Regression and artificial neural network (ANN) (5, 39) were used as
complementary approaches to model the relationship between gray leaf spot
severity and the predictors. As a preliminary step, Mallow's Cp (28) variable
selection criterion was used to determine the best subset of the 11 predictor
variables (selected based on correlation coefficient) to be used in the input layer of
the ANN. Variable selection prior to model development is useful for removing
redundant predictors from the model, reducing noise in the data set due to
unnecessary predictors, and avoiding problems of collinearity caused by having too
many variables fulfilling the same function in the model (15). To identify the best
subset of potentially useful predictors, all-subset regressions by leaps and bounds
(17) was performed using the /eaps function in S-plus 6.1 (Academic Site Edition,
Insightful, Corp. Seattle, WA). Using this modeling approach, different numbers and
combinations of input variables were used to develop regression models, and the
best model was selected based on Mallow's Cp criteria defined as: