How to subtract a variability from regression

[#1]

Hello everyone,

I’m learning regression and have some questions about variability.

Suppose I want to study the impact of a factor X on a process response Y. The regression results suggest that moving from condition level A to B of X changes Y by about 10%. However, I also know that the process itself has variability — for example, even at the same condition level of X, Y might fluctuate by around 5%. Below are my questions:

• In the regression summary table, is there a way to tell what percentage of the variability comes from X versus what percentage comes from the process itself? Would this be reflected in the residuals?
• If I have a past study on the repeatability of the process that gave me an estimate of the process variability, would it be possible to subtract that from the regression results in order to isolate the variability that truly comes from X?

Thank you

[#2]

Assuming that your model is correct, then the R square metric estimates the proportion of the variability in Y that is associated with the variation in X.

The process variation and the measurement variation are inseparable unless you perform a study that varies both of these sources of variation.

You have the 'fixed effect' of X and you have the 'random effect' of the process and measurement. The random effect can be decomposed further with a properly designed study and analysis.