1 Bob, a church warden, decides to investigate the lifetime of a particular manufacturer's brand of beeswax candle. Each candle is 30 cm in length. From a box containing a large number of such candles, he selects one candle at random. He lights the candle and, after it has burned continuously for \(x\) hours, he records its length, \(y \mathrm {~cm}\), to the nearest centimetre. His results are shown in the table.

1. State the value that you would expect for \(a\) in the equation of the least squares regression line, \(y = a + b x\).
2. 1. Calculate the equation of the least squares regression line, \(y = a + b x\).
   2. Interpret the value that you obtain for \(b\).
   3. It is claimed by the candle manufacturer that the total length of time that such candles are likely to burn for is more than 50 hours. Comment on this claim, giving a numerical justification for your answer.