Suppose you don't know the estimates of a linear regression model (b0, b1 are unknown) and you are given a 95% prediction interval at x = 6 to be [5,15].
Then, since prediction intervals are numerically symmetric you find the midpoint and this is your Y^hat at that given value of x.
(15 + 5) / 2 = 10.
So here, Y^hat = 10.
Is the statistically correct or can you not find the estimated Y-value of the regression line using a prediction interval?
Sorry if this doesn't make sense, I am a bit confused.