4. A drilling machine can run at various speeds, but in general the higher the speed the sooner the drill needs to be replaced. Over several months, 15 pairs of observations relating to speed, \(s\) revolutions per minute, and life of drill, \(h\) hours, are collected.
For convenience the data are coded so that \(x = s - 20\) and \(y = h - 100\) and the following summations obtained.
\(\Sigma x = 143 ; \Sigma y = 391 ; \Sigma x ^ { 2 } = 2413 ; \Sigma y ^ { 2 } = 22441 ; \Sigma x y = 484\).
- Find the equation of the regression line of \(h\) on \(s\).
- Interpret the slope of your regression line.
Estimate the life of a drill revolving at 30 revolutions per minute.
(2)