Which test would be appropriate to test multiple variables?

I have a data on users with 5 personality variables. The users had to pick a logo for three different projects (most likely, may be, least likely). The question is why the users chose the logo they did - is it the color, the shape, etc.

There are 3 data sets - the personality test results, logo characteristics, and social achievement characteristics.

The t-test on each of the aspect of personality test and each of the avatar characteristics didn't bring much.

Is there a test that could be run on all of the variables together in order to reach the results which would explain why the user chose a certain logo?

The software used is SPSS Statistics 22