Agriculture Reference
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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
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