Is there any way to represent these coordinates with a formula? I can't think of a function that would work. I know the data doesn't yield a function because it would pass the vertical line test, but is there anything close? What do you think?

29.84 39.39
28.96 46.01
26.74 41.84
24.52 41.86
24.04 45.91
24.2 49.58
24.49 52.5

Question

Is there any way to represent these coordinates with a formula?  I can't think of a function that would work.  I know the data doesn't yield a function because it would pass the vertical line test, but is there anything close?  What do you think? 


29.84	39.39
28.96	46.01
26.74	41.84
24.52	41.86
24.04	45.91
24.2	        49.58
24.49	52.5

anonymous · Answer

|dw:1386548824766:dw|

anonymous · Answer

it looks a little like that

anonymous · Answer

Sorry.... *wouldn't* pass the vertical line test

ranga · Answer

Is this statistics?  Are you supposed to find the "best-fit"?

anonymous · Answer

I want to just find some sort of model.

anonymous · Answer

But yes, best-fit of some sort

anonymous · Answer

It looks sort of cubic...

ranga · Answer

In the fourth and the last pair of points, the x-coordinates are very close and yet the y coordinates are different.  Does not pass vertical line test.  No function.

anonymous · Answer

Well, I know it's not a function, but this is data that I collected, and it is obviously not a random mess.  There must be some sort of function I can use to best-fit this, right? Do you think there is some way to do that?

ranga · Answer

You can find a function that comes close to some of the points but some of them might be way off.  Also, the sample size is too small (just 7 points) to meaningfully extrapolate.

anonymous · Answer

Hmmm... I think you're right.  Thank you!  My problem was lack of accessible data when doing this.

ranga · Answer

29.84 39.39 28.96 46.01 26.74 41.84 24.52 41.86 24.04 45.91 24.20 49.58 24.49 52.50 Copy and paste the above data and see if you can fit a polynomial. This link allows you to try various degrees of polynomial from 2 to 10. Start with cubic as this is definitely not linear or quadratic: http://www.xuru.org/rt/PR.asp#CopyPaste

anonymous · Answer

I'll try that!  Oh my gosh, thank you!

ranga · Answer

You are welcome.

anonymous · Answer

The cubic does fit the data best.  My next question is: Is it reasonable to use this equation to model future points?  I realize that I don't have anywhere near enough data to do so, but it's kind of that or nothing for me...