3. Consider the model of the form Yjk =p+a; +7; + Bitijk + Eijk for i = 1,...,1, j = 1,...,Jk=1,..., Nij and Eijk ~ N(0,

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3 Consider The Model Of The Form Yjk P A 7 Bitijk Eijk For I 1 1 J 1 Jk 1 Nij And Eijk N 0 1 (109.23 KiB) Viewed 33 times

3. Consider the model of the form Yjk =p+a; +7; + Bitijk + Eijk for i = 1,...,1, j = 1,...,Jk=1,..., Nij and Eijk ~ N(0,0%) independently for all 2, j and k. (a) This model can be regarded as extending a special case of linear regression models, by combining it with elements from another special case. Write downlthe names of those two special cases. [2 MARKS] (b) What does the absence of an interaction term between the a and y terms imply about the effects of these factors in this model? [1 MARK) (c) Write down the model in matrix-vector form for case where I=2 and J=2, defining each element. [5 MARKS] (a) State with justification whether or not the design matrix you wrote down in part (c) is of full rank and why this is important. [3 MARKS] (e) In order for these to be data from an experiment that is balanced with respect to the ox and terms, what condition(s) must be met? [1 MARK (f) What assumption is required for the usual estimation procedure to deliver maxi- mum likelihood estimates for this model? [1 MARK (g) An examination of some plots has shown 3 observations that may be outliers, Describe two plots that may have revealed these outliers. Suggest what the next step in the analysis should be. (3 MARKS] (h) Give an example of a study that this model could be used to analyse clearly stating the response variable and the variables that the o, and 3 terms refer to (4 MARKS