(b) A factory manager measures the amount of power used by a machine each hour, pro- viding a series of observations {X,}. A proposed model for this is X, = C+1X,-1 + 42X4-2+ i. What sort of model is this? [2 marks] ii. What assumption about {Xf} has been made to model the data this way? [2 marks] iii. If this assumption turns out to be false, give three ways the data might be trans- formed to make it true. [3 marks] iv. If the assumption is true, but the model is still a poor fit, give two ways the model could be modified. Write down an example of each of these modified models. [4 marks]