I have table with 500 rows where I have a row number and cost value. Here is first 100 of them.
0,25
0,30
0,35
0,40
0,45
0,50
0,55
0,60
0,65
0,70
0,75
0,75
0,80
0,85
0,90
0,95
0,95
1,00
1,05
1,10
1,15
1,20
1,25
1,35
1,40
1,50
1,55
1,60
1,70
1,75
1,85
1,90
2,00
2,05
2,15
2,25
2,30
2,40
2,50
2,60
2,70
2,80
2,90
3,00
3,10
3,25
3,35
3,45
3,55
3,65
3,80
3,90
4,05
4,20
4,35
4,50
4,60
4,75
4,90
5,05
5,20
5,35
5,50
5,65
5,80
6,00
6,15
6,30
6,50
6,65
6,85
7,05
7,25
7,45
7,65
7,85
8,05
8,25
8,45
8,65
8,85
9,10
9,35
9,60
9,85
10,10
10,35
10,60
10,85
11,10
11,35
11,60
11,90
12,20
12,50
12,80
13,10
13,40
13,70
14,00
When I graph them, it looks exponential.
But when I look at difference between each row value, graph looks jittery.
Log of value
Factor (division) of value
What steps should be made if I wan't to create formula so that I can predict next 1000 (or more) values?
EDIT: Manually, I have got so far to use 0,178*SQRT(x)-0,730 to predict values, but it has an error in range of 0..25% with strange pattern.
It seems that there is something more to it than this simple formula.
How and what best fit curve software to use to get as close as possible?
PS: These are cost of stat points in RPG game. It could be that there is custom function with some sort of balancing. How to determine if it is custom?
As seen from the logplot, your function $f(x)$ is not exponential (the line is not straight). However, observe that it looks a bit like a square root, so
$$f(x)=ae^{b\sqrt{x}}$$ would be a potential model to fit after. But note how your function actually is zero (for $x=1$ it seems). An exponential function can't do this ($e^0=1$). This hints that the function may instead be of the form $$f(x)=axe^{b\sqrt{x}},$$ which would be my best guess (it has this form - ignore the orange lines). To find the coefficients $a,b$ that fits your data the best, you need to usage some dedicated software (Excel might be able to fit after custom functions, I don't know) to find the best guess.
Good luck!