I'm not sure how to ask this question to Google, so I'm coming here.
Learning (some) stats long ago, I was shown that once you've calculated your regression results and built a new model (in plain English: equation) with the coefficients as your betas, you could "predict" the value of the outcome for a hypothetical set of values for the inputs/covariates/independent variables. I recall being able to do this for all sorts of variations on regression, even logistic regression.
My question is: while I'm pretty sure this works to get a number for an outcome, how can I (or can I?) get an estimate of the precision of such a "prediction"?
Here's an example logistic regression result in Stata. I'm trying to model the log odds of being admitted to university (
admit) as a linear combination of the predictors
GRE (GRE test score),
GPA (Grade point average), and
rank (High school rank, factor variable, range: 1 - 4, with 1 being highly ranked). (Here's the source dataset: data)
Crudely, the regression model looks like this before analysis (dummy variables used for
admit) = b0 + b1(
GRE) + b2(
GPA) + b3(
rank=2) + b4(
rank=3) + b5(
Here are the results:
And here's the complete model:
admit) = -3.989 + .00226(
GRE) + .804(
GPA) - .675(
rank=2) - 1.34(
rank=3) - 1.55(
All normal so far, I think. Now, say that I wanted to know what the log odds of getting admitted to college were for a student with a 650 GRE, a 3.24 GPA, and who went to a rank-1 high school. Plug and chug, right?
admit) = -3.98+0.0022(650)+.804(3.24) = .05496
(Which in odds ratio form is exp(.05496) = 1.056 )
So: how precise is this estimate? Can I get a 95% CI for it somehow, or even an SE?