The R value for this prediction was 0.37 that is, the prediction explains 37% of the variations in Urner Barry quotes. Using the same 3 predictor variables, the Urner Barry quote (a market indicator of egg price) was predicted over 91 wk and results are presented in Figure 3.
An R 2 of 0.36 is moderate in our case of egg price determination that explains 36% of the variations in egg price due to the 3 predictor variables used in the analysis. A perfect fit would result in an R 2 value of 1, a very good fit near 1, and a very poor fit less than zero. The R 2 value is the coefficient of multiple determination and is a statistical indicator applied to multiple regression analysis. The R 2 (a measure of degree of fit) value for this prediction was 0.36. Using the 3 independent (predictor) variables (number of egg laying hens, US egg export, and number of egg-type chicks hatched in com- mercial hatcheries), egg price was predicted over 91 wk, and is shown in Figure 2. The results of multiple linear regressions are presented in Figures 2 and 3. Three different architectures, namely Ward, back propagation ( BPNN ), andGRNN were used on the test data and results were compared for the best-fit lines and statistical analysis. The 2001 data were organized in the similar fashion as the training data for a total of 52 test examples and is given in Table 3. The 2001 egg quote data were used as a test case to determine the validity of the training of network and the 2002 data were used to compare the NN-predicted results on 2001 test data for market validation. The networks, using Neuro Shell 2 (Ward Systems Group, 1993), were trained on these training sets until no further improvements were noticed in the network. This process was iterated until all the weeks from January 1991 to December 2000 were included as inputs and outputs in all the training examples for a total of 518 examples. The second training example consisted of the second, third, fourth, and fifth weeks’ egg prices as inputs, with the egg price in the sixth week as output. This procedure consti- tuted one training example or epoch. Starting from the first week of January 1991, the egg prices for wk 1 through 4 were used as inputs, and the egg prices for wk 5 were used as the output. To recognize all possible patterns within the egg quote data set, we manipulated the data set to create its own inputs and output rather than taking along the other variables.
Alternatively, only the Urner Barry egg quote data were used as the sole data set. Initially, the 3 variables, namely, number of egg laying hens, US egg export, and number of egg-type chicks hatched in commercial hatcheries (independent variables), were used with farm egg price or Urner Barry egg quotes (dependent variable) as 3 inputs and 1 output for back-propagation neural network. An NN model can be developed em- ploying different architecture and manipulating data sets within such architecture.
To develop a viable and logical neural network ( NN ) model, various approaches were tried, two of which are reported here. Using the GLM procedure of SAS (SAS Institute, 2004, v 9.1), multiple regression analysis was performed with egg prices and Urner Barry egg quotes as dependent or regressor variables and number of egg-laying hens, US egg export, and number of egg-type chicks hatched in commercial hatcheries as independent or predictor variables. The monthly USDA data from Jan 1993 to Dec 2000 are given in Table 1, and weekly Urner Barry quotes (Egg Prices, 2004) from Jan 1, 1991, to Dec 31, 2002, are given in Table 2. The data for egg prices received by farmers, number of egg-laying hens, US egg export, and number of egg-type chicks hatched in commercial hatcheries were collected from the Poultry Yearbook (USDA, 2004). data of egg prices and related variables were used for the regression analysis and neural network training in this research project.
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