When using an mth degree polynomial
to approximate the given set of data, 
,
,
..., 
,
where 
,
the best fitting curve 
has the least square error, i.e.,
Please note that 
,
,
,
..., and 
are unknown coefficients while all 
and 
are given. To obtain the least square error, the unknown coefficients ,
,
,
..., and
must yield zero first derivatives.
Expanding the above equations, we have
The unknown coefficients ,
,
,
..., and
can hence be obtained by solving the above linear equations.