz that gets you to estimate the r value for different graphs</p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#6f4552fb"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="6f4552fb"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> Bi-variate data 1 <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="11-536-1926" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following gives the best estimate for the r value for this y-on-x regression line</p><p><img alt="" src="../../files/data-handling/bivariate-data/q1" style="width: 600px; height: 551px;"></p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>-0.6</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.9</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>0.6</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.3</span></label> </p></div><div class="q-explanation"><p> </p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following gives the best estimate for the r value for this y-on-x regression line</p><p><img alt="" src="../../files/data-handling/bivariate-data/q2" style="width: 600px; height: 551px;"></p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>0</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.6</span></label> </p><p><label class="radio"> <input type="radio"> <span>-0.6</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>0.9</span></label> </p></div><div class="q-explanation"><p> </p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following gives the best estimate for the r value for this y-on-x regression line</p><p><img alt="" src="../../files/data-handling/bivariate-data/q3" style="width: 600px; height: 551px;"></p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>0.9</span></label> </p><p><label class="radio"> <input type="radio"> <span>-0.7</span></label> </p><p><label class="radio"> <input type="radio"> <span>-0.9</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>-0.4</span></label> </p></div><div class="q-explanation"><p> </p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following gives the best estimate for the r value for this y-on-x regression line</p><p><img alt="" src="../../files/data-handling/bivariate-data/q4" style="width: 600px; height: 551px;"></p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>-0.4</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.4</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>0</span></label> </p><p><label class="radio"> <input type="radio"> <span>-1</span></label> </p></div><div class="q-explanation"><p>r = 0</p><p>This means that there is no correlation. In these cases, we should NOT draw a line of regression.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following gives the best estimate for the r value for this y-on-x regression line</p><p><img alt="" src="../../files/data-handling/bivariate-data/q5" style="width: 600px; height: 551px;"></p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>-0.5</span></label> </p><p><label class="radio"> <input type="radio"> <span>1</span></label> </p><p><label class="radio"> <input type="radio"> <span>0</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>-1</span></label> </p></div><div class="q-explanation"><p> </p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following gives the best estimate for the r value for this y-on-x regression line</p><p><img alt="" src="../../files/data-handling/bivariate-data/q6" style="width: 600px; height: 551px;"></p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>-0.6</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.6</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>-0.9</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.9</span></label> </p></div><div class="q-explanation"><p> </p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following gives the best estimate for the r value for this y-on-x regression line</p><p><img alt="" src="../../files/data-handling/bivariate-data/q7" style="width: 600px; height: 551px;"></p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>-1</span></label> </p><p><label class="radio"> <input type="radio"> <span>0</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>1</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.5</span></label> </p></div><div class="q-explanation"><p> </p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following gives the best estimate for the r value for this y-on-x regression line</p><p><img alt="" src="../../files/data-handling/bivariate-data/q8" style="width: 600px; height: 551px;"></p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>0.4</span></label> </p><p><label class="radio"> <input type="radio"> <span>0</span></label> </p><p><label class="radio"> <input