Find the linear portion of a curve

[RandomGuy88]

Hi,

So I have a set of experimental data and I would like to find the slope of the linear portion of the data. For example, say I have set of points, the first few points are not linear, then there is a chunk of data in the middle that is linear, and then the last several points are very non-linear. I would like to find the slope of this linear portion in the middle but the location and length of the linear portion will be different for each experiment. I could easily do this by just manually removing the non-linear portions of the curve but I would like for the computer to be able to do this automatically. Does anyone have any suggestions on the best way to do this?

Thanks

 

[hotvette]

Tricky business I would think. What the human brain can easily do isn't necessarily so easy to replicate with a computer program.

http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=05716374

http://en.wikipedia.org/wiki/Robust_regression

http://www.mendeley.com/research/empirical-analysis-software-effort-estimation-outlier-elimination/

http://pubs.acs.org/doi/abs/10.1021/ed082p1472.2

 

[Bob S]

Will the curve fitting program mentioned in post #8 in https://www.physicsforums.com/showthread.php?t=364600 work?

Diffferentiate the result for the slope.

Bob S

 

[jack action]

You calculate the http://en.wikipedia.org/wiki/Differentiation_(mathematics)#Definition_via_difference_quotients" will be equal to zero (which means «no change in slope»).

 

[alphy]

for your question. As a scientist, there are a few ways you could approach finding the linear portion of a curve in your experimental data. One method is to use a statistical approach, such as linear regression, to fit a line to your data points and determine the slope of that line. This can be done using software such as Excel or R. Another approach is to visually inspect your data and manually identify the linear portion. However, as you mentioned, this can be time-consuming and subjective.

If you would like the computer to automatically identify the linear portion, you could also use algorithms such as piecewise linear fitting or spline interpolation to determine the linear portion of your data. These methods involve dividing your data into smaller segments and fitting a line to each segment to determine the slope. This can be done using software such as MATLAB or Python.

Overall, the best approach for finding the linear portion of your data will depend on the specific characteristics of your data and the resources available to you. It may be helpful to consult with a statistician or data analyst for further guidance on the most appropriate method for your specific experiment.