Why do we need clearly defined variables as response/dependent variables? This is not a homework question, just sort of a mental block. Why do statistical analyses require clearly defined variables as response/dependent variable? Why can't my response variable be something [vague] like "Likely High Value Customer" or a yes/no question?
 A: EDIT: This answer was directed at the original question: Why does logistic regression require a clearly defined dichotomous variable as response/dependent variable? It is likely to read very strangely as an answer to the question which is currently Why do we need clearly defined variables as response/dependent variables?
One could always define logit or logistic regression as requiring the response to be a binary or dichotomous variable, conventionally coded 0 or 1. Some software embodies such a definition in so far as data not satisfying such a definition will not be accepted as input or will be coerced to that form (e.g. all nonzero values are mapped on the fly to 1). 
But such a definition would be perverse, or at least narrow-minded. A main point about logit regression even for such input is that we can think of the response as being, or as representing, an underlying probability that varies continuously in a particular way, at least for continuous predictors. Consider, for example, precipitation falling as solid (snow) or liquid (rain) as temperature varies. As the temperature gets colder, the probability of snow goes to 1, and as it gets warmer it goes to 0: it's the probability that we are modelling and the 0 and 1 observed values are just grist for the mill. Furthermore, it also makes sense to apply such a model to a proportion that is inherently (or practically) a continuous response (e.g. the fraction or proportion of forest cover in a set of small areas). 
Historically, such interpretation came first! Logit or logistic treatments of responses came before the idea of using the logit as link function for binary responses. 
A minor classic dataset of this kind includes data on the incidence of Rhynchosporium secalis (leaf blotch) on the leaves of 10 varieties of barley grown at 9 sites in 1965 from Wedderburn, R.W.M. 1974. Quasilikelihood functions, generalized linear models and the Gauss-Newton method. Biometrika 61: 439–47. Blotch incidence is measured as a percent cover. Naturally, the usual assumptions of binomial distribution don't carry over, which is why a different approach is needed.  
Pedagogically, there is often a minor problem in so far as logit models for continuous responses often fall between texts or courses on categorical data analysis on the one hand and regression on the other hand. 
That said, your examples are puzzling. In a particular, a Yes-No question would seem to be another example of a clearly defined dichotomous variable. 
A: Statistical analyses do not require a response variable.  There's an entire class of problems called "unsupervised learning" where one only works with a set of known features.  Also much of exploratory data analysis doesn't concern itself with singling out one variable as the response.  It's primarily when we're building predictive models that it's important to identify a dependent variable, but in these cases it should be pretty obvious why.
A: The answer to your question has two elements.


*

*Operationalinalization of scientific concepts to make them measurable

*Statistics estimated on measured quantities


In step 1 of the process you would define what you mean by the 'vaguely' defined concept, such as customer value. In science you need to be clear on what you mean by a concept before you can systematically observe it. Second you need to come to an operational definition: how can you make the concept you theoretically defined measurable? For example you could take answers to the question "Do you like brand xyz?" (yes/no) from a survey questionnaire as operational definition of high customer value. If that's a good operationalization is then debatable, but you have made it clear.
In step 2 you start the statistics and their use always depends on your goal (research question). If you want to predict when a brand has high customer value, then the variable measuring that concept becomes the dependent variable in an analysis, which could be logistic regression, for example. Which is the appropriate staistical method often depends on the distribution of the variable, which in case of dichotomous variables like answers to yes/no questions is often binomial, and hence logistic regression is appropriate.
