Which Analysis is Appropriate?

[jnet7]

I have collected data on different furniture type purchases and feel that there may be some underlying correlations between the items chosen and the type of residence the consumer wants to furnish.

The items to choose from are couch, table, pillow, and chair. What I am assuming is that if the consumer has selected a couch, they are likely to choose a pillow as well. Similarly, if the consumer has selected a table, they are likely to purchase a chair. There is a chance that those needing a pillow will select a chair as well, but it is less likely. 

The types of residences the consumers are looking to furnish are either an apartment, house, or dormitory. Depending on the type of residence, I assume that only certain furniture is likely to be needed. For instance, a dormitory is less likely to need a couch as most dorms come furnished. An unfurnished apartment may need all furniture options. 

Which type of statistical analysis should be performed? I have data representing the frequency of each item purchased below:

Residence	Couch	Table	Pillow	Chair
Dorm	30	10	32	12
Apartment	103	40	99	34
House	25	11	23	15

[PGStats]

For a graphic representation of the relationship between furniture type and residence type, try correspondence analysis:

data have;
length Residence $16;
input Residence Couch Table Pillow Chair;
datalines;
Dorm 30 10 32 12 
Apartment 103 40 99 34 
House 25 11 23 15 
;

ods graphics / height=600 width=600;
proc corresp data=have deviation;
var couch -- chair;
id residence;
run;

Configuration plot

Proximity on the graph indicates stronger correspondence.

[Ksharp]

Or check Bayes Choice Model.

PROC BCHOICE