Compare a linear trend with a transformed quadratic

In a country, a government agency tracks the number of cases of dengue fever ($N$) each month ($T$). The number of cases prior to May 2017 are shown in the table below.

$T$	1	2	3	4	5	6	7	8	9	10	11	12
$N$	711	647	584	501	407	350	281	222	197	141	133	129

(i) Sketch a scatter diagram to illustrate the data.2 marks

(ii) Calculate the value of the product moment correlation coefficient and find the equation of the regression line of $N$ on $T$, in the form $N=a+bT$, giving the values of $a$ and $b$ correct to 3 significant figures.2 marks

(iii) A statistician suggested that the model $N=k(T-30)^2+c$ would be more appropriate. Find the values of $k$ and $c$. State whether you agree, justifying your answer.3 marks