i got 30 binary variables and i want to find out if there is any combination of this variables which leads to a high value on a metric variable.
For example: i got the binary variables "loud", "hot", "new", "nice", "hard" and i got the dependent metric variable "liking" (1-100).
I want to find out which combination of "loud", "hot", "new", "nice" and "hard" leads to the highest ratings on "liking". If it was just 2 binary variables i would think a 2-factorial anova would do the job? But i got 30 binary variables and i have no idea how to do this.
i could calc 30 t-tests to finde out which binary has an effect alone. But if i do so, i wont finde out how they interact with each other. i could calc a regression with all the 30 variables and have the same problem.
Is there any method to finde out the best combination of binary-ratings for a high liking value?
And as a second theoretical question: If there is any combination of binary variables which leads to a high rating, does that imply that all the binary variables in this combination are correlated? If yes, i could look for correlations.
thanks a lot for all your help!