tregr()

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 regression of expr2 (the dependent variable) onto expr1 (the independent variable). tregr gives the expected value of the expr2 departure given a 1 unit departure in expr1.

Usage Notes

1. If both expr1 and expr2 vary only in time, the output is a single value.

2. The regression is sensitive to the units of the input expressions. In the examples below, the variable SLP is in units of mb and the variable elnino is in units of K, so the regression coefficient of SLP upon elnino is in units of mb per K.

3. 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 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

   Where

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

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

4. Use the sregr function to do regression over the spatial domain.

Example

1. This example calculates the expected departure from the slp mean given a unit departure in the defined variable elnino.

   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)
   

2. This example builds on the previous example by calculating the regression estimate of slp based on the defined variable elnino.

   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