Re: Method to fit data with equation Y = C1*e^(C2*X) + C3


draccarlawpet a écrit :

Suppose that you have data that you want to fit with the curve: Y =
C1*e^(C2*X) + C3 . I found that to manually do this is very difficult.
However, I have this idea how to make this transformation, which for
some reason, doesn't work. My method is this:

1. Take the log of the dependent variable, Y.
2. Regress ln (Y) against X.
3. The equation will be in the form: ln Y = C1*X + C2
4. Therefore, Y = k2 * e^(k1*X)....or another words, Y=C1*e^(C2*X).
5. Finally, regress Y against Y_predicted - which in this case is
Y_predicted = C1*e^(C2*X). The computed equation will be of the form
Y_predicted_2 = Y = C1*e^(C2*X) + C3 .

However, this equation is not the greatest fit for the data of the form
Y = C1*e^(C2*X) + C3. You would think that this is the case, but it's
not.

Bonjour,
I would start with ln(y - c3) =c2*x + ln (c1) , a straight line
try a value for c3 and adjust it till you obtain a x ,y line
Alain
Another method to fit the data is by manual trial and error with C1 and
C2.
1. Fit various C1s and C2s for the data and regress.
2. The output will calculate the C3.

You will see that the manual method of fitting the data with Y =
C1*e^(C2*X) + C3 is much more better than my first method of taking ln
Y.

Why is my first method of regressing Y against C1*X + C2 not robust?
Can you think of a way, using MS Excel, to fit Y = C1*e^(C2*X) + C3 to
data sets?

.

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