What is the exact difference between regression and correlation maps?

I know that they are often used in climate science but which is the difference in the information they provide? Here an example I found online:

Is the regression map between two quantities $A(t)$ and $B(x,y,t)$, the map of the following index:

$$r = \frac{corr( A(t), B(x,y,t) )}{var( A(t) )}$$

while the correlation simply the map of

$$corr(A(t), B(x,y,t))$$ ?

  • $\begingroup$ From the units given, it appears that the Correlation map shows the r values while the Regression map shows the standard deviation of the correlation, so roughly the spread in the data. Seems backwards to me. $\endgroup$ – haresfur Jul 22 '18 at 22:06

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