Significance levels of combined coefficients

[Frank de Vries]

Dear Stata users,

My regression looks as follows: y = x0 x1 x2 x3 x4 x5

Where x4 = x3 * dummy (indicating top quartile) and x5 = x3 * dummy (indicating bottom quartile)
I follow the methodology by Easterwood & Nutt (1999) where they sum up the coefficients to get the total effect of the top (x3 + x4) and bottom (x3+x5) quartiles.
I don't know how to compute the significance levels of these combined coefficients though.

All help is greatly appreciated!

Kind regards,

Frank

[Carlo Lazzaro]

Frank:
a temptative reply might be:

sysuse auto.dta
. reg price mpg turn

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     10.08
       Model |   140436412         2  70218206.1   Prob > F        =    0.0001
    Residual |   494628984        71  6966605.41   R-squared       =    0.2211
-------------+----------------------------------   Adj R-squared   =    0.1992
       Total |   635065396        73  8699525.97   Root MSE        =    2639.4

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -259.6967   76.84886    -3.38   0.001     -412.929   -106.4645
        turn |  -38.03857   101.0624    -0.38   0.708    -239.5513    163.4742
       _cons |   13204.27   5316.186     2.48   0.015       2604.1    23804.45
------------------------------------------------------------------------------

. sum mpg turn

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
         mpg |         74     21.2973    5.785503         12         41
        turn |         74    39.64865    4.399354         31         51

. test mpg+turn=(41+51)

 ( 1)  mpg + turn = 92

       F(  1,    71) =    5.57
            Prob > F =    0.0211

.

As an aside, FAQ recommend to provide full reference of any quoted contribution (multidisciplinarity, you know...).