  In the paper the interval least squares approach to estimate/fit data with
interval uncertainties is introduced. The solution of this problem is discussed
from the perspective of interval linear algebra. Using the interval linear
algebra carefully, it is possible to significantly speed up the computation in
specialized cases. The interval least squares approach is then applied to lung
function testing method - Multiple breath washout test (MBW). It is used for
algebraic handling of uncertainties arising during the measurement.
Surprisingly, it sheds new light on various aspects of this procedure - it
shows that the precision of currently used sensors does not allow verified
prediction. Moreover, it proved the most commonly used curve to model the
nitrogen washout process from lung to be wrong. Such insight contributes to the
ongoing discussions on the possibility to predict clinically relevant indices
(e.g., LCI).
