- A clothes shop manager records the weekly sales figures, \(\pounds s\), and the average weekly temperature, \(t ^ { \circ } \mathrm { C }\), for 6 weeks during the summer. The sales figures were coded so that \(w = \frac { s } { 1000 }\)
The data are summarised as follows
$$\mathrm { S } _ { w w } = 50 \quad \sum w t = 784 \quad \sum t ^ { 2 } = 2435 \quad \sum t = 119 \quad \sum w = 42$$
- Find \(\mathrm { S } _ { w t }\) and \(\mathrm { S } _ { t t }\)
- Write down the value of \(\mathrm { S } _ { s s }\) and the value of \(\mathrm { S } _ { s t }\)
- Find the product moment correlation coefficient between \(s\) and \(t\).
The manager of the clothes shop believes that a linear regression model may be appropriate to describe these data.
- State, giving a reason, whether or not your value of the correlation coefficient supports the manager's belief.
- Find the equation of the regression line of \(w\) on \(t\), giving your answer in the form \(w = a + b t\)
- Hence find the equation of the regression line of \(s\) on \(t\), giving your answer in the form \(s = c + d t\), where \(c\) and \(d\) are correct to 3 significant figures.
- Using your equation in part (f), interpret the effect of a \(1 ^ { \circ } \mathrm { C }\) increase in average weekly temperature on weekly sales during the summer.