Dear Josep,

If you are looking for an association between two scale variables then the best place to start is drawing a scatter plot. If the dispersion of points is approximately "cigar shaped", i.e. in the shape of an ellipse rotated on its axis, then you can run a Pearson correlation and a simple linear regression.

If there appears to be an underlying relationship between the two variables but it is not linear then you can attempt a transformation to make it linear.

There are also exceptions to the normality assumption for linear regression but the following are still required:

You can use the Kolmogorov-Smirnov normality test to test the normality of the residuals once you have calculated them by fitting a linear model but a better normality test is Shapiro-Wilk because it is usually more sensitive.

If all this fails then use Spearman rank correlation.

Have a look at our study guides:

https://www.researchgate.net/publication/274635640_Pearson_Correlation

https://www.researchgate.net/publication/275018503_Simple_Linear_Regression

https://www.researchgate.net/publication/275018646_Simple_Linear_Regression_Additional_Information

Technical Report Pearson Correlation

Technical Report Simple Linear Regression

Technical Report Simple Linear Regression – Additional Information

Thank you for your answer. It will be very useful in my research

But I was referring to multivariate regression model. Some kind of linear model or generalized model like poisson or similar. To introduce independent variables such as  age, sex, level income, tourist typology on so on.

If I understood you correctly, you want to make a regression not on unidimensional data, but on points with two dimensional information each (i.e. x and y).

Then, clearly (!), BIDIMENSIONAL REGRESSION is the only probbaly regression model as it takes into account both coordinates simultaneously.

I have wriitten a very comfortable toolbox for conducting such analyses (which are NOT part of any other statistical package) for R:

http://www.experimental-psychology.de/publications-peerreviewed.html

--< Publication [066]

http://www.jstatsoft.org/v52/c01/paper

The link to the R routine can be found in the paper itself.

All the best, hope this helps!

CCC

Thank you for your answer but I guess it was not exactly what I need.

I have quantitative variables and factors. I want to run a generalized linear model with a ten-point likert scale as dependent and several variables as independent. And I don't know wich is the best link function and the best family of distribution for it.

I hope I had explained better this way. I apologize for not being specific enough.

Ah, okay, now I got it; then I would fully follow Peter's advice, especially the VISUAL INSPECTION at first hand---this is essential becase most people used to conduct regression analyses just only trust in the data output; but this is dangerous, so ALWAYS inspect your data by a scatterplot to reduce the possibility of generating artefacts such as cluster effects beforehand.

All the best!

CCC