A common and simple approach to evaluate model is to regress predicted vs observed values (or vice versa) and compare slope and intercept parameters against the 1:1 line

Present mathematical evidence that evaluating the model based on the regression of predicted (y-axis) (PO) and observed (x-axis) leads to erroneous estimates of the slope and intercept

Observed (y-axis) vs predicted (x-axis) (OP) should be used

There is no consensus on which variable should be placed in each axis to present the results

The scatter plot of predicted and observed values (and vice versa) is still the most frequently used approach

R^2 remains the same for PO or OP

The slope and the intercept must be calculated only by regressing OP data because in tat case the residuals are independent of the predicted value (while they are independent of the observed values in PO)

Recommends to test the significance of slope =1 and intercept = 0

The difference between the two slopes increases as R^2 decreases

The lack of symmetry in the computation of several parameters when regression OP or PO has been noted by several authors (Kobayashi and Salam, 2000; Gauch et al, 2003; Mitchell, 1997)

The root mean square error (RMSE) should not be applied for the regression of OP data, use the root mean squared deviation instead (RMSD)

The deviation of each predicted values should be made against the 1:1 slope and not against the regression line for either OP or PO

RMSE will always be smaller than the RMSD and is thus an underestimation of the real error