Hello. Kindly help solving these questions

B3. 1) The linear model for n observations on a response and p explanatory variables may be written in matrix form as Y = X8 +6, where ( ~ No(0. o'1,) (o' > 0). Assume that the known design matrix X is of full rank. a) Denote H = X(XTX) 'X". Show that # is symmetric and idempotent, and further show that 0 S ha S 1 using the idempotent property. where , is the ith diagonal element of # (i = 1, ..., n).\fConsider the problem on multiple linear regression in which you have p predictor variables z(1),..., I(P) The model is given by Y = So + Biz(1) + . .. + for(P) + . where e ~ N(0,?). Suppose that we have n random samples of Y, i.e. Y, for i = 1, . .., n that satisfy with 0 and f" (k) 0 the economy will eventually converge to a constant value for k denoted by k". (d) Define the long-run equilibrium concept of the Balanced Growth Path (BGP). Derive the growth rates of capital (K), output (Y), capital per worker (K/L) and output per worker (Y/L) along the BGP.Consider the standard version of the Solow growth model discussed in class. The production function is Y (t) = F(K(t), A(t) I(t) ), (1) while the rate of change of capital is given by K (t ) = BY (t) - 8K (t) . (2) Labor L (t) and the "effectiveness of labor" A (t) are assumed to grow at the exogenous rates n and 9, respectively. (a) Assuming that (1) exhibits constant returns to scale, show that the production function can be written in intensive form as y (t ) = 1 (k (t) ), (3) where y ( t ) = Y (t) / ( A (t) L (t)) and k (t) = K (t) / (A (t) L (t)). (b) Show that (2) can be written in intensive form as k ( t ) = of ( k (t) ) - (n+ g + 8) k(t). (4) What is the interpretation of (4)