Question

please help me to solve part b and c .

and please dont copy my answer in part a and then post it as an answer.

thanks

Consider two separate linear regression models and For concreteness, assume that the vector yi contains observations on the wealth ofn randomly selected individuals in Australia and y2 contains observations on the wealth of n randomly selected individuals in New Zealand. The matrix Xi contains n observations on ki explanatory variables which are believed to affect individual wealth in Australia, and he matrix X2 contains n observations on k2 explanatory variables which are believed to affect individual wealth in New Zealand. Notice that we are not assuming that the same regressors appear in both X and X2. For simplicity, we assume that Var(u1,2. In econometrics we often wish to combine two or more linear regression equations into a single equation. (a) Combine the linear regression models given by (1) and (2) into a single model of the form where y, u and B are partitioned vectors and Xis a partitioned matrix. Carefully specify the dimensions of each sub-matrix (sub-vector) of y.u, B and Xin (3). Note: The partitioning must satisfy the conformability conditions for matrix addition and matrix multiplication. (b) The formula for the OLS estimator of B in (3), which we denote by b, is i) Derive the partitioned matrix X X.Specify the dimensions of each element of the partitioned matrix. Hint: Let the partitioned matrix Ai A2 Then ii) Use the properties of partitioned matrices stated in lectures to derive the partitioned matrix (Xx)-1.Specify the dimensions of each element of the matrix iii) Derive the partitioned vector X'y. Specify the dimensions of each element of the vector. iv) Show that the partitioned vector b in (4) may be written as (kixl) b2 (k2x) where (c) What is the practical implication of the result in (b) iv) above? (d) Assume that the matrix X in (3) is an nxk matrix. Prove that if the column rank of Xis less than k, then X'X is a singular matrix and the OLS estimator of B in (3) is not defined. Consider y-Po +Ax be the estimated regression line We know that, y,x, 1 -1 572 x 43 1697.80 A14 43- 14 157.42- -2.33 yi 12 572 1 A-1-3) -(-2.33 P 48.01 Thus the linear regression can be given by, 48.01- 2.33r for x -3.7 y 48.01-2.33x3.7 v = 39.389 Thus the point estimate of mean permeability when compressive strength is 3.7 is 39.389 Residual 46.1-39.389 Residual = 6.71 1 Hence the corresponding residual is 6.711

Answer 1

Solotion Consilertp, be the estimades vegression ne 1672.80- S.413 凫恤' -A 늡러 Po48. the 3 The linear ㆆeyvesion can be given by Y= 48.01-2.33 x ye 48.01-2.33 3구 Y32-389 7 Thus the point ostimate af mean pesmeability Residua/-46小39.389 Hence the cote pending esiais