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How to derive an equation from a graph

  1. Nov 5, 2013 #1
    1. The problem statement, all variables and given/known data

    Hello! I have two graphs which I need to find if there is relationship between them (all in one).

    I have to create a formula/equation that can show and prove that there is this relationship between them.


    I am really confused at the moment since I do not know if there is any correlation, I have examined the two graphs and so far I don't think there is any correlation.


    The graph represents Prey and Predators number. X axis is time (weeks), Y axis is numbers. When the pre

    y number starts to increase the predator number starts to increase as well.

    Here are the numbers of Prey from week 15 to 25:

    495, 550, 560, 620, 720, 690, 750, 740, 950, 800, 650

    And here are the number of population for Predators from week 15 to week 25:

    15, 20, 50, 80, 110, 190, 200, 250, 360, 380, 650,


    2. Relevant equations

    Can I also use LinReg (for Prey graph) and ExpReg (for Predator graph) on a GDC? (Ti-84+)

    3. The attempt at a solution

    I created a scatter plot which can be found to the attached documents so it can be easier for me to illustrate if there is any correlation.
    Also it is clearly visible on the predator graph that it is Exponential however the prey graph is not.

    About the formula I was thinking of something like P = a.e^Inb.t
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

    Last edited: Nov 5, 2013
  2. jcsd
  3. Nov 5, 2013 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    Note: the first graph shows very clearly that the word is "prey", not "pray".
     
  4. Nov 5, 2013 #3

    berkeman

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    Staff: Mentor



    There clearly is a correlation. The number of predators follows the number prey with some ratio, and with a time lag (and maybe some other correction factors).

    Try out a formula that shows the ratio of prey to predators (it's a ratio >1), and include some time lag in the function. Then calculate your overall error versus the graph, and see if you can adjust the ratio and time lag parameters to give you a good correlation. Then for whatever errors you still have, see if you can figure out smaller correction factors to put into the equation. For example, the seasons of the year may be a factor in their populations as well...
     
  5. Nov 6, 2013 #4
    Thanks for the reply, I'll try that. If it doesn't work out I will come back for more help!
     
  6. Nov 6, 2013 #5
    How come you only included weeks 15-25 on the scatter plot? You should include all the data on the scatter plot, and you will see a much better correlation.

    Chet
     
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