4 The time taken for a fax machine to scan an A4 sheet of paper is dependent, in part, on the number of lines of print on the sheet. The table below shows, for each of a random sample of 8 sheets of A4 paper, the number, \(x\), of lines of print and the scanning time, \(y\) seconds, taken by the fax machine.

1. Calculate the equation of the least squares regression line of \(y\) on \(x\).
2. The following table lists some of the residuals for the regression line.

   Sheet	\(\mathbf { 1 }\)	\(\mathbf { 2 }\)	\(\mathbf { 3 }\)	\(\mathbf { 4 }\)	\(\mathbf { 5 }\)	\(\mathbf { 6 }\)	\(\mathbf { 7 }\)	\(\mathbf { 8 }\)
   Residual	- 0.174	0.418		0.085	- 0.254	0.906		- 0.157

   1. Calculate the values of the residuals for sheets 3 and 7 .
   2. Hence explain what can be deduced about the regression line.
3. The time, \(z\) seconds, to transmit an A4 page after scanning is given by: $$z = 0.80 + 0.05 x$$ Estimate the total time to scan and transmit an A4 page containing:
   1. 15 lines of print;
   2. 75 lines of print. In each case comment on the likely reliability of your estimate.