When the intercept term is present in any given regression equation, it forces the average of the error term to be equal to zero. This occurs because the intercept, when included, will account for the fixed portion change of the dependent variable and the explanatory variables will account for the non-fixed portion. Therefore, the error term must be falling in size as both variable and fixed changes are accounted for. Therefore when an intercept is included and the sample size approaches infinity, then the average of the included will approach a zero population mean.
When assessing the stochastic error term and you have a series of possible values for that particular error term, if you were to add them all up and then get the average, this average number should be equal to zero. This probably would not be the case when assessing a small sample but when dealing with a large scale of numbers approaching infinity, this is what should occur.
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