Don't waste your time .. a multivariate regression won't work to a sensible accuracy in most all cases. Run regressions on each of the lines separately (and that might require the lines to be segmented), use that to look up some values for the independent variable of interest ... and then run a sensible interpolation or regression to get the final answer ... works real well.
The end requirement is negligible to no detectable delta betwixt the line data as she is read .. and the calculation as she is run .. and any delta must be conservative.