Linearity is pretty simple and obvious to guess. However, in some cases, the scenario gets totally different. IF you see the following attached graph, would you consider it linear association or not?
if linear then why?
If nonlinear then why?
Looks pretty nonlinear to me. The graph of a linear function must have a constant first derivative, f'(x) = const for all x. That means, it can only be a function f of the general type f(x) = mx + b (where m, b are both constants), which is not the case in the graph of your image.
Agree with Armin Fugenschuh. Looks like the closest model would be a sinusoidal curve... or possibly... possibly a polynomial of degree 6 or 7 at least...
Dear Hasan Bin Sohail
The graph is nonlinear. If your mathematical model requires a straight line for the attached image, then you can approximate the data (if exists) to find the best straight line that fits the available data. The least-square fitting can do the job.
Best regards
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