ABSTRACT

As considered in Chapter 3, all theoretical results apply to it. So, for example, the least squares (maximum likelihood) estimate of the regression coefficients has the form

βˆ = (XTW−1X)−1XTW−1y (10.7)

and its mean vector is E(βˆ) = β, (10.8)

variance matrix var(βˆ) = σ2(XTW−1X)−1, (10.9)

and if the response y is normally distributed it has the following normal distribution:

βˆ = (XTW−1X)−1XTW−1y ∼ MultivariateNormalModel[d, β, σ2(XTW−1X)−1].