It is believed that there is a correlation between the number of fogging sessions and the number of

Question

It is believed that there is a correlation between the number of fogging sessions and the number of new dengue cases. To test the effectiveness of fogging on controlling the spread of dengue, a particular neighbourhood is subjected to a number of fogging sessions ($x$) spread out regularly in a month and the corresponding number of new dengue cases ($y$) is recorded. The results are summarised in the following table:

No. of fogging sessions, $x$	$2$	$4$	$6$	$8$	$10$	$12$	$14$
No. of new dengue cases, $y$	$20$	$14$	$9$	$6$	$7$	$2$	$1$

Calculate the product moment correlation coefficient between $x$ and $y$, and explain whether your answer suggests that a linear model is appropriate.[2]
Draw a scatter diagram for the data.[1]

One of the data points appears to be incorrect.

Indicate this point by labelling it as P, and explain why the scatter diagram for the remaining points may be consistent with a model of the form $y=A{{\mathrm{e}}^{bx}}$.[2]
Omitting $P$, use an appropriate regression line to give the best estimate, to the nearest whole number, of the number of fogging sessions in a month when the number of new dengue cases is $7$.[2]

Accepted Answer

(i) $r=-0.955$; the coefficient suggests that a linear model is appropriate (ii) Scatter diagram plotted (iii) $P=(10,7)$; the remaining points are consistent with $y=A\mathrm{e}^{bx}$ (iv) $7$ fogging sessions

2015 AJC P2 Q8

2015 AJC P2 Q8

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