iSixSigma

Y=f(X)

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  • #54525

    Sheldon
    Member

    So Y=f(X), Y is the outcome I desire, f is the function performed on the inputs to produce the outputs. Y is a function of x. Is x the inputs?

    I get this but maybe I’m looking at its as a math equation because in my math mind I see the equation as Y= f multiplied by x. This is wrong, right?

    In layman’s terms how should i be reading this equation?

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    #195888

    Robert Butler
    Participant

    What you are looking at is standard notational shorthand for designating Y as a function of an x. The shorthand has nothing to do with multiplication. The actual form of the function – that is the expression involving the X’s is some specific expression which is to be found elsewhere, to be determined, specified somewhere in the text, etc.

    As an example say you have Y = 3.1 + 2*x + 4.5*x*x

    The shorthand version in a discussion would be something like this: Y is a quadratic function of x. It should be noted that the general solution for f(x) is x = [-b +-sqrt(b**2 – 4ac)]/2a where b = 2, a = 3.1 and c = 4.5.

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    #195889

    Brian
    Participant

    f(x) isn’t a mathematical formula. It simply represents the concept that “X” functions as a variable in any formula used to determine “Y”. The formula can be as simple as 2X or as complex as one can imagine but Y will always be dependent on the variable X.

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    #195890

    Chris Seider
    Participant

    @Sheldon18

    Consider the following example and 2 inputs might impact the output.

    Ice Cream Sales = (Outside temperature in Fahrenheight – 75)*150 + Number of trucks selling * 50

    Notice that Temperature is an uncontrolled variable and number of trucks is a variable in control of the company. This is another example of y = f(x1, x2) or y=f(x) as R. Butler did a nice job explaining.

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    #195892

    Sheldon
    Member

    @cseider So the f really just means function, it holds no weight on the equation except to signify function?

    In your example Y would be Ice Cream Sales, x would be outside temperature and Number of trucks selling?

    Thank you everyone for your replies, much appreciated.

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    #195893

    Chris Seider
    Participant

    @Sheldon18 Yes, f is often referred to “a function of” when referred to y=f(x).

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    #195894

    Sheldon
    Member

    Very cool, got it. Thanks again.

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    #195900

    Darth
    Participant

    @sheldon18 As has been explained, the notation of Y=f(x) is not really mathematical but a conceptual description. In the LSS context I like to describe it as “Outputs are a function of the inputs” since we often use Y to describe out outputs or response and X as the inputs. That is why we don’t try to improve the Y. We must identify and improve the Xs. We don’t improve “Profit”. There is no profit dial to turn. It is a result or function of the various inputs of costs and revenues. I find this explanation, while obvious, seems to help clarify things.

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    #195932

    Danny Kee
    Guest

    Y is output, f is the function or the process of transforming x to became a Y, in a real world, the result are not simple, so just treat is Y= f(Xn), where n represent constant, could be any no.

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