How Can I test the joint significance of the variables not selected?

[Gabriella Miniero]

Hi Forum!
I started a multiple regression with 10 predictors. I checked the linearity assumption and the significance of the model and now I have just 4 predictors but I have to test the joint significance of variables that were not selected. How Can I do that? I think that using F test and comparing the unrestricted model with the restricted model could be a good option. What do you think about?

[Andrew Musau]

You can do this with nestreg (nested regression) since the restricted model is nested in the full model. However, this is just equivalent to conducting a Wald test on the joint significance of the non-selected variables in the full model.

*NESTED REGRESSION
sysuse auto, clear
nestreg: reg mpg (weight trunk) (turn disp gear)
*WALD TEST AFTER REGRESSION
regress mpg weight trunk turn disp gear
testparm turn disp gear

Res.:

.
. nestreg: reg mpg (weight trunk) (turn disp gear)

Block  1: weight trunk

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     67.19
       Model |  1598.76953         2  799.384767   Prob > F        =    0.0000
    Residual |  844.689926        71  11.8970412   R-squared       =    0.6543
-------------+----------------------------------   Adj R-squared   =    0.6446
       Total |  2443.45946        73  33.4720474   Root MSE        =    3.4492

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0056527   .0007016    -8.06   0.000    -.0070516   -.0042537
       trunk |   -.096229   .1274771    -0.75   0.453    -.3504112    .1579531
       _cons |   39.68913    1.65207    24.02   0.000       36.395    42.98327
------------------------------------------------------------------------------

Block  2: turn displacement gear_ratio

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(5, 68)        =     26.29
       Model |  1610.39046         5  322.078091   Prob > F        =    0.0000
    Residual |  833.069003        68  12.2510148   R-squared       =    0.6591
-------------+----------------------------------   Adj R-squared   =    0.6340
       Total |  2443.45946        73  33.4720474   Root MSE        =    3.5001

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0056276   .0015025    -3.75   0.000    -.0086258   -.0026295
       trunk |  -.0927874   .1296839    -0.72   0.477    -.3515677    .1659929
        turn |  -.1261096   .1818657    -0.69   0.490    -.4890169    .2367977
displacement |   .0079344   .0116608     0.68   0.499    -.0153343    .0312031
  gear_ratio |   .5938431   1.612433     0.37   0.714    -2.623718    3.811404
       _cons |   41.21048   8.278612     4.98   0.000     24.69076    57.73019
------------------------------------------------------------------------------


  +-------------------------------------------------------------+
  |       |          Block  Residual                     Change |
  | Block |       F     df        df   Pr > F       R2    in R2 |
  |-------+-----------------------------------------------------|
  |     1 |   67.19      2        71   0.0000   0.6543          |
  |     2 |    0.32      3        68   0.8136   0.6591   0.0048 |
  +-------------------------------------------------------------+

.
. *WALD TEST AFTER REGRESSION

.
. regress mpg weight trunk turn disp gear

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(5, 68)        =     26.29
       Model |  1610.39046         5  322.078091   Prob > F        =    0.0000
    Residual |  833.069003        68  12.2510148   R-squared       =    0.6591
-------------+----------------------------------   Adj R-squared   =    0.6340
       Total |  2443.45946        73  33.4720474   Root MSE        =    3.5001

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0056276   .0015025    -3.75   0.000    -.0086258   -.0026295
       trunk |  -.0927874   .1296839    -0.72   0.477    -.3515677    .1659929
        turn |  -.1261096   .1818657    -0.69   0.490    -.4890169    .2367977
displacement |   .0079344   .0116608     0.68   0.499    -.0153343    .0312031
  gear_ratio |   .5938431   1.612433     0.37   0.714    -2.623718    3.811404
       _cons |   41.21048   8.278612     4.98   0.000     24.69076    57.73019
------------------------------------------------------------------------------

.
. testparm turn disp gear

 ( 1)  turn = 0
 ( 2)  displacement = 0
 ( 3)  gear_ratio = 0

       F(  3,    68) =    0.32
            Prob > F =    0.8136

[Gabriella Miniero]

thanks a lot! it's very helpful!