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Table 5. Spearman rank correlation coefficients for the chemical components of feeds used to perform Monte Carlo simulations 1,2 Item CP SP ADICP NDICP NDF Lignin Starch WSC EE Ash Corn silage CP 1.00 SP 0.11 1.00 ADICP −0.19 −0.27 1.00 NDICP −0.12 −0.55 0.39 1.00 NDF 0.18 −0.10 0.41 0.46 1.00 Lignin 0.08 −0.09 0.25 0.15 0.05 1.00 Starch −0.37 0.09 −0.39 −0.38 −0.91 −0.10 1.00 WSC 0.07 −0.30 0.09 0.11 0.09 −0.06 −0.25 1.00 EE 0.18 0.37 −0.27 −0.27 −0.29 −0.01 0.30 −0.28 1.00 Ash 0.35 −0.08 0.26 0.12 0.35 0.30 −0.50 0.07 −0.16 1.00 Alfalfa silage CP 1.00 SP 0.18 1.00 ADICP −0.52 −0.23 1.00 NDICP −0.31 −0.57 0.67 1.00 NDF −0.62 −0.18 0.54 0.56 1.00 Lignin 0.27 0.13 0.23 −0.02 −0.21 1.00 Starch −0.25 −0.15 0.01 0.01 −0.08 −0.13 1.00 WSC 0.17 −0.62 −0.27 −0.14 −0.42 −0.10 0.18 1.00 EE 0.27 0.45 −0.16 −0.14 −0.12 −0.16 −0.07 −0.56 1.00 Ash 0.18 0.20 0.02 −0.16 −0.12 0.22 −0.18 −0.17 0.05 1.00 Grass hay CP 1.00 SP 0.07 1.00 ADICP −0.43 −0.21 1.00 NDICP −0.11 −0.42 0.48 1.00 NDF −0.51 −0.11 0.27 0.36 1.00 Lignin 0.04 −0.03 0.55 0.25 −0.04 1.00 Starch −0.10 −0.07 0.10 −0.04 −0.24 0.10 1.00 WSC 0.09 0.24 −0.48 −0.46 −0.65 −0.31 0.13 1.00 EE 0.51 −0.13 −0.27 −0.11 −0.60 0.05 0.09 0.34 1.00 Ash 0.50 0.10 −0.16 −0.06 −0.55 −0.18 −0.01 0.01 0.23 1.00 Corn grain CP 1.00 SP 0.17 1.00 ADICP −0.10 −0.19 1.00 NDICP −0.18 −0.11 0.43 1.00 NDF 0.05 0.02 0.10 0.34 1.00 Lignin 0.19 −0.07 0.17 −0.07 −0.24 1.00 Starch −0.40 −0.16 0.13 0.00 −0.56 0.01 1.00 WSC 0.03 0.34 −0.11 −0.05 0.04 0.16 −0.20 1.00 EE 0.21 0.22 −0.25 −0.16 0.24 0.14 −0.48 0.23 1.00 Ash 0.15 0.23 0.00 0.03 −0.01 −0.02 −0.14 0.00 0.22 1.00 Soybean meal CP 1.00 SP −0.03 1.00 ADICP 0.10 −0.62 1.00 NDICP −0.36 −0.39 0.14 1.00 NDF −0.15 −0.31 0.06 0.20 1.00 Lignin −0.03 −0.09 0.32 −0.35 −0.18 1.00 Starch −0.02 0.00 −0.16 −0.54 −0.18 0.27 1.00 WSC 3 EE 0.08 −0.24 −0.03 0.44 0.21 −0.14 −0.19 1.00 Ash −0.26 −0.06 0.04 −0.01 −0.34 0.10 0.04 0.03 1.00 1 WSC = water-soluble carbohydrates; SP = soluble protein; ADICP = acid detergent-insoluble CP; NDICP = neutral detergent-insoluble CP; EE = ether extract. 2 Chemical components are expressed as % of DM except: SP = % of CP; ADICP = % of CP; NDICP = % of CP; Lignin = % of NDF. 3 Row left blank because insufficient data was available to perform the analysis. AOAC Research Institute ERP Use Only

with n entries, A is the intercept arranged in an n × p matrix, B is the predictor variable arranged in an n × p matrix, and X is the regression coefficient and row vector for the i th component with n entries:

to construct a matrix of regression estimates in the arrangement shown below and according to the general form Y ij = A + BX i , where Y is the response variable and column vector for the i th component in the j th feed

Journal of Dairy Science Vol. 98 No. 9, 2015