you should use normalization transformation to normalize your data before applying these concepts

If your sample size is large enough application of the Central Limit Theorem could make the test robust against violations of underlying assumptions like the normality assumption. I therefore suggest increase in the sample size before using these parametric methods.

Dear Laura

Try to transformation your data for normality, and in the case that your data stay in not normal distribution you can use spearman rank correlation which not need assumption for normality, and you can use logistic regression does not require a linear relationship between the dependent and independent variables.  Second, the error terms (residuals) do not need to be normally distributed. 

Good Luck

Dear Rafa and Khalid, I've sugested transformation to my boss but she doesn't want to go that way, me either..

Dear Ette my sample is large but the hipothesis of normality rejected the hypothesis of normally still.

I will try the non parametric test that Khalid have suggested

Thanks.

(I'm answering this way and not individually because I'm new here and I dont know how to do it)

Laura -

I am not sure of your application, but if it is appropriate to use linear regression, then data do not need to be normally distributed. 

[It may be helpful in case of prediction interval estimation for your estimated residuals to be approximately  normally distributed so that it does not take such a large sample to invoke the Central Limit Theorem, but we are still just talking about the estimate residuals ... or look at the random factors of the estimated residuals in weighted least squares regression.] 

I am not so familiar with time series data, but I think you are probably misunderstanding the usefulness of "normality."   It is often a misleading name. 

Cheers - Jim

Dear James,

I'm quite aware of what are you talking about. Nontehless, neither residues, nor QQplots or Cook's distance show any evidence of certain normality.

Anyway, I've been looking around and reading some books and publications and I´ve decided to use Theil's regression wich is a non parametric type of regression used in time series.

Thanks to all of you for your time. It's been very helpfull.

Best regards,

Laura