<!--Copyright (C) 1988-2005 by the Institute of Global Environment and Society (IGES). See file COPYRIGHT for more information.--> <html> <head> <title>GrADS Function: sregr</title> </head> <body bgcolor="e0f0ff" text="#000000"> <h2><b>sregr()</b></h2> <p> <p> This function calculates the linear least-squares regression between two variables over an X-Y domain. It returns a single number. The syntax is: <ul> <code>sregr(<i>expr1, expr2, xdim1, xdim2, ydim1, ydim2</i>)</code> </ul> <p> where: <p> <ul> <code><i>expr1</i> </code>- a valid GrADS expression varying in X and Y<br> <code><i>expr2</i> </code>- a valid GrADS expression varying in X and Y<br> <code><i>xdim1</i> </code>- starting X dimension expression <br> <code><i>xdim2</i> </code>- ending X dimension expression <br> <code><i>ydim1</i> </code>- starting Y dimension expression <br> <code><i>ydim2</i> </code>- ending Y dimension expression <br> </ul> <p> To do the regression over the global domain, a shorthand may be used: <ul> <code>sregr(<i>expr1, expr2</i>, global)</code> or<br> <code>sregr(<i>expr1, expr2</i>, g)</code> </ul> is the same as <ul> <code>sregr(<i>expr1, expr2</i>, lon=0, lon=360, lat=-90, lat=90)</code> </ul> <p> The result from <code>sregr</code> is the expected value of the <code><i>expr2</i></code> departure given a 1 unit departure in <code><i>expr1</i></code>. <p> <h3>Usage Notes</h3> <ol> <li> <code><i>expr1</i></code> is the independent variable and <code><i>expr2</i></code> is the dependent variable. <p> <li>The regression is sensitive to the units of the input expressions. In the examples below, the sensible heat flux (shtfl) is in units of W m^-2 and the surface temperature (tsfc) is in units of K, so the regression coefficient of shtfl on tsfc is in units of W m^-2 K^-1. <p> <li> <code>sregr</code> may be used in conjunction with <a href="gradfunctloop.html"><code>tloop</code></a> or <a href="gradcomddefine.html"><code>define</code></a> to create time series or time/height plots. <p> <li><code>sregr</code> assumes that the world coordinates are longitude in the X dimension and latitude in the Y dimension, and does weighting in the latitude dimension by the delta of the sin of the latitudes. Weighting is also performed appropriately for unequally spaced grids. <p> <li>The result of the least squares regression of Y on X is often expressed as a linear equation: <p> <ul><code>Y = slope * X + intercept</code></ul> <p> where X is the independent variable, Y is the dependent variable, and the slope and intercept are calculated using complicated algebraic formulas. The calculation is simplified if the means are removed. If we define x and y to be the departures from the areal averages of X and Y: <p> <ul><code>x = X - Xave</code><br><code>y = Y - Yave</code></ul> <p> then the regression equation becomes: <p> <ul><code>y = <i>coefficient</i> * x</code></ul> <p> Where <p> <ul><code><i>coefficient</i> = (sum of x*y over area)/(sum of x*x over area)</code></ul> <p> This <code><i>coefficient</i></code> is the output from the <code>sregr</code> function. The second example below shows how to construct the regression estimate of Y based on X. <p> <li>Use the <a href="gradfunctregr.html"><code>tregr</code></a> function to do regression over the time domain. <p> </ol> <p> <h3>Example</h3> <ol> <li>This example calculates the expected departure from the mean of the sensible heat flux (shtfl) in the North Pacific given a unit departure from the mean surface temperature (tsfc). The units are W m^-2 K^-1. <p> <pre> set lon 120 250 set lat 15 60 define ivar = tsfc ;* surface temperautre define dvar = shtfl ;* sensible heat flux set z 1 set t 1 d sregr(ivar, dvar, lon=120, lon=250, lat=15, lat=60) </pre> <p> <li>This example builds on the previous example by calculating the regression estimate of sensible heat flux based on the surface temperature. <p> <pre> define coeff = sregr(ivar, dvar, lon=120, lon=250, lat=15, lat=60) define dvarave = aave(dvar, lon=120, lon=250, lat=15, lat=60) define ivarave = aave(ivar, lon=120, lon=250, lat=15, lat=60) d coeff * (ivar - ivarave) + dvarave </pre> </ol> </body> </html>
