5 A shop manager recorded the maximum daytime temperature \(T ^ { \circ } \mathrm { C }\) and the number \(C\) of ice creams sold on 9 summer days.
The results are given in the table and illustrated in the scatter diagram.
| \(T\) | 17 | 21 | 25 | 26 | 27 | 27 | 29 | 30 | 30 |
| \(C\) | 21 | 16 | 20 | 38 | 32 | 37 | 35 | 39 | 42 |
\includegraphics[max width=\textwidth, alt={}]{64d7ed6d-fadd-4c59-afb0-97d1788ba369-3_661_1189_1320_431}
$$n = 9 , \Sigma t = 232 , \Sigma c = 280 , \Sigma t ^ { 2 } = 6130 , \Sigma c ^ { 2 } = 9444 , \Sigma t c = 7489$$
- State, with a reason, whether one of the variables \(C\) or \(T\) is likely to be dependent upon the other.
- Calculate Pearson's product-moment correlation coefficient \(r\) for the data.
- State with a reason what the value of \(r\) would have been if the temperature had been measured in \({ } ^ { \circ } \mathrm { F }\) rather than \({ } ^ { \circ } \mathrm { C }\).
- Calculate the equation of the least squares regression line of \(c\) on \(t\).
- The regression line is drawn on the copy of the scatter diagram in the Printed Answer Booklet. Use this diagram to explain what is meant by "least squares".