7. An ice cream seller believes that there is a relationship between the temperature on a summer day and the number of ice creams sold. Over a period of 10 days he records the temperature at 1 p.m., \(t ^ { \circ } \mathrm { C }\), and the number of ice creams sold, \(c\), in the next hour. The data he collects is summarised in the table below.
| \(t\) | \(c\) |
| 13 | 24 |
| 22 | 55 |
| 17 | 35 |
| 20 | 45 |
| 10 | 20 |
| 15 | 30 |
| 19 | 39 |
| 12 | 19 |
| 18 | 36 |
| 23 | 54 |
[Use \(\left. \Sigma t ^ { 2 } = 3025 , \Sigma c ^ { 2 } = 14245 , \Sigma c t = 6526 .\right]\)
- Calculate the value of the product moment correlation coefficient between \(t\) and \(c\).
- State whether or not your value supports the use of a regression equation to predict the number of ice creams sold. Give a reason for your answer.
- Find the equation of the least squares regression line of \(c\) on \(t\) in the form \(c = a + b t\).
- Interpret the value of \(b\).
- Estimate the number of ice creams sold between 1 p.m. and 2 p.m. when the temperature at 1 p.m. is \(16 ^ { \circ } \mathrm { C }\).
(3) - At 1 p.m. on a particular day, the highest temperature for 50 years was recorded. Give a reason why you should not use the regression equation to predict ice cream sales on that day.
(1)