I am doing an assignment in which a set of data and a function is given. One of the questions ask for me to estimate and interpret the parameters of the function. I have already estimated them accurately, but what does it mean to interpret them? Does this mean to explain what they are in words in terms of the context?

Thank-you in advance.

## Answers (1)

What do they mean?

Example: I found the best fit to the curve of the bent beam was a cubic. I tried several fits, and based on the RMSE, the large number of measurement along the curve, and the number of parameters in the fit I was able to compute the AICc (okay model selection criteria) and it indicated the cubic was the best fit.

So what? Why does it mean anything that the cubic made the fit and not Gaussian, or a Quadratic? Well the small beam deflection theory says the curve should be cubic, and the system I measured could qualify as a beam. If I knew the modulus and geometry I could determine the applied load. It's a physically consistent example.

If I find areas of deviation from the cubic, I can start looking for local damage. The cubic answer leads me somewhere - it gives clues as to the next step in the investigation. I also need to account for the Confidence Interval - I use 95% - so that I know not just the mean of the estimate, but the reasonable range, or an estimate in the variability .. like the standard deviation.

In the real world everything is noisy. There is always a mean and a standard deviation if you have a good measurement system. Account for that. In mechanical designs for 6-sigma (or the more common 5-sigma) you must account for not just the means but the interactions of your standard deviations - your uncertainties too.

Questions to ask yourself:

what do you learn from the analysis? What do the coefficients of your fit equation tell you? Do they give you clues that lead somewhere?

what is your uncertainty? Does it stack up? How does it impact your inferences, conclusions.

always ask yourself what you would do if you could start over knowing what you now know. You really should have an answer here. If you aren't making some sort of mistake, or able to come up with some sort of improvement .. then you aren't loving what you are doing, and you might be wasting your time and the time of someone else too

Best of luck.