Skewness/Standard deviation

[Prathvajeeth Rajmohan]

Hi there, I am doing summary statistics of explanatory variables in a regression and was interested to know in terms of skewness and standard deviation:

Are they there any (implicit) acceptable levels in terms how high these can get?

For example if you have a variable with a skew of roughly 5/6 and a std of 12 for example are both these values considered quite high/bad?

or is it accepted that variables can't obviously be normally distributed?

Thanks

[Nick Cox]

A standard deviation of 12 could be anything from extraordinarily low to extraordinarily high.

There is no requirement in regression that any marginal distribution be normal. A skewness of 5/6 (assuming you mean the moment-based measure) could be fine or associated with a problem: more depends on whether data follow the functional form closely than on univariate summaries alone.

[Prathvajeeth Rajmohan]

A skewness of 5/6 (assuming you mean the moment-based measure) could be fine or associated with a problem: more depends on whether data follow the functional form closely than on univariate summaries alone.

sorry very elementary econometrics learner here, is there any chance you could perhaps elaborate a bit more as to what you mean by follow the functional form? thanks

[Prathvajeeth Rajmohan]

. sum rnd_rev_w1 if inlist(year,2015,2016) & inlist(FXDerivatives10,0,1), detail

                          Grate
-------------------------------------------------------------
      Percentiles      Smallest
 1%            0              0
 5%            0              0
10%            0              0       Obs                 722
25%            0              0       Sum of Wgt.         722

50%            0                      Mean           4.422812
                        Largest       Std. Dev.      18.23743
75%     1.379152        156.126
90%     8.004015        156.126       Variance       332.6038
95%     17.07221        156.126       Skewness        7.03823
99%      156.126        156.126       Kurtosis       56.09734

. sum rnd_rev_w1 if inlist(year,2015,2016), detail

                           Yrate
-------------------------------------------------------------
      Percentiles      Smallest
 1%            0              0
 5%            0              0
10%            0              0       Obs                 759
25%            0              0       Sum of Wgt.         759

50%            0                      Mean           4.574741
                        Largest       Std. Dev.       18.4524
75%     1.490596        156.126
90%     8.101542        156.126       Variance        340.491
95%     17.91488        156.126       Skewness       6.781072
99%      156.126        156.126       Kurtosis       52.42444

Sorry should have provided some context initially here you go, if any one could please have a look and let me know regarding the skewness/kurtosis of these figures.

Thanks

[Nick Cox]

Evidently you meant 5 or 6 when you wrote 5/6. not a fraction; and in fact 5 or 6 means 6 or 7.

Clearly you have substantially skewed distributions with >50% zeros and clutches of outliers.

Following functional form means that Y = Xb is a good idea when you fit Y = Xb or that Y = exp(XB) is a good idea when you fit Y = exp(XB), etc.