QUESTION 1 [23 Marks] Consider the following data from an oil company concerning 3 refineries and 2 processes. The recorded values are percentages of measure of efficiency (y). Process Refinery 1 2 31, 33 37, 59, 41 44. 36 39 42 1.1 Write out the equations for a regression on dummy variables considering the effect of refinery (a) and process () on efficiency. (6) 1.2 Rewrite the model equations in terms of the data and matrix notation. (5) 1.3 Write down the normal equations of the linear models for this situation. (6) 1.4 Carry out the analysis assuming no interaction model and present the results in an ANOVA table. (6)