We consider arbit,rary regression modelsy=Xβ+ ϵ, where the covariance matrix from ϵ can also be singulary. First we determine optimal homogeneous and inhomogeneous linear predictions fory*where the true equation fory*bey*=Xβ+ϵ*As the risk we use a mean quadratic (not necessary) distance. Then we study the possibilities for improving the best homogeneous unbiased prediction. We show, that this is possible, if there are additional informations aboutX βif for instance ∣X β∣ is bounded. After this me consider the improvement of a homogeneous prediction by admitting inhomogeneous predictions. In a further section we determine for (may be even singulary) modelsy=X β+ ϵ a GAUSS-MARKOV estimation for β and we get also statements of the question in which cases this estimation can be improved. Thereby the strict connection between unbiased predictions and G.-M. estimations is used.