# Residual deviance for normal distribution with unknown variance?

An older post defines a saturated model as one having as many parameters as observations. I understand how you calculate residual deviance (and its relation to scaled deviance) when the scale is known. What about the alternative?

Suppose, for example, you wish to assume that two independent observations are defined by a normal distributions with unknown means and equal but unknown variance. It seems like you have to choose some mapping from two to three parameters before the saturated model can be defined. Is there a correct choice?

• The reference to "as many parameters as observations" relates to the parameters in the model for the mean. You're quite right that in a GLM for a family with a free variance parameter, the variance parameter is not determined by that. – Glen_b May 28 '15 at 0:11