type="radio"> <span>-0.6</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.6</span></label> </p></div><div class="q-explanation"><p> </p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following gives the best estimate for the r value for this y-on-x regression line</p><p><img alt="" src="../../files/data-handling/bivariate-data/q9" style="width: 600px; height: 551px;"></p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>0.95</span></label> </p><p><label class="radio"> <input type="radio"> <span>1</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.6</span></label> </p><p><label class="radio"> <input type="radio"> <span>-0.9</span></label> </p></div><div class="q-explanation"><p> </p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following gives the best estimate for the r value for this y-on-x regression line</p><p><img alt="" src="../../files/data-handling/bivariate-data/q10" style="width: 600px; height: 551px;"></p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>-0.9</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.9</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>-0.6</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.6</span></label> </p></div><div class="q-explanation"><p> </p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div> </div> </div> <div class="modal-footer slide-quiz-actions"> <div class=""> <div class="pull-left pull-xs-none mb-xs-3"> <button class="btn btn-default d-xs-none btn-prev"> <i class="fa fa-arrow-left"></i> Prev </button> </div> <div class="pull-right pull-xs-none"> <button class="btn btn-success btn-xs-block text-xs-center btn-results" style="display: none"> <i class="fa fa-bar-chart"></i> Check Results </button> <button class="btn btn-default d-xs-none btn-next"> Next <i class="fa fa-arrow-right"></i> </button> <button class="btn btn-default btn-xs-block text-xs-center btn-close" data-dismiss="modal" style="display: none"> Close </button> </div> </div> </div> </div> </div></div> <hr class="hidden-separator"> <p>Here is a quiz that tests your understanding of linear correlation</p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#85d30451"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="85d30451"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> Bivariate Data 2 <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="11-537-1926" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>What does this graph demonstrate?</p><p><img alt="" src="../../files/data-handling/bivariate-data/quiz2/q1" style="width: 600px; height: 512px;"></p></div><div class="q-answer"><p><label class="checkbox"><input type="checkbox"> positive correlation</label></p><p><label class="checkbox"><input type="checkbox"> x on y regression</label></p><p><label class="checkbox"><input class="c" type="checkbox"> y on x regression</label></p><p><label class="checkbox"><input class="c" type="checkbox"> negative correlation</label></p></div><div class="q-explanation"><p>Vertical residuals are for y on x regression</p><p>The line of best fit is sloping down (negative gradient), so the correlation is negative. In this case <strong><em>r </em></strong> would have a negative value.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>What does this graph demonstrate?</p><p><img alt="" src="../../files/data-handling/bivariate-data/quiz2/q2" style="width: 600px; height: 440px;"></p></div><div class="q-answer"><p><label class="checkbox"><input type="checkbox"> 0 < r < 1</label></p><p><label class="checkbox"><input type="checkbox"> y on x correlation</label></p><p><label class="checkbox"><input class="c" type="checkbox"> x on y regression</label></p><p><label class="checkbox"><input class="c" type="checkbox"> -1 < r < 0</label></p></div><div class="q-explanation"><p>Horizontal residuals are for x on y regression</p><p>The line of best fit is sloping down (negative gradient), so the correlation is negative. In this case <strong><em>r </em></strong> would have a negative value.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Use your graphical calculator to calculate the y on x regression line, y = ax + b for the data below</p><table border="0" cellpadding="0" cellspacing="0" height="135" width="262"><tbody><tr><td style="text-align: center;"><em><strong>x</strong></em></td><td style="text-align: center;"><em><strong>y</strong></em></td></tr><tr><td style="text-align: center;">2.5</td><td style="text-align: center;">12.1</td></tr><tr><td style="text-align: center;">3.3</td><td style="text-align: center;">15.6</td></tr><tr><td style="text-align: center;">3.7</td><td style="text-align: center;">14.9</td></tr><tr><td style="text-align: center;">4.0</td><td style="text-align: center;">18.8</td></tr><tr><td style="text-align: center;">4.9</td><td style="text-align: