# Are there problems with inference using linear regression on observational data with highly skewed distributions of predictor values?

I am using a linear regression model to perform inference on some observational data. The samples are from an observational study and highly skewed along some of the dummy variables in the regression.

My understanding is this is okay as long as the the errors are uncorrelated and have unequal variance. The predictions for the poorly sampled regions of the independent variable may not be very accurate, but it shouldn't affect the validity of the inference. Is this correct?

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Could you clarify "highly skewed along some of the dummy variables"? –  onestop Feb 28 '12 at 15:53
I have several discrete indicators - some of these are for a covariates that I'm adjusting for. eg I have 30,000 observations of X=1, and 1,000 observations for X=0. This is true of predictor I'm making inferences on as well (available observational data is unbalanced). –  user4733 Feb 28 '12 at 16:41

Yes, there shouldn't be any problem given your description in comments of skewed predictor as actually meaning a 0/1 dummy variable that just has many more values of 1 than 0. There's no reason why this should be a problem; at most it will mean you just have a relatively high degree of uncertainty about your estimates of the coefficient for that variable, and this will just come up automatically in your results no particular problem there.

But in my world, even 1,000 observations of X=0 and 30,000 of X=1 is still lots of data... :-)

The fishhook with skewed continuous data is that you may end up with a few extreme points for one of your continuous variables. These points have high degrees of leverage and potentially of influence which can cause you problems. But this is not likely to be a problem in your case.

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The empirical distribution of a binary dataset in which 30/31 of the values are 1's and the rest are 0's has a standardized central third moment ("skewness") of -5.3, which is quite large: "skewed" seems like an accurate characterization here (although "unbalanced" might be clearer to some). –  whuber Feb 28 '12 at 19:18
ok, good point, I was wondering about this myself on the train after writing my answer. I've edited the answer accordingly to remove my comment on the use of "skew". –  Peter Ellis Feb 28 '12 at 19:33
+1 in anticipation :-) –  whuber Feb 28 '12 at 19:34