2015 DHS P2 Q10
2015 DHS P2 Q10
In an experiment, different quantities of fertilizer, \(x\) ml, were given to seven radish plants of the same height. The heights, \(y\) mm, of the plants were measured after ten days. The results are given in the table.
\(x\) | \(10\) | \(15\) | \(20\) | \(25\) | \(30\) | \(35\) | \(40\) |
|---|---|---|---|---|---|---|---|
\(y\) | \(407\) | \(412\) | \(420\) | \(434\) | \(450\) | \(465\) | \(490\) |
- Draw a scatter diagram to illustrate the data. [1]
It is suggested that the height \(y\) can be modelled by one of the formulae
\(y=a+bx\) or \(\text{}\hspace{0.5em}y=c+d{{x}^{2}}\)
where \(a\), \(b\), \(c\) and \(d\) are constants.
- Find, correct to 4 decimal places, the value of the product moment correlation coefficient between
- \(x\) and \(y\),
- \({{x}^{2}}\)and \(y\).[2]
- Use your answers to parts (i) and (ii) to explain which of \(y=a+bx\) or \(y=c+d{{x}^{2}}\) is the better model.[1]
- It is desired to estimate the value of \(x\) for which \(y=440.\) Explain why neither the regression line of \(x\) on \(y\) nor the regression line of \({{x}^{2}}\) on \(y\) should be used.[1]
- By finding the equation of a suitable regression line, find the required estimate in part (iv). Comment on the reliability of your estimate.[3]
Solution:
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(i) Scatter diagram shown.
(ii)(a) \(0.9781\). (b) \(0.9985\), both to 4 decimal places.
(iii) \(y=c+dx^2\). (iv) \(x\) is controlled and \(y\) is the response.
(v) \(y\approx399.60+0.055326x^2\); \(x\approx27.0\) ml. Reasonably reliable interpolation under the fitted model.
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