I would argue that saying the error follows a second degree polynomial is an erroneous way of thinking. Unless derived from some sort of first principals as to why it should be a second order polynomial we have no reason to think so. If you just look at r squared then fit a n+1 polynomial where n is the number of data points and you get a perfect r squared. Give more data points the trend could look linear with a fair degree of variation from the mean, or not.
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