Agriculture Reference
In-Depth Information
Table 8.14
Comparison between the correlation coeffi-
cient and the regression coefficient
Sl
no. Correlation coefficient
varieties to find out the degree of linear associa-
tion between the yield and the panicle length of
paddy and to find out the linear relationship of
yield on the panicle length of paddy.
Regression coefficient
1
Correlation coefficient
(
Regression coefficient
(
r
XY
) measures the degree
of linear association
between any two given
variables
b
XY
; b
YX
) measures the
change in dependent
variable due to per unit
change in independent
variable when the
relation is linear
X
18 20 20 22
22
25
26
28
35
40
Y
14 14 15 15
16
18
17
20
22
21
Solution. Let us make the following table:
2
2
X
Y
X
Y
XY
2
Correlation coefficient
does not consider the
dependency between the
variables
One variable is
dependent on the other
variable
18
14
324
196
252
20
14
400
196
280
20
15
400
225
300
3
Correlation coefficient is
a unit-free measure
Regression coefficient
(
22
15
484
225
330
b
XY
; b
YX
) has the unit
depending upon the units
of the variables under
consideration
22
16
484
256
352
25
18
625
324
450
26
17
676
289
442
4
Correlation coefficient is
independent of the
change of origin and
scale
Regression coefficient
(
28
20
784
400
560
b
XY
; b
YX
) does not
depend on the change of
origin but depends on the
change of scale
35
22
1,225
484
770
40
21
1,600
441
840
Mean
25.6
17.2
Variance
44.84
7.76
5
1
r
XY
þ
1
b
XY
; b
YX
does not have
any limit
Covariance 17.28
Correlation coefficient 0.926
We have a no. of observations “
10, and
the mean and variances and covariance are cal-
culated as per the formula given in Chap.
3
.So
the correlation coefficient between the yield and
the panicle length is given by
n
”
¼
y
Now, the total sum of squares (
)
2
X
n
i¼
1
y
i
y
X
n
2
_
_
TSS
¼
ð
Þ
¼
y
i
y
þ y
y
i¼
1
r ¼
Cov(
X
,
Y
)/sd
X
n
X
n
2
2
(
X
).sd(
Y
). Now, the regression equation of yield
_
_
¼
1
ðy
i
y
Þ
þ
1
ðy
yÞ
;
(
Y
) on the panicle length (
X
) is given by
i¼
i¼
_
is the estimate of
where
y
Y
ðY YÞ¼b
yx
ðX XÞ
¼
Residual sum of squares
þ
Regression sum of squares
Cov
ðX:YÞ
s
)ðY
:
Þ¼
ðX
:
Þ
17
2
25
6
2
X
¼
þ
RSS
R
g
SS
17
:
28
¼
84
ðX
25
:
6
Þ
RSS
TSS
þ
R
g
SS
TSS
44
:
¼
þ
)
¼
;
TSS
RSS
R
g
SS
1
¼
0
:
385
ðX
25
:
6
Þ¼
0
:
385
x
9
:
865
RSS
TSS
þ r
) Y ¼
:
þ
:
X
:
17
2
0
385
9
865
2
¼
:
) Y ¼
:
þ
:
X:
7
335
0
385
R
g
SS
TSS
¼ r
2
and
Now, we
observe
that
RSS
2
TSS
¼
:
If we get the calculated value of
1
r
Example 8.31.
The following data give the num-
ber of insects per hill (
2
as 0.55,
we mean that 55% variations are explained by
the regression line, and the remaining 45%
variations are unexplained (Table
8.14
).
r
X
) and the corresponding
yield (
) of nine different varieties of rice. Work
out the linear relationship between the yield and
the number of insects per hill.
Y
Variety V1 V2 V3 V4 V5 V6 V7 V8 V9
X
Example 8.30.
The following table gives the
16
16
22
23
24
24
25
28
29
