Can the dependency between variables be deduced from data? And if so, how?
Yes, We can do that. We can measure the linear relation between two variables by correlation metric to know more see this. If you want to identify the linear relationship between more than two variables we can do it by VIF scores. If a VIF score of a variable is >5 we can say this variable can be expressed as linear combination of other variables to know more see this. If you want to implement in python consider this.