- The production cost, \(\pounds c\) million, of a film and the total ticket sales, \(\pounds t\) million, earned by the film are recorded for a sample of 40 films.
Some summary statistics are given below.
$$\sum c = 1634 \quad \sum t = 1361 \quad \sum t ^ { 2 } = 82873 \quad \sum c t = 83634 \quad \mathrm {~S} _ { c c } = 28732.1$$
- Find the exact value of \(\mathrm { S } _ { t t }\) and the exact value of \(\mathrm { S } _ { c t }\)
- Calculate the value of the product moment correlation coefficient for these data.
- Give an interpretation of your answer to part (b)
- Show that the equation of the linear regression line of \(t\) on \(c\) can be written as
$$t = - 5.84 + 0.976 c$$
where the values of the intercept and gradient are given to 3 significant figures.
- Find the expected total ticket sales for a film with a production cost of \(\pounds 90\) million.
Using the regression line in part (d)
- find the range of values of the production cost of a film for which the total ticket sales are less than \(80 \%\) of its production cost.