# Find best fit function for different data set with errors

I have the following 3 data sets for the same quantity with errors as shown in the figure in different colors. How to find the best fit function of 1) each data set separately 2) combined of the 3 data set. Suppose I find the best fit function of each data set separately; then how to combine the three best-fit functions correctly so that I can have a single fit function. Which method will give the more accurate results; finding one single fit function for all the data sets or finding separately each and then adding them up? How I would check the accuracy.

ListPlot[{{Around[0.2, 0.1], Around[1, 0.1], Around[2, 0.2],
Around[3, 0.3]}, {Around[0.5, 0.1], Around[2.5, 0.1],
Around[3.5, 0.2], Around[3.5, 0.3]}, {Around[0.8, 0.1],
Around[1.5, 0.1], Around[2.8, 0.2], Around[1.8, 0.3],
Around[5, 0.5]}}, Frame -> True]


• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Mar 25 at 22:18
• Isn't every described above? If any other information is needed, I can explain. The main goal is to find a single fit-function for the different data sets given above where the data corresponds to the measurement of the same quantity, but with different experiments. Mar 25 at 23:55
• The other information needed would be an explanation as to what exactly is meant by "different experiments". Different persons taking observations from same device? Do the values 1, 2, 3, 4, and 5 represent time? Are those measurements serially correlated? Is there a single underlying function with measurement and replication error? What do you plan to do with the results? And by that last question I mean do you need to predict a future set of observations and need confidence bands on those predictions? The point is that the objectives are essential as well as the analysis procedure.
– JimB
Apr 29 at 2:23