# [Gretl-users] Heteroskedasticity / correction

Ana Amaro ISG anaamaro at isg.pt
Fri Jan 10 13:29:48 EST 2014

```Yeap
It doesn't use the constant:(

In adition i don't understand the meaning of the r-squared when the regression has no constant :(

Sent from my iPhone
Apologize for the brevity/grammar/spelling

No dia 10/01/2014, às 18:18, "Riccardo (Jack) Lucchetti" <r.lucchetti at univpm.it> escreveu:

>> On Fri, 10 Jan 2014, Ana Amaro ISG wrote:
>>
>>
>>
>> Sent from my iPhone
>> Apologize for the brevity/grammar/spelling
>>
>> No dia 10/01/2014, às 17:48, Sven Schreiber <svetosch at gmx.net> escreveu:
>>
>>> Am 10.01.2014 18:38, schrieb Ana Amaro ISG:
>>>> Hi everyone
>>>> I need some help on this topic:
>>>> 1- simple model one regressor (x)
>>>> 2- error is heteroskedastic (and residual analysis shows that the error variance increases with x variable)
>>>> 3- rerun the analysis dividing both model members by the sqrt(x) - no constant
>>>
>>> why no constant here? usually you need to have good reasons for that --
>>> if you had a constant in step 1, dividing everything by some number does
>>> not eliminate the constant.
>> When dividing the original constant by sqrt(x) the constant disapears:(
>
> Sure?
>
> <hansl>
> nulldata 100
> set seed 987
> x = uniform()
> e = normal()
> y = x + e
> ols y const x
> modtest --white
>
> sqrtx = sqrt(x)
> ymod = y / sqrtx
> cmod = 1 / sqrtx
> ols ymod cmod sqrtx
> modtest --white
> </hansl>
>
> here gives
>
> <output>
> Model 1: OLS, using observations 1-100
> Dependent variable: y
>
>             coefficient   std. error   t-ratio   p-value
>  --------------------------------------------------------
>  const       −0.183247     0.195633    −0.9367   0.3512
>  x            1.77855      0.322094     5.522    2.75e-07 ***
>
> Mean dependent var   0.750871   S.D. dependent var   1.119396
> Sum squared resid    94.61446   S.E. of regression   0.982575
> R-squared            0.237299   Adjusted R-squared   0.229516
> F(1, 98)             30.49066   P-value(F)           2.75e-07
> Log-likelihood      −139.1259   Akaike criterion     282.2517
> Schwarz criterion    287.4621   Hannan-Quinn         284.3604
>
> ? modtest --white
>
> White's test for heteroskedasticity
> OLS, using observations 1-100
> Dependent variable: uhat^2
>
>             coefficient   std. error   t-ratio   p-value
>  -------------------------------------------------------
>  const        1.13073      0.439983     2.570    0.0117  **
>  x           −1.77980      2.08494     −0.8536   0.3954
>  sq_x         2.03353      1.96553      1.035    0.3034
>
>
> Test statistic: TR^2 = 1.613760,
> with p-value = P(Chi-square(2) > 1.613760) = 0.446248
>
> ? sqrtx = sqrt(x)
> Generated series sqrtx (ID 5)
> ? ymod = y / sqrtx
> Generated series ymod (ID 6)
> ? cmod = 1 / sqrtx
> Generated series cmod (ID 7)
> ? ols ymod cmod sqrtx
>
> Model 2: OLS, using observations 1-100
> Dependent variable: ymod
>
>             coefficient   std. error   t-ratio   p-value
>  --------------------------------------------------------
>  cmod       −0.0735086     0.118736    −0.6191   0.5373
>  sqrtx       1.56961       0.342301     4.585    1.34e-05 ***
>
> Mean dependent var   0.923079   S.D. dependent var   1.916162
> Sum squared resid    340.0252   S.E. of regression   1.862698
> R-squared            0.242205   Adjusted R-squared   0.234472
> F(2, 98)             15.66129   P-value(F)           1.25e-06
> Log-likelihood      −203.0863   Akaike criterion     410.1727
> Schwarz criterion    415.3830   Hannan-Quinn         412.2814
>
> ? modtest --white
>
> White's test for heteroskedasticity
> OLS, using observations 1-100
> Dependent variable: uhat^2
>
>             coefficient   std. error   t-ratio   p-value
>  -------------------------------------------------------
>  cmod         12.3469      19.7685      0.6246   0.5337
>  sqrtx       −14.3832     121.333      −0.1185   0.9059
>  sq_cmod      −1.25675      1.57423    −0.7983   0.4267
>  X1_X2       −12.8604      78.7441     −0.1633   0.8706
>  sq_sqrtx     18.2010      62.4175      0.2916   0.7712
>
>
> Test statistic: TR^2 = 33.927864,
> with p-value = P(Chi-square(4) > 33.927864) = 0.000001
> </output>
>
>
>
> -------------------------------------------------------
>  Riccardo (Jack) Lucchetti
>  Dipartimento di Scienze Economiche e Sociali (DiSES)
>
>  Università Politecnica delle Marche
>  (formerly known as Università di Ancona)
>
>  r.lucchetti at univpm.it
>  http://www2.econ.univpm.it/servizi/hpp/lucchetti
> -------------------------------------------------------
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