{smcl}
{* 4mar2005}{...}
{hline}
help for {hi:variog2}
{hline}

{title:Semi-variogram for point-based data in two dimensions}

{p 8 17 2}
{cmd:variog2}
{it:yvar} 
{it:coord1} {it:coord2} 
[{cmd:if} {it:exp}] 
[{cmd:in} {it:range}] 
, 
{cmdab:w:idth(}{it:#}{cmd:)} 
[
{cmdab:g:enerate(}{it:newvar}{cmd:)}
{cmdab:l:ags(}{it:#}{cmd:)} 
{cmd:list} 
{it:graph_options}
]
   
   
{title:Description} 

{p 4 4 2} 
{cmd:variog2} calculates, graphs, and optionally lists the first {cmd:lags}
values of the semi-variogram for a series of observations in
two spatial dimensions. That is, we have measurements of a response {it:yvar} 
(rainfall, ore grade, soil depth) at points whose horizontal map coordinates
are {it:coord1} and {it:coord2}. The response must be named first; the order
of the two coordinate variables is immaterial. 

{p 4 4 2} 
The semi-variogram is a plot of the semi-variance

       1                       2
    {hline 8}   SUM    (y  - y )   = gamma(h)
    2 #pairs  i, j in   i    j
             same band 
	     
{p 4 4 2}against the lag or band number h = 1, ... , {cmd:lags}. In words, it shows 
half the mean difference squared for pairs of points in various distance bands. 
Given {cmd:width} w, 
successive bands are for distances up to w, between w and 2w, between 2w and 3w, 
and so forth. Note that the units of the semi-variogram are the units of the response 
variable, squared. 


{title:Options} 

{p 4 8 2}{cmd:width()} specifies the width of successive distance bands in 
the units linked to the coordinate variables. It is a required option. 

{p 4 8 2}{cmd:generate(}{it:newvar}{cmd:)} saves the semi-variances in 
{it:newvar}.

{p 4 8 2}{cmd:lags()} specifies the number of lags.  If not specified, the first
    int(_N/2) semi-variances are graphed: that is, the number of 
    lags is about half the number of observations. 

{p 4 8 2}{cmd:list} lists the semi-variances and the number of 
pairs of measurements on which they are based. This may help in identifying
parts of the variogram based on rather few pairs of data. 

{p 4 8 2} 
{it:graph_options} refers to any of the options of {help line}.


{title:Examples} 

{p 4 8 2}{cmd:. variog2 height easting northing, width(10)}{p_end}
{p 4 8 2}{cmd:. variog2 height easting northing, w(10) list}{p_end}
{p 4 8 2}{cmd:. variog2 height easting northing, w(10) recast(scatter)}


{title:Author} 

{p 4 4 2}Nicholas J. Cox, University of Durham, U.K.{break} 
         n.j.cox@durham.ac.uk


{title:Also see} 

{p 4 13 2}
On-line: help for {help variog}