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6346 HIGGS ET AL.
Journal of Dairy Science Vol. 98 No. 9, 2015
to construct a matrix of regression estimates in the
arrangement shown below and according to the general
form Yij = A + BXi, where Y is the response variable
and column vector for the ith component in the jth feed
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 ith component with n entries:
Table 5. Spearman rank correlation coefficients for the chemical components of feeds used to perform Monte Carlo simulations1,2
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
WSC3
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
1WSC = water-soluble carbohydrates; SP = soluble protein; ADICP = acid detergent-insoluble CP; NDICP = neutral detergent-insoluble CP;
EE = ether extract.
2Chemical components are expressed as % of DM except: SP = % of CP; ADICP = % of CP; NDICP = % of CP; Lignin = % of NDF.
3Row left blank because insufficient data was available to perform the analysis.