As part of a statistics project, Gill collected data relating to the length of time, to the nearest minute, spent by shoppers in a supermarket and the amount of money they spent. Her data for a random sample of 10 shoppers are summarised in the table below, where \(t\) represents time and \(\pounds m\) the amount spent over \(\pounds 20\).
\(t\) (minutes)
£m
15
-3
23
17
5
-19
16
4
30
12
6
-9
32
27
23
6
35
20
27
6
Write down the actual amount spent by the shopper who was in the supermarket for 15 minutes.
Calculate \(S _ { t t } , S _ { m m }\) and \(S _ { t m }\).
$$\text { (You may use } \Sigma t ^ { 2 } = 5478 \Sigma m ^ { 2 } = 2101 \Sigma t m = 2485 \text { ) }$$
Calculate the value of the product moment correlation coefficient between \(t\) and \(m\).
Write down the value of the product moment correlation coefficient between \(t\) and the actual amount spent. Give a reason to justify your value.
On another day Gill collected similar data. For these data the product moment correlation coefficient was 0.178
Give an interpretation to both of these coefficients.
Suggest a practical reason why these two values are so different.