T-test

[Sally Ahmed]

Hello, what is the code to compare between two regression coefficients using t-test

[Carlo Lazzaro]

Sally:
you may want to consider the following toy-example:

. sysuse auto.dta
(1978 automobile data)

. regress price mpg trunk

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     10.14
       Model |   141126459         2  70563229.4   Prob > F        =    0.0001
    Residual |   493938937        71  6956886.44   R-squared       =    0.2222
-------------+----------------------------------   Adj R-squared   =    0.2003
       Total |   635065396        73  8699525.97   Root MSE        =    2637.6

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |  -220.1649   65.59262    -3.36   0.001    -350.9529    -89.3769
       trunk |   43.55851   88.71884     0.49   0.625    -133.3418    220.4589
       _cons |   10254.95   2349.084     4.37   0.000      5571.01    14938.89
------------------------------------------------------------------------------

. test mpg=trunk

 ( 1)  mpg - trunk = 0

       F(  1,    71) =   12.87
            Prob > F =    0.0006

. lincom mpg - trunk

 ( 1)  mpg - trunk = 0

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         (1) |  -263.7234    73.5159    -3.59   0.001    -410.3099   -117.1368
------------------------------------------------------------------------------

.

[Sally Ahmed]

Hi Carlo,

Thank you but is there anyway to test two variables from different regressions for example

regress price mpg
regress price trunk

[Carlo Lazzaro]

Sally:
yes, there is; see: https://www.stata.com/support/faqs/s...-coefficients/

[Sally Ahmed]

I have checked the link and it made me confused so please let me know if what I understood is correct:


reg AQ green y z
estimates store Y1

regress AQ yellow y z
estimates store Y2
suest Y1 Y2

test [Y1_mean = Y2_mean]

or lincom [Y1_mean]:green - [Y2_mean]:yellow

[Carlo Lazzaro]

Sally:
1) you cannot use -suest- after -regress- (see why in -suest-);
2) if you have different regressands (ie, y variables) and the very same set of predictors, go -sureg-;
3) otherwise go -test- or -lincom- (the latter is probably waht you're looking for).

[Sally Ahmed]

Hi Carlo,


thanks for your reply. I have different independent variables but same dependent variable and when I do after the regress lincom this error appears:
lincom Y1-Y2
Y1 not found
r(111);

[Sally Ahmed]

I had to split my independent variable into two variables to see how the two different directions affect my dependent variable and I want to compare between the two coefficients using ttest

[Carlo Lazzaro]

Sally: so you have one regression only:

 sysuse auto.dta
. reg price c.mpg##i.foreign

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =      9.48
       Model |   183435281         3  61145093.6   Prob > F        =    0.0000
    Residual |   451630115        70  6451858.79   R-squared       =    0.2888
-------------+----------------------------------   Adj R-squared   =    0.2584
       Total |   635065396        73  8699525.97   Root MSE        =    2540.1

-------------------------------------------------------------------------------
        price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
          mpg |  -329.2551   74.98545    -4.39   0.000    -478.8088   -179.7013
              |
      foreign |
     Foreign  |  -13.58741   2634.664    -0.01   0.996    -5268.258    5241.084
              |
foreign#c.mpg |
     Foreign  |   78.88826   112.4812     0.70   0.485    -145.4485     303.225
              |
        _cons |   12600.54   1527.888     8.25   0.000     9553.261    15647.81
-------------------------------------------------------------------------------

. mat list e(b)

e(b)[1,6]
                          0b.           1.  0b.foreign#   1.foreign#             
            mpg      foreign      foreign       co.mpg        c.mpg        _cons
y1   -329.25507            0   -13.587408            0    78.888255    12600.538

. lincom (0b.foreign+0b.foreign#co.mpg)-(1.foreign+1.foreign#co.mpg)

 ( 1)  0b.foreign - 1.foreign + 0b.foreign#co.mpg - 1.foreign#c.mpg = 0

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         (1) |  -65.30085   2526.435    -0.03   0.979    -5104.116    4973.514
------------------------------------------------------------------------------

.

Please note that -test- compares variables, not (regression) coefficients, which are adjusted for the other predictors incklude din the right-hand side of your regressione equation. If what above does not hel, please provide (as per FAQ) an example/excerpt of your dataset via dataex.

[Sally Ahmed]

Hi Carlo,

No I have two regressions because I have divided one of my independent variables into two separate variables green and brown. I run the first regression to see the effect of green on the quality then in another regression the effect of brown on the quality and now I want two compare the two coefficients

