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We still need the variances vj. Since each error is evenly distributed in the range , the variances of the parameters are given by
. The variance of the inputs and
desired outputs can be assumed to be zero, or they can be assigned
some values if there is prior knowledge about, for example, the
equipment used to measure the values.
In order to compute the variance of the function fi, we shall
approximate it with first order Taylor's series expansion.
According to this approximation, , which yields
Again we can drop out the cross terms if all are mutually
uncorrelated. This yields our final approximation for the variance of
Notice that when computing the variance, one cannot mix the first and
second order approximation for , since that might result in
negative values for vi.