b_OLS = inv(X'X)*X'y

b = inv(10X'*10X)*10*X'y

  = (1/100)*inv(X'X)*10*X'y

  = (1/10)*b_OLS

因此，某个变量数值变为其原值的10倍，相应的OLS估计系数会变为原来的1/10.

*--------------------------------------

. sysuse auto,clear
(1978 Automobile Data)

. gen mpg10 = 10*mpg

. reg price wei mpg,noheader
------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |   1.746559   .6413538     2.72   0.008      .467736    3.025382
         mpg |  -49.51222   86.15604    -0.57   0.567    -221.3025     122.278
       _cons |   1946.069    3597.05     0.54   0.590    -5226.245    9118.382
------------------------------------------------------------------------------

. reg price wei mpg10,noheader
------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |   1.746559   .6413538     2.72   0.008      .467736    3.025382
       mpg10 |  -4.951222   8.615604    -0.57   0.567    -22.13025     12.2278
       _cons |   1946.069    3597.05     0.54   0.590    -5226.245    9118.382
------------------------------------------------------------------------------