Comparison of predicted values after OLS regression

[Daniel Graeber]

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

[Carlo Lazzaro]

Daniel:
you may want to take a look at: https://stats.idre.ucla.edu/stata/co...s-using-suest/

[Daniel Graeber]

Dear Carlo,

thank you for your suggestion. II was already familiar with that. But I did not know about the possibility of testing more involved hypotheses.

My approach now looks as follows:

sysuse auto, clear

xtile price_cat = price, nquantiles(3)

reg displacement mpg if price_cat == 1
est store cat1
reg displacement mpg if price_cat == 2
est store cat2
reg displacement mpg if price_cat == 3
est store cat3

**** Significance of difference between groups

suest cat1 cat2 cat3
test ([cat1_mean]_cons + [cat1_mean]mpg*20) = ([cat2_mean]_cons + [cat2_mean]mpg*20)
test ([cat3_mean]_cons + [cat3_mean]mpg*20) = ([cat2_mean]_cons + [cat2_mean]mpg*20), accum



************************************************** **********

Thanks so far

Daniel

[Carlo Lazzaro]

Daniel:
your approach makes sense.
What else are you after?

[Daniel Graeber]

Dear Carlo,

I am okay. I just wanted to double check. Thank you very much.

Best

Daniel