Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.
Given a set of observations xi,yi, for i=1,2,…,n, with corresponding weights wi, G10ZAF rearranges the observations so that the xi are in ascending order.
For any equal xi in the ordered set, say xj=xj+1=⋯=xj+k, a single observation xj is returned with a corresponding y′ and w′, calculated as
w′=∑l=0kwi+l
and
y′=∑l=0kwi+lyi+lw′.
Observations with zero weight are ignored. If no weights are supplied by you, then unit weights are assumed; that is wi=1, for i=1,2,…,n.
In addition, the within group sum of squares is computed for the tied observations using West's algorithm (see West (1979)).
4 References
Draper N R and Smith H (1985) Applied Regression Analysis (2nd Edition) Wiley
West D H D (1979) Updating mean and variance estimates: An improved method Comm. ACM22 532–555
5 Parameters
1: WEIGHT – CHARACTER*1Input
On entry: indicates whether user-defined weights are to be used.
If WEIGHT='W', user-defined weights are to be used and must be supplied in WT.
On entry: IFAIL must be set to 0, -1 or 1. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
On exit: IFAIL=0 unless the routine detects an error (see Section 6).
For environments where it might be inappropriate to halt program execution when an error is detected, the value -1 or 1 is recommended. If the output of error messages is undesirable, then the value 1 is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is 0. When the value -1 or 1 is used it is essential to test the value of IFAIL on exit.
6 Error Indicators and Warnings
If on entry IFAIL=0 or -1, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
IFAIL=1
On entry,
WEIGHT≠'W' or 'U',
or
N<1.
IFAIL=2
On entry,
WEIGHT='W' and at least one element of WT is <0.0, or all elements of WT are 0.0.
7 Accuracy
For a discussion on the accuracy of the algorithm for computing mean and variance see West (1979).
8 Further Comments
G10ZAF may be used to compute the pure error sum of squares in simple linear regression along with G02DAF; see Draper and Smith (1985).
9 Example
A set of unweighted observations are input and G10ZAF used to produce a set of strictly increasing weighted observations.