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Am I allowed to use multiple regression analysis on a sample size of 21? I did the Shapiro - Wilik test on all four of my variables (p>0,05 on all of them). I also checked their linear distribuon and possible outliers in the screeplots, and everything seems fine. So my question is can i use the multiple regression analysis even though my sample size is less than 30, but the conditions of normality and linear relationships are satisfied?

Thank you in advance!

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  • $\begingroup$ Sample size of 30 is irrelevant here. A sample size of 30 is for approximating an exact t-test with an approximate Z-test but even in that case you could just use the exact t-test for a sample size of 4. Likewise, you're using the exact sharipo-wilik test and you don't need a large sample size to apply any approximation. $\endgroup$ – Hugh Dec 4 '16 at 17:03
  • $\begingroup$ Neither IVs nor the raw (i.e. marginal) DVs are assumed normal in regression -- you shouldn't be testing what is not assumed; it will lead you to mistaken actions. $\endgroup$ – Glen_b -Reinstate Monica Dec 4 '16 at 22:03
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You are allowed to do this analysis but you will have to accept that your estimates of the coefficients will be rather imprecise. You also need to revisit the introductory material from which you learned regression as you do not check the predictor variables for their properties but instead examine the residuals from your model. With your sample size this is only likely to show gross deviations anyway.

The sample size issue has been covered in some depth on this site for instance in this Q&A How can I assess many explanatory variables with a sample small enough for in-depth qualitative (case-study) analysis?

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