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I want to establish the uncertainty in my fitted model to my data

I can evaluate the variance for the predicted model, but I'm getting very confused as to how the variance can then give me the uncertainty in my model :S

I know that the standard error of the mean may be taken as the standard deviation divided by the root of the number of measurements, and that the square root of the variance gives the standard deviation- but I am really struggling to see how from these I could interpretate an uncertainty. I am very baffled at the moment- so any help would be massively appreciated :-)

Cheers