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?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.