.\" -*-nroff-*-
.\"
.\" Manual for linear regression
.\"
.\" (c) 2024 Straylight/Edgeware
.\"
.
.\"----- Licensing notice ---------------------------------------------------
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.\"--------------------------------------------------------------------------
.so ../defs.man \" @@@PRE@@@
.
.\"--------------------------------------------------------------------------
.TH linreg 3mLib "9 March 2024" "Straylight/Edgeware" "mLib utilities library"
.\" @linreg_init
.\" @linreg_update
.\" @linreg_fit
.\" @LINREG_INIT
.
.\"--------------------------------------------------------------------------
.SH NAME
lineag \- linear regression
.
.\"--------------------------------------------------------------------------
.SH SYNOPSIS
.nf
.B "#include <mLib/linreg.h>"
.PP
.B "struct linreg { ...\& };"
.B "#define LINREG_INIT ..."
.PP
.BI "void linreg_init(struct linreg *" lr );
.BI "void linreg_update(struct linreg *" lr ", double " x ", double " y );
.ta \w'void linreg_fit('u
.BI "void linreg_fit(struct linreg *" lr ,
.BI "	double *" m_out ", double *" c_out ", double *" r_out );
.fi
.
.\"--------------------------------------------------------------------------
.SH DESCRIPTION
.
The functions declared in the
.B <mLib/linreg.h>
header perform simple linear regression.
.PP
The state for a linear regression is held in a
.BR "struct linreg" .
Such a structure can be initialized statically,
using the
.B LINREG_INIT macro,
or dynamically, by calling the
.B linreg_init
function.
.PP
Once a state is initialized,
points
.RI ( x ",\ " y )
can be added by calling
.BR linreg_update .
Each call just performs a small and constant amount of computation;
the linear regression state uses a constant amount of storage
independent of the number of points.
.P
Finally, the
.B linreg_fit
function will return the results of the regression.
It calculates quantities
.I m
and
.I c
such that the line
.IR y "\ =\ " m "\ " x "\ +\ " c
is a reasonable approximation to the data points provided,
and a correlation coefficient
.I r
quantifying how good this approximation is.
These quantities are stored in
.BI * m_out \fR,
.BI * c_out \fR,
and
.BI * r_out \fR,
respectively;
any (or all, but that wouldn't be useful) of these pointers may be null,
to discard the corresponding output.
.PP
The linear regression state can be discarded without need for ceremony:
it holds no external resources.
.PP
Any half-decent introduction to statistics will explain these concepts.
.
.\"--------------------------------------------------------------------------
.SH SEE ALSO
.
.BR mLib (3).
.
.\"--------------------------------------------------------------------------
.SH AUTHOR
.
Mark Wooding, <mdw@distorted.org.uk>
.
.\"----- That's all, folks --------------------------------------------------