sregr()

This function calculates the linear least-squares regression between two variables over an X-Y domain. It returns a single number. The syntax is:

sregr(expr1, expr2, xdim1, xdim2, ydim1, ydim2)

where:

expr1   - a valid GrADS expression varying in X and Y
expr2   - a valid GrADS expression varying in X and Y
xdim1   - starting X dimension expression
xdim2   - ending X dimension expression
ydim1   - starting Y dimension expression
ydim2   - ending Y dimension expression

To do the regression over the global domain, a shorthand may be used:

sregr(expr1, expr2, global) or
sregr(expr1, expr2, g)

sregr(expr1, expr2, lon=0, lon=360, lat=-90, lat=90)

The result from sregr is the expected value of the expr2 departure given a 1 unit departure in expr1.

Usage Notes

1. expr1 is the independent variable and expr2 is the dependent variable.

2. 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.

3. sregr may be used in conjunction with tloop or define to create time series or time/height plots.

4. sregr 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.

5. The result of the least squares regression of Y on X is often expressed as a linear equation:
   Y = slope * X + intercept

   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:

   x = X - Xave
y = Y - Yave

   then the regression equation becomes:

   y = coefficient * x

   Where

   coefficient = (sum of x*y over area)/(sum of x*x over area)

   This coefficient is the output from the sregr function. The second example below shows how to construct the regression estimate of Y based on X.

6. Use the tregr function to do regression over the time domain.

Example

1. 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.

   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)
   

2. This example builds on the previous example by calculating the regression estimate of sensible heat flux based on the surface temperature.

   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