1. For the clinical trial considered in Tutorial 5, Question 3, treat the operation as a single factor and the four combinations of operation A and B as the levels, i.e., treat (no,no); (yes, no), (no, yes) and (yes, yes) respectively as level 1, 2, 3 and 4. The data is re- described as follows: Level | Measurements 1 31.02 24.03 28.37 26.57 25.83 25.87 26.08 24.89 28.32 29.98 20.41 20.31 23.45 13 35.71 34.83 35.13 38.30 33.12 42.07 38.69 43.16 33.11 42.47 40.45 31.95 38.69 42.26 14 25.85 39.77 32.88 46.29 33.07 29.23 31.39 28.28 22.43 38.42 TO 49.47 42.29 48.60 47.10 33.63 32.00 49.31 50.81 (i) [5 marks] Write R-codes to fit the following model: y = Po + Bruz + Bous + PAULA + E, where uj's are the dummy variable defined in the conventional way for the factor operation. Provide the summary table and the estimated variance matrix of the estimated regression parameters. (ii) [10 marks] Do a general exploring to find out whether there are any significant contrasts among the four treatment means. Identify at least FOUR apparently significant contrasts. Give reasons why you identify them. Test their significance by controlling the family-wise type I error rate at level of = 0.05. (iii) [5 marks] Construct 95% simultaneous confidence intervals for the contrasts iden- tified in (ii). (iv) The clinician was only concerned with whether or not operation A and B have significant main effect and whether or not there is significant interaction between the two operations. These correspond to whether or not the following contrasts are significantly nonzero: (a) me + pa - (me + pa), (b) * + me - (pa + p4) and (c) #1 - M2 - (#3 - HA). (iva) [5 marks] Express the contrasts in terms of the regression parameters. (ivb) [5 marks] Test the significance of the contrasts using a proper criterion to control the overall type I error rate at o = 0.05