One sided t-test between two regression coefficients (H0: b1 >= b2)

[Olaf Hotte]

Hi,

How do I perform an one sided t-test between two regression coefficients? Of course, it should take into account the different beta coefficient and its corresponding standard error.

Example:

. sysuse auto
(1978 Automobile Data)

. reg mpg headroom weight displacement gear_ratio

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(4, 69)        =     32.72
       Model |  1599.93693         4  399.984232   Prob > F        =    0.0000
    Residual |  843.522532        69  12.2249642   R-squared       =    0.6548
-------------+----------------------------------   Adj R-squared   =    0.6348
       Total |  2443.45946        73  33.4720474   Root MSE        =    3.4964

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    headroom |  -.2543924   .5562903    -0.46   0.649    -1.364161    .8553762
      weight |  -.0064504   .0011968    -5.39   0.000    -.0088379   -.0040629
displacement |   .0082948   .0117199     0.71   0.481    -.0150858    .0316754
  gear_ratio |   .6764766   1.608566     0.42   0.675    -2.532525    3.885478
       _cons |   37.85946   6.633312     5.71   0.000     24.62637    51.09256
------------------------------------------------------------------------------

Now, I would like to test if "weight" has a greater (5 times greater) coefficient than "headroom".

H0: b[weight] >= b[headroom]

(H0: 5*b[weight] >= b[headroom]

How do I perform an one sided t-test between these two regression coefficients?

[Clyde Schechter]

test 5*weight = headroom

Then divide the p-value that Stata reports by 2 to get the 1-tailed value.