Continuous and Categorical variable data analysis

I have three variables:

• distance (continuous, variable range negative infinity to positive infinity)
• isLand (discrete categorical/ Boolean, variable range 1 or 0)
• occupants (discrete categorical, variable range 0-7)

I want to answer the following statistical questions:

• How to I compare distributions that have both categorical and continuous variable. For example, I like to determine if the data distribution of distance vs occupants varies depending on the value of isLand.
• Given two of the three variables, can I predict the third using some equation?
• How can I determine independence with more than two variables?
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I would recommend that you to split this across three separate questions. –  Shane Sep 13 '10 at 15:20
Actually, now that I read this a little closer, I see that the answer for each is very closely related. –  Shane Sep 13 '10 at 15:25
I felt that the heart of the question is comparing two different distributions, I just happen to list three different ways to do it. –  Elpezmuerto Sep 13 '10 at 16:14
For occupants what you've got is an ordinal variable, so I wouldn't think of it as categorical. Especially with 8 values, it's almost continuous. –  Mike Dunlavey Sep 14 '10 at 0:07

I would recommend reading about logistic or log-linear models in particular, and methods of categorical data analysis in general. The notes on the following course are pretty good for a start: Analysis of Discrete Data. The textbook by Agresti is quite good. You might also consider Kleinbaum for a quick start.

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I actually have the Agresti textbook on my desk right now and I have been using it. The problem is that I didn't know what specific methodology I should be using. –  Elpezmuerto Sep 13 '10 at 16:32
@Elpezmuerto Very briefly, to complement @ars answer, question 1 can be answered with a conditional or trellis plot, e.g. sth like dist ~ occ | isLand using Lattice, or see the coplot() function in the vcd package -- this is for exploratory purpose; question 2 calls for a prediction model; depending on the variable you consider as your outcome, it may be logistic regression (e.g. if Y=isLand), a linear regression (e.g. if Y=distance), or directly a log-linear model providing you categorize your continuous measurement; question 3 is clearly a log-linear model as suggested by @ars. –  chl Sep 13 '10 at 19:10
@Elpezmuerto @ars Thanks to the work of Laura Thompson, Agresti's book is available in R too, j.mp/9fXheu :-) –  chl Sep 13 '10 at 19:12
@chl: that's a great find! Thank you. @Elpezmuerto: There's a series of examples in Agresti concerning crabs -- I'm pretty sure there's a continuous variable (size of crab?) along with a color (range) and a boolean (can't recall). So fairly close to your case -- it's probably instructive to read through those examples which span at least 2 chapters (one chapter is logistic regression I believe). –  ars Sep 13 '10 at 19:33
@ars These are esp. chapters 4 and 5, with carapace width and weight as continuous variables and spine condition as another categorical (ordinal) variable, used in Poisson and Logistic regression :) –  chl Sep 13 '10 at 19:51