# Thread: Plotting observations to form equation

1. ## Plotting observations to form equation

Hello. This is my first time with this website. Please let me know if this topic should have been placed in another forum group.

I have a set of observed numerical data. It is composed of lots of x,y coordinates. I can create a graph and the data forms a curved line. I would like to know how to enter the data into my HP 48GX (or a computer program?) so it can analize the curve and give me the equation that it represents. So I can take x and the equation will calculate y. I don't know if any graphing calculator can even do that. I have the User's Guied and the Advanced User's Manual, but I'm not even sure what terminology to refer to. Arrays? Matrices? It's been a while since I was in school and I'm getting back into math. Any comments or help in pointing me in the right direction would help.

Thanks!

2. Originally Posted by e6bwhiz
Hello. This is my first time with this website. Please let me know if this topic should have been placed in another forum group.

I have a set of observed numerical data. It is composed of lots of x,y coordinates. I can create a graph and the data forms a curved line. I would like to know how to enter the data into my HP 48GX (or a computer program?) so it can analize the curve and give me the equation that it represents. So I can take x and the equation will calculate y. I don't know if any graphing calculator can even do that. I have the User's Guied and the Advanced User's Manual, but I'm not even sure what terminology to refer to. Arrays? Matrices? It's been a while since I was in school and I'm getting back into math. Any comments or help in pointing me in the right direction would help.

Thanks!
The answer to your question is, "it depends."

If you know what form the function should be (polynomial, logarithmic, sinusoidal, etc.) then the answer is probably yes. You can usually do some kind of linear regression, or log-log plot, or something to determine the parameters. However if you don't know the form of the function ahead of time, all you can do is guess at the form and hope for the best.

The nice thing is that if you don't care about anything except for modeling the points you have, then you can always fit your data to a sufficiently high polynomial function.

Now whether your calculator can best fit your data to, say, a sinusoidal curve is going to depend on the kind of calculator and the software you can get for it.

-Dan

3. Thanks for the advice.

How can I find the form of function? I have the x coordinates 2,3,4,5...132. For each x I have y: 130, 152, 177...1000. The curve begins steep and slowly tapers off as the y numbers become closer together.

Should I put this in another forum, like pre-calc?

4. Originally Posted by e6bwhiz
Thanks for the advice.

How can I find the form of function? I have the x coordinates 2,3,4,5...132. For each x I have y: 130, 152, 177...1000. The curve begins steep and slowly tapers off as the y numbers become closer together.

Should I put this in another forum, like pre-calc?
I don't think there's a problem with the forum.

Since you don't know what the form of the function is to be all you can do is to start taking guesses. If the data look like an exponential, try an exponential function:
$f(x) = Ae^{Bx}$

If it looks like a parabola, try to fit it to:
$f(x) = ax^2 + bx + c$

etc.

-Dan

5. This is a statistics problem. It is very long to do by hand. Just run a program on your computer that try different forms: exponential, power, polynomial, ... And pick the one that looks best.

6. Thanks for the further help. It's beginning to sound like this is harder than I thought.

Does anyone know of a program or calculator that will allow input of the observations and it will do all the work and estimate the form or equation?

7. Originally Posted by e6bwhiz
Thanks for the further help. It's beginning to sound like this is harder than I thought.

Does anyone know of a program or calculator that will allow input of the observations and it will do all the work and estimate the form or equation?
Here.

8. Just wanted to thank you for showing me that graphing program. It works great and I was able to find the function for my ploynomial. Quick question about the Graph program. When I went to Insert Trendline the Logarithmic, Power and Exponential options are not clickable. Is this not offered in this program version or does it automatically know from the start that the point series is not one of those? Just curious because I had another point series that looked logarithmic, but it won't let me try. I tried the other options, but the trend line won't fit right.

Thanks!

**EDIT: I figured it out. I had to remove the 0,0 point and it opened up all the other trendlines. Thanks again!