Under the assumptions of the Simple Linear Regression (SLR) model:a. Show that Cov(Bo, B₁) = = [Hint: write Cov(ŝo, ß₁) = Cov(Ỹ – Î₁T, Î₁).]Sxx-b. Use the answer from part (a) to show that Bo and B₁ are independent ifx=0. [Hint: if W and X are linear combinations of independentnormal random variables, then Cov(W, X) = 0 W and X independent.]

Using the simple linear regression model We have to show that Cov(β0^,β1^)=-x¯/(σ2/Sxx)And based on…

Answered: Under the assumptions of the Simple…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Compute the coefficients b₁ and b₂ for the regression model y₁ = 60+ b₁x₁₁ +b2×21 given the summary statistics shown below. a. Tx₁y b. rx₁y c. Tx₁y d. = 0.80, x2y=0.60, =200, Sx2 = 0.40, Sx₁ 0,5x1x2 =-0.80, гx2y=0.60, rx₁x2 = -0.40, Sx₁ = 200, Sx2 = 100, sy = 500 = 100, 0, Sy = 500 100, Sy = 500 =0.80, x2y = -0.20, 0, rx₁x2 = -0.10, Sx₁ =200, Sx2 = 100, Sy = 500 =0.50, rx2y=0.75, x₁x2 = 0.70, Sx₁ =200, Sx2 =
q7-
4. Consider the Normal regression problem: Y,- N(a + Br, o) where a, 3. are unknown. Recall the following: a = Y- 37 S = SY = En - F)(Y - Y). Show that S,y E,(r, - 2)Y- Show that Cov(Y, Y) = for all i. Use part a and b and linearity of Covariance to show that Cov(8, Y) = 0. Show that Var(3) = ) „how that Cov(a, B) = - (Hint: part a , b and d may be useful in this cauculation).
Consider the regression model Y₁ = BX; +u; Y Where ui and X; satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ = Show that ẞ is a linear function of Y₁, Y2,..., Yn. Show that ẞ is conditionally unbiased. 1. E (YiX1, X2,..., Xn) = == X + +Yn) 2. E(B|×1, X2,..., Xn) = E = B Χ | (X1, X2,..., Xn) = where Y and X are the sample means of Y; and X;, respectively.
A linear multiple regression model is given as: Y = βo + β1 X1 + β2 X2 + μ a. Determine the parameters of this model b. Explain the circumstance under which X1 be called an endogenous variable?
1. Consider two least-squares regressions and y = Xíễ tế y = Xí$i+ XzB2 tê Let R2 and R2 be the R-squared from the two regressions. Show that R22 R2.
Use the following linear regression equation to answer the questions. x1 = 2.0 + 3.6x2 – 7.8x3 + 2.1x4 a) Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1?b) Suppose x2 increased by 2 units. What would be the expected change in x1?c) Suppose x2 decreased by 4 units. What would be the expected change in x1?

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