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(Quality green brown SIZE)
-.023498783     .      . 13.259064
 -.04692965     . -.2446 13.569432
 -.04860371     . -.3123 15.105076
          .     .      .         .
 -.02689968     . -.1947 16.305819
 -.10176031     .      . 13.618954
  -.0828585     .      . 14.658607
          .     .      .         .
-.015844844 .2016      .  18.38984
          .     .      .         .
-.012508074     .   -.22  15.67468
 -.06576106     . -.4193  15.28486
 -.10900471     .      . 13.461156
 -.04421114     . -.2358 16.230042
 -.06064047     .      .  12.04105
  -.0840023     . -.0765  13.60215
 -.09142987 .1034      .  12.72466
 -.02763558     .      .  14.44713
 -.06822613     .      .         .
 -.07659444     .      . 13.439718
 -.02508457     .      . 11.168207
 -.10666119     . -.4175  15.79195
 -.06840717     . -.1121 14.878547
-.011925415     . -.3017  14.86093
 -.10588618     .      . 14.823525
 -.04781695     . -.1684 14.893375
 -.04020242     . -.2402 17.383379
-.020710016     .      . 16.073341
 -.10175898     .      . 13.751846
 -.09382027     .      . 15.056574
 -.05675267 .1838      . 16.072336
 -.06355513 .1967      . 16.058983
 -.09535021     .  -.332  15.86111
          .     .      .         .
 -.07131862     . -.2379 15.943108
 -.05375332     .      . 12.790956
 -.13221191     .      .  13.98439
  -.1091644     .      .   14.5308
 -.12223452 .0658      .  18.38984
-.034990136     .      . 10.951087
          .     .      .         .
 -.09104384     .      . 13.654697
  -.0537772     . -.2774 17.266705
          .     .      .         .
 -.13631308     .      . 12.994676
 -.02458645 .2012      .  18.38984
-.035449382     . -.3014  14.73208
 -.08436283     . -.3456 13.689683
          .     .      .         .
 -.05060596     .      .  18.38984
 -.19048506     .      . 13.128886
 -.08916418     .      . 13.336082
 -.14970775     .      . 14.118113
 -.05141915     . -.0407 17.211285
 -.13723621     . -.1248 13.560867
 -.10945213     . -.1814  13.60244
  -.0797871     .      . 14.359032
-.033043083     .      . 13.967512
 -.06982245     .      .  13.56478
-.014638564     . -.2011 17.244064
-.018109797     .      . 15.453828
 -.04712491     .      . 12.940494
 -.07557642     . -.2246  14.75085
          .     .      .         .
 -.04852199     .      . 13.014318
 -.04596049     .      . 11.283085
 -.06070792 .0861      . 15.679855
 -.05885315     .      . 12.741495
 -.04884082     .      . 14.349708
-.065595314     .      .  12.88035
 -.06822452     .  -.043   14.8816
-.018667955     .      .  12.53987
 -.05273695     . -.0861 14.634684
 -.11064856     . -.3254 12.936993
 -.04161104     .      . 14.200109
 -.04297802     .      . 15.278043
 -.02390868     . -.2583 16.257566
  -.1600706     .      . 14.006145
          .     .      . 11.133435
-.063129105     .      . 11.755165
  -.1822904     .      . 10.510886
 -.04943193 .0653      .  17.63981
 -.04682806     . -.3785 15.085893
 -.07877155     . -.0658 14.462242
 -.02141324     .      . 13.635972
 -.02927202     .      .  15.84666
 -.12802325     .      . 11.962395
          .     .      .         .
 -.10383837     . -.2313  15.46607
 -.03622859     . -.0418 16.531675
 -.02274577     . -.1936 14.094083
-.030762667     .      . 12.615934
          .     .      . 13.589437
  -.0384847     . -.1754 12.645885
-.017075129     . -.2707 14.179723
 -.08459768     . -.3994 15.067476
 -.02081717     .      .  14.31284
-.014353865 .1628      .  15.09948
 -.03222968     . -.1756 14.639038
-.021212853     .  -.338 17.669416
end

[Carlo Lazzaro]

Sally:
I would go as follows:

. gen green_brown=green if green!=.
. replace green_brown=brown if brown!=.
. g indicator=0 if green!=.
. replace indicator=1 if brown!=.
. regress Quality c.green_brown##i.indicator SIZE
. regress Quality c.green_brown##i.indicator SIZE, allbase

      Source |       SS           df       MS      Number of obs   =        45
-------------+----------------------------------   F(4, 40)        =      2.22
       Model |  .008460312         4  .002115078   Prob > F        =    0.0835
    Residual |  .038024205        40  .000950605   R-squared       =    0.1820
-------------+----------------------------------   Adj R-squared   =    0.1002
       Total |  .046484517        44  .001056466   Root MSE        =    .03083

-----------------------------------------------------------------------------------------
                Quality | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
------------------------+----------------------------------------------------------------
            green_brown |   .3528698   .1830436     1.93   0.061    -.0170751    .7228147
                        |
              indicator |
                     0  |          0  (base)
                     1  |    .060665   .0303915     2.00   0.053    -.0007584    .1220885
                        |
indicator#c.green_brown |
                     0  |          0  (base)
                     1  |  -.3361346   .1895475    -1.77   0.084    -.7192244    .0469552
                        |
                   SIZE |   .0069765   .0032989     2.11   0.041     .0003092    .0136437
                  _cons |  -.2201662   .0594042    -3.71   0.001    -.3402265   -.1001059
-----------------------------------------------------------------------------------------

. mat list e(b)

e(b)[1,7]
                              0b.             1.  0b.indicator#   1.indicator#                              
      green_brown      indicator      indicator   co.green_b~n   c.green_br~n           SIZE          _cons
y1      .35286979              0      .06066501              0      -.3361346      .00697646     -.22016619


. lincom(green_brown)-(green_brown+1.indicator#c.green_brown)

 ( 1)  - 1.indicator#c.green_brown = 0

------------------------------------------------------------------------------
     Quality | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         (1) |   .3361346   .1895475     1.77   0.084    -.0469552    .7192244
------------------------------------------------------------------------------

.