I'm studying some variances ($\sigma^2$), that in my case, they must depend by velocity squared $v^2$.
So, in my experimental proofs, I have plotted a graph of $\sigma^2/v^2$, and I was hoping to find a horizontal line.
But, my data seem to be constants in $\sigma^2/v$, and now I find myself in times of trouble: I have to choose which one is the best fit.
In each cases ($\sigma^2/v^2$ or $\sigma^2/v$), I obtain a nearly straight line.
So, I look the equation of best fit lines as $y = mx +q$, where $m$ is his angular coefficient.
The angular coefficient $m$ is less, in the case of $\sigma^2/v^2$ (by about an order of magnitude), but in the case of $\sigma^2/v$, the range of the best fit line (from its maximum and minimum in the graph) is relatively more lower.
At this point, to choose the best fit, the best solution is:
- Choose the case where $m$ is lower.
- Or I have to choose the dynamic case (maximum value minus minimum value), where the best fit line is more flat in the graph (not by absolute value)?
Here are an example: in the first graph $m$ is greater (see the equation in the plot), but the line varies of 0.01.
In the second case $m$ is lower, but the line varies of 0.15.
What is the best fit? The first or the second?
EDIT
For Matt L. - Your approximation error $e$ is very similar to the $R^2$ parameter, that I define so (now I use your notation):
$$R^2 = 1 - \frac{\sum_i \left[d_i-f(v_i)\right]^2}{\sum_i \left[d_i-\overline{d_i}\right]^2}$$,
where $\overline{d_i}$ is the average value of $d_i$.
Maybe you would like say that I must simply see where I have the minimum error $e$ or the best fit parameter, e.g. $R^2$.