1 A manufacturer of playground safety tiles is testing a new type of tile. Tiles of various thicknesses are tested to estimate the maximum height at which people would be unlikely to sustain injury if they fell onto a tile. The results of the test are as follows.
| Thickness \(( t \mathrm {~mm} )\) | 20 | 40 | 60 | 80 | 100 |
| Maximum height \(( h \mathrm {~m} )\) | 0.72 | 1.09 | 1.62 | 1.97 | 2.34 |
- Draw a scatter diagram to illustrate these data.
- State which of the two variables is the independent variable, giving a reason for your answer.
- Calculate the equation of the regression line of maximum height on thickness.
- Use the equation of the regression line to calculate estimates of the maximum height for thicknesses of
(A) 70 mm ,
(B) 120 mm .
Comment on the reliability of each of these estimates. - Calculate the value of the residual for the data point at which \(t = 40\).
- In a further experiment, the manufacturer tests a tile with a thickness of 200 mm and finds that the corresponding maximum height is 2.96 m . What can be said about the relationship between tile thickness and maximum height?