Chi-square and weights
Syntax: |
FIT\WEIGHTS w y=expression
|
The weight at each point defaults to one (1
), if a weight vector
is not entered. Weights only make sense with a normal distribution, and
are ignored when used with the \POISSON
qualifier.
To make use of a weight array, the \WEIGHTS
qualifier must be entered. If the
\WEIGHTS
qualifier is used, the weight vector, w, will then be expected. The
weights are assigned to the dependent variable in a one-to-one fashion, that is, the
weight vector must be the same length as the data vector, y. If the \ITMAX
qualifier is used, the weight comes before the iteration maximum in the command parameter list. If the
\TOLERANCE
qualifier is used, the iteration maximum comes before the tolerance in
the command parameter list.
By default, the zero elements of the weight vector are used when calculating the number of degrees of
freedom. If the \-ZEROS
qualifier is used with the \WEIGHTS
qualifier, then
the zero elements of the weight vector will not be used when calculating the number of degrees of
freedom. This could have an affect on the calculation of the confidence level, the
χ2
per degrees of freedom, and E2
, the root mean square total
errors of estimate.
If the \CHISQ
qualifier is used, a new scalar, named
FIT$CHISQ
, will be made with value equal to the total
χ2 = ∑
wk[yk - f(xk,pmin)]2
where wk
represents the optional weight at each data point
yk
, f is the expression to be fitted, and pmin
are the best values of the parameters, p
.