Regression line of soup sales on temperature, a prediction, the mean point and drawing the line on a scatter diagram
Regression line of soup sales on temperature, a prediction, the mean point and drawing the line on a scatter diagram
7 marks
On eight winter days, a café recorded the midday temperature, \(x\) degrees Celsius, and the volume of hot soup sold, \(y\) litres. The results are given in the table.
| \(x\) | \(2.4\) | \(5.1\) | \(7.8\) | \(10.2\) | \(13.5\) | \(15.9\) | \(18.6\) | \(22.5\) |
|---|---|---|---|---|---|---|---|---|
| \(y\) | \(27.6\) | \(25.2\) | \(23.9\) | \(20.6\) | \(19.5\) | \(16.4\) | \(15.8\) | \(11.0\) |
These eight data points are plotted on the scatter diagram below.
The regression line of \(y\) on \(x\) for these data has equation \(y=ax+b\).
- Write down \(a\) and \(b\), correct to 3 significant figures.[2]
- Use the regression line to estimate the volume of soup sold on a day when the midday temperature is \(16\) degrees Celsius.[2]
- State the mean temperature, \(\bar{x}\), and the mean volume of soup, \(\bar{y}\).[1]
- On the scatter diagram, draw the regression line of \(y\) on \(x\).[2]
Solution:
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Answer:(a) \(a=-0.793,\ b=29.5\) (b) \(16.8\) litres (c) \(\bar{x}=12,\ \bar{y}=20\) (d) straight line through \((12,\ 20)\) and \((0,\ 29.5)\)
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