Geoscience Reference
In-Depth Information
or
n
⎛
⎜
n
⎞
⎟
⎛
⎜
n
⎞
⎟
∑∑∑
n
xy
−
x
y
ii
i
i
i
=
1
i
=
1
i
=
1
r
=
⎡
2
⎤
⎡
2
⎤
n
−
⎛
⎝
n
⎞
⎟
n
−
⎛
n
⎞
⎟
∑∑
∑∑
⎢
⎢
⎥
⎥
⎢
⎢
⎥
⎥
nx
2
x
ny
2
y
⎜
⎜
i
i
i
i
i
=
1
i
=
1
i
=
1
i
=
1
⎣
⎦
⎣
⎦
The correlation matrix for the above three variables given in
Table 4.2 are as follows:
Minimum
temperature
Maximum
temperature
Rainfall
Minimum temperature
1
0.847
−0.508
(0.001)
(0.092)
Maximum temperature
0.847
1
−0.677
(0.001)
(0.016)
Rainfall
−0.508
−0.677
1
(0.092) (0.016)
Note:
Values in parenthesis are the significance level.
It is seen that the minimum and maximum temperatures
show a strong positive correlation whereas maximum tem-
perature and rainfall shows a negative correlation and are
significant.
In a multi-variate setup, the partial correlation is the correla-
tion between two variables after eliminating the effects on other
variables. Partial correlation coefficient between minimum and
maximum temperature after controlling the variability due to
rainfall is found to be 0.794 and is significant (0.004), which
shows that rainfall has indirect effect on correlation between
minimum and maximum temperature.
Regression
analysis
The correlation coefficient measures the extent of interrelation
between two variables that are simultaneously changing with
mutually extended effects. In certain cases, changes in one
variable are due to changes in a related variable, but there need
not be any mutual dependence. One variable is considered to be
dependent on the other as it changes. The relationship between
variables of this kind is known as regression. Regression anal-
ysis is a statistical tool for the investigation of relationships
between variables (Draper 1998; Montgomery 2006). When
