Data sampling prior to fit linear regression is an efficient way for accurate modeling and prediction. Does that work in Experimental Design? Has that been done?
could you add some detail to your question so we understand what exactly you want to do. As stated the simple answer is yes, it is done all the time, but I think you have a more complex idea in mind?
I use multi-variable linear regression when I am not sure what is causing an effect; it is a good way to objectively rule out unimportant parameters.
Others use Kalman filtering to distinguish a transducer fault, from a real experimental change.
Particularly when there is a complex system under experiment, with lots of measurements, these techniques are very useful. One example is experiments on gas turbines, where a change in one area can affect lots of measurements. (Opening compressor bleed valves changes: Turbine mass flow rates, spool speeds, TET and change the compressor stall line.)
Actually what I am thinking is once I collect the response factor with independent variables and prior to fit MLR for Experimental Design, I sample the data by mixing the observation rows with changing the order.
Along with, I can split the data into train and test. Fit the model given the train data to predict the test data. It is kind of external prediction and checking for the validity of linear modeling for experimental design model.
The case I have is regarding the CO2 injection in oil field for Enhanced Oil Recovery Processes. CO2 EOR flooding is affected by many factors that influence its performance and effectiveness and I want to optimize Oil Recovery by Experimental Design.