The FAQ at https://stats.idre.ucla.edu/stat/stata/faq/compreg3.htm shows how you can compare regression coefficients across three groups using xi and by forming interactions. This can also be done using suest as shown below.
use https://stats.idre.ucla.edu/stat/stata/faq/compreg3
regress weight height if age==1
Source | SS df MS Number of obs = 10
-------------+------------------------------ F( 1, 8) = 0.24
Model | 42.657257 1 42.657257 Prob > F = 0.6396
Residual | 1440.94274 8 180.117843 R-squared = 0.0288
-------------+------------------------------ Adj R-squared = -0.0927
Total | 1483.6 9 164.844444 Root MSE = 13.421
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weight | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
height | -.3768309 .7743341 -0.49 0.640 -2.162449 1.408787
_cons | 170.1664 49.43018 3.44 0.009 56.18024 284.1526
------------------------------------------------------------------------------
est store age1
regress weight height if age==2
Source | SS df MS Number of obs = 10
-------------+------------------------------ F( 1, 8) = 359.81
Model | 1319.56112 1 1319.56112 Prob > F = 0.0000
Residual | 29.3388815 8 3.66736019 R-squared = 0.9782
-------------+------------------------------ Adj R-squared = 0.9755
Total | 1348.9 9 149.877778 Root MSE = 1.915
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weight | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
height | 2.095872 .110491 18.97 0.000 1.84108 2.350665
_cons | -2.39747 7.053272 -0.34 0.743 -18.66234 13.8674
------------------------------------------------------------------------------
est store age2
regress weight height if age==3
Source | SS df MS Number of obs = 10
-------------+------------------------------ F( 1, 8) = 669.93
Model | 3882.53627 1 3882.53627 Prob > F = 0.0000
Residual | 46.3637317 8 5.79546646 R-squared = 0.9882
-------------+------------------------------ Adj R-squared = 0.9867
Total | 3928.9 9 436.544444 Root MSE = 2.4074
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weight | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
height | 3.189727 .1232367 25.88 0.000 2.905543 3.473912
_cons | 5.601677 8.930197 0.63 0.548 -14.99139 26.19475
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est store age3
suest age1 age2 age3
Simultaneous results for age1, age2, age3
Obs = 30
------------------------------------------------------------------------------
| Robust
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age1_mean |
height | -.3768309 .496919 -0.76 0.448 -1.350774 .5971124
_cons | 170.1664 31.30796 5.44 0.000 108.804 231.5289
-------------+----------------------------------------------------------------
age1_lnvar |
_cons | 5.193611 .3232765 16.07 0.000 4.560001 5.827222
-------------+----------------------------------------------------------------
age2_mean |
height | 2.095872 .0862164 24.31 0.000 1.926891 2.264853
_cons | -2.39747 5.668326 -0.42 0.672 -13.50719 8.712246
-------------+----------------------------------------------------------------
age2_lnvar |
_cons | 1.299472 .2573396 5.05 0.000 .7950958 1.803848
-------------+----------------------------------------------------------------
age3_mean |
height | 3.189727 .1008442 31.63 0.000 2.992077 3.387378
_cons | 5.601677 7.218938 0.78 0.438 -8.547181 19.75054
-------------+----------------------------------------------------------------
age3_lnvar |
_cons | 1.757076 .2637826 6.66 0.000 1.240072 2.27408
------------------------------------------------------------------------------
test [age1_mean]height=[age2_mean]height
( 1) [age1_mean]height - [age2_mean]height = 0
chi2( 1) = 24.04
Prob > chi2 = 0.0000
test [age2_mean]height=[age3_mean]height, accum
( 1) [age1_mean]height - [age2_mean]height = 0
( 2) [age2_mean]height - [age3_mean]height = 0
chi2( 2) = 102.25
Prob > chi2 = 0.0000