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(c) Show that V(3) = o²(X'V-¹X)-¹.

(c) Show that V(3) = o²(X'V-¹X)-¹.

MATLAB: An Introduction with Applications
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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Please solve question 3c
Heb54003f794/8531422?X-Blackboard-Expiration=1651449600000&X-Blackboard-Signature=LCRFiaXEwbV4rx%2FU1D8814E 1 / 2 100% + Po or as you need) to linearize the functions below. x1 y= B11+ Bo- 3. Consider a multiple linear regression model Y = X3 + € (n x 1) (n xp) (p x 1) (n x 1) where n is the sample size, p=k+1 with k is the number of regressors and E(e) = 0, V(e) = o²V. Consider the transformed model B3+ g with new variables. 2= K-¹₂ y₂ B = K-¹X, g= K ¹e with K'KKK' = KK = V (K is symmetric ). (a) Show that (B'B)-¹B'z = (X'V-¹X)-¹X'V-¹y. (b) Show that = (X'V-¹X)-¹X'V-¹y is an unbiased estimator of 3. k (c) Show that V(B) = o²(X'V-¹X)-¹. 4. Consider a multiple linear regression model Y (n x 1) = XB + (n xp) (P x 1) € (nx 1) where n is the sample size, p=k+1 with k is the number of regressors and E(e) = 0, V(e) = o² In- M DELL а
Transcribed Image Text:Heb54003f794/8531422?X-Blackboard-Expiration=1651449600000&X-Blackboard-Signature=LCRFiaXEwbV4rx%2FU1D8814E 1 / 2 100% + Po or as you need) to linearize the functions below. x1 y= B11+ Bo- 3. Consider a multiple linear regression model Y = X3 + € (n x 1) (n xp) (p x 1) (n x 1) where n is the sample size, p=k+1 with k is the number of regressors and E(e) = 0, V(e) = o²V. Consider the transformed model B3+ g with new variables. 2= K-¹₂ y₂ B = K-¹X, g= K ¹e with K'KKK' = KK = V (K is symmetric ). (a) Show that (B'B)-¹B'z = (X'V-¹X)-¹X'V-¹y. (b) Show that = (X'V-¹X)-¹X'V-¹y is an unbiased estimator of 3. k (c) Show that V(B) = o²(X'V-¹X)-¹. 4. Consider a multiple linear regression model Y (n x 1) = XB + (n xp) (P x 1) € (nx 1) where n is the sample size, p=k+1 with k is the number of regressors and E(e) = 0, V(e) = o² In- M DELL а
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