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- Consider a multiple linear regression model Y - XB + (nx p) (p x 1) € (n 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) = 0²V. Consider the transformed model z = вз + 9 with new variables 4 z = K-¹y, B = K-¹X, g= K ¹e with K'K - KK' = KK = V (K is symmetric ). (a) Show that (B'B)−¹B'z = (X'V-¹X)-¹X'V−¹y. (b) Show that B = (X'V-¹X)-¹X'V-¹y is an unbiased estimator of 3.

- Consider a multiple linear regression model Y - XB + (nx p) (p x 1) € (n 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) = 0²V. Consider the transformed model z = вз + 9 with new variables 4 z = K-¹y, B = K-¹X, g= K ¹e with K'K - KK' = KK = V (K is symmetric ). (a) Show that (B'B)−¹B'z = (X'V-¹X)-¹X'V−¹y. (b) Show that B = (X'V-¹X)-¹X'V-¹y is an unbiased estimator of 3.

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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Regression analysis class
- Consider a multiple linear regression model XB (n x 1) (n x p)(p x 1) (n x 1) where n is the sample size, p k+ 1 with k is the number of regressors and %3D E(e) = 0, V(e) =o²V. Consider the transformed model BB with new variables z = K-'y, B= K-'X, g = K-'e with K'K = KK' = KK = V (K is symmetric ). (a) Show that (B'B)-'B'z = (X'V-1X)-1X'V-ly. (b) Show that B = (X'V-'X)-'X'V-!y is an unbiased estimator of ß.
Transcribed Image Text:- Consider a multiple linear regression model XB (n x 1) (n x p)(p x 1) (n x 1) where n is the sample size, p k+ 1 with k is the number of regressors and %3D E(e) = 0, V(e) =o²V. Consider the transformed model BB with new variables z = K-'y, B= K-'X, g = K-'e with K'K = KK' = KK = V (K is symmetric ). (a) Show that (B'B)-'B'z = (X'V-1X)-1X'V-ly. (b) Show that B = (X'V-'X)-'X'V-!y is an unbiased estimator of ß.
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