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(c) Normal linear regression model, The regression equations can be written in matrix form as y=XB+e where y is the Nx 1 vector of observations of the dependent variable, X is the Nx K matrix of regressors, and is the Nx 1 error terms. With the i.i.d assumption, multivariate normal distribution of e on X, and full rank X, we can construct that the likelihood function of the linear regression model is (16-2189²) i=1 Show that the MLE of the regression coefficients 3 and the variance of the error terms o² are L(3,0²; y, X) = (2no²) -N/2 exp BN * = (M-TION) (XX)-¹XTy N i=1

(c) Normal linear regression model, The regression equations can be written in matrix form as y=XB+e where y is the Nx 1 vector of observations of the dependent variable, X is the Nx K matrix of regressors, and is the Nx 1 error terms. With the i.i.d assumption, multivariate normal distribution of e on X, and full rank X, we can construct that the likelihood function of the linear regression model is (16-2189²) i=1 Show that the MLE of the regression coefficients 3 and the variance of the error terms o² are L(3,0²; y, X) = (2no²) -N/2 exp BN * = (M-TION) (XX)-¹XTy N i=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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(c) Normal linear regression model The regression equations can be written in matrix form as y = XB+e where y is the Nx 1 vector of observations of the dependent variable, X is the N x K matrix of regressors, and is the Nx 1 error terms. With the i.i.d assumption, multivariate normal distribution of e on X, and full rank X, we can construct that the likelihood function of the linear regression model is L(3,0²; y, X) = (2no²) -N/2 exp 20² Show that the MLE of the regression coefficients 3 and the variance of the error terms o² are BN o = = N (XTX)-¹XTy N Σ Σ( i=1 (Yi - TiBN) (Yi-xi3)²
Transcribed Image Text:(c) Normal linear regression model The regression equations can be written in matrix form as y = XB+e where y is the Nx 1 vector of observations of the dependent variable, X is the N x K matrix of regressors, and is the Nx 1 error terms. With the i.i.d assumption, multivariate normal distribution of e on X, and full rank X, we can construct that the likelihood function of the linear regression model is L(3,0²; y, X) = (2no²) -N/2 exp 20² Show that the MLE of the regression coefficients 3 and the variance of the error terms o² are BN o = = N (XTX)-¹XTy N Σ Σ( i=1 (Yi - TiBN) (Yi-xi3)²
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