hettest : Different results from regression

[Poomthan Rangkakulnuwat]

Hi, I have a model with 3 nominal independent variables. Three dummy variables are used for the first nominal variable. Two dummy varaibles are used for the second nominal variable. And two dummy variables are used for the third dummy variables. I test for heteroskedasticiy by 2 methods.
(1) Use stata command : hettest. The chi(1) = 6.21 and its p-value = 0.0127.
(2) Use the regular regression: Run resdidual^2 on all dummy variables. The F-statistics = 1.492 and its p-value = 0.2106.
The two methods give different conclusion about heteroskedasticity.
Can somebody explain this different results?
Thank You.

[Richard Williams]

Showing commands and output would give people a better chance at answering your question. Use code tags. See pt 12 of the Statalist FAQ on asking Qs effectively.

Your procedure does not sound right to me. See

https://www3.nd.edu/~rwilliam/stats2/l25.pdf

Specifically, pp. 9-10 show how to manually reproduce the results of hettest,

[Poomthan Rangkakulnuwat]

Dear Williams,
Thank you for your help. Here is the commands:
Method 1:reg pref i.time i.capnew i.price, beta
estat hettest

Source | SS df MS Number of obs = 36
-------------+---------------------------------- F(7, 28) = 90.72
Model | 3757.22222 7 536.746032 Prob > F = 0.0000
Residual | 165.666667 28 5.91666667 R-squared = 0.9578
-------------+---------------------------------- Adj R-squared = 0.9472
Total | 3922.88889 35 112.08254 Root MSE = 2.4324

------------------------------------------------------------------------------
pref | Coef. Std. Err. t P>|t| Beta
-------------+----------------------------------------------------------------
time |
4 Mins | -1.333333 1.146654 -1.16 0.255 -.055308
6 Mins | -6.777778 1.146654 -5.91 0.000 -.2811488
8 Mins | -14.11111 1.146654 -12.31 0.000 -.5853425
|
capnew |
8 cups | 11.75 .9930313 11.83 0.000 .5306154
10 cups | 19.08333 .9930313 19.22 0.000 .8617796
|
price |
32000 | -2.083333 .9930313 -2.10 0.045 -.0940807
38000 | -8.083333 .9930313 -8.14 0.000 -.3650333
|
_cons | 17.11111 1.146654 14.92 0.000 .
------------------------------------------------------------------------------

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity
Ho: Constant variance
Variables: fitted values of pref

chi2(1) = 6.21
Prob > chi2 = 0.0127

Method 2: predict e, residual
gen e2 = e*e
reg e2 ib4.time ib3.capnew ib38000.price

. reg e2 ib4.time ib3.capnew ib38000.price

Source | SS df MS Number of obs = 36
-------------+---------------------------------- F(7, 28) = 1.49
Model | 715.4564 7 102.208057 Prob > F = 0.2106
Residual | 1917.89019 28 68.4960781 R-squared = 0.2717
-------------+---------------------------------- Adj R-squared = 0.0896
Total | 2633.34659 35 75.2384739 Root MSE = 8.2762

------------------------------------------------------------------------------
e2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
time |
2 Mins | -4.549383 3.901455 -1.17 0.253 -12.54115 3.442385
4 Mins | -4.808642 3.901455 -1.23 0.228 -12.80041 3.183126
6 Mins | -1.76e-07 3.901455 -0.00 1.000 -7.991768 7.991768
|
capnew |
4 cups | 1.280093 3.378759 0.38 0.708 -5.640981 8.201167
8 cups | 1.12963 3.378759 0.33 0.741 -5.791444 8.050704
|
price |
28000 | -7.881945 3.378759 -2.33 0.027 -14.80302 -.9608705
32000 | -8.027778 3.378759 -2.38 0.025 -14.94885 -1.106704
|
_cons | 11.44136 3.901455 2.93 0.007 3.44959 19.43313
------------------------------------------------------------------------------

Thank You

[Richard Williams]

Hi Poomthan. Your posting is very hard to read. You should use code tags. See the faq.

Your two approaches are not equivalent. Perhaps both are legitimate tests, but they are not the same test.

[Richard Williams]

If you want hettest and your regression approach to yield the same results, I believe you need the rhs and fstat options on hettest:

webuse nhanes2f, clear
reg health i.race i.female i.diabetes
predict e if e(sample), resid
gen esquare = e^2
estat hettest, rhs fstat
reg esquare i.race i.female i.diabetes

. estat hettest, rhs fstat

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity 
         Ho: Constant variance
         Variables: 1b.race 2.race 3.race 0b.female 1.female 0b.diabetes 1.diabetes

         F(4 , 10330) =     8.72
         Prob > F     =   0.0000

. reg esquare i.race i.female i.diabetes

      Source |       SS           df       MS      Number of obs   =    10,335
-------------+----------------------------------   F(4, 10330)     =      8.72
       Model |  82.2864077         4  20.5716019   Prob > F        =    0.0000
    Residual |  24360.9941    10,330  2.35827629   R-squared       =    0.0034
-------------+----------------------------------   Adj R-squared   =    0.0030
       Total |  24443.2805    10,334  2.36532616   Root MSE        =    1.5357

Also notice how much easier it is to read when you use code tags.

[Eric de Souza]

If you do not list the regressors in the auxiliary regression, Stata defaults to the fitted value of the original regression as regressor. This is why your Chi squared has only one degree of freedom.