Geoscience Reference
In-Depth Information
Correlation
analysis
Given a pair of related measures (X and Y) on each of a set of
items, the correlation coefficient (r) provides an index of the
degree to which the paired measures co-vary in a linear fashion.
In general, r will be positive when items with large values of X
also tend to have large values of Y, whereas items with small
values of X tend to have small values of Y. Correspondingly, r
will be negative when items with large values of X tend to have
small values of Y whereas items with small values of X tend
to have large values of Y. Numerically, r can assume any value
between −1 and +1 depending upon the degree of the linear
relationship. Plus and minus one indicate perfect positive and
negative relationships whereas zero indicates that the X and Y
values do not co-vary in any linear fashion. This is also called
as
Pearson product-moment correlation coefficient.
. The val-
ues of the correlation coefficient have no units. A scatter plot
provides a picture of the relation, the value of the correlation
is the same if you switch the Y (vertical) and X (horizontal)
measures.
Let (x
i
, y
i
), i = 1,2, …, n denote a random sample of n obser-
vations from a bivariate population. The sample correlation
coefficient r is estimated by the formula
Covxy
VxVy
(, )
() ()
r
=
table 4.2
Station-wise maximum and minimum
temperature and rainfall in India for the year 2012
Minimum
temperature
(°C)
Maximum
temperature
(°C)
Highest
24-hour
rainfall (mm)
Stations
Agartala AP
7.0
37.8
102.3
Cherrapunji
0.8
27.2
772.2
Dibrugarh AP
6.6
37.0
137.2
Guwahati AP
6.4
37.4
111.3
Imphal AP
2.0
35.6
84.8
Passighat
8.5
35.9
261.1
Shillong
2.1
28.9
134.0
Tezpur
7.0
36.4
161.3
Baghdogra AP
5.3
36.8
134.0
Berhampore
9.3
43.4
91.0
Kolkata
10.0
40.5
87.4
Cooch Behar AP
5.0
36.5
259.6
Source:
Indiastat.com.
