CORRELATION
Correlation