- Pat is investigating the relationship between the height of professional tennis players and the speed of their serve. Data from 9 randomly selected professional male tennis players were collected. The variables recorded were the height of each player, \(h\) metres, and the maximum speed of their serve, \(v \mathrm {~km} / \mathrm { h }\).
Pat summarised these data as follows
$$\sum h = 17.63 \quad \sum v = 2174.9 \quad \sum v ^ { 2 } = 526407.8 \quad S _ { h h } = 0.0487 \quad S _ { h v } = 5.1376$$
- Calculate the product moment correlation coefficient between \(h\) and \(v\)
- Explain whether the answer to part (a) is consistent with a linear model for these data.
- Find the equation of the regression line of \(v\) on \(h\) in the form \(v = a + b h\) where \(a\) and \(b\) are to be given to one decimal place.
Pat calculated the sum of the residuals for the 9 tennis players as 1.04
- Without doing a calculation, explain how you know Pat has made a mistake.
Pat made one mistake in the calculation. For the tennis player of height 1.96 m Pat misread the residual as 2.27
- Find the maximum speed of serve, in km/h, for the tennis player of height 1.96 m