Determining Constants of Best Fit Curve

I have a dataset (x,y) that I would like to fit a curve to. The curve must be of the form:

y = a + b*c^d*x^e

where a,b,c,d,e are constants and constants a and c are known.

Is there a way to numerically determine these constants in matlab?

Answer 1

[Steven Lord]

No. You can't decouple b and d: consider that (b)*c^(d) and (b*c)*c^(d-1) are the exact same value. So let's say you determine for your particular data set that b*c^d is 8 and you know c is 2. We could have (assuming b and d were restricted to take on only nonnegative integer values.)

• b = 1 and d = 3
• b = 2 and d = 2
• b = 4 and d = 1
• b = 8 and d = 0

All of those result in a value for b*c^d of 8. Which solution is the "correct" solution? Without other information, they all are.

If you want to try to determine e and b*c^d search the documentation for "curve fitting" and you'll find descriptions of many different tools that you can use for this application.

[Ian]

I see!

If I fix one of the constants, say b, such that a,b, and c are now known, will I be able to get a unique solution?

I tried doing this using the curve fitting tool app in matlab and it appears to be working.