center;">23</td></tr></tbody></table><p>Give the values correct to 2 significant figures</p></div><div class="q-answer"><p>y = ax + b</p><p><strong><em>a</em></strong> <span class="math-tex">\(\approx\)</span> <input type="text" style="height: auto;" data-c="4.5"> <span class="review"></span></p><p><strong><em>b</em></strong> <span class="math-tex">\(\approx\)</span> <input type="text" style="height: auto;" data-c="0.21"> <span class="review"></span></p></div><div class="q-explanation"><p>Enter the data into your GDC</p><p>Ensure that x variable is list 1 and y variables is list 2</p><p>Round the answers carefully</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Use your graphical calculator to calculate the correlation coefficient <strong><em>r</em></strong> for the data below</p><table border="0" cellpadding="0" cellspacing="0" height="135" width="262"><tbody><tr><td style="text-align: center;"><em><strong>x</strong></em></td><td style="text-align: center;"><em><strong>y</strong></em></td></tr><tr><td style="text-align: center;">2.5</td><td style="text-align: center;">12.1</td></tr><tr><td style="text-align: center;">3.3</td><td style="text-align: center;">15.6</td></tr><tr><td style="text-align: center;">3.7</td><td style="text-align: center;">14.9</td></tr><tr><td style="text-align: center;">4.0</td><td style="text-align: center;">18.8</td></tr><tr><td style="text-align: center;">4.9</td><td style="text-align: center;">23</td></tr></tbody></table><p>Give your answer correct to 3 significant figures</p></div><div class="q-answer"><p><strong><em>r</em></strong> <span class="math-tex">\(\approx\)</span> <input type="text" style="height: auto;" data-c="0.961"> <span class="review"></span></p></div><div class="q-explanation"><p>Enter the data into your GDC</p><p>The full answer displayed on your calculator is r <span class="math-tex">\(\approx\)</span> 0.905784809</p><p>Ensure that you round this answer correctly</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Use your graphical calculator to calculate the x on y regression line, x = ay + b for the data below</p><table border="0" cellpadding="0" cellspacing="0" height="133" width="257"><tbody><tr><td style="text-align: center;"><strong><em>x</em></strong></td><td style="text-align: center;"><strong><em>y</em></strong></td></tr><tr><td style="text-align: center;">43</td><td style="text-align: center;">10</td></tr><tr><td style="text-align: center;">33</td><td style="text-align: center;">15</td></tr><tr><td style="text-align: center;">39</td><td style="text-align: center;">22</td></tr><tr><td style="text-align: center;">25</td><td style="text-align: center;">24</td></tr><tr><td style="text-align: center;">21</td><td style="text-align: center;">27</td></tr></tbody></table><p>Give the values correct to 2 significant figures</p></div><div class="q-answer"><p>x = ay + b</p><p><strong><em>a</em></strong> <span class="math-tex">\(\approx\)</span> <input type="text" style="height: auto;" data-c="-1.1"> <span class="review"></span></p><p><strong><em>b</em></strong> <span class="math-tex">\(\approx\)</span> <input type="text" style="height: auto;" data-c="53"> <span class="review"></span></p></div><div class="q-explanation"><p>Enter the data into your GDC</p><p>Ensure that x variable is list 2 and y variables is list 1</p><p>Round the answers carefully</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The relationship between the volume in <span class="math-tex">\(cm^3\)</span> of a parcel (x) and the mass in g of the parcel (y) is given by the y on x regression line</p><p><em><strong>y = 2.1x - 15</strong></em></p><p>A parcel has volume 250<span class="math-tex">\(cm^3\)</span>. Calculate the mass.</p></div><div class="q-answer"><p>mass = <input type="text" style="height: auto;" data-c="510"> <span class="review"></span></p></div><div class="q-explanation"><p>y = 2.1x - 15</p><p>y = 2.1x250 - 15</p><p>y = 510</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The x on y line of regression for the two variables x and y is given by</p><p><strong><em>x = -3.2y + 48</em></strong></p><p>Find <strong><em>x</em></strong> when <strong><em>y</em></strong> = 12</p></div><div class="q-answer"><p><strong><em>x</em></strong> = <input type="text" style="height: auto;" data-c="9.6"> <span class="review"></span></p></div><div class="q-explanation"><p>x = -3.2y + 48</p><p>x = -3.2x12 + 48</p><p>x = 9.6</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The world record times for men's 100m over time is given below. The time in seconds (y) in the year (x) can be modelled by the equation <strong>y = -0.010x + 30</strong></p><p>Find the world record time in 1900.