Abstract: Analysis of positive observations is generally done using log-normal and gamma models. For constant variance, log-normal and gamma model fits give almost same regression coefficient estimates, except the intercept. It is difficult to interpret about the estimates from these two model fits for non-constant variance. This article focuses the discrepancy in fitting between log-normal and gamma models for non-constant variance. It shows that for non-constant variance, even though the measures of fitting criteria and estimates are almost same in both the models, but the fittings may not always be identical. Moreover, this article points that some insignificant effects may also be sometimes very important in fitting. An example illustrates this point.