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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
Y
ij
=
A
+
BX
i
, where
Y
is the response variable
and column vector for the
i
th component in the
j
th 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
i
th component with
n
entries:
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.