If the equation for the best straight line is
the expression for the square of the differences is
In order to minimize D, the derivatives with respect to the adjustable parameters, m and
b, are set equal to zero
and for each of the n experimental points xi, two simultaneous equations containing the
unknowns, m and b, are obtained
These expressions define a series of simultaneous equations (referred to as “normal equations”)
from which the adjustable parameters m and b can be calculated:
