2024 TMJC H1 Q10
2024 TMJC H1 Q10
10 marks
The table below shows the average retail prices of white pomfret sold (per kilogram) in Singapore from Year 2011 to Year 2020.
| Year | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 |
|---|---|---|---|---|---|---|---|---|---|---|
| \(t\) years after \(2010\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) |
Average retail prices of white pomfret (per kilogram), \($y\) | \(24.28\) | \(24.76\) | \(24.70\) | \(25.02\) | \(26.29\) | \(27.66\) | \(28.69\) | \(29.68\) | \(29.06\) | \(30.15\) |
- Give a sketch of the scatter diagram for the data.[2]
- Find the product moment correlation coefficient and comment on its value in the context of the data.[2]
- Find the equation of the regression line of \(y\) on \(t\) in the form of \(y = a + bt\), giving the values of \(a\) and \(b\) correct to \(3\) significant figures. Sketch this line on your scatter diagram.[2]
- Explain why we cannot use the regression line of \(t\) on \(y\) to estimate the average retail price of white pomfret. Hence, predict the average retail price of white pomfret in Year \(2023\) and comment on the validity of this prediction.[3]
- Based on actual data, the average retail price of white pomfret in Year \(2023\) is \(\$29.11\) per kilogram. Give a possible reason, in context, why the actual price is much lower than the predicted price in part (iv).[1]
Solution:
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Answer:(i) Scatter diagram shown. (ii) \(r\approx0.968\): strong positive linear correlation. (iii) \(y=23.0+0.729t\), coefficients to 3 s.f. (iv) Use price-on-time regression: \(\$32.49\) per kilogram; extrapolation is unreliable. (v) Increased supply could lower the price.
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