Agriculture Reference
In-Depth Information
(continued)
Y
X
X
X
X
Y
X
X
X
X
1
2
3
4
1
2
3
4
117.29
8.20
4.16
8.80
6.20
52.98
3.40
6.26
7.20
5.00
121.30
7.80
3.63
10.20
5.40
97.58
4.60
7.42
8.20
4.00
121.38
5.60
6.76
8.20
10.20
93.69
3.80
6.43
7.40
5.00
Solution. From the given data, we calculate the
following correlation coefficient and prepare the
correlation table.
Y
X
X
X
X
1
2
3
4
Y
0.2977
1.0000
0.6861
0.1929
0.4559
X
0.6861
1.0000
0.5945
0.0580
0.4085
1
X
0.2977
0.5945
1.0000
0.0826
0.0447
2
X
0.1929
0.0580
0.0826
1.0000
0.0360
3
X
4
0.4559
0.4085
0.0447
0.0360
1.0000
From the above correlation table, we have the
following correlation matrices:
0
@
1
A
0
:
6861
0
@
1
A
1
:
0000
0
:
5945
0
:
0580
0
:
4085
0
:
2977
0
:
5945
1
:
0000
0
:
0826
0
:
0447
0
:
1929
B
~
0
:
0580
0
:
0826
1
:
0000
0
:
0360
0
:
4559
0
:
4085
0
:
0447
0
:
0360
1
:
0000
A
~
0
1
2
:
0328612
1
:
1896280
0
:
1884937
0
:
7704334
@
A
1
:
1896280
1
:
7053523
0
:
1954023
0
:
4026777
:
:
:
:
0
1884937
0
1954023
1
0259480
0
0313676
:
:
:
:
0
7704334
0
4026777
0
0313676
1
2955812
1
.
Now the direct and indirect effects of different
yield components are given as follows:
Table of path coefficients
The inverse matrix of
B
, that is, B
~
0
1
0
:
725755792
@
A
0
:
162659179
1
is given by
So P
~
¼
A
~
:
B
~
.
:
0
254770092
:
0
175887089
r
yx
X
X
X
X
1
2
3
4
r
y
1
¼
0.6861
0.72575579
0.09669818
0.014779644
0.071848
r
y
2
¼
0.2977
0.431449783
0.16265918
0.021045259
0.007860
r
y
3
¼
0.1929
0.042102321
0.01343644
0.254770090
0.006320
r
y
4
¼
0.4559
0.296462008
0.00727221
0.009161656
0.175890
Note
: Diagonal elements are the direct effects and the off-diagonal elements are the indirect effects.
