Linear regression of hot drink sales on air temperature, correlation coefficient, prediction and the reverse regression line
Linear regression of hot drink sales on air temperature, correlation coefficient, prediction and the reverse regression line
IB Year 6 | Grade 12
6 marks
A café records the midday air temperature, \(C\) degrees Celsius, and the number of hot drinks sold, \(N\), on eight randomly chosen days.
| Temperature (\(C\ ^\circ\text{C}\)) | \(12\) | \(15\) | \(9\) | \(18\) | \(21\) | \(14\) | \(17\) | \(10\) |
|---|---|---|---|---|---|---|---|---|
| Hot drinks sold (\(N\)) | \(72\) | \(67\) | \(85\) | \(55\) | \(51\) | \(66\) | \(62\) | \(79\) |
The regression line of \(N\) on \(C\) has equation \(N=pC+q\).
- Find the values of \(p\) and \(q\).[2]
- Write down \(r\), the product-moment correlation coefficient of the data.[1]
- Use your regression line to predict the number of hot drinks sold on a day when the midday air temperature is \(16^\circ\text{C}\).[2]
- The regression line of \(C\) on \(N\) has equation \(C=sN+t\).Find the values of \(s\) and \(t\).[1]
Solution:
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Answer:(a) \(p=-2.74,\ q=107\) (b) \(r=-0.982\) (c) \(63\) hot drinks (d) \(s=-0.352,\ t=38.1\)
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