(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
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Author:Amos Gilat
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13208dfc-6768-4a76-8aab-4a6fbb561297%2Fde2f86b4-91b7-4a14-93cd-43f76dfb7bcf%2F7rx6mt_processed.jpeg&w=3840&q=75)
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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