# How to check dependency on nominal variables?

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?

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Can you show us the data (using graphs)? – Roman Luštrik Feb 27 '13 at 8:52
@Roman Luštrik, I am not sure what graph you need. How should I build it? The only graph that I have is y as function of x (it ignores values of other variables). It looks like y linearly depends on x with a lot of noise. The second problem, I think I am not allowed to post the data on line, since it is property of the company that I am working on. – Roman Feb 27 '13 at 8:59

## 1 Answer

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).

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thank you for the answer. Unfortunately, I do not understand the data. There are four columns which of them is function and which are arguments. If I assume that the last (or fist) columns is the function than I have one real-valued argument and two (not one as you say) nominal-valued variables (or factors). I also do not understand the first plot. It looks like there are four plots. Why four? And what is x and what is y. What is "priorlmp" and what is "Improv"? – Roman Feb 27 '13 at 10:23
Improv is the $y$, PriorImp is the $x$. RDExp is a factor (nominal). The other one is actually a replicate number but I have treated it kind of like it was a factor in the second plot. As for what the data measure, I have no clue. The fourth plot (lower right) combines the two plots on the left. Don't worry about it - just try to comprehend the general idea of doing a separate y vs x for each level of a factor (that's called a coplot). The second plot is called an interaction plot. If you gave some sample data, someone might be able to generate one for you. – Glen_b Feb 27 '13 at 10:36