Dear all,

I am interested in predicted values after an OLS regression. Moreover, I am curious how these vary across groups (number of groups varies from 2-3, depending on the dimension). I would like to perform this via a significance test. The intuition is that,

H0: yhat_1 = yhat_2 v.s. H1: yhat_1 uneq yhat_2

t (or z) = (yhat_1 - yhat_2) /(sqrt(var_1 + var_2)

And now three questions:

1. Is this intuition right?
2. If yes, is there a pre build option to omplement this test.
3. And how do I perform the joint hypothesis that all three predictions are equal?

Below a minimal working example.

Thank you very much.

Daniel

******************************************* MWE ************************************************** *******

sysuse auto, clear

xtile price_cat = price, nquantiles(3)

reg displacement mpg if price_cat == 1
lincom _cons + mpg*20
reg displacement mpg if price_cat == 2
lincom _cons + mpg*20
reg displacement mpg if price_cat == 3
lincom _cons + mpg*20

**** Significance of difference between groups

* e.g. via test