difference between mean and response

Mean response:    it’s the inference interval for  E(Y(x)) = B0+B1x+B2x^2

My understanding is, mean response interval is the interval for the estimate mean. It indicates the probability that the mean is in the interval

Prediction interval:  it’s the inference interval Y(x) = B0+B1x+B2x^2+epsilon

is the interval for prediction the real data or population. So it will have the wider range.

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