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3. Let y = (91, .... ) be a set of responses, and consider the linear model where u = (u. .... p) and e is a vector of zero mean, uncorrelated errors with variance a?. This is a linear model in which the responses have a constant but unknown mean . We will call this model the location model. (a) If we write the location model in the usual form of the general linear model V = XA+6. then what is the design matrix X? What is 3? (b) Find XX, (X X] and XTy. (c) Using the results we have proved for the general linear models, find the least squares estimator of B. What is the estimator of unknown mean ? Is this estimator unbiased? (d) Using the results we have proved for the general linear models, derive an expression for an unbiased estimator of o' in the location model