Agriculture Reference
In-Depth Information
Let us consider the simple correlation
coefficients among the variables under consider-
ation as given below:
X1
X2
X3
Y
X1
Pearson correlation
1
.282
.708(*)
.656(*)
Sig. (2-tailed)
.
.430
.022
.039
N
10
10
10
10
X2
Pearson correlation
.282
1
.417
.724(*)
Sig. (2-tailed)
.430
.
.231
.018
N
10
10
10
10
X3
Pearson correlation
.708(*)
.417
1
.854(**)
Sig. (2-tailed)
.022
.231
.
.002
N
10
10
10
10
Y
Pearson correlation
.656(*)
.724(*)
.854(**)
1
Sig. (2-tailed)
.039
.018
.002
.
N
10
10
10
10
*Correlation is significant at the 0.05 level (2-tailed)
**Correlation is significant at the 0.01 level (2-tailed)
Thus, from the above, it is clear that in all the
three cases, the simple correlation coefficients
are different from the partial correlation
coefficients of yield and other three variables,
individually.
Partial correlation coefficient can also be
worked out using SAS.
unmanageable by judging huge number of bivari-
ate correlations between sets of variables.
In social or agricultural studies, the innovation
index, motivation index, adoption index, etc., of
farmers are dependent on age, gender, education,
income, family size, etc. Multiple regression
equation of innovation index with age, gender,
education, income, family size, etc., can predict
the innovation index only. Similarly one can pre-
dict motivation index and/or adoption index using
the independent variables mentioned above. But
if the researcher wants to evaluate/identify/index
farmers taking all the three indices at a time
by assessing the relationship of these groups
of dependent variables with the independent
variables' group consisting of age, gender, educa-
tion, income, family size, etc., then canonical
correlation analysis could be the possible way out.
C
12.7
Canonical Correlation
During regression analysis, generally one depen-
dent variable is taken at a time to find out its
relationship with independent variables. But in
many situations, the researchers need to consider
a group of dependent and independent variables.
The researchers become interested in getting the
relationship between a group of dependent
variables and a group of independent variables.
Canonical correlation analysis facilitates in get-
ting the interrelationship between these two
groups of variables. Canonical correlation is a
powerful multivariate technique which provides
the information of higher quality and in a more
interpretable manner. Canonical analysis suggests
the number of ways in which two groups (inde-
pendent and dependent) of variables are related,
their strength of linear relationship, and the nature
of the relationship which otherwise might be
anonical correlation measures the intensity of
relationship between the linear combinations of the
dependent variables with those of the independent
variables
. The weighted linear combinations of two
or more (either for independent or for dependent)
variables are known as
(also
known as linear composites, linear compounds).
Thus, the canonical correlation measures the
strength of relationship between two canonical
variates (two sets of variables).
canonical variates
The canonical cor-
relation analysis searches for optimum structure of
