The linear regression model in matrix format is Y Xe, with the usual definitions. Let E(elX)- 0 a...
2. The linear regression model in matrix format is Y Χβ + e, with the usual definitions Let E(elX) 0 and T1 0 0 01 0 r2 00 0 0 0 0.0 0 γΝ 0 00 Notice that as a covariance matrix, Σ is bymmetric and nonnegative definite () Derive Var (0LS|x). (ii) Let B- CY be any other linear unbiased estimator where C' is an N x K function of X. Prove Var (BIX) 2 (X-x)-1 3. An oracle...
1.Given the Multiple Linear regression model as Y-Po + β.X1 + β2X2 + β3Xs + which in matrix notation is written asy-xß +ε where -έ has a N(0,a21) distribution + + ßpXo +ε A. Show that the OLS estimator of the parameter vector B is given by B. Show that the OLS in A above is an unbiased estimator of β Hint: E(β)-β C. Show that the variance of the estimator is Var(B)-o(Xx)-1 D. What is the distribution o the...
Consider the simple linear regression model y - e, where the errors €1, ,en are iid. random variables with Eki-0, var(G)-σ2, i-1, .. . ,n. Solve either one of the questions below. 1. Let Bi be the least squares estimator for B. Show that B is the best linear unbiased estimator for B1. (Note: you can read the proof in wikipedia, but you cannot use the matrix notation in this proof.) 2. Consider a new loss function Lx(A,%) 71 where...
linear stat modeling & regression please , i need the solution for Q3, but i copy Q2 because you need info from Q2 in order to answer Q3. 2) Suppose you have multiple regression set up YxXBp The ridge regression estimator is given by Here, llell'-Σ.< where is a vector of Vik. a) Find the expectation and variance-covariance matrix of Bridge, when X'X is a diagonal matrix with each diagonal entry is eqal to. Com pare these variances with the...
linear stat modeling & regression 1) Consider n data points with 3 covariates and observations {xn, ^i2, xi3,yid; i,,n, and you fit the following model, y Bi+Br2+Br+e that is yi A) +Ari,1 +Ari,2 +Buri,3 + єї where є,'s are independent normal distribution with mean zero and variance ơ2 . H the vectors of (Y1, . . . ,Yn). Assume the covariates are centered: Σίχί,,-0, k = 1,2,3. ere, n = 50, Let L are Assume, X'X is a diagonal matrix...
1. Consider the following linear model y Xp+ €, where Cor(e)-021 with ơ e R+ being unknown. an estimable function, where C is a full column rank matrix of rank s. Let T'y be the Let C. β BLUE for CB Write down an explicit expression for T. It should be only in terms of C, y and X. a. basic result do you use to justify your answer? V Cov(Ty). hypothesis is H CB o. (Ty- d), where b....
Exercise 1 Answer the following questions: a. Consider the multiple regression model y-Xe subject to a set of linear constraints of the form Cß-γ, where C is mx (k + 1) matrix. The Gauss-Markov conditions hold and also ε ~ N(0, σ21) Is it true that we can test the hypothesis C9-γ using a k¿SSRfillm d SKreducedmodel Please explain b. Refer to question (a). Let H and Hi be the hat matrices of the full and reduced model respectively. Show...