2025 EJC P2 Q7
2025 EJC P2 Q7
9 marks
An investigation into the relationship between two variables \(x\) and \(y\) results in the following data.
| \(x\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) | \(13\) |
|---|---|---|---|---|---|---|---|
| \(y\) | \(1.1\) | \(5.7\) | \(9.3\) | \(9.8\) | \(8.6\) | \(6.4\) | \(0.9\) |
- Calculate the product moment correlation coefficient between \(x\) and \(y\).[1]
- Draw a scatter diagram of the data and comment on the relationship between \(x\) and \(y\) based on the scatter diagram.[3]
Several possible models for the relationship between \(x\) and \(y\) are proposed; one is chosen for further investigation.
- Calculate the product moment correlation coefficient between \(y\) and \((x-10)^2\), and comment on its value.[2]
- Find the equation of the regression line of \(y\) on \((x-10)^2\). Use the equation of the regression line to estimate the value of \(y\) when \(x=17\) and comment on the reliability of this estimate.[3]
Solution:
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Answer:(a) \(r\approx0.00208\). (b) Strong nonlinear, approximately inverted-parabolic association. (c) \(r\approx-0.997\); strong negative linear correlation with \((x-10)^2\). (d) \(y\approx9.92-0.987(x-10)^2\); estimate \(-38.4\), unreliable extrapolation.
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