Can you answer following question, I need solution for my practice exam.

Consider the full rank linear model y = X ,8 + a with p parameters. Now suppose that we transform the design variables :1: in a linear manner: :9 zi=2ajimj, z=1,...,p. i=1 (Note that the :1: variables include the intercept term.) Now consider the linear model y = Z162 + 52, which also has 1) parameters. (a) [2 marks] Express the design matrix Z in terms of X, and state a condition under which the second linear model is also full rank. (b) [3 marks] Calculate the least squares estimators for z from the second model, and express them in terms of b, the least squares estimators for [3. (c) [2 marks] Consider a subject with design variables x* (for the rst model). Calculate a point estimate for the average response for this subject, using the second model, and express it in terms of b. (d) [3 marks] Calculate the sample variance for the second model, and express it in terms of the sample variance for the rst model. (e) [2 marks] Briey discuss the implications of the results you have derived above in the context of tting a linear model, with particular reference to variable standardisation