tregr (expr1, expr2, tdim1, tdim2)
This function calculates the least-squares regression between two time-dependent variables.
expr1- a valid GrADS expression that varies in time
expr2- a valid GrADS expression that varies in time and may also vary in X and Y
tdim1- starting time dimension expression
tdim2- ending time dimension expression
The result is a grid that matches the X and Y dimensions of
expr2 where each grid point is the temporal
expr2 (the dependent variable) onto
expr1 (the independent variable).
tregr gives the expected value of
expr2 departure given a 1 unit departure in
expr2vary only in time, the output is a single value.
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 time means are removed. If we define x and y to be the departures from the time averages of X and Y:
x = X - Xave
y = Y - Yave
then the regression equation becomes:
y = coefficient * x
coefficient = (sum of x*y over time)/(sum of x*x over time)
coefficient is the output from the
The second example below shows how to construct the regression estimate of Y based on X.
sregrfunction to do regression over the spatial domain.
set y 1 set z 1 set t 1 100 define elnino = aave(ts, lon=-160, lon=-80, lat=-20, lat=10) set lon 0 360 set lat -90 90 set z 1 set t 1 d tregr(elnino, slp, t=1, t=100)
define coeff = tregr(elnino, slp, t=1, t=100) define slpave = ave(slp, t=1, t=100) define ninoave = ave(elnino, t=1, t=100) d coeff * (elnino - ninoave) + slpave