The Jargon File (version 4.4.7, 29 Dec 2003):

coefficient of X
 n.

    Hackish speech makes heavy use of pseudo-mathematical metaphors. Four
    particularly important ones involve the terms coefficient, factor, index of
    X, and quotient. They are often loosely applied to things you cannot really
    be quantitative about, but there are subtle distinctions among them that
    convey information about the way the speaker mentally models whatever he or
    she is describing. Foo factor and foo quotient tend to describe something
    for which the issue is one of presence or absence. The canonical example is
    fudge factor. It's not important how much you're fudging; the term simply
    acknowledges that some fudging is needed. You might talk of liking a movie
    for its silliness factor. Quotient tends to imply that the property is a
    ratio of two opposing factors: ?I would have won except for my luck
    quotient.? This could also be ?I would have won except for the luck factor?
    , but using quotient emphasizes that it was bad luck overpowering good luck
    (or someone else's good luck overpowering your own). Foo index and
    coefficient of foo both tend to imply that foo is, if not strictly
    measurable, at least something that can be larger or smaller. Thus, you
    might refer to a paper or person as having a high bogosity index, whereas
    you would be less likely to speak of a high bogosity factor. Foo index
    suggests that foo is a condensation of many quantities, as in the mundane
    cost-of-living index; coefficient of foo suggests that foo is a fundamental
    quantity, as in a coefficient of friction. The choice between these terms
    is often one of personal preference; e.g., some people might feel that
    bogosity is a fundamental attribute and thus say coefficient of bogosity,
    whereas others might feel it is a combination of factors and thus say
    bogosity index.