Doing a t test on regression coefficients

[Ryan Whetstine]

Hi,

I am trying to do a t test that the null hypothesis is B2= -B1 where B2 is the coefficient on a variable called lexpendB and B1 is the coefficient on lexpendA.

My stata output is as follows:

regress voteA lexpendA lexpendB prtystrA

Source | SS df MS Number of obs = 173
-------------+---------------------------------- F(3, 169) = 215.23
Model | 38405.1089 3 12801.703 Prob > F = 0.0000
Residual | 10052.1396 169 59.4801161 R-squared = 0.7926
-------------+---------------------------------- Adj R-squared = 0.7889
Total | 48457.2486 172 281.728189 Root MSE = 7.7123

------------------------------------------------------------------------------
voteA | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lexpendA | 6.083316 .38215 15.92 0.000 5.328914 6.837719
lexpendB | -6.615417 .3788203 -17.46 0.000 -7.363247 -5.867588
prtystrA | .1519574 .0620181 2.45 0.015 .0295274 .2743873
_cons | 45.07893 3.926305 11.48 0.000 37.32801 52.82985
------------------------------------------------------------------------------

But when I do ttest lexpendB=-lexpendA it gives me an error. What would be the code for testing this hypothesis?

[Joro Kolev]

Post some subset of your data, and what exactly error Stata gives you.

Because to me it does not give an error:

. sysuse auto, clear
(1978 Automobile Data)

. reg price mpg head

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     10.44
       Model |   144280501         2  72140250.4   Prob > F        =    0.0001
    Residual |   490784895        71  6912463.32   R-squared       =    0.2272
-------------+----------------------------------   Adj R-squared   =    0.2054
       Total |   635065396        73  8699525.97   Root MSE        =    2629.2

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -259.1057   58.42485    -4.43   0.000    -375.6015   -142.6098
    headroom |  -334.0215   399.5499    -0.84   0.406    -1130.701    462.6585
       _cons |   12683.31   2074.497     6.11   0.000     8546.885    16819.74
------------------------------------------------------------------------------

. test mpg = - head

 ( 1)  mpg + headroom = 0

       F(  1,    71) =    1.93
            Prob > F =    0.1692

[Joro Kolev]

I got it now. You are using the wrong command. It is not -ttest-. You have to write -test- as I have done above.

[Ryan Whetstine]

I want a t test, not an F test.

ttest lexpendB=-lexpendA
- invalid name
r(198);

[Ryan Whetstine]

I know I can get the t statistic from the F statistic, but there must be a command to do a t test on this.

[William Lisowski]

You can find out about the "postestimation commands" available after running an estimation command by using the help command; for example help regress postestimation points us to the lincom command.

. sysuse auto, clear
(1978 Automobile Data)

. regress price mpg headroom

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     10.44
       Model |   144280501         2  72140250.4   Prob > F        =    0.0001
    Residual |   490784895        71  6912463.32   R-squared       =    0.2272
-------------+----------------------------------   Adj R-squared   =    0.2054
       Total |   635065396        73  8699525.97   Root MSE        =    2629.2

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -259.1057   58.42485    -4.43   0.000    -375.6015   -142.6098
    headroom |  -334.0215   399.5499    -0.84   0.406    -1130.701    462.6585
       _cons |   12683.31   2074.497     6.11   0.000     8546.885    16819.74
------------------------------------------------------------------------------

. test mpg = - headroom

 ( 1)  mpg + headroom = 0

       F(  1,    71) =    1.93
            Prob > F =    0.1692

. lincom mpg + headroom

 ( 1)  mpg + headroom = 0

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |  -593.1271   427.0515    -1.39   0.169    -1444.644    258.3893
------------------------------------------------------------------------------

[Joro Kolev]

I know I can get the t statistic from the F statistic, but there must be a command to do a t test on this.

The command that you might be looking for is either -lincom-, or the Square Root Command:

. sysuse auto, clear
(1978 Automobile Data)

. reg price mpg head, noheader
------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -259.1057   58.42485    -4.43   0.000    -375.6015   -142.6098
    headroom |  -334.0215   399.5499    -0.84   0.406    -1130.701    462.6585
       _cons |   12683.31   2074.497     6.11   0.000     8546.885    16819.74
------------------------------------------------------------------------------

. test mpg = - head

 ( 1)  mpg + headroom = 0

       F(  1,    71) =    1.93
            Prob > F =    0.1692

. dis sqrt(r(F))
1.3888891

. lincom mpg + head

 ( 1)  mpg + headroom = 0

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |  -593.1271   427.0515    -1.39   0.169    -1444.644    258.3893
------------------------------------------------------------------------------

. dis r(t)
-1.3888891

As one can see the two are the same except for the sign which gets lost when you do t^2=F.

But I agree that it would have been cute if Stata could return the t-version of the F-test for a single constraint if you instruct her to do so by something like (imaginary code follows, this does not exist in Stata) -test mpg = - head, ttest-.