How to check dependency on nominal variables?

Question

I have data that map one real (float) and several nominal arguments to one real value:

y = f(r, n1, n2, n3, n4)

If I check dependency of y on r (r is my real-valued variable), I see that y depends linearly on r with a lot of noise on top of this dependency.

Now I want to check if there is any dependency of y on nominal variables: n1, n2, n3, n4. I also would like to know what nominal variable has the largest influence on y. So, my question is: What methods can I used to do that?

Answer 1

Regression with dummy variables for the levels of the nominal variables (factors) would probably be an obvious first thought, but as @RomanLuštrik points out the first thing to do is plot the data.

An example plot with one linear variable and one factor:

(That data is from this page)

There are various other plots that can be done.

Here's another example:

(Same data, somewhat different kind of plot)

Here is a document that discusses some other plots for this kind of data (like boxplots).