In polynomial regression, what assumptions underlie the (strict) validity of the various p-values and confidence intervals?

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In polynomial regression, what assumptions underlie the (strict)validity of the various p-values and confidence intervals?

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The full set of assumptions is embodied in a statistical model that underpins the method This model is a mathematical representation of data variability and thus ideally would capture accurately all sources of such variability Many problems arise however because this statistical model often incorporates unrealistic    See Answer
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