easy to implement method to fit a power function (regression)?

Question

I want to fit to a dataset a power function ($y=Ax^B$). What is the best and easiest method to do this. I need the $A$ and $B$ parameters too. I'm using in general financial data in my project, which looks like this: 8553600 458.2 17193600 373.6 25833600 694.16 34646400 738.33 44064000 817.89 54259200 1040.67 67910400 1032.69 76291200 1222.1 84844800 1245.65 94089600 1217.44 102211200 1579.38 110592000 1859.24 118886400 1711.67 127612800 2303.62 136684800 2658.26 219196800 3669.23 225676800 3525.02 225763200 3749.27 I need to implement the algorithm in a Java similar language called ActionScript.

Answer 1

y = c * B^x

takes the log of both sides:

log y = log C + logB^x

log y = log C + x * log B <--- this is linear with slope m=logB and intercept k=log C

Then you do the LINEAR REGRESSION on x vs. log Y.

Once done, you have base B = 10^m and intercept k= 10^c

========================================================

There are MANY online calculators and hand-held calculators that will do these

calculations for you. It is a shame you have to "REINVENT the Wheel" by having to

implement it yourself. It would probably be easier to do it with the spreadsheet (Excel/google sheets).

Oh well... I have uploaded the source code written in Java for you. The filename is REGRESSION.java

in the RESOURCES section under the TOOLKIT menu. THe code is too long to display here.

You need to create the input file like this:

N=6

X y

0 , 3

1 , 6

2 , 12

3 , 24

4 , 48

5 , 96

The equal sign in the first line states there are six ordered pairs. The equal sign is REQUIRED.

It then reads the ordered pairs, loads the data into memory arrays, sets up the table, calculates, and

outputs the results.

The output is correct here at y = 3*2^x

You will also need to change the filename in the Go() routine. I hard-coded the filename because you need to translate this code into another script language anyway. Just take the algorithm and "heart and soul" or "meat and potatoes" out of the code, use what you need, and discard the rest...

Good Luck

Answer 2

Just us the power law fit in Excel.

Jim