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Is there an explanation why there are 2 different results for Fit?
Liste1 = {A, B, C, D}
f(x) = FitExp[Liste1]
g(x) = a ℯ^(-b x)
h(x) = Fit[Liste1, g]
f and h should be the same?!
Andreas
ggb 4.2.28
Files:
Trend_exp.png
The same problem 
IANAGGP (I am not a GeoGebra programer), but I think I can explain what is probably going on. In a nutshell, they use two different algorithms.
The FitExp[] command linearizes the data by taking the natural log of the y values and then finding the best-fit line from all the (x,ln(y)) points. The process for doing this type of regression is very simple and fast. This best-fit line will produce results that will be fairly close to the actual best-fit exponential curve. This is what your calculator's ExpReg command does.
The Fit[] command attempts to find the best-fit curve based on the given function without doing any linearizing. It's a much more complicated process, but if done correctly will result in a curve that is the actual best-fit curve. I don't know what GG does, but the method usually involves systematically trying different values for a,b,c... until the sum of the squares of the differences between the actual and predicted y values is a minimum (the method of least-mean-squares). (If I'm not mistaken, I think that your calculator's Logistic Regression uses a similar technique which is why it takes so long to calculate.)
If you plug the data points you gave into a calculator and use ExpReg, the calculator will give you an equation equivalent to FitExp[] and report that the r^2 = 0.89318. But this is the r^2 of the line using the linearized points. If you calculate the r^2 of the suggested exponential curve, you get r^2 = 0.89459. However, if you find the r^2 of the exponential curve from Fit[], you get r^2 = 0.92381.
In other words, Fit[] gives you a better "fit" than FitExp[].
Hope this helps,
-Wes L
Did you try g(x) = a e^(b x) without the minus sign? It shouldn't matter but maybe this is what throws off the more complicated algorithm fot Fit[]?
Have you tried other comparisons, like linear, polynomial, trigonometric, logistic...?
Yes, I have tried g(x) = a e^(b x) - same result as for g(x) = a e^(-b x).
Andreas
IANAGGP (I am not a GeoGebra programer), but I think I can explain what is probably going on. In a nutshell, they use two different algorithms.
The FitExp[] command linearizes the data by taking the natural log of the y values and then finding the best-fit line from all the (x,ln(y)) points. The process for doing this type of regression is very simple and fast. This best-fit line will produce results that will be fairly close to the actual best-fit exponential curve. This is what your calculator's ExpReg command does.
The Fit[] command attempts to find the best-fit curve based on the given function without doing any linearizing. It's a much more complicated process, but if done correctly will result in a curve that is the actual best-fit curve. I don't know what GG does, but the method usually involves systematically trying different values for a,b,c... until the sum of the squares of the differences between the actual and predicted y values is a minimum (the method of least-mean-squares). (If I'm not mistaken, I think that your calculator's Logistic Regression uses a similar technique which is why it takes so long to calculate.)
If you plug the data points you gave into a calculator and use ExpReg, the calculator will give you an equation equivalent to FitExp[] and report that the r^2 = 0.89318. But this is the r^2 of the line using the linearized points. If you calculate the r^2 of the suggested exponential curve, you get r^2 = 0.89459. However, if you find the r^2 of the exponential curve from Fit[], you get r^2 = 0.92381.
In other words, Fit[] gives you a better "fit" than FitExp[].
Hope this helps,
-Wes L
Well, it helped me at least. Thanks for a clear and concise explanation.
:-)
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