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Cubic Regression

  1. Aug 25, 2011 #1
    Hi,

    I have the following population figures for a five year interval:

    554.8, 609, 657.5, 729.2, 830.7, 927.8, 998.9, 1070, 1155.3, 1220.5

    The graph has an exponential growth from the first value to the fourth value and then the population starts to decay.

    I found that a Cubic Regression best illustrates these figures but I have to describe it and, since I've never worked with them I am a bit wary.

    Is it correct to say that the cubic correctly illustrates the initial exponential growth of the population but also manages to reflect the leveling off of the population in the latter segment of the plot?

    Thanks
     
  2. jcsd
  3. Aug 25, 2011 #2

    Mark44

    Staff: Mentor

    A cubic would get steeper over time, not decay. A logistic function might be the better choice.
     
  4. Aug 25, 2011 #3
    Yes, a Logistic is my next step, but this function here:

    -0.0056755x^3+0.4186x^2+7.35529x+555.2542

    Seems to me like it's leveling off towards the end, or is that impossible? It looks like it is possible from google images but you are probably a more trustworthy source :smile:
     
    Last edited: Aug 25, 2011
  5. Aug 25, 2011 #4

    Mark44

    Staff: Mentor

    No, that one isn't leveling off. Because the coefficient of x3 is negative, the graph of this function is heading to negative infinity as x gets large.
     
  6. Aug 25, 2011 #5
    Um,

    Look :redface:
     

    Attached Files:

  7. Aug 25, 2011 #6

    Mark44

    Staff: Mentor

    That's a pretty good fit, but is it likely that the population will die out in another 50 years? That's what modeling this data with a cubic spline is predicting. On the other hand, if the population is more likely to approach some stable value, then a logistic model is the way to go.
     
  8. Aug 25, 2011 #7

    Mark44

    Staff: Mentor

    BTW, your first post says the data is for a five-year interval, but you graph uses about a 45-year interval. I suspect that you meant that the data represent populations at five year intervals.
     
  9. Aug 25, 2011 #8

    NascentOxygen

    User Avatar

    Staff: Mentor

    Are you just wanting a curve of good fit for these points, or do you plan on extrapolating for the next couple of years?
     
  10. Aug 26, 2011 #9
    This is what my assignment says:

    What types of function could model the behavior of the graph

    and a bit later:

    Analytically develop one model function that fits the data points on your graph

    Furthermore, I am restricting the domain of my graph too.
     
    Last edited: Aug 26, 2011
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