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# Is the difference between an OLS regression and a GLS regression qualitative or quantitative?

It is quantitative

Ordinary least squares is a technique for estimating unknown parameters in a linear regression model. OLS yield the maximum likelihood in a vector ##β##, assuming the parameters have equal variance and are uncorrelated, in a noise ε - homoscedastic.

##vec(y)=Xvec(β)+vec(ε)##

Generalized least squares allows this approach to be generalized to give the maximum likelihood estimate ##β## when the noise is of unequal variance (heteroscedasticity). Typically this leads to mathematical treatment that presents the two as follows: OLS: ##vecY=Xbeta+ε " where " ε~N(0,σ²I)## GLS: ##vecY=Xbeta+η " where " η~N(0,σ²Cov)## Note the formulation for the two approaches results in real structural and quantitative difference. Notice the two are governed by two different Gauss distribution the ##N(0, sigma^2M); M = I " or " M=Cov## part Where: ##I = ## "Identity Matrix and " ##Cov =## "Covariance Matrix

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