4. An internet service provider runs a series of television adverts at weekly intervals. To investigate the effectiveness of the adverts the company recorded the viewing figures in millions, \(v\), for the programme in which the advert was shown, and the number of new customers, \(c\), who signed up for their service the next day.
The results are summarised as follows.
$$\bar { v } = 4.92 , \quad \bar { c } = 104.4 , \quad S _ { v c } = 594.05 , \quad S _ { v v } = 85.44 .$$
- Calculate the equation of the regression line of \(c\) on \(v\) in the form \(c = a + b v\).
- Give an interpretation of the constants \(a\) and \(b\) in this context.
- Estimate the number of customers that will sign up with the company the day after an advert is shown during a programme watched by 3.7 million viewers.
- State two other factors besides viewing figures that will affect the success of an advert in gaining new customers for the company.