- Two students, Olive and Shan, collect data on the weight, \(w\) grams, and the tail length, \(t \mathrm {~cm}\), of 15 mice.
Olive summarised the data as follows
$$\mathrm { S } _ { t t } = 5.3173 \quad \sum w ^ { 2 } = 6089.12 \quad \sum t w = 2304.53 \quad \sum w = 297.8 \quad \sum t = 114.8$$
- Calculate the value of \(\mathrm { S } _ { t w }\) and the value of \(\mathrm { S } _ { w w }\)
- Calculate the value of the product moment correlation coefficient between \(w\) and \(t\)
- Show that the equation of the regression line of \(w\) on \(t\) can be written as
$$w = - 16.7 + 4.77 t$$
- Give an interpretation of the gradient of the regression line.
- Explain why it would not be appropriate to use the regression line in part (c) to estimate the weight of a mouse with a tail length of 2 cm .
Shan decided to code the data using \(x = t - 6\) and \(y = \frac { w } { 2 } - 5\)
- Write down the value of the product moment correlation coefficient between \(x\) and \(y\)
- Write down an equation of the regression line of \(y\) on \(x\) You do not need to simplify your equation.