N2010 P2 Q10
N2010 P2 Q10
Junior College 2
9 marks
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.
| \(v\) | \(0\) | \(4\) | \(8\) | \(12\) | \(16\) | \(20\) | \(24\) | \(28\) | \(32\) | \(36\) |
| \(F\) | \(0\) | \(2.5\) | \(5.1\) | \(8.8\) | \(11.2\) | \(13.6\) | \(17.6\) | \(22\) | \(27.8\) | \(33.9\) |
- 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.
- Find, correct to 4 decimal places, the value of the product moment correlation coefficient between[2]
- \(v\) and \(F\),
- \(v^2\) and \(F\).
- 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]
- 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]
Solution:
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Answer:(ii) \(0.9860,0.9907\). (iii) \(F=c+dv^2\). (iv) \(F=3.19565217+0.02424199085v^2\), \(v\approx30.7\).
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