I want to build a linear model to predict a scalar output from a vector of noisy scalar variable measurements.
I have two separate training data sets. One has output data and corresponding exact variable measurements. The other has exact variable measurements and corresponding noisy variable measurements. The noisy measurements of some variables are noisier (higher error variance) than others, and the noisy measurements of some variables are biased. I do not have a single data set with output data and corresponding noisy variable measurements.
How should I build my linear model? Should I use the exact variable measurements and ignore the fact that when the model is applied/used, noisy measurements of the variables will be input to the model? Or is there some way I can make use of what I can figure out about the noisy measurements of each variable when building the model? Can R help me with this problem?