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iid is an acronym for independent and identically distributed. Many statistical methods assume that the data are iid; that is, that each observation comes from the same distribution and is independent of other observations.

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When using a gaussian link in GLM, what are the assumptions?

In R, when I am fitting a model glm(y~x, family = gaussian(link="log")), do I assume that $Y \stackrel{iid}\sim N(\mu, \sigma^2)$ or do I assume that $Y \stackrel{indep}\sim N(\mu, \sigma^2)$? … I guess the point where I am confused is that I recall that in OLS regression, the Y is iid but in GLM Y is only independent. …
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