<p>The table below gives the values of a set of bivariate data comprising ten observations of $x$ and $y$.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center">$x$</th><th style="text-align: center; --cell-justify: center">$0.5$</th><th style="text-align: center; --cell-justify: center">$1.0$</th><th style="text-align: center; --cell-justify: center">$1.5$</th><th style="text-align: center; --cell-justify: center">$2.0$</th><th style="text-align: center; --cell-justify: center">$2.5$</th><th style="text-align: center; --cell-justify: center">$3.0$</th><th style="text-align: center; --cell-justify: center">$3.5$</th><th style="text-align: center; --cell-justify: center">$4.0$</th><th style="text-align: center; --cell-justify: center">$4.5$</th><th style="text-align: center; --cell-justify: center">$5.0$</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">$y$</td><td style="text-align: center; --cell-justify: center">$13.1$</td><td style="text-align: center; --cell-justify: center">$12.9$</td><td style="text-align: center; --cell-justify: center">$12.5$</td><td style="text-align: center; --cell-justify: center">$11.7$</td><td style="text-align: center; --cell-justify: center">$10.9$</td><td style="text-align: center; --cell-justify: center">$9.9$</td><td style="text-align: center; --cell-justify: center">$8.9$</td><td style="text-align: center; --cell-justify: center">$7.7$</td><td style="text-align: center; --cell-justify: center">$6.0$</td><td style="text-align: center; --cell-justify: center">$4.1$</td></tr></tbody></table></div></div>
<ol class="i-list"><li><div class="list-item-paragraph">Sketch the scatter diagram and determine the value of the product moment correlation coefficient between $y$ and $x$.</div></li><li><div class="list-item-content"><span class="list-item-text">Determine which of the following is the best model for this set of data, justifying your choice clearly.</span></div><div class="list-item-paragraph" style="text-align: center">(A) $y=ax+b$    (B) $y=c{{x}^{2}}+d$   (C) $y=e\sqrt{x}+f$</div></li><li><div class="list-item-paragraph">Find the equation of the least-squares regression line of your selected best model in part (ii). Use your equation to estimate the value of $y$ when&nbsp;$x = 3.8$. Comment on the reliability of the estimation.</div></li></ol>

The table below gives the values of a set of bivariate data comprising ten observations of $x$ and $y$.

Sketch the scatter diagram and determine the value of the product moment correlation coefficient between $y$ and $x$.

Determine which of the following is the best model for this set of data, justifying your choice clearly.

(A) $y=ax+b$    (B) $y=c{{x}^{2}}+d$   (C) $y=e\sqrt{x}+f$

Find the equation of the least-squares regression line of your selected best model in part (ii). Use your equation to estimate the value of $y$ when $x = 3.8$. Comment on the reliability of the estimation.

2012 NJC P2 Q6

2012 NJC P2 Q6

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