7. Pipes-R-us manufacture a special lightweight aluminium tubing.
The price \(\pounds P\), for each length, \(l\) metres, that the company sells is shown in the table.
| \(l\) (metres) | 0.5 | 0.8 | 1.0 | 1.5 | 2 | 4 | 6 |
| \(P ( \pounds )\) | 2.50 | 3.40 | 4.00 | 5.20 | 6.00 | 10.50 | 15.00 |
- Represent these data on a scatter diagram.
You may use
$$\Sigma l = 15.8 , \quad \Sigma P = 46.6 , \quad \Sigma l ^ { 2 } = 60.14 , \quad \Sigma l P = 159.77$$
- Find the equation of the regression line of \(P\) on \(l\) in the form \(P = a + b l\).
- Give a practical interpretation of the constant b.
In response to customer demand Pipes- \(R\)-us decide to start selling tubes cut to specific lengths. Initially the company decides to use the regression line found in part (b) as a pricing formula for this new service.
- Calculate the price that Pipes- \(R\)-us should charge for 5.2 metres of the tubing.
- Suggest a reason why Pipes- \(R\)-us might not offer prices based on the regression line for any length of tubing.