Provided by: gmt-common_5.4.3+dfsg-1_all 
NAME
gmtregress - Linear regression of 1-D data sets
SYNOPSIS
gmtregress [ table ] [ -Amin/max/inc ] [ -Clevel ] [ -Ex|y|o|r ] [ -Fflags ] [ -N1|2|r|w ] [ -S[r]
] [ -Tmin/max/inc | -Tn ] [ -W[w][x][y][r] ] [ -V[level] ] [ -aflags ] [ -bbinary ] [ -dnodata ] [
-eregexp ] [ -ggaps ] [ -hheaders ] [ -iflags ] [ -oflags ]
Note: No space is allowed between the option flag and the associated arguments.
DESCRIPTION
gmtregress reads one or more data tables [or stdin] and determines the best linear regression model y = a
+ b* x for each segment using the chosen parameters. The user may specify which data and model
components should be reported. By default, the model will be evaluated at the input points, but
alternatively you can specify an equidistant range over which to evaluate the model, or turn off
evaluation completely. Instead of determining the best fit we can perform a scan of all possible
regression lines (for a range of slope angles) and examine how the chosen misfit measure varies with
slope. This is particularly useful when analyzing data with many outliers. Note: If you actually need
to work with log10 of x or y you can accomplish that transformation during read by using the -i option.
REQUIRED ARGUMENTS
None
OPTIONAL ARGUMENTS
table One or more ASCII (or binary, see -bi[ncols][type]) data table file(s) holding a number of data
columns. If no tables are given then we read from standard input. The first two columns are
expected to contain the required x and y data. Depending on your -W and -E settings we may expect
an additional 1-3 columns with error estimates of one of both of the data coordinates, and even
their correlation.
-Amin/max/inc
Instead of determining a best-fit regression we explore the full range of regressions. Examine
all possible regression lines with slope angles between min and max, using steps of inc degrees
[-90/+90/1]. For each slope the optimum intercept is determined based on your regression type
(-E) and misfit norm (-N) settings. For each segment we report the four columns angle, E, slope,
intercept, for the range of specified angles. The best model parameters within this range are
written into the segment header and reported in verbose mode (-V).
-Clevel
Set the confidence level (in %) to use for the optional calculation of confidence bands on the
regression [95]. This is only used if -F includes the output column c.
-Ex|y|o|r
Type of linear regression, i.e., select the type of misfit we should calculate. Choose from x
(regress x on y; i.e., the misfit is measured horizontally from data point to regression line), y
(regress y on x; i.e., the misfit is measured vertically [Default]), o (orthogonal regression;
i.e., the misfit is measured from data point orthogonally to nearest point on the line), or r
(Reduced Major Axis regression; i.e., the misfit is the product of both vertical and horizontal
misfits) [y].
-Fflags
Append a combination of the columns you wish returned; the output order will match the order
specified. Choose from x (observed x), y (observed y), m (model prediction), r (residual = data
minus model), c (symmetrical confidence interval on the regression; see -C for specifying the
level), z (standardized residuals or so-called z-scores) and w (outlier weights 0 or 1; for -Nw
these are the Reweighted Least Squares weights) [xymrczw]. As an alternative to evaluating the
model, just give -Fp and we instead write a single record with the model parameters npoints xmean
ymean angle misfit slope intercept sigma_slope sigma_intercept.
-N1|2|r|w
Selects the norm to use for the misfit calculation. Choose among 1 (L-1 measure; the mean of the
absolute residuals), 2 (Least-squares; the mean of the squared residuals), r (LMS; The least
median of the squared residuals), or w (RLS; Reweighted Least Squares: the mean of the squared
residuals after outliers identified via LMS have been removed) [Default is 2]. Traditional
regression uses L-2 while L-1 and in particular LMS are more robust in how they handle outliers.
As alluded to, RLS implies an initial LMS regression which is then used to identify outliers in
the data, assign these a zero weight, and then redo the regression using a L-2 norm.
-S[r] Restricts which records will be output. By default all data records will be output in the format
specified by -F. Use -S to exclude data points identified as outliers by the regression.
Alternatively, use -Sr to reverse this and only output the outlier records.
