1.  (Worth 100 marks) Introduction To do something useful with big data, models are devised from the large numbers of observations in order to predict what will occur for some other observation(s). A simple linear model1 is of the form: where yi is the dependent variable, i is the observation number (there are a total of M observa- tions), xij is the set of independent variables, N is the number of independent variables (for big data, M N ), and aj are the set of model coefficients. Equation (1) lends itself to a matrix formulation: Y = X... More