I'm doing research and I have some data (attached  'y' = first column, 'x' = second column in CSV format) that I need to find a general curve fit for (function = f(x)/x). This will help me do future predictions.
Here are my stipulations:
The fit curve must have the format of f(x)/x. Two examples I've tried are sqrt(x)/x and log(x)/x > and of course they have more general forms such as [(b*x+a)^n]/x and {[log(x+a)]^n}/x. However, these functions do not "bend" in the way that fits the data best so there must be better (see "sqrt.jpg").
The function f(x) MUST behave well at zero and be positive for 'x' > 0. E.g., for the log function this can be done by shifting the x data by '1'. The sqrt function is naturally well behaved with no modifications obviously.
The curve needs to fit the general shape but use as FEW of parameters as possible. E.g., the sqrt function (x^n) is attractive because it only uses 1 parameter, "n", but just not quite right.
Thanks!
Here are my stipulations:
The fit curve must have the format of f(x)/x. Two examples I've tried are sqrt(x)/x and log(x)/x > and of course they have more general forms such as [(b*x+a)^n]/x and {[log(x+a)]^n}/x. However, these functions do not "bend" in the way that fits the data best so there must be better (see "sqrt.jpg").
The function f(x) MUST behave well at zero and be positive for 'x' > 0. E.g., for the log function this can be done by shifting the x data by '1'. The sqrt function is naturally well behaved with no modifications obviously.
The curve needs to fit the general shape but use as FEW of parameters as possible. E.g., the sqrt function (x^n) is attractive because it only uses 1 parameter, "n", but just not quite right.
Thanks!
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