Chi-square and weights

Syntax: FIT\WEIGHTS w y=expression
FIT\WEIGHTS\-ZEROS w y=expression
FIT\WEIGHTS\TOLERANCE w eps y=expression
FIT\WEIGHTS\ITMAX w n y=expression
FIT\WEIGHTS\ITMAX\TOLERANCE w n eps y=expression
FIT\WEIGHTS\-ZEROS\ITMAX w n 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.

  Normal distribution
  Hint for physicists