Re: [Gretl-users] Heteroskedasticity / correction

> 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(a)gmx.net&gt; 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 Unadjusted R-squared = 0.016138 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 Unadjusted R-squared = 0.339279 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(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti ------------------------------------------------------- _______________________________________________ Gretl-users mailing list Gretl-users(a)lists.wfu.edu http://lists.wfu.edu/mailman/listinfo/gretl-users