E250: Least-Squares Fit to Straight Line

Author(s): M. Metcalf	Library: MATHLIB
Submitter:	Submitted: 01.05.1977
Language: Fortran	Revised: 27.11.1984

Given a vector of values Y measured at the points X, LFIT and LFITW find the best least-squares fit to the linear relationship Y=aX+b. LFIT performs an unweighted fit and LFITW takes account of a given vector of weights. Both subroutines have an option for skipping missing points without shifting the points of the vector X.

Structure:

SUBROUTINE subprogram
User Entry Names: LFIT, LFITW

Usage:

CALL LFIT(X,Y,L,KEY,A,B,VAR) or

CALL LFITW(X,Y,W,L,KEY,A,B,VAR)

X

(REAL) Vector of abscissae.

Y

(REAL) Vector of values corresponding to points X.

W

(REAL) Vector of weights (for LFITW only).

L

(INTEGER) Length of vectors X, Y and W.

KEY

(INTEGER)
indicates that any points where are to be skipped,
indicates that all L points are to be used.

A

(REAL) Fitted slope a.

B

(REAL) Fitted constant term b.

VAR

(REAL) Residual sum of squares divided by ( ) indicating the badness of fit.

References:

1. D.H. Menzel, Fundamental Formulas of Physics, Dover Publ., New York (1960) 116.