- Tomas is studying the relationship between temperature and hours of sunshine in Seapron. He records the midday temperature, \(t ^ { \circ } \mathrm { C }\), and the hours of sunshine, \(s\) hours, for a random sample of 9 days in October. He calculated the following statistics
$$\sum s = 15 \quad \sum s ^ { 2 } = 44.22 \quad \sum t = 127 \quad \mathrm {~S} _ { t t } = 10.89$$
- Calculate \(\mathrm { S } _ { s s }\)
Tomas calculated the product moment correlation coefficient between \(s\) and \(t\) to be 0.832 correct to 3 decimal places.
- State, giving a reason, whether or not this correlation coefficient supports the use of a linear regression model to describe the relationship between midday temperature and hours of sunshine.
- State, giving a reason, why the hours of sunshine would be the explanatory variable in a linear regression model between midday temperature and hours of sunshine.
- Find \(\mathrm { S } _ { s t }\)
- Calculate a suitable linear regression equation to model the relationship between midday temperature and hours of sunshine.
- Calculate the standard deviation of \(s\)
Tomas uses this model to estimate the midday temperature in Seapron for a day in October with 5 hours of sunshine.
- State the value of Tomas' estimate.
Given that the values of \(s\) are all within 2 standard deviations of the mean,
- comment, giving your reason, on the reliability of this estimate.