- A random sample of 24 adults is taken. The height, \(h\) metres, and the arm span, \(s\) metres, for each adult are recorded.
These data are summarised below.
$$\mathrm { S } _ { h h } = 0.377 \quad \mathrm {~S} _ { s h } = 0.352 \quad \bar { s } = 1.70 \quad \bar { h } = 1.68$$
The least squares regression line of \(h\) on \(s\) is
$$h = a + 0.919 s$$
where \(a\) is a constant.
- Calculate the product moment correlation coefficient.
A doctor uses the least squares regression line of \(h\) on \(s\) as a model to predict a person's height based on their arm span.
- Use the model to predict the height of an adult with arm span 1.79 metres.
Ewan has an arm span of 1.70 metres and a height of 1.75 metres. His information is added to the sample as the 25th adult.
- Explain how the gradient of the regression line for the sample of 25 adults compares with the gradient of the regression line for the original sample of 24 adults.
Give a reason for your answer.