Consider the linear regression modelYt = Bo + B1(x1)e + ..+ Bk(Xx)t + Ut, t 1,... T,where the regressors 1, x1,...,X and errors u satisfy the Gauss-Markov assumptions.Let R? be the (centered) R2 of the regression of xj on all other regressors including aconstant. Show that for the OLS estimators of B1,...Bk it holdsvar ß, =T. Sx(1-R)Remark: The factorRis called the variance inflation factor and is used as an indicator of multicollinearityHint. Use the Frisch-Waugh theorem to partial out all other regressors,

The ideal regression model with various assumptions is given as Description of an ideal dataset…

Answered: Yt = Bo + B1(x1)t + ·…· + Bx(Xx)t + Ue,…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

See similar textbooks

Similar questions

If Kt = B2t - t, where B is standard Brownian Motion, show that Kt is a martingale, and a markov process
Which of the following processes (Xt)t is weakly stationary? A: Xt = 1:6 + Xt 1 + V tB: Xt = 0:6 Xt-1 +V tC: Xt = 0:8 Xt-1 + V tD: Xt = 0:8 t + 0:6 V t – 1 The term (t) is always assumed to be white noise with variance one
Let A be an n × n positive stochastic matrix withdominant eigenvalue λ1 = 1 and linearly independenteigenvectors x1, x2, . . . , xn, and let y0 be aninitial probability vector for a Markov chainy0, y1= Ay0, y2= Ay1, . . . Show that if y0 = c1x1 + c2x2 +· · ·+cnxn then the component c1 in the direction of the positive eigenvector x1 must be nonzero.
Find the matrix for the D-H parameter -90 beta, d =0,a=0 , alpha = -90 using Niku
31 - Find the regression model. Regresyon modelini bulunuz. Y X 2 5 5 9 7 4 4 11A) y=-3,21+2,11xB) y=2,56+5,43xC) y=5,27+0,11x
Suppose that X k is a time-homogenous Markov chain. Show thatP{X3= j3, X2= j2|X0= j0,X1 = j1}= P{X3 = j3 | X2 = j2} P{X2 = j2|X1 = j1}.
Find the general solution of the linear system (1) when A is then x n diagonal matrix A = diag[Aj, A21... ,An]- What condition onthe eigenvalues Al, ... , An will guarantee that limt_,,. x(t) = 0 for allsolutions x(t) of (1)?
Consider the Markov chain with transition matrix: 0 0 0.1 0.9 0 0 0.6 0.4 0.8 0.2 0 0 0.4 0.6 0 0 Find the limit of p2n(x,x) as n -> infinity.
Pij = P(Xn+1 =j|Xn=i) Xn is a Markov chain Show that for a fixed i, Sum of jPij = 1
The function f (x, y) = 2xy certainly has a saddle point and not a minimum at (0, 0). What symmetric matrix S produces this f? What are its eigenvalues?
Suppose we have collected a random sample from our population, denoted by (xi , yi), i = 1, . . . , n. We now fit a least squares line: yˆi = βˆ 0 + βˆ 1xi (i = 1, . . . , n). What additional assumption do we need in order to carry out statistical inference on our least square estimators βˆ 0 and βˆ 1? c. Using the results we’ve derived in class, prove that the sum of residuals is zero (Pn i=1 ei = 0)
Starting from the linearly independent functions yn(x) = xn where n = 0, 1, · · · , use Gram–Schmidt orthogonalisation to construct the first three orthonormal functions over the range −1 < x < 1, assuming a weight function of unity, and verify that they are mutually orthogonal.

SEE MORE QUESTIONS

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS