Agriculture Reference
In-Depth Information
Table 12.1
Regression output through SPSS
Variables Entered/Removed
b
Model
Variables Entered
Variables Removed
Method
x3, x2, x1
a
1
Enter
a. All requested variables entered.
b. Dependent Variable: y
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
.949
a
1
.900
.850
19.37018
a. Predictors: (Constant), x3, x2, x1
ANOVA
b
Model
Sum of Squares
df
Mean Square
F
Sig.
.002
a
1
Regression
20200.591
3
6733.530
17.946
Residual
2251.222
6
375.204
Total
22451.814
9
a. Predictors: (Constant), x3, x2, x1
b. Dependent Variable: y
Coefficients
a
Model
Unstandardized Coefficients
Standardized Coefficients
B
Std. Error
Beta
t
Sig.
1
(Constant)
-212.072
83.573
-2.538
.044
x1
.149
.236
.115
.629
.552
x2
.183
.058
.447
3.145
.020
x3
4.132
1.363
.586
3.032
.023
a. Dependent Variable: y
2
,isa
nondecreasing function of the number of
variables in the regression equation. Thus, as
we go on introducing more and more number of
variables in the regression equation, the
2. The coefficient of determination, that is,
R
12.4
Stepwise Regression
From the above example, it is clear that the rela-
tionship of yield with three yield components
having
2
is
supposed to increase or at least remain constant.
So one may be tempted to include more and
more number of variables in the regression
model in order to maximize
R
2
0.900 is sufficient to explain more
than 90 of the variation in yield. The ANOVA
table also shows the significance of the overall
relationship as depicted by the significance value
of 0.002 that means the
R
R
¼
2
and thereby
increase the possibility of significance of the
overall regression equation. This phenomenon
is sometimes known as
R
2
vis-a-vis the relation-
ship is
significant
at 2
probability
level
2
(
0.02). Now, while analyzing the signifi-
cance of the individual coefficients, it is found
that
P ¼
.
It must be clearly understood that the variables
to be included in the regression model should
be guided by the knowledge about the variables
in relation to the response variable, never
should be guided towards maximizing
game of maximizing R
X
3
significant as depicted by respective significance
levels of 0.02 and 0.023. But the coefficient of
t
-test declares the coefficients of
X
2
and
X
1
is not found to be significant. So the question is
whether to retain
2
value. The experimenter should include or try
to incorporate only those variables which have
got significant coefficients and instead of con-
centrating on the value of
R
R
X
1
in the model or not. At this
juncture, the readers should note that:
1. The one-to-one relationship vis-a-vis the
nature of the coefficients in linear relationship
may change under multiple variable condition.
2
rather concentrate
