<p>In an experiment, different quantities of fertilizer, $x$ ml, were given to seven radish plants of the same height. The heights, $y$ mm, of the plants were measured after ten days. The results are given in the table.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$x$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$10$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$15$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$20$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$25$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$30$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$35$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$40$</p></th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$y$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$407$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$412$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$420$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$434$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$450$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$465$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$490$</p></td></tr></tbody></table></div></div>
<ol class="i-list"><li><div class="list-item-paragraph">Draw a scatter diagram to illustrate the data.			<span class="inline-marks">[1]</span></div></li></ol>
<p>It is suggested that the height $y$ can be modelled by one of the formulae</p>
<p style="text-align: center">$y=a+bx$ or $\text{}\hspace{0.5em}y=c+d{{x}^{2}}$</p>
<p>where&nbsp;$a$, $b$, $c$ and $d$ are constants.</p>
<ol class="i-list" start="2"><li><div class="list-item-paragraph">Find, correct to 4 decimal places, the value of the product moment correlation coefficient between</div><ol class="abc-list"><li><div class="list-item-paragraph">$x$ and $y$,</div></li><li><div class="list-item-paragraph">${{x}^{2}}$and $y$.<span class="inline-marks">[2]</span></div></li></ol></li><li><div class="list-item-paragraph">Use your answers to parts <strong>(i)</strong> and <strong>(ii)</strong> to explain which of $y=a+bx$ or $y=c+d{{x}^{2}}$ is the better model.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">It is desired to estimate the value of $x$ for which $y=440.$ Explain why neither the regression line of $x$ on $y$ nor the regression line of ${{x}^{2}}$ on $y$ should be used.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">By finding the equation of a suitable regression line, find the required estimate in part <strong>(iv)</strong>. Comment on the reliability of your estimate.<span class="inline-marks">[3]</span></div></li></ol>

In an experiment, different quantities of fertilizer, $x$ ml, were given to seven radish plants of the same height. The heights, $y$ mm, of the plants were measured after ten days. The results are given in the table.

Draw a scatter diagram to illustrate the data.			

It is suggested that the height $y$ can be modelled by one of the formulae

where $a$, $b$, $c$ and $d$ are constants.

Find, correct to 4 decimal places, the value of the product moment correlation coefficient between

Use your answers to parts **(i)** and **(ii)** to explain which of $y=a+bx$ or $y=c+d{{x}^{2}}$ is the better model.

It is desired to estimate the value of $x$ for which $y=440.$ Explain why neither the regression line of $x$ on $y$ nor the regression line of ${{x}^{2}}$ on $y$ should be used.

By finding the equation of a suitable regression line, find the required estimate in part **(iv)**. Comment on the reliability of your estimate.

Hypothesis Testing

International Baccalaureate Higher Level Mathematics

2015 DHS P2 Q10

2015 DHS P2 Q10