I work for a commercial printing company, and am collecting data regarding the quality of our printing over time (density and dot gains). Essentially, for every job I have a date, a density, and a dot gain. I would like to be able to analyze a date range and check to see if our quality seems to be getting consistently worse.
From a math perspective, I somewhat understand what I need to do. I need to get a best fit curve for our data, and then find the derivative of that curve. The slope of that derivative should give some insight as to if our quality is getting better or worse, and how quickly.
My biggest hiccup here is how to find the best fit curve for a scatter plot. Certainly I can work out a way to find the derivative after that, but I can't think of any good way to find the original curve.
So - how do you find the best fit curve of a scatter plot? And bonus points if you can give me a quick and (relatively) easy way to get the derivative/slope of that curve.