2024 YIJC H1 Q10
2024 YIJC H1 Q10
11 marks
A PE teacher is investigating the relationship between the height and the shoe size of students. The height, \(x\) cm, and the shoe size, \(y\), for a random sample of \(8\) students are given in the following table.
| Student | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| \(x\) | \(150\) | \(155\) | \(160\) | \(165\) | \(170\) | \(175\) | \(180\) | \(190\) |
| \(y\) | \(6.5\) | \(7.0\) | \(8.0\) | \(8.0\) | \(9.0\) | \(10.0\) | \(9.5\) | \(11.5\) |
- Give a sketch of the scatter diagram for the data, as shown on your calculator.[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 \(x\) in the form \(y = mx + c\), giving the values of \(m\) and \(c\) correct to \(3\) significant figures. Sketch this line on your scatter diagram.[2]
- Use the equation of your regression line to calculate an estimate for the shoe size of a student of height \(171\) cm. State two reasons why you would expect this to be a reliable estimate.[2]
The regression line of \(y\) on \(x\) changes to \(y = 0.121x - 11.7\) when data from a new student is added. However, the shoe size data for the new student is missing, and only the height, which is \(166\) cm, is available.
- Find the shoe size of the new student.[3]
Solution:
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Answer:(a) Scatter and line shown. (b) \(r\approx0.977\), strong positive correlation. (c) \(y=0.121x-11.6\). (d) \(9.03\), interpolation and strong correlation. (e) About\(8.03\).
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