-Tmin/max/inc | -Tn
Evaluate the best-fit regression model at the equidistant points implied by the arguments. If -Tn
is given instead we will reset min and max to the extreme x-values for each segment and determine
inc so that there are exactly n output values for each segment. To skip the model evaluation
entirely, simply provide -T0.
-W[w][x][y][r]
Specifies weighted regression and which weights will be provided. Append x if giving 1-sigma
uncertainties in the x-observations, y if giving 1-sigma uncertainties in y, and r if giving
correlations between x and y observations, in the order these columns appear in the input (after
the two required and leading x, y columns). Giving both x and y (and optionally r) implies an
orthogonal regression, otherwise giving x requires -Ex and y requires -Ey. We convert
uncertainties in x and y to regression weights via the relationship weight = 1/sigma. Use -Ww if
the we should interpret the input columns to have precomputed weights instead. Note: residuals
with respect to the regression line will be scaled by the given weights. Most norms will then
square this weighted residual (-N1 is the only exception).
-V[level] (more …)
Select verbosity level [c].
-acol=name[…] (more …)
Set aspatial column associations col=name.
-bi[ncols][t] (more …)
Select native binary input.
-bo[ncols][type] (more …)
Select native binary output. [Default is same as input].
-d[i|o]nodata (more …)
Replace input columns that equal nodata with NaN and do the reverse on output.
-e[~]”pattern” | -e[~]/regexp/[i] (more …)
Only accept data records that match the given pattern.
-g[a]x|y|d|X|Y|D|[col]z[+|-]gap[u] (more …)
Determine data gaps and line breaks.
-h[i|o][n][+c][+d][+rremark][+rtitle] (more …)
Skip or produce header record(s).
-icols[+l][+sscale][+ooffset][,…] (more …)
Select input columns and transformations (0 is first column).
-ocols[,…] (more …)
Select output columns (0 is first column).
-^ or just -
Print a short message about the syntax of the command, then exits (NOTE: on Windows just use -).
-+ or just +
Print an extensive usage (help) message, including the explanation of any module-specific option
(but not the GMT common options), then exits.
-? or no arguments
Print a complete usage (help) message, including the explanation of all options, then exits.
ASCII FORMAT PRECISION
The ASCII output formats of numerical data are controlled by parameters in your gmt.conf file. Longitude
and latitude are formatted according to FORMAT_GEO_OUT, absolute time is under the control of
FORMAT_DATE_OUT and FORMAT_CLOCK_OUT, whereas general floating point values are formatted according to
FORMAT_FLOAT_OUT. Be aware that the format in effect can lead to loss of precision in ASCII output, which
can lead to various problems downstream. If you find the output is not written with enough precision,
consider switching to binary output (-bo if available) or specify more decimals using the
FORMAT_FLOAT_OUT setting.
EXAMPLES
To do a standard least-squares regression on the x-y data in points.txt and return x, y, and model
prediction with 99% confidence intervals, try
gmt regress points.txt -Fxymc -C99 > points_regressed.txt
To just get the slope for the above regression, try
slope=`gmt regress points.txt -Fp -o5`
To do a reweighted least-squares regression on the data rough.txt and return x, y, model prediction and
the RLS weights, try
gmt regress rough.txt -Fxymw > points_regressed.txt
To do an orthogonal least-squares regression on the data crazy.txt but first take the logarithm of both x
and y, then return x, y, model prediction and the normalized residuals (z-scores), try
gmt regress crazy.txt -Eo -Fxymz -i0-1l > points_regressed.txt
To examine how the orthogonal LMS misfits vary with angle between 0 and 90 in steps of 0.2 degrees for
the same file, try
gmt regress points.txt -A0/90/0.2 -Eo -Nr > points_analysis.txt
REFERENCES
Draper, N. R., and H. Smith, 1998, Applied regression analysis, 3rd ed., 736 pp., John Wiley and Sons,
New York.
Rousseeuw, P. J., and A. M. Leroy, 1987, Robust regression and outlier detection, 329 pp., John Wiley and
Sons, New York.
York, D., N. M. Evensen, M. L. Martinez, and J. De Basebe Delgado, 2004, Unified equations for the slope,
intercept, and standard errors of the best straight line, Am. J. Phys., 72(3), 367-375.
SEE ALSO
gmt, trend1d, trend2d
COPYRIGHT
2018, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe