Table 2 RMSE in t/ha (and RRMSE in %) of the interaction regression model for the extrapolation of crop yield for unseen counties at the year 2018.

Crop	Training and validation sets	Test set	Training RMSE (RRMSE)	Validation RMSE (RRMSE)	Test RMSE (RRMSE)
Corn	IA and IN	IA and IN	0.56 (6.19%)	1.20 (10.3%)	1.52 (12.82%)
	IA and IN	IL	0.56 (6.19%)	1.20 (10.3%)	0.83 (6.67%)
	IA and IL	IA and IL	0.60 (6.61%)	0.82 (6.80%)	1.15 (9.37%)
	IA and IL	IN	0.60 (6.61%)	0.82 (6.80%)	0.79 (6.79%)
	IL and IN	IL and IN	0.59 (6.75%)	0.66 (5.93%)	0.71 (5.90%)
	IL and IN	IA	0.59 (6.75%)	0.66 (5.93%)	1.08 (8.98%)
	193 random counties	193 random counties	0.62 (6.85%)	0.68 (5.89%)	0.75 (6.23%)
	193 random counties	The other 100 counties	0.62 (6.85%)	0.68 (5.89%)	0.75 (6.30%)
Soybean	IA and IN	IA and IN	0.19 (6.51%)	0.20 (5.42%)	0.30 (7.86%)
	IA and IN	IL	0.19 (6.51%)	0.20 (5.42%)	0.37 (8.94%)
	IA and IL	IA and IL	0.19 (6.54%)	0.18 (4.81%)	0.30 (7.55%)
	IA and IL	IN	0.19 (6.54%)	0.18 (4.81%)	0.64 (16.77%)
	IL and IN	IL and IN	0.20 (6.87%)	0.18 (4.97%)	0.24 (6.09%)
	IL and IN	IA	0.20 (6.87%)	0.18 (4.97%)	0.85 (22.47%)
	193 random counties	193 random counties	0.20 (6.95%)	0.18 (4.96%)	0.30 (7.71%)
	193 random counties	The other 100 counties	0.20 (6.95%)	0.18 (4.96%)	0.29 (7.39%)

Each row shows the dataset by removing all historical information of counties. The rest of the dataset was partitioned into validation and training sets as two previous years from the test year 2018 (years 2016 and 2017) and dataset corresponding to the rest of the years to 1990 (years 1990–2015). First test set refers to the prediction of counties with historical datasets in training and validation set at the test year 2018 (temporal extrapolation). Second test set refers to the prediction of unseen counties with no historical dataset in training and validation set at the test year 2018 (temporal and spatial extrapolation).

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