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The distribution of my residuals or dependant variable where not normal (skewness to the right and Kurtosis). the lnskew0 command in STATA transformed my dependent variable (DV) for solving the problem by doing ln (-DV - (-k) ) where K is calculated by stata. Now the skewness has disapeared, but some kurtosis is still presente. 1) Do you know how to solve the Kurtosis problem? 2) Now that I have a different B coefficients, p values and R2 for the regression before and after the transformation of my DV, which ones should I show as a result? the p values and R2 of the regression after the transformation, but the coefficients of the regression before transformation or other? B coeffcients of the regression after transformation are not easy to interpret for the readers and they are very different from the original values.

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Even with non-normal residuals, the coefficient estimates are consistent. Non-normal residuals are not the biggest evil in model construction. Your main objective is capturing the dependence between the dependent variable and independent variables most accurately. It is not clear if the original model was better or if the transformation has improved the fit. To check that, you should use a model selection criterion, like Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC).

In my experience, if the residuals are not normal, fighting that fully is difficult. In most cases a transformation just mitigates the problem. Therefore, you should use bootstrap-based tests to assess statistical significance of the parameter estimates.

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  • $\begingroup$ After the transformation of my dependent variable, the residuals of the regression are normal distributed. $\endgroup$
    – César
    Feb 4, 2018 at 20:55
  • $\begingroup$ According to the skewness test of my residuals,after the transformation they are normal distributed, if I'm not mistaken the concepts! If as you say the coefficient estimates are consistent, so I guess I can take the coefficients of the first regression before the transformation, but the p values and R2 of the second regression with the transformed values ? $\endgroup$
    – César
    Feb 4, 2018 at 21:56
  • $\begingroup$ FOR MY REGRESSION WITH NOT TRANSFORMED DEPENDENT VARIABLE . predict r, residuals (1316 missing values generated) . sktest r Skewness/Kurtosis tests for Normality ------- joint ------ Variable | Obs Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 -------------+--------------------------------------------------------------- r | 907 0.0000 0.4707 47.52 0.0000 $\endgroup$
    – César
    Feb 4, 2018 at 21:59
  • $\begingroup$ FOR MY REGRESSION WITH TRANFORMED DEPENDENT VARIABLE . predict rr, residuals (1316 missing values generated) . sktest rr Skewness/Kurtosis tests for Normality ------- joint ------ Variable | Obs Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 -------------+--------------------------------------------------------------- rr | 907 0.8416 0.0000 39.75 0.0000 $\endgroup$
    – César
    Feb 4, 2018 at 22:02
  • $\begingroup$ Sorry stans, it is not well shown, but the skewness test for my residuals went from 0,000 to 0,8416 and the histrogram of the residuals show that its distribution is now normalmy. What do you think? $\endgroup$
    – César
    Feb 4, 2018 at 22:05

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