A car dealer published the following data on the engine capacity measured in cubic centimetres (\(x\

Question

A car dealer published the following data on the engine capacity measured in cubic centimetres ($x$) and the prices in thousand dollars ($y$) of eight new car models.

Engine capacity and price data for eight car models
Model	$A$	$B$	$C$	$D$	$E$	$F$	$G$	$H$
$x$	$1000$	$1230$	$1700$	$2230$	$1990$	$1450$	$1650$	$1500$
$y$	$131.0$	$144.2$	$154.6$	$178.5$	$165.3$	$149.9$	$152.6$	$145.7$

Give a sketch of the scatter diagram for the data, as shown on your calculator.[2]
Find the product moment correlation coefficient and comment on its value in the context of the data.[2]
Find the equation of the regression line of $y$ on $x$, giving your answers in the form $y = mx + c$, with the values of $m$ and $c$ correct to $3$ significant figures. Sketch this line on your scatter diagram.[2]
Use the equation of your regression line to estimate the price for a car model with an engine capacity of $2080$ cubic centimetres. Explain why you would expect this estimate to be reliable.[2]

All the prices of the eight new car models increased by $3$% due to inflation.

Without any further calculations, state what will happen to the value of the product moment correlation coefficient found in part (b).[1]

Accepted Answer

(a) Eight-point scatter shown. (b) $r\approx0.979$, strong positive linear correlation. (c) $y=0.0354x+96.3$ (coefficients to 3 s.f.). (d) Approximately$170000, reasonably reliable interpolation. (e) Correlation unchanged.

Model	\(A\)	\(B\)	\(C\)	\(D\)	\(E\)	\(F\)	\(G\)	\(H\)
\(x\)	\(1000\)	\(1230\)	\(1700\)	\(2230\)	\(1990\)	\(1450\)	\(1650\)	\(1500\)
\(y\)	\(131.0\)	\(144.2\)	\(154.6\)	\(178.5\)	\(165.3\)	\(149.9\)	\(152.6\)	\(145.7\)

2024 NYJC H1 Q9

2024 NYJC H1 Q9

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