2024 RI H1 Q9
2024 RI H1 Q9
Heat strokes precautions include measuring the body temperatures of students before and after Physical Education (PE) lessons. The table below shows the body temperature readings of a random sample of \(8\) students, taken before a particular PE lesson (\(x\) \({}^\circ\)C) and taken immediately after the PE lesson (\(y\) \({}^\circ\)C).
| Student | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) |
|---|---|---|---|---|---|---|---|---|
| \(x\) | \(36.1\) | \(35.9\) | \(36.3\) | \(37.0\) | \(37.2\) | \(36.8\) | \(35.7\) | \(36.6\) |
| \(y\) | \(37.0\) | \(36.6\) | \(37.1\) | \(39.9\) | \(38.5\) | \(38.0\) | \(36.5\) | \(38.0\) |
- Give a sketch of the scatter diagram for the data, as shown on your calculator.[2]
- One of the points does not seem to follow the trend. Write down the coordinates of this point.[1]
For the rest of the question, this point is removed.
- Find the value of \(r\), the product moment correlation coefficient.[1]
- 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.[1]
- The body temperature of Teo before this PE lesson is \(36.7\) \({}^\circ\)C. Use your regression line in part (d) to calculate an estimate of his body temperature immediately after the PE lesson. Comment on the reliability of your estimate.[3]
Solution:
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(a) Scatter shown. (b) \((37.0,39.9)\).
(c) \(r\approx0.981\). (d) \(y\approx1.44x-15.1\), coefficients to 3 significant figures.
(e) \(37.7^\circ\mathrm C\) from the displayed rounded line; \(37.9^\circ\mathrm C\) with unrounded coefficients. Reasonably reliable interpolation with strong correlation.
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