</p><p><img alt="" src="../../files/data-handling/bivariate-data/quiz2/q8" style="width: 600px; height: 560px;"></p><p> </p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>Don't know. You should not use y on x regression to predict a y value</span></label> </p><p><label class="radio"> <input type="radio"> <span>Don't know. You should not interpolate data</span></label> </p><p><label class="radio"> <input type="radio"> <span>11.0</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>Don't know. You should not extrapolate data</span></label> </p></div><div class="q-explanation"><p>1900 is outside of the range of data that is given. We cannot assume that the linear model would be appropriate before the 1930s. We should not extrapolate.</p><p>This is a good example of why we should not extrapolate. If world record times continue to follow this linear model, then at some point in the future the world record time would be 0s. Clearly this cannot happen!</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The following graph shows the distances hit by a golfer. X represents loft angle in degrees and y represents the distance in metres.</p><p>The y on x line of repression is <strong>y = - 3.7x + 320</strong></p><p>Work out the distance hit by a club with loft angle = 30°</p><p><img alt="" src="../../files/data-handling/bivariate-data/quiz2/q9" style="width: 600px; height: 448px;"></p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>Don't know. We need the x on y regression line.</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>209 metres</span></label> </p><p><label class="radio"> <input type="radio"> <span>Don't know. You should not extrapolate.</span></label> </p><p><label class="radio"> <input type="radio"> <span>Don't know. You should not interpolate.</span></label> </p></div><div class="q-explanation"><p>Here we are interpolating a result from data given</p><p>y = - 3.7x + 320</p><p>y = - 3.7x30 + 320</p><p>y = 209</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The following graph shows the distances hit by a golfer. X represents loft angle in degrees and y represents the distance in metres.</p><p>The y on x line of repression is <strong>y = - 3.7x + 320</strong></p><p>Work out the distance hit by a club with loft angle = 70°</p><p><img alt="" src="../../files/data-handling/bivariate-data/quiz2/q9" style="width: 600px; height: 448px;"></p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>Don't know. You should not interpolate.</span></label> </p><p><label class="radio"> <input type="radio"> <span>Don't know. We need the x on y regression line.</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>Don't know. You should not extrapolate</span></label> </p><p><label class="radio"> <input type="radio"> <span>61</span></label> </p></div><div class="q-explanation"><p>Here we are using a model to predict a value that is outside of the range of values given. We do not know if the model will continue in this linear pattern for values of x greater than 60°. We should not extrapolate.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div> </div> </div> <div class="modal-footer slide-quiz-actions"> <div class=""> <div class="pull-left pull-xs-none mb-xs-3"> <button class="btn btn-default d-xs-none btn-prev"> <i class="fa fa-arrow-left"></i> Prev </button> </div> <div class="pull-right pull-xs-none"> <button class="btn btn-success btn-xs-block text-xs-center btn-results" style="display: none"> <i class="fa fa-bar-chart"></i> Check Results </button> <button class="btn btn-default d-xs-none btn-next"> Next <i class="fa fa-arrow-right"></i> </button> <button class="btn btn-default btn-xs-block text-xs-center btn-close" data-dismiss="modal" style="display: none"> Close </button> </div> </div> </div> </div> </div></div> </div> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Exam-style Questions</p> </div> </div> <div class="panel-body"> <div class="panel panel-has-colored-body panel-default panel-has-border"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <div> <div class="smart-object center" data-id="882"> <p><img class="sibico" src="../../../img/sibico/hl-green.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="HL easy"> <img class="sibico" src="../../../img/sibico/sl-green.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="SL easy"> <img class="sibico" src="../../../img/sibico/no-calc.