I have values of dependent variable (y) and independent variable (x). x and y are exponentially related. I want to fit an exponential curve with a DC shift. ie,fit a curve between x and y in the form, y=A.exp(B.x)+ C . I have methods to fit y=A.exp(B.x). If you know the procedure to fit in the form y=A.exp(B.x)+C , please replay here
As I understand it you want the form: y = a exp(bx) and is C an error term for the least-squares fit, or an extra coefficient? But really for an uncomplicated exponential you won't need an additional coefficient C unless you actually have a sigmoidal curve (which you may well do, if you have biological variables).
A linear transform will give: loge y = loge a + bx (with just two coefficients, a and b.)
So you'd convert your Ys to their loge, the Xs would remain linear, then plug both vectors into your least-square program SPSS or whatever. This will yield their a and b coefficients relating loge of Ys to Xs, though the a coefficient will be a loge value of a. And I'm assuming now your C is an error term (variance around the line of best fit).
Jeez, it's been 40 years since I've done this stuff, and I'm doing it now from an imperfect memory, so I'm really digging deep here.
I'm hoping this will provide the solution for you.
Cheers, Don
Dear Nabeel,
If you want to fit the function y=A exp(B x)+C which cannot be converted to the least-squares fit by transformation given by Donald I recommend you Mathematica Wolfram or free product called Wolfram Alpha. The last you can find here
https://www.wolframalpha.com/
You should make two steps in Mathematica.
1. Create variable “data” with your values
data={{x1,y1},{x2,y2},……{xn,yn}}
2. Write command
FindFit[data, a exp[b x]+c,{a,b,c},x]
And you can enjoy your results.
More info about FindFit you can find here
https://reference.wolfram.com/language/ref/FindFit.html
If you need my help send me your data
Thank you guys. I got the method to do in LabVIEW and it is working well. Similear to MATLAB and Mathematica.
Now, you can do it in R software in one step code. And the R package named "basicTrendline".
Link1:
https://cran.r-project.org/web/packages/basicTrendline/index.html
Link2 with README file:
https://github.com/PhDMeiwp/basicTrendline
You also can use the solver tool in Excel. See a tutorial in https://www.youtube.com/watch?v=DOCzyB8zj-8
Best regards!
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