N2010 P2 Q10

A car is placed in a wind tunnel and the drag force \(F\) for different wind speeds \(v\), in appropriate units, is recorded. The results are shown in the table.

1. Draw the scatter diagram for these values, labelling the axes clearly.[2]

It is thought that the drag force \(F\) can be modelled by one of the formulae \(F=a+bv\) or \(F=c+dv^2\), where \(a\), \(b\), \(c\) and \(d\) are constants.

2. Find, correct to 4 decimal places, the value of the product moment correlation coefficient between[2]
   1. \(v\) and \(F\),
   2. \(v^2\) and \(F\).
3. Use your answers to parts (i) and (ii) to explain which of \(F=a+bv\) or \(F=c+dv^2\) is the better model.[1]
4. It is required to estimate the value of \(v\) for which \(F=26.0\). Find the equation of a suitable regression line, and use it to find the required estimate. Explain why neither the regression line of \(v\) on \(F\) nor the regression line of \(v^2\) on \(F\) should be used.[4]