National Oceanic and
Atmospheric Administration
United States Department of Commerce

Least Squares Regression

Least Squares Regression

Question:

How can I compute a regression line?

The script regresst.jnl defines variables "SLOPE", "INTERCEP", "RSQUARE", and"QHAT" given a dependent and independent variable. If you have a variable definedon the X axis, (or you can use RESHAPE to put it on an X axis) then use the script regressx.jnl

regresst.jnl offeres the following coaching lines about its inputs and outputs:

... Linear Regression Along the T Axis
... Instructions:
Use the LET command to define new variables
Define the variable P as your independent (X) variable
Define the variable Q as your dependent (Y) variable
Results will be variables "SLOPE", "INTERCEP" and "RSQUARE"
QHAT will be the regression estimate
Note: If "T" is your independent variable then
... "SET GRID Q" after defining Q.
...

Define variables P and Q as the inputs to the script.

 yes? USE rainfall.nc
yes? LET p = t[gt=rain]
yes? LET q = rain
yes? SET GRID q
yes? GO regresst

Here are our definitions of P and Q, and some of the variables that the script definesOne might want to use QAVE or QVAR, the mean and variance of variable Q.

 yes? SHOW VAR
Created by DEFINE VARIABLE:
>>> Definitions that replace any file variable of same name:
P = T[GT=RAIN]
Q = RAIN
...
PAVE = PMASKED[T=@AVE]
QAVE = QMASKED[T=@AVE]

PVAR = PPAVE - PAVE*PAVE
QVAR = QQAVE - QAVE*QAVE

SLOPE = PQVAR / PVAR
INTERCEP = QAVE - SLOPE*PAVE
QHAT = SLOPE*P + INTERCEP
RSQUARE = (PQVAR*PQVAR) / (PVAR*QVAR)

Show the input data as a scatter point, and the regression line

 yes? SET VIEW upper
yes? PLOT/SYM q
yes? PLOT/OVER qhat

Subtract qhat from the variable to get the series, minus its mean and trend.

 
yes? SET VIEW lower
yes? LET/TITLE="rainfall - mean, trend" detrended = rain - qhat
yes? PLOT rain, detrended