Agriculture Reference
In-Depth Information
p
n
r
uv
1
spraying, the null hypothesis would be
H
0
: σ
x
¼
t ¼
p
ðn
Þ
:
:
2
with
2
d
f
r
uv
2
σ
y
against
H
0
: σ
x
6¼ σ
y
.Thisisequivalenttotest
ρ
uv
¼
,
respectively. The test statistic for the same will be
0where
u
and
v
are
x
+
y
and
x y
We have
X
:
114
113
119
116
119
116
117
118
Y
:
220
217
226
221
223
221
218
224
U ¼
(
X
+
Y
):
334
330
345
337
342
337
335
342
V ¼
(
X Y
):
106
104
107
105
104
105
101
106
P
uv nuv
P
u
be rejected. We conclude that population regres-
sion coefficient may be zero.
14.
;r
uv
¼
q
¼
0
:
4647
:
P
v
2
2
2
nu
2
nv
Test for Significance of the Population
Multiple Correlation Coefficients
Let
p
1
ð
0
:
4647
Þ
4647
p
ðx
1
; x
2
; ...x
p
Þ
there be
variables
t ¼
0
:
8
2
Thus,
q
¼
1
:
2855 at 6 d
:
f
:
following a
-variate normal distribution and
the multiple correlation of
p
2
x
1
on
x
2
; x
3
; ...x
p
From the table we get
t
0
:
025
;
6
¼
2
:
447. Thus,
be given by
ρ
12
:
34
;...p
and the corresponding
sample multiple correlation coefficient being
R
1
:
2
;
3
;...p
based on a random sample of size
the observed value of
jj
is less than the table
value. That is,
t
ca
j j < t
tab
. So we cannot reject the
null hypothesis of equality of variances.
13.
.
The problem is to test whether the population
multiple correlation is zero or not, that is, to
test
n
Test for Significance and Regression Coeffi-
cient in a Simple Linear Regression.
To test the
H
0
: ρ
1
:
2
;
3
;...;p
¼
0 against the alternative
H
0
:
b ¼ 0
, we have the test sta-
hypothesis
H
1
: ρ
1
:
2
;
3
;...;p
>
0. Under
H
0
the
t ¼ bSEðbÞ
n
tistic
=
with
1 d.f.:
if the
test statistic is
at
2
calculated value of
H
tab
ðn
1
Þ
d
:
f
:
level of significance,
then it cannot be
R
2
1
:
23
...p
ðp
=
1
Þ
ðn pÞ
F ¼
rejected; otherwise
t
is rejected.
R
2
1
:
23
...p
=
1
with
ðp
1
; n pÞ
d
:
f
:
Example 9.13.
The relation between yield and
expenditure on plant protection measure was
found to be
If cal
F>F
α; p
1
;np
, then H
0
is rejected, else
it is accepted}.
It is noted that in this problem, alternative
hypothesis
15.6 + 0.8 PP with standard
error estimates for the intercept and the regres-
sion coefficients being 6.2 and 0.625, respec-
tively, from ten varieties of paddy. Test for
significance of regression coefficient of plant
protection.
Y ¼
is always one sided (right)
because
ρ
12
:
3
;
4
;...;p
cannot be negative.
Example 9.14.
In a yield component analysis,
the relationship of yield with five-yield compo-
nent was worked out for 20 plants. The multiple
correlation coefficients were found to be 0.98.
Test for significance of multiple correlation
coefficients.
Solution.
To rest the
H
0
:
b ¼
0 the test statistic
is
t ¼ b
=
SE
ðbÞ
¼
0
:
80
=
:
625
¼
1
:
28. The table
value of
statistic at 5% level of significance is
greater than the table value. Hence, the test is
nonsignificant and the null hypothesis cannot
t