Need help with #5, please. Thank you
Need help with #5, please. Thank you For the following problems assume y = Χβ +...
For the following problems assume y = Χβ + ε and assume E(e) 0 and var(e) σ21. 3. Show that έ (1-X (XTX)-XT) ε. (Hint: Use the assumption that y + ε)
For the following problems assume y = Χβ + ε and assume E(e) 0 and var(e) σ21. 2. The vector of predicted values is defined as У-Xß. Show var(y) = σ2X(XTX)-XT.
For the following problems assume y-Xß + ε and assume E(e)-0 and var(e)-σ21 1. We are often interested in estimating where r. is a (p+ 1)x 1 vector of predictors. We will find that a reasonable estimator is Find var(y*).
Let y = Xß + ε where ε ~ N(0, σ21). Let β = (XTX)-"XTy and let è-y-X β. (a) Show that è-(1-Pxje where Px (b) Compute Ee -e 2. X(XTX)-1x" (1 (c) Compute Varle-e. Let y = Xß + ε where ε ~ N(0, σ21). Let β = (XTX)-"XTy and let è-y-X β. (a) Show that è-(1-Pxje where Px (b) Compute Ee -e 2. X(XTX)-1x" (1 (c) Compute Varle-e.
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...
2. In the regression model Y-Χβ+ E, Xis a fixed n x k matrix of rank k S11, E(c)-0 and E(es')-σ2Ω where Ω is a known non-singular matrix. The GiLS estimator of B is given by the formula Consider the following data 16 31 2 3 51 4 10 Assuming that Ay a) b) Calculate the GLS estimate of β in the model Y,Xß + ε Calculate the OLS estimate c) Compare it the two estimates and comment on efficiency.
In need of help with these problems, can you please show work to know how it was done please and thank you 10. For the function (x) = 6sinx - 3 cos 2x on (0,2x) Find all critical numbers. You will want to recall the identity sin 2x=2 sin .xcosx 11. Find the indefinite integrals 10x + 4x +5 12. Find the indefinite integral ſ3x sin(2x) dx
e. Consider the multiple regression model y X 3+E. with E(e)-0 and var (e) ơ21 Assume that ε ~ N(0 σ21), when we test the hypothesis Ho : βί-0 against Ha : βί 0 we use the t statistic with n-k-1 degrees of freedom. When Ho is not true find the expected value and variance of the test onsider the genera -~ 0 gains 0 1S not true find the expected value and variance of the test statistic. e. Consider...
Please help me finish these two problems, I really have no way. Thank you for your patience! thank you! 3. -/2 points SCalcET7 14.8.004. Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.) f(x, ) = 6x + 6y; x2 + y2 = 18 maximum minimum Need Help? Talk to a Tutor Show My Work (Optional) 4. -12 points ScalcET7 14.8.005. Use Lagrange...
please help if you know Optimization with Quadratic Functions Could you please prove 89. Thank you so much ! Quadratic Functions A quadratic function is a mapping Q R R that is a scalar combination of single variables and pairs of variables. Thus, there are coefficients Cli,] and Ell, and a real number q, such that for X E IRn, we have The m atrix notation for C is suggestive. Indeed, C is n × n, and we take E...