E250 Least-Squares Fit to Straight Line

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)
$=\; 0:$ indicates that any points where $Y=0$ are to be skipped,
$=\; 1:$ 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 ($L-2$ ) indicating the badness of fit.

References:

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

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