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="No calculator"></p> <p><span calibri="" style="font-size:11.0pt;line-height: 115%;font-family:">The world record times in seconds for the women’s 100m sprint from 1970 onwards are given below</span></p> <p><img alt="" src="../../files/data-handling/bivariate-data/esq1.png" style="width: 600px; height: 77px;"></p> <p>Use your calculator to write down</p> <p>a) <span class="math-tex">\(\bar{x}\)</span> , the mean year</p> <p>b) <span class="math-tex">\(\bar{y}\)</span> , the mean time</p> <p>c) <span class="math-tex">\(r\)</span>, <span calibri="" style="font-size:11.0pt;line-height:115%; font-family:">Pearson’s product-moment correlation coefficient</span></p> <p>The equation of the regression line y on x is y = ax + b</p> <p>d) Find the values of a and b for these data</p> <p>e) Show that <span class="math-tex">\((\bar{x},\bar{y})\)</span> lies on this line</p> <p>f) Use the regression line to estimate the world record time in 2024</p> <hr class="hidden-separator"> <h4><span class="fa fa-support" style="color:rgb(0, 0, 0);"></span> Hint</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden">Enter the data carefully into your calculator. Then double check that you have typed them in correctly.<content></content></section> <h4><span class="fa fa-pencil" style="color:rgb(0, 0, 0);"></span> Full Solution</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p><span class="fa fa-print" style="color:rgb(0, 0, 0);font-size:14px;"></span> Print from <a href="../../files/data-handling/bivariate-data/esq_bivariate_data1.pdf" target="_blank">here</a></p> <p><iframe align="middle" frameborder="0" height="480" scrolling="yes" src="../../files/data-handling/bivariate-data/esq_bivariate_data1.pdf" width="640"></iframe></p> </section> <h4> </h4> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 2</p> </div> </div> <div class="panel-body"> <div> <div class="smart-object center" data-id="883"> <p><img class="sibico" src="../../../img/sibico/hl-green.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="HL easy"> <img class="sibico" src="../../../img/sibico/sl-orange.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="SL moderate"> <img class="sibico" src="../../../img/sibico/no-calc.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="No calculator"></p> <p><span calibri="" style="font-size:11.0pt;line-height:115%; font-family:">The table below shows the test scores of SL students following a six-week revision period using studyib.</span></p> <p><img alt="" src="../../files/data-handling/bivariate-data/esq2.png" style="width: 600px; height: 77px;"></p> <p>a) Work out r, Pearson’s correlation coefficient</p> <p>The y on x regression line is y = ax + b</p> <p>b) Find a and b</p> <p>c) A student scores 80 marks before revision. Use the regression line to estimate the score after revision</p> <p>The x on y regression line is x = cx + d</p> <p>d) Find c and d</p> <p>e) A student scores 90 marks after revision. Use the regression line to estimate the score before revision</p> <p>f) Find the point of intersection of the y on x and the x on y regression lines</p> <hr class="hidden-separator"> <h4><span class="fa fa-support" style="color:rgb(0, 0, 0);"></span> Hint</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p><content> </content>Enter the data carefully into your graphical calculator.</p> <p>Give answers to 3 significant figures, but use a higher degree of accuracy for calculations.</p> </section> <h4><span class="fa fa-pencil" style="color:rgb(0, 0, 0);"></span> Full Solution</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p><span class="fa fa-print" style="color:rgb(0, 0, 0);font-size:14px;"></span> Print from <a href="../../files/data-handling/bivariate-data/esq_bivariate_data2.pdf" target="_blank">here</a></p> <p><iframe align="middle" frameborder="0" height="480" scrolling="yes" src="../../files/data-handling/bivariate-data/esq_bivariate_data2.pdf" width="640"></iframe></p> </section> <h4> </h4> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-default panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 3</p> </div> </div> <div class="panel-body"> <div> <div class="smart-object center" data-id="881"> <p><img class="sibico" src="../../../img/sibico/hl-green.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="HL easy"> <img class="sibico" src="../../../img/sibico/sl-orange.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="SL moderate"> <img class="sibico" src="../../../img/sibico/calc.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Calculator"></p> <p><span calibri="" style="font-size:11.0pt;line-height:115%; font-family:">The following table shows the hand spans and the heights of eight basketball players on a team</span></p> <p><img alt="" src="../../files/data-handling/bivariate-data/esq3.png" style="width: 600px; height: 73px;"></p> <p>The relationship between x and y can be modelled by the x on y line of regression x = ay + b</p> <ul> <li>Find the values of a and b</li> <li>Write down the correlation coefficient</li> <li>Another basketball player is 193cm tall. Use this regression line to estimate the handspan of this player.