2015 HCI P2 Q9

The number of reported cases, \(x\) (in hundreds) of a virus in the \({{n}^{\text{th}}}\) month are given in the table below.

It is given that the least squares regression line of \(x\) on \(n\) is \(x=0.943n+0.484\).

1. Show that the value of \(k\) to two decimal places is \(5.50\). [1]

Use the value of \(k\) in part (i) for the rest of the question.[1]

2. Draw a scatter diagram to illustrate the data. [1]
3. Explain why a linear model is inappropriate. [1]
4. Explain clearly which of the following models (A) or (B), where \(a\) and \(b\) are positive constants, is more appropriate to model these values.
   (A) \(x=a+b\ln n\),
   (B) \(x=a+b{{n}^{2}}\).
   Use the model that you have identified, calculate the values of \(a\) and \(b\), and use them to predict the month in which the number of reported cases is at least \(1000\). [1]
5. Give an interpretation, in context, of the value of \(a\) for the model you have identified in part (iv).[1]