Traditional regression analyses assume normality of observations and independence of mean and variance. However, there are many examples in science and Technology where the observations come from a skewed distribution and moreover there is a functional dependence between variance and mean.

In this article, we propose a method for regression analysis under Inverse Gaussian model when there are repeated observations for a fixed value of explanatory variable. The problem is treated by likelihood, Bayes, and empirical Bayes procedures, using conjugate priors. Inferences are provided for regression analysis.