<p>An investigation into the relationship between two variables \(x\) and \(y\) results in the following data.</p>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr><th style="text-align: left; --cell-justify: flex-start">\(x\)</th><th style="text-align: left; --cell-justify: flex-start">\(7\)</th><th style="text-align: left; --cell-justify: flex-start">\(8\)</th><th style="text-align: left; --cell-justify: flex-start">\(9\)</th><th style="text-align: left; --cell-justify: flex-start">\(10\)</th><th style="text-align: left; --cell-justify: flex-start">\(11\)</th><th style="text-align: left; --cell-justify: flex-start">\(12\)</th><th style="text-align: left; --cell-justify: flex-start">\(13\)</th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start">\(y\)</td><td style="text-align: left; --cell-justify: flex-start">\(1.1\)</td><td style="text-align: left; --cell-justify: flex-start">\(5.7\)</td><td style="text-align: left; --cell-justify: flex-start">\(9.3\)</td><td style="text-align: left; --cell-justify: flex-start">\(9.8\)</td><td style="text-align: left; --cell-justify: flex-start">\(8.6\)</td><td style="text-align: left; --cell-justify: flex-start">\(6.4\)</td><td style="text-align: left; --cell-justify: flex-start">\(0.9\)</td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Calculate the product moment correlation coefficient between \(x\) and \(y\).</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Draw a scatter diagram of the data and comment on the relationship between \(x\) and \(y\) based on the scatter diagram.</span><span class="inline-marks">[3]</span></div></li></ol>
<p>Several possible models for the relationship between \(x\) and \(y\) are proposed; one is chosen for further investigation.</p>
<ol class="abc-list" start="3"><li><div class="list-item-content"><span class="list-item-text">Calculate the product moment correlation coefficient between \(y\) and \((x-10)^2\), and comment on its value.</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the equation of the regression line of \(y\) on \((x-10)^2\). Use the equation of the regression line to estimate the value of \(y\) when \(x=17\) and comment on the reliability of this estimate.</span><span class="inline-marks">[3]</span></div></li></ol>

An investigation into the relationship between two variables \(x\) and \(y\) results in the following data.

Calculate the product moment correlation coefficient between \(x\) and \(y\).

Draw a scatter diagram of the data and comment on the relationship between \(x\) and \(y\) based on the scatter diagram.

Several possible models for the relationship between \(x\) and \(y\) are proposed; one is chosen for further investigation.

Calculate the product moment correlation coefficient between \(y\) and \((x-10)^2\), and comment on its value.

Find the equation of the regression line of \(y\) on \((x-10)^2\). Use the equation of the regression line to estimate the value of \(y\) when \(x=17\) and comment on the reliability of this estimate.

Correlation & Regressions

International Baccalaureate Higher Level Mathematics

2025 EJC P2 Q7

2025 EJC P2 Q7