Consider the simplified classical normal linear regression problem written in matrix notation:y = Xβ + u, u ∼ N (0, σ 2 I n ), β ∈ R K , σ > 0

Consider the simplified classical normal linear regression problem written in matrix notation:y = Xβ + u, u ∼ N (0, σ 2 I n ), β ∈ R K , σ > 0,where y is an n-vector of endogenous variables, and X is a n × k matrix of regressors. Under whatcondition(s) is the parameter β point-identified in this model? Explain

Write a program to find the normal of a matrix.Input format :The first line of the input consists of the value of N.The second line of the input consists of matrix elements.Output format :The output prints the normal of the given matrix.Refer to the sample input and output for format specifications.Sample test cases :Input 1 :51 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 5Output 1 :16Input 2 :41 2 3 45 6 7 89 10 11 1213 14 15 16Output 2 :38

(a) Consider the classical linear regression model: y = Xβ + u under the Gauss Markov assumptions, such that E uu = σ 2 I . Consider the estimator for σ 2 given by s2∗ = e e/(T − 10) where e is the OLS residual vector: is this an unbiased estimator? If not, how can we correct it to get an unbiased estimator of σ 2 . (b) Consider the generalized linear regression model. State the model in matrix algebra form. Show that there exists a transformation of the model that satisfies all the Gauss Markov assumptions. Derive the GLS estimator and compute its variance-covariance matrix.

consider y=(y1, y2, ... yn) and X= (1 x1, 1 x2, ..., 1 xn). a) show that i) (X^T)X = (n nx, nx Σxi^2). ii) det((X^T)X) = n Sxx. b) state a necessary and sufficient condition on x1, x2, ..., xn for (X^T)X to be invertible. c) show that if (X^T)X is invertible, then (((X^t)X)^-1)(X^T)y = (y-(Sxy/Sxx)x Sxy/Sxx). Hint use the facts that Sxx = Σn, i=1 (xi^2-nx^2), Sxy = Σn,i=1 (xiyi - nxy).

(b) Consider the generalized linear regression model. State the model in matrix algebra form. Show that there exists a transformation of the model that satisfies all the Gauss Markov assumptions. Derive the GLS estimator and compute its variance-covariance matrix.