6. A physics student recorded the length, \(l \mathrm {~cm}\), of a spring when different masses, \(m\) grams, were suspended from it giving the following results.
| \(m ( \mathrm {~g} )\) | 50 | 100 | 200 | 300 | 400 | 500 | 600 | 700 |
| \(l ( \mathrm {~cm} )\) | 7.8 | 10.7 | 16.5 | 22.1 | 28.0 | 33.9 | 35.2 | 35.6 |
- Represent these data on a scatter diagram with \(l\) on the vertical axis.
The student decides to find the equation of a regression line of the form \(l = a + b m\) using only the data for \(m \leq 500 \mathrm {~g}\).
- Give a reason to support the fitting of such a regression line and explain why the student is excluding two of his values.
(2 marks)
You may use
$$\Sigma m = 1550 , \quad \Sigma l = 119 , \quad \Sigma m ^ { 2 } = 552500 , \quad \Sigma l ^ { 2 } = 2869.2 , \quad \Sigma m l = 39540 .$$ - Find the values of \(a\) and \(b\).
- Explain the significance of the values of \(a\) and \(b\) in this situation.