In Myers and Montgomery (2002), a data set. Is discussed in which a 23 factorial is used by an engineer to study the effects of cutting speed (A), tool geometry (B) and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each factor are chosen, and duplicates were run at, each design point with the: order of the runs being random. The data are presented here.(a) Calculate all seven effects. Which appear, based on their magnitude, to be important?(b) Do an analysis of variance and observe P-values.(c) Do your results in (a) and (b) agree?(d) The engineer felt confident, that cutting speed and cutting angle should interact. If this interaction is significant, draw an interaction plot and discuss the engineering meaning of theinteraction.

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Life (1) 22. 31 32, 43 35. 34 35. 47 ab 44, 45 40. 37 60, 50 ac be abc 39, 41 OIIII + ++ + . +. +.