</li> </ul> <p>Another player is 180cm tall. Use this regression line to estimate the handspan of this player.</p> <hr class="hidden-separator"> <h4><span class="fa fa-support" style="color:rgb(0, 0, 0);"></span> Hint</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden">Take care how you set up your calculator to find the <strong>x on y</strong> repression line<content></content></section> <h4><span class="fa fa-pencil" style="color:rgb(0, 0, 0);"></span> Full Solution</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p><span class="fa fa-print" style="color:rgb(0, 0, 0);font-size:14px;"></span> Print from <a href="../../files/data-handling/bivariate-data/esq_bivariate_data3.pdf" target="_blank">here</a></p> <p><iframe align="middle" frameborder="0" height="480" scrolling="yes" src="../../files/data-handling/bivariate-data/esq_bivariate_data3.pdf" width="640"></iframe></p> </section> <h4> </h4> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 4</p> </div> </div> <div class="panel-body"> <div> <div class="smart-object center" data-id="884"> <p><img class="sibico" src="../../../img/sibico/hl-green.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="HL easy"> <img class="sibico" src="../../../img/sibico/sl-orange.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="SL moderate"> <img class="sibico" src="../../../img/sibico/no-calc.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="No calculator"></p> <p><span calibri="" style="font-size:11.0pt;line-height:115%; font-family:">The following table shows the age in days (x) and length of new-born babies in cm (y).</span></p> <p><img alt="" src="../../files/data-handling/bivariate-data/esq4.png" style="width: 600px; height: 78px;"></p> <p>The relationship between the variables is modelled by the regression line with equation y = ax + b</p> <p>a) Find the values of a and b</p> <p>b) Write down the correlation coefficient</p> <p>c) Use your equation to estimate the length of a baby that is 40 days old</p> <p>d) Use your equation to estimate the length of a baby that is 150 days old</p> <p>e) Use your equation to estimate the age of a child that is 54 cm long.</p> <hr class="hidden-separator"> <h4><span class="fa fa-support" style="color:rgb(0, 0, 0);"></span> Hint</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden">Think carefully about when you can use y on x regression line for predictions</section> <h4><span class="fa fa-pencil" style="color:rgb(0, 0, 0);"></span> Full Solution</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p><span class="fa fa-print" style="color:rgb(0, 0, 0);font-size:14px;"></span> Print from <a href="../../files/data-handling/bivariate-data/esq_bivariate_data4.pdf" target="_blank">here</a></p> <p><iframe align="middle" frameborder="0" height="480" scrolling="yes" src="../../files/data-handling/bivariate-data/esq_bivariate_data4.pdf" width="640"></iframe></p> </section> <h4> </h4> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="1926"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>Linear Correlation</strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider self-assessment " data-value="1" data-percentage=""></div></div> <label class="label-lg">My notes</label> <textarea name="page-notes" class="form-control" rows="3" placeholder="Write your notes here..."></textarea> </div> <div class="panel-footer text-xs-center"> <span id="last-edited" class="mb-xs-3"> </span> <div class="actions mt-xs-3"> <button id="save-my-progress" type="button" class="btn btn-sm btn-primary text-center btn-xs-block"> <i class="fa fa-fw fa-floppy-o"></i> Save </button> </div> </div></div> <div id="modal-feedback" class="modal fade" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <h4 class="modal-title">Feedback</h4> <button type="button" class="close hidden-xs hidden-sm" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> <div class="modal-body"> <div class="errors"></div> <p><strong>Which of the following best describes your feedback?</strong></p> <form method="post" style="overflow: hidden"> <div class="form-group"> <div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Recommendation"> Recommend</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Problem"> Report a problem</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Improvement"> Suggest an improvement</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Other"> Other</label></div> </div> <hr> <div class="row"> <div class="col-md-6"> <div class="form-group"> <label for="feedback-name">Name</label> <input type="text" class="form-control" name="feedback-name" placeholder="Name" value=" "> </div> </div> <div class="col-md-6"> <div class="form-group"> <label for="feedback-email">Email address</label> <input