I am currently working on a research project based on the data of a big survey. I derived a variable set, which I would like to investigate. Before starting with it, I would like to check the assumptions of the OLS.

I read quite a bit about these assumptions but I am still not sure how I can interpret my output. I am currently hanging on the assumption "errors are normally distributed" I read that this assumption is not important if the sample size is big enough. Is it correct in this case? What would be your interpretation of the model's output and my attached plots? Is it enough to test the assumption?

I can´t do a log transformation of my DV as it ranges from 0 to 26 and I obviously would lose the observations which contain 0.

My Model

My P Plot + Q Plot

  • $\begingroup$ I agree broadly with @Hadi's answer. You should be concerned with whether the overall functional form of the model makes sense. A residual versus fitted plot and added variable plots would be higher up my list of diagnostics than checking normality of residuals. In Stata, which you are using, those are rvfplot and avplots. Zeros in the response are no problem to generalised linear models with logarithmic link. Does your model ever predict negative values for the response in the range of the data? Can you remove some predictors without weakening the model much? It isn't very parsimonious. $\endgroup$ – Nick Cox Sep 6 '16 at 8:45
  • $\begingroup$ Thank you @NickCox. How do I do logarithmic link of my DV without losing with a 0? No, the DV never turns negativ. Is it an Issue? Most of them add to the R2. I will check on that. Thanks for the mentioned plots. I will have a look on that. Thank You! Best, Carsten $\endgroup$ – Michael Meyer Sep 6 '16 at 15:13
  • $\begingroup$ Carsten/Michael Check out glm, link(log) or poisson in Stata. blog.stata.com/2011/08/22/… should interest non-Stata users too. $\endgroup$ – Nick Cox Sep 6 '16 at 15:23

Regression modelling is not sensitive to the normally distributed errors. The normal assumption is used for inference about your fitted model such as prediction and control. As I see from your results and based on your P-P and Q-Q plots the normal assumption is valid for your modelling. (If your fitted model shows approximately near to the theoretical line, then your normal assumption on the errors are valid.)

You would use other diagnostic tests for more validation about your regression modelling, such as the constant variance assumptions of the errors and zero means behaviour of the errors.

Moreover, based on machine learning approach, it is better to use k-fold cross validation approach for computing the accuracy of your fitted model.

  • $\begingroup$ Thank you @Hadi! I´ll check for the other assumptions aswell. Your comment regarding k fold cross validation is concering the design and the validation of my survey, am I correct? I am using a data set, which was created in big survey. I am not part of this research team. Do I need to do it under these circumstances? Best $\endgroup$ – Michael Meyer Sep 6 '16 at 15:22
  • $\begingroup$ @Michael your welcome. About k-fold cross validation, when we are computing the model error using all of data, your reported accuracy( root MSE in your output) is overfitted to these data and mybe won't be as good as for the next data. In data mining and machine learning the k-fold CV is an standard approach for reporting accuracy of the fitted model. I recommend to apply the k-fold CV as well as your current results to produce more robust results about the output model. $\endgroup$ – Hadi Sep 6 '16 at 18:11

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