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[QUOTE="FactChecker, post: 6853080, member: 500115"] I struggled with how to distinguish between the statistical mean, ##\hat{Y}## versus the deterministic, ##y(x)##. Of course, for a repeatable experiment, given a fixed variable, x, the question would be whether the result, y, always gives the same value or varies randomly. But what about something that is not repeatable, such as values (e.g. daily temperature highs) versus calendar dates? For that, the x values can not be repeated. Conversely, what about something that we would consider deterministic, but the details are so complicated that we might consider them random? So I guess the best I can do is to refer to how one decides to model the process and whether a random term, ##\epsilon## is included in the model. I don't know if there is a good study or reference on this issue. My thoughts on it seem rather amateurish. [/QUOTE]
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