2012 NJC P2 Q6
2012 NJC P2 Q6
Prelims
The table below gives the values of a set of bivariate data comprising ten observations of \(x\) and \(y\).
| \(x\) | \(0.5\) | \(1.0\) | \(1.5\) | \(2.0\) | \(2.5\) | \(3.0\) | \(3.5\) | \(4.0\) | \(4.5\) | \(5.0\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(y\) | \(13.1\) | \(12.9\) | \(12.5\) | \(11.7\) | \(10.9\) | \(9.9\) | \(8.9\) | \(7.7\) | \(6.0\) | \(4.1\) |
- Sketch the scatter diagram and determine the value of the product moment correlation coefficient between \(y\) and \(x\).
- Determine which of the following is the best model for this set of data, justifying your choice clearly.(A) \(y=ax+b\) (B) \(y=c{{x}^{2}}+d\) (C) \(y=e\sqrt{x}+f\)
- Find the equation of the least-squares regression line of your selected best model in part (ii). Use your equation to estimate the value of \(y\) when \(x = 3.8\). Comment on the reliability of the estimation.
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Answer:(i) \(r=-0.973\) (ii) Model B, \(y=cx^2+d\) (iii) \(y=-0.359x^2+13.2\), giving \(y=8.04\) when \(x=3.8\). The estimate is reliable because it is interpolation and \(|r(y,x^2)|\) is close to \(1\).
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