# regcoef

Calculates the linear regression coefficient (trend, slope,...)
between two series. Missing data are allowed.

## Synopsis

function regcoef(
x : float,
y : float,
tval : float,
nptxy : integer
)

## Arguments

*x*
- Input vector array of any dimensionality (last dimension is
*npts*). Missing values should be indicated by
*x*@_FillValue. If *x*@_FillValue is not set, then the NCL
default (-999) will be assumed.
*y*
- Input vector array of any dimensionality. The right-most
dimensions of
*y* must the same as the dimensions of *x*.
Missing values should be indicated by *y*@_FillValue. If
*y*@_FillValue is not set, then the NCL default (-999) will be
assumed.
*tval*
- t-statistic (assuming null hypothesis) array (output) of the same
dimensionality as
*y*, minus the last dimension, *npts*. Space
for this must be explicity allocated by the user (see example below).
*nptxy*
- number of points used (output), same dimensionality as
*tval*. Space for this must be explicity allocated by the user
(see example below).

## Description

`regcoef` computes the regression coefficient (trend,
slope,...) and returns it as a float array, for which the space is
automatically allocated by NCL.

## Example

In the example below, the regression coefficient for the case with no
missing data is 0.97, the number of points used (*nptxy*) was 18
which yields 16 degrees of freedom (=*nptxy*-2). A test of the
null hypothesis (i.e., that the regression coefficient is zero) yields
a t-statistic of 38.7, which is distributed as t(16). Obviously, the
null hypothesis would be rejected.

begin
x = (/ 1190.,1455.,1550.,1730.,1745.,1770. \
, 1900.,1920.,1960.,2295.,2335.,2490. \
, 2720.,2710.,2530.,2900.,2760.,3010. /)
y = (/ 1115.,1425.,1515.,1795.,1715.,1710. \
, 1830.,1920.,1970.,2300.,2280.,2520. \
, 2630.,2740.,2390.,2800.,2630.,2970. /)
x@_FillValue = -999.
y@_FillValue = -999.
tval = 0.
nptxy = 0
rc = regcoef(x,y,tval,nptxy)
print ("NO MSG DATA: rc="+rc+" tval="+tval+" nptxy="+nptxy)
x(2) = x@_FillValue
y(8) = y@_FillValue
rc = regcoef(x,y,tval,nptxy)
print ("MSG DATA: rc="+rc+" tval="+tval+" nptxy="+nptxy)
end

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* $Revision: 1.7 $ $Date: 1999/03/22 20:49:10 $ *