Measurement error is ubiquitous in astronomy. In the astronomical literature, discussion on measurement error problems is almost entirely confined to linear regression. We introduce a linear regression measurement error model (LRMM) highlighting the distinguishing features of the model and the data that typically arise in astronomy. Standard methods, proposed in the statistics literature for tackling measurement error problems in regression analysis, are not useful for the analysis of astronomical data. We briefly discuss the methods, and their appropriateness, commonly used by the astronomers for analysis of data using LRMM. A short discussion, on their relative performances based on the available numerical studies, is given. We conclude with some remarks on data characteristics typical to astronomical data and on an emerging measurement error problem in astronomy.