1 A geography student chose a certain point in a stream and took measurements of the speed of flow, \(v \mathrm {~ms} ^ { - 1 }\), of water at various depths, \(d \mathrm {~m}\), below the surface at that point. The results are shown in the table.
| \(d\) | 0.1 | 0.15 | 0.2 | 0.25 | 0.3 | 0.35 | 0.4 | 0.45 | 0.5 |
| \(v\) | 0.8 | 0.5 | 0.7 | 1.2 | 1.1 | 1.3 | 1.6 | 1.4 | 0.4 |
\(n = 9 \quad \sum d = 2.7 \quad \sum v = 9.0 \quad \sum d ^ { 2 } = 0.96 \quad \sum v ^ { 2 } = 10.4 \quad \sum \mathrm {~d} v = 2.85\)
- Explain why \(d\) is an example of an independent, controlled variable.
- Use two relevant terms to describe the variable \(v\) in a similar way.
A statistician believes that the point ( \(0.5,0.4\) ) may be an anomaly.
- Calculate the equation of the least squares regression line of \(v\) on \(d\) for all the points in the table apart from ( \(0.5,0.4\) ).
- Use the equation of the line found in part (b) to estimate the value of \(v\) when \(d = 0.5\).
- Use your answer to part (c) to comment on the statistician’s belief.
- Use the diagram in the Printed Answer Booklet (which does not illustrate the data in this question) to explain what is meant by "least squares regression line".