A weight is suspended in mid-air by means of a string of length $x$ cm. In an experiment, the weig

Question

A weight is suspended in mid-air by means of a string of length $x$ cm. In an experiment, the weight was displaced slightly and the time, $y$ s, taken to complete $10$ oscillations was recorded. The results are shown in the table.

$x$	$10$	$30$	$50$	$100$	$150$	$200$
$y$	$7.05$	$9.85$	$15.53$	$18.86$	$25.91$	$28.31$

Draw a scatter diagram to illustrate the data.[1]

It is thought that the time taken $y$ can be modelled by one of the formulae $y=a+bx$ or $y=c+d\sqrt{x}$ where $a$, $b$, $c$ and $d$ are constants.

Find the value of the product moment correlation coefficient between
1. $y$ and $x$,
2. $y$ and $\sqrt{x}$.[2]
Use your answers to (i) and (ii) to explain which formula is the better model.[1]
Find the equation of a suitable regression line and use it to estimate the value of $y$ when $x=45$. Comment on the reliability of the estimate.[3]
The addition of a data point will not change the equation of the regression line found in (iv). State the coordinates of such a point.[1]

Accepted Answer

(ii)(a) $0.980$ (b) $0.991$ (iii) $y=c+d\sqrt{x}$ (iv) $y=0.121+2.01\sqrt{x}$, giving $y=13.6\text{ s}$ (v) $(75.4,17.6)$

2015 YIJC P2 Q10

2015 YIJC P2 Q10

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