(c) Show that V(3) = o²(X'V-¹X)-¹.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Related questions
Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fb8d2d8-3257-4894-91bc-492e5f32e00a%2F29c04879-8b01-4a6f-b3c4-7f61afcb1d80%2F6fpldn_processed.jpeg&w=3840&q=75)
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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