type="email" class="form-control" name="feedback-email" placeholder="Email" value="@airmail.cc"> </div> </div> </div> <div class="form-group"> <label for="feedback-comments">Comments</label> <textarea class="form-control" name="feedback-comments" style="resize: vertical;"></textarea> </div> <input type="hidden" name="feedback-ticket" value="082b9c9c4ae3624d"> <input type="hidden" name="feedback-url" value="https://studyib.net/mathsanalysis/page/1926/linear-correlation"> <input type="hidden" name="feedback-subject" value="11"> <input type="hidden" name="feedback-subject-name" value="Maths: Analysis & Approaches"> <div class="pull-left"> </div> </form> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary btn-xs-block feedback-submit mb-xs-3 pull-right"> <i class="fa fa-send"></i> Send </button> <button type="button" class="btn btn-default btn-xs-block m-xs-0 pull-left" data-dismiss="modal"> Close </button> </div> </div> </div></div> </article> <hr class="hidden-md hidden-lg"> <div class="hidden-md hidden-lg mt-xs-3"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <input type="hidden" id="user-id" value="38342"></div><input id="ticket" type="hidden" value="082b9c9c4ae3624d"><input id="tzoffset" type="hidden" value="new"><input id="fp" class="fp" type="hidden" value=""></div><div id="std-footer"> <div class="wmap"> <div class="layout-wrapper"> <p> <a href="https://www.inthinking.net"> © <span id="footer-year"></span> <em>InThinking</em> <script>document.getElementById("footer-year").innerHTML = new Date().getFullYear();</script> </a> | <a target="_self" href="../../../about.html"> About us </a> | <a target="_self" href="../../../terms-and-conditions.html"> Legal </a> | <a target="_self" href="../../../contact.html"> Contact </a> </p> <p> <a class="social" target="_blank" href="https://twitter.com/#!/inthinker"> <img src="../../../img/social/twitter-square.svg"> Twitter </a> <a class="social" target="_blank" href="https://www.facebook.com/inthinking.net"> <img src="../../../img/social/facebook-square.svg"> Facebook </a> <a class="social" target="_blank" href="https://www.linkedin.com/profile/view?id=139741989"> <img src="../../../img/social/linkedin-square.svg"> LinkedIn </a> </p> </div> </div></div><script src="../../../js/jquery-1.11.3.min.js"></script><script src="../../../js/bootstrap.min.js"></script><script src="../../../js/jquery-fancybox/jquery.fancybox.min.js"></script><script>var pageId = 1926;</script><script type="text/javascript" src="../../../js/jqueryui/jquery-ui-custom.min.js"></script><script type="text/javascript" src="../../../js/jqueryui/jquery.ui.touch-punch.js"></script><script type="text/javascript" src="../../../js/std-quizzes-helpers.min.js?v=20220406"></script><script src="../../../ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script><script type="text/javascript" src="../../../js/slick-carousel/slick.min.js"></script><script type="text/javascript" src="../../../js/std-slide-quizzes.min.js?v=20220406"></script><script type="text/javascript" src="../../../js/jqueryui/jquery-ui.min.js"></script><script type="text/javascript" src="../../../js/jqueryui/jquery.ui.touch-punch.min.js"></script><script src="../../../js/user/page-my-progress.min.js?v=202211221000"></script><script>var sAJAX='/pages/subjects/activity/user-stats-page.php?t=082b9c9c4ae3624d&p=1926&s=11&x=10726';var sData='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';var loopSecs = 30;var minSecsLog = 60;var lsKey = '11-83608-1926';</script><script src="../../../js/subjects/activity/user-stats-page.min.js?v=202205311700"></script><script src="../../../js/subjects/activity/my-favorites.min.js?v=20220610"></script><script src="../../../js/subjects/feedback.min.js?v=202211221000"></script><script>var sessionUpdateSecs = 300;</script><script type="text/javascript" src="../../../js/session-updater.js"></script><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');ga('create', 'UA-98480796-4', 'auto');ga('send', 'pageview');</script><script src="../../../js/devicefp/devicefp.min.js"></script><script src="../../../js/jq-quickfit/jq-quickfit.min.js?v=20220201"></script><script src="../../../js/frontpage-subjects.min.js?v=202211161300"></script><script type="text/javascript" src="../../../js/studyib-jq.min.js?v=202211241300"></script><script type="text/javascript">$(document).ready(function(){ $('#trigger-modal-video-overview').click(function() { if( $('#modal-video-overview .modal-body iframe').attr('src').length == 0 ) { $('#modal-video-overview .modal-body iframe').attr('src', 'https://www.youtube.com/embed/hxxtdiLdTFk?rel=0'); } }); $('#modal-video-overview').on('hidden.bs.modal', function() { $('#modal-video-overview .modal-body iframe').attr('src', ''); }); });</script></body></html>