Agriculture Reference
In-Depth Information
Slide 12.19: Portion of output for canonical analysis using SAS
(Canonical loading)
12.8 Multiple Regression Analysis
and Multicollinearity
of the conclusion.
There are different techniques
to avoid/overcome the problem of multicol-
linearity. One of the techniques is to use principal
component analysis before conducting regres-
sion analysis. The principal component analysis
is a type of factor analysis.
During the regression analysis, we have assumed
that the predictor variables are independent not
only with each other but also with the distur-
bance terms. But in real-life situation, hardly
one can find any variable which is independent
of other variables. Actually, in social, economic,
business, biological, and other fields, the
variables tend to move together. As a result, the
variables will be correlated with each other,
thereby violating the assumptions of the regres-
sion analysis. This phenomenon of linear associ-
ation among the explanatory variables during
regression analysis is known as multicollinearity.
As a result of multicollinearity, the regression
estimates sometimes become inestimable, and
the standard errors of the estimates become
exceptionally high, giving rise to nonsignificance
of
12.9
Factor Analysis
One of the most powerful multivariate techniques
is the factor analysis aimed at simplifying and
analyzing the interrelationship among a set of
variables in the form of a relatively few number
of hypothetical variables known as factors, which
are orthogonal or uncorrelated among them-
selves. Factor analysis helps in getting an insight
into the otherwise hidden structure of the data.
The essence of factor analysis lies in explaining
the interrelationship among a large number of
variables to a small number of factors without
losing any essential information or with mini-
mum loss of information.
the
relationships worked out, and subsequently the
conclusion drawn in the presence of multicol-
linearity may hamper/effect the quality/validity
the
regression
estimates.
Thus,
