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+.help tlinear Aug2000 tables
+.ih
+NAME
+tlinear -- Fit a linear function to one or two table columns by linear
+regression.
+.ih
+USAGE
+tlinear intable outtable xcol ycol
+.ih
+DESCRIPTION
+This task generates fitted Y values and their residuals in two columns.
+These columns may be written to an output table, but cannot be written
+to STDOUT--only the fit parameters can be written to STDOUT.
+If there is more than one table in the input list then a separate fit
+is made for each table.
+
+When a column of weights is used (see 'wcol'),
+the weights will be applied when computing the
+coefficients of the fit (a, b),
+their standard deviations (siga2, sigb2),
+and chi squared (chi2),
+where the names in parentheses are the headings in
+the output printed to STDOUT.
+If any row has a weight that is exactly zero,
+that row will not be counted in the "pts in fit" value.
+The weights will NOT be used when computing
+the RMS of the residuals and mean of the residuals
+(residual rms, residual mean);
+these are unweighted averages
+except that rows with exactly zero weight will not be included.
+.ih
+PARAMETERS
+.ls intable [file name template]
+A list of input tables containing the columns to be fit.
+A fit will be made of the columns specified by the 'xcol' and 'ycol'
+parameters.  If more than one file name is passed to 'intable', all of
+the files must use the same column names.
+.le
+.ls outtable = STDOUT [file name template]
+File names for creating output files, or STDOUT to send output to the screen.
+If the value of this parameter is "STDOUT" then the parameters of the fit will
+be written to STDOUT preceded by a header line (beginning with #) in tabular
+form.
+If 'outtable' is not "STDOUT" then the number of file
+names must match the number
+of names in 'intable', and the fitted Y values and residuals will be written
+to an output table with the specified name.  The parameters of the fit will
+be written to the table header.
+.le
+.ls xcol [string]
+Column name in the input tables to be fit.
+The values in this column will be fit for the X axis.
+(The same column name is used for each input table.)  If a name is not specified
+for the X values then row number is used.  The values in the 'xcol' column will
+be copied to 'outtable' unless the output is being directed to STDOUT.
+.le
+.ls ycol [string]
+Column name in the input tables containing value to be fit for the Y axis.
+(The same column name is used for each input table.)  Values in 'ycol' will
+be copied to 'outtable' unless 'outtable = STDOUT'.
+.le
+.ls (wcol) [string]
+Column name in 'intable' that contains weight values for X and Y.
+(The same column name is used for each input table.)  If no column
+name is passed to either the 'wcol' or 'scol' parameters, then a weight
+of 1. is used.  The value of the 'wcol' column is copied to 'outtable' unless
+'outtable = STDOUT'.
+.le
+.ls (scol) [string]
+Column in 'intable' containing the standard deviation of X and Y.
+The X and Y values are weighted by the values in 'scol'
+as the reciprocal of the values squared.  (The same column name is used for each
+input table.)  If no value is passed to 'wcol' or 'scol', then
+a weight of 1. is used.  This task can accept either a weight value or a
+standard deviation value, but not both.  If both 'wcol' and 'scol' are
+specified, then the weight column (i.e., 'wcol') will be used.
+The value in the 'scol' column is written to 'outtable' unless 'outtable'
+= STDOUT.
+.le
+.ls (rows = "-") [string]
+Range of rows to use for fitting the data.
+The default "-" means that all rows are used.
+(Type "help xtools.ranges" for more information.)
+.le
+.ls (outcoly = "yfit") [string]
+Column name for fitted Y values.
+This parameter is not used if 'outtable' = STDOUT.
+This column will be double data type.
+.le
+.ls (outcolr = "yres") [string]
+Name of the column to contain residuals.
+This parameter is ignored if 'outtable' = STDOUT.
+This column will be of double data type.
+.le
+.ih
+EXAMPLES
+1. Fit the values in the "flux" column in every table whose name begins with
+"hr"; put all parameters of the fits in the ASCII file "fit.lis".
+
+.nf
+  tt> tlinear hr*.tab STDOUT "" flux > fit.lis
+.fi
+
+2. Generate the same fits as in the previous example, but put the
+results in tables, one output for each input table.  For example,
+the fitted Y values and
+residuals for an input table named "hr465.tab" would be put in "hr465h.tab".
+
+.nf
+  tt> tlinear hr*.tab hr*%%h%.tab "" flux
+.fi
+
+3. Fit the values in the "flux" column as a function of the values in the
+"wavelength" column and write all the parameters of the fit to STDOUT.
+
+.nf
+  tt> tlinear hr*.tab STDOUT wavelength flux
+.fi
+.ih
+BUGS
+.ih
+REFERENCES
+This task was written by Betty Stobie.
+.ih
+SEE ALSO
+ranges
+.endhelp