<p style="margin-bottom: 1.5rem">The number of reported cases, $x$ (in hundreds) of a virus in the ${{n}^{\text{th}}}$ month are given in the table below.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 350px;"><colgroup><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"></colgroup><thead><tr style="height: 33px;"><th style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$n$</p></th><th style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$1$</p></th><th style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$2$</p></th><th style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$3$</p></th><th style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$4$</p></th><th style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$5$</p></th><th style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$6$</p></th></tr></thead><tbody><tr style="height: 33px;"><td style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$x$</p></td><td style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$0.26$</p></td><td style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$3.05$</p></td><td style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$4.12$</p></td><td style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$4.63$</p></td><td style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$5.15$</p></td><td style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$k$</p></td></tr></tbody></table></div></div>
<p>It is given that the least squares regression line of $x$ on $n$ is $x=0.943n+0.484$.  </p>
<ol class="i-list"><li><div class="list-item-paragraph">Show that the value of $k$ to two decimal places is $5.50$.		<span class="inline-marks">[1]</span></div></li></ol>
<p>Use the value of $k$ in part <strong> (i) </strong> for the rest of the question.<span class="inline-marks">[1]</span></p>
<ol class="i-list" start="2"><li><div class="list-item-paragraph">Draw a scatter diagram to illustrate the data.	<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Explain why a linear model is inappropriate.	<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Explain clearly which of the following models <strong>(A) </strong>or <strong> (B)</strong>, where&nbsp;$a$ and $b$ are positive constants, is more appropriate to model these values.</div><div class="list-item-paragraph" style="text-align: center"><strong>(A)</strong>   $x=a+b\ln n$,</div><div class="list-item-paragraph" style="text-align: center">				<strong>	(B)</strong>   $x=a+b{{n}^{2}}$.		</div><div class="list-item-paragraph">Use the model that you have identified, calculate the values of $a$ and $b$, and use them to predict the month in which the number of reported cases is at least $1000$.	<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Give an interpretation, in context, of the value of $a$ for the model you have identified in part <strong> (iv)</strong>.<span class="inline-marks">[1]</span></div></li></ol>

The number of reported cases, $x$ (in hundreds) of a virus in the ${{n}^{\text{th}}}$ month are given in the table below.

It is given that the least squares regression line of $x$ on $n$ is $x=0.943n+0.484$.  

Show that the value of $k$ to two decimal places is $5.50$.		

Use the value of $k$ in part ** (i) ** for the rest of the question.

Draw a scatter diagram to illustrate the data.	

Explain why a linear model is inappropriate.	

Explain clearly which of the following models **(A) **or ** (B)**, where $a$ and $b$ are positive constants, is more appropriate to model these values.

Use the model that you have identified, calculate the values of $a$ and $b$, and use them to predict the month in which the number of reported cases is at least $1000$.	

Give an interpretation, in context, of the value of $a$ for the model you have identified in part ** (iv)**.

2015 HCI P2 Q9

2015 HCI P2 Q9