We consider the following linear calibration problem. Two scalar quant
ities X and Y are related by a simple linear regression of Y on X, and
at the calibration step repeated measurements on both X and Y are ava
ilable for a number of sampling units. At the prediction step a Y meas
urement, possibly together with previously obtained Y measurements, is
available for a new sampling unit, and we wish to estimate the corres
ponding unknown X. Both the intercept and the slope of the regression
are allowed to vary between units, resulting in a random regression co
efficient model at the calibration step. As a result, at the predictio
n step the unknown X affects both the mean and covariance structure of
Y. Point and interval estimates for X are obtained and illustrated on
a set of biomedical data.