2024 VJC H1 Q11
2024 VJC H1 Q11
9 marks
A scientist is investigating the relationship between the average daily temperature \(x\) (in \({}^\circ\mathrm{C}\)) and her household's daily energy consumption \(y\) (in \(\mathrm{kWh}\)), in winter. The results for a random sample of \(10\) winter days are shown in the table.
| \(x\) | \(-0.4\) | \(-0.2\) | \(0.3\) | \(0.8\) | \(1.1\) | \(1.4\) | \(1.8\) | \(2.1\) | \(2.5\) | \(2.6\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(y\) | \(32\) | \(30\) | \(28\) | \(29\) | \(26\) | \(27\) | \(26\) | \(24\) | \(22\) | \(21\) |
- 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]
- Explain the meaning of \(m\) in the context of the data.[1]
- Use the equation of your regression line to calculate an estimate of the scientist's household's daily energy consumption when the average daily temperature is \(0.5{}^\circ\mathrm{C}\) and comment on the reliability of your estimate.[2]
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Answer:(b)r=-0.954
(c)\(y=-3.09x+30.2\)
(e)estimated = 28.7 kWh, reliable.
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