For instance, if the x-axis data is known to have no error, but the y data does, (such as a population estimate (y), at a known time (x)), simple linear regression would work.
If both sets of data contained error, for instance the relationship between concentrations of two substances in blood, Deming regression would be more appropriate.
The disadvantage with Deming regression, is that it is mathematically more complex to do. This means doing the calculations, either on paper, or by writing a formula for a spreadsheet, are more difficult.
This article is a stub.