Geoscience Reference
In-Depth Information
explanatory variables. Out of these p explanatory variables,
suppose apart from the first explanatory variable rainfall, all
other (p − 1) variables are quantitative climatic explanatory
variables wherein rainfall is a categorical variable with three
levels mentioned as above normal, normal and below normal.
In this situation, to quantify the attribute, one has to use two
dummy variables Z
1
and Z
2
. One of the possible ways of defin-
ing the two dummy variables may be
Z
1
= 0 and Z
2
= 0
Below normal rainfall
Normal rainfall
Z
1
= 0 and Z
2
= 1
Above normal rainfall
Z
1
=
1 and Z
2
=
1
Then a multiple regression model of crop yield that might
describe this relationship can be written as
y
=+ +
ββ β
z
z
+
β
x
++x
β
+
ε
,
for i
=
12
,
,
…
,
n
i
0
11i
2
2i
32i
p
pi
i
(4.4)
where the symbols have their usual meaning as defined earlier.
Generally, when there are m levels of qualitative explanatory
variables, then one has to employ m − 1 dummy variables for
that particular qualitative explanatory variable. Sometimes,
more than one qualitative climatic explanatory variable exists
in the dataset. In such situations, more than one dummy vari-
able may have to be used.
Logistic
regression
analysis
In all the above cases discussed so far, it is generally assumed
that the dependent variable, that is, the crop yield is quantita-
tive in nature. But situations may arise when, in the available
dataset, the yield of crop is not quantitative in nature; rather, it
is qualitative in nature. For example, suppose data related to the
yield of crop are not numeric; rather, in the available dataset, it
is expressed as high yield and low yield. In that situation, yield
is a qualitative response variable with two levels: high yield and
low yield. Further, let high yield be denoted by 1 and low yield
be denoted by 0. In such cases, the usual multiple linear regres-
sion theory is not appropriate. Rather, the statistical model pre-
ferred for the analysis of such binary (dichotomous) responses
is the binary logistic regression model, developed primarily
by Cox (1958) and Walker and Duncan (1967). Thus, binary
logistic regression is a mathematical modelling approach that
can be used to describe the relationship of several indepen-
dent variables to a binary (dichotomous) dependent variable.
