Dear teachers and friends,
Can anybody please help me in this problem ?? For a Given set of n- data points {(x1,y1), (x2,y2), (x3,y3), ......., (xn,yn)}, how can i fit an exponentially growing Regression fit, of the form
y = k0 (1-e-x/Τ)
(following the principle of least Square, as shown in figure), where k0 and τ are constand of Regression. In text book i can find Regresion of the form
y = k0 e-x/Τ , which is nothing but a special case of linear regression. but I am looking for the above mentioned exponentially growing form. Can anybody suggest me any algorithm or any mathematical formula ?? Your help will be highly appreciated.
Thank You
you can use non-linear least squares algorithm (see wikipedia link for an introduction). R is really easy to use as it has a build-in function called nls for non-linear least squares, you can see how to use it in an example I have attached.
https://en.wikipedia.org/wiki/Non-linear_least_squares
https://stat.ethz.ch/R-manual/R-devel/library/stats/html/nls.html
you can use non-linear least squares algorithm (see wikipedia link for an introduction). R is really easy to use as it has a build-in function called nls for non-linear least squares, you can see how to use it in an example I have attached.
https://en.wikipedia.org/wiki/Non-linear_least_squares
https://stat.ethz.ch/R-manual/R-devel/library/stats/html/nls.html
Yes, I agree with the above. You do have to supply starting values for the parameters, so you can try plotting guesses manually to see that they fit the data reasonably well.
For a simple example in R, see the section:
"Nonlinear regression"
in
http://rcompanion.org/rcompanion/e_03.html
For another example that is based on an exponential model, see:
"Mitscherlich–Bray model"
in
http://rcompanion.org/documents/RHandbookProgramEvaluation.pdf
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