The usual regressio or correlation analysis uses a straight line relationship between the two variables

Y = a+bX.

The Climate Explorer fit routine can also fit other functions, such as the parabola

Y = a+bX(1+cX).

In this case the correlation indicates the correlation between the fitted right-hand side and Y and is therefore always positive.

For correlations between two time series, a cubic fit (Y = a+BX+cX²+dX³) and a straight line plus time derivative (Y = a+bX+cY') are also available.

The option "phase diagram" does not perform a fit and connects all (X_i,Y_i) pairs by a line.