# Which statistics to use calculating prediction interval of dummy linear regression?

I have performed a linear regression and found a model of the form: $$\hat{Y} = \alpha + \beta_1 x+ \delta_{high} + \delta_{low} + \epsilon\\$$ Where:

$\beta_1$ is a continuously distributed variable

$\delta_{high}$ and $\delta_{low}$ are dummy variables, each levels of 'high' or 'low'

To use the model I would like to predict the most likely value and provide a confidence interval around the estimate. I am not sure how to properly calculate the standard error of the estimate. Since, for example, $\delta_{high}$ only applies in a "high" scenario and is zero otherwise I am tempted to use standard deviation/mean of only those records where the factor is actually "high" for the purpose calculating the standard error of the estimate.

Therefore, should I use standard deviation and means over the whole sample or use only those records showing the dummies levels when calculating the standard error of the estimate and prediction interval?