Below, I'm showing a hypothetical simple linear regression case. There are $5000$ datapoints in each of the 4 sub-populations stacked over the top of each predictor value. Each subpopulation is normally distributed. And all subpopulations have the same $\sigma^2$. However, the subpopulations' $\mu$ are different leading to an upward-sloping regression line.
When I compute the $99.999999999\%$ confidence interval for the regression line, nothing basically shows (i.e., the line is super precise due to huge number of datapoints).
However, When I compute the $99.999999999\%$ prediction interval for predicting a future observation (the light green surrounding the 4 subpopulations as well as the regression line), the prediction interval becomes hugely wide.
Why when datapoint are so huge (about the size of a population), setting the confidence interval around the regression line to about $1$, doesn't make the such confidence interval to even show BUT
setting the prediction interval for observations to about $1$, is still so huge? (Is there really any other far-away observation than the ones currently existing in each subpopulation)