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The better the fit of the data to the line, the lower the uncertainty.
For further information on fitting of lines to data (also known as regression analysis), see: Note that the methods used by isotope geologists (as described by York) are much more complicated than those described by Gonick.
This will be discussed in more detail in the section on Gill's paper below.
In many cases, there are independent cues (such as geologic setting or the chemistry of the specimen) which can suggest that such assumptions are entirely reasonable.Consider some molten rock in which isotopes and elements are distributed in a reasonably homogeneous manner.Its composition would be represented as a single point on the isochron plot: Note that the above is somewhat simplified.The simplest form of isotopic age computation involves substituting three measurements into an equation of four variables, and solving for the fourth.The equation is the one which describes radioactive decay: If one of these assumptions has been violated, the simple computation above yields an incorrect age.