Agriculture Reference
In-Depth Information
The indirect path coefficients are obtained
by multiplying each element of
the example are efficient enough to explain as
much as 58% variation in the response variable.
Character one (
the
row
concerned in matrix
(correlation matrix) by
the respective elements of the
B
X
1
) has high positive direct
effect commensurating with high positive corre-
lation coefficient; hence, this character may be
utilized for direct selection. On the other hand,
the negative correlation and positive direct
effect of
P
matrix. Thus,
the indirect effect of
X
1
through
X
2
on
Y
is
- 0.5945
0.096698.
The diagonal elements of the table are the
direct effects, whereas the off-diagonal elements
are the indirect effects. It may be noted that the
sum of the direct and indirect effects of any
character is equal to its correlation coefficients
with the response variables.
The residual is worked with the help of the
formula
0.1626
¼
X
2
are mainly
attributed by the indirect effect of
the character
two
X
1
.
The other characters though have low positive
correlation coefficients but are associated with
positive direct effects; hence, these cannot be
ignored during selection.
With the help of the MS Excel program, how
one can work out
X
2
via
the path coefficients
is
h
2
2
y
2
y
2
y
2
y
R
¼
1
p
þ p
þ p
þ p
þ
2
r
12
p
y
1
p
y
2
presented in the following example.
1
2
3
4
þ
r
13
p
y
1
p
y
3
þ
r
14
p
y
1
p
y
4
þ
r
23
p
y
2
p
y
3
2
2
2
Example 11.4.
Data given in the example are
pertaining to the yield and three yield
components per plant in six different varieties.
We are to find out the path coefficients for yield
per plant on other characters.
þ
2
r
24
p
y
2
p
y
4
þ
2
r
34
p
y
3
p
y
4
i
¼
0
:
42113
:
Thus, from the above analysis, it is clear that
the yield-contributing characters considered in
Yield
Branch no
Test wt
Pod/plant
Var no
Replication
Ch1
Ch2
Ch3
Ch4
1
1
14.5
1.8
34
27.2
2
13.8
2.6
32.8
29.2
3
14.8
2.8
35.1
18.6
2
1
14.9
2.9
38.3
24.8
2
15.8
2.3
38.5
23.6
3
17.3
3.2
40.2
17.4
3
1
15.1
2.8
48.5
25.2
2
15.2
3.1
45.3
28.8
3
16.3
3.3
45.2
25.6
4
1
15.7
2
36.2
29.2
2
16.5
2.5
38.1
18.4
3
17.5
3.1
44.2
24.8
5
1
17.6
3.3
46.1
24.8
2
17.1
3.5
55.3
22.2
3
18.3
3
58.6
20.2
6
1
17.2
3.7
60.8
20.8
2
17.3
3.4
62
20.2
3
18.5
4.1
59.4
28
Solution. We are provided with replicated data of
four characters, including yield per plant for six
varieties. One can use the variance-covariance
analysis to get the correlation at the phenotypic,
genotypic, and environmental levels. But for this
coefficient from simple correlations considering
that there is 6
18 number of observations
per character. In a stepwise manner, we shall
demonstrate how path analysis can be done
using the MS Excel program in the MS Office
3
¼
