- The age, \(t\) years, and weight, \(w\) grams, of each of 10 coins were recorded. These data are summarised below.
$$\sum t ^ { 2 } = 2688 \quad \sum t w = 1760.62 \quad \sum t = 158 \quad \sum w = 111.75 \quad S _ { w w } = 0.16$$
- Find \(S _ { t t }\) and \(S _ { t w }\) for these data.
- Calculate, to 3 significant figures, the product moment correlation coefficient between \(t\) and \(w\).
- Find the equation of the regression line of \(w\) on \(t\) in the form \(w = a + b t\)
- State, with a reason, which variable is the explanatory variable.
- Using this model, estimate
- the weight of a coin which is 5 years old,
- the effect of an increase of 4 years in age on the weight of a coin.
It was discovered that a coin in the original sample, which was 5 years old and weighed 20 grams, was a fake.
- State, without any further calculations, whether the exclusion of this coin would increase or decrease the value of the product moment correlation coefficient. Give a reason for your answer.