Table 2.

Results of regression models created with random forest. The R² values of random forest model with entire set of variables and those with only most important variables are presented for the bean and maize aggregate phene metrics.

Aggregate phenotypic metric	R 2 (% variance explained)
	Bean		Maize
	Model with all variables	Model with most important variables	Model with all variables	Model with most important variables
Total length	89.5	91.6	82	85
Total area	87	87	78	81
Total volume	81.7	88.5	79	81.6
Volume distribution	87	91	61	66
Max no. of roots	78.8	84	67	72.8
Median no. of roots	79.9	87	71	75
Bushiness	62	67	36	41
Max depth	98.6	99.6	79	84
Max width	91	90	95	99
Convex hull area	97.8	97	90	93.4
Convex hull volume	97.6	97.6	87	89.9
Ellipse minor axis	94.9	93.6	80	85
Ellipse major axis	96.7	97.3	95	98.6
Ellipse aspect ratio	85.9	87.4	51.9	62
Solidity	97.4	97.5	89	89
FD	67	68	16	20
FA	93.5	94.9	88	90

Random forest possesses its own reliable statistical characteristics, which could be used for validation and model selection. The major criterion for estimation of internal predictive ability of the random forest models and model selection is the value of R². R² in random forest is interpreted as a measure of predictive quality of random forest model on independent samples. Random forest models were run with the aggregate phenotype as dependent variable and all the phenes as predictor variables. Most important variables were chosen based on the % increase in mean square, and random forest models were run with only the most important variables.