1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solving response surface for 0

  1. Oct 5, 2011 #1
    Hi,

    I've done a response surface analysis, resulting in an equation of the form:

    P= A + B*X + C*X^2 + D*Y + E*Y^2 + F*X*Y

    Where A,B,C,D,E, and F are known values.

    I want to rearrange the equation so I can get a polynomial describing when P=0, but I'm stuck.

    Any suggestions?

    Thanks,

    Jono
     
  2. jcsd
  3. Oct 5, 2011 #2

    Mute

    User Avatar
    Homework Helper

    Your equation is a quadratic form. You generally will not be able to solve it in the form y = f(x). Such an equation (with P = 0) describes a conic section (ellipses, hypberbolas, etc).

    See this wikipedia page for details about how to identify which conic section your equation gives you.
     
  4. Oct 7, 2011 #3
    I see... So I guess I need to re-think how I've done things.

    I have a bunch of bacteria growth rates at different temperatures and water levels, and want to whack a curve on it that describes the boundary between growth and no growth for x (temp) and y(water). I've been playing around with response surfaces and binary logistic regressions, but I can't figure out how to get the resulting equations to give me an y=f(x) that describes the boundary.

    Thanks for your help, it has been very useful.

    J.
     
  5. Oct 7, 2011 #4

    Mute

    User Avatar
    Homework Helper

    Why does the boundary have to be a function? Couldn't there be regions of growth and non-growth that are bounded by curves that can't be described by a form y = f(x)?

    If you plot P(x,y) = 0 (e.g., using the contour-plot in Mathematica), what does the curve look like given your numbers A...E? Depending on your constants, it could be possible that the resulting curve could be described by a function for x > 0 and y > 0. For example, the curve

    (x-2)^2 + y^2 = 4

    is a conic section, and obviously a circle. You can't solve it exactly as y = f(x), although you can split it into two functions: [itex]y = \pm \sqrt{4-(x-2)^2}[/itex]. In this case, if you only care about x > 0, y > 0, you only need the [itex]y = + \sqrt{4-(x-2)^2}[/itex] solution.

    Depending on your parameters, something similar could happen for your case, but in general it won't. However, again, I'm not sure why your boundary must be a function y = f(x)?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solving response surface for 0
  1. Solve e^x+2x-5=0 (Replies: 11)

Loading...