Table 4.

Error metrics considered for comparison of interpolation methods.

Metric	Formula	Interpretation
Correlation coefficient, r	Correlation between $Z_i^{\prime }$ and Zi	High correlation between observed and interpolated values suggests accurate interpolation
Mean Absolute Error (MAE)	$\frac{{\sum }_{i=1}^n\mid Z_i^{\prime }-Z_i\mid }{n}$	A measure of the average magnitude of prediction errors
Root Mean Square Error (RMSE)	$\sqrt{\frac{{\sum }_{i=1}^n{\left(Z_i^{\prime }-Z_i\right)}^2}{n}}$	Another measure of the average prediction error. Compared to MAE, RMSE is more sensitive to large outliers.
Mean Bias Error (MBE)	$\frac{{\sum }_{i=1}^n{Z}_i^{\prime }-Z_i}{n}$	By including the sign of individual residuals, MBE shows whether (on average) the interpolation tends to over- or under-predict
Median Symmetric Accuracy (MSA)	$exp\left(Median\left({|\log }_e\left(Z_i/Z_i^{\prime }\right)|\right)\right)-1$	Measure of ‘typical’ proportional error, symmetric and robust to outliers

Z_i is the observed value at a point, $Z_i^{\prime }$ is the value interpolated for that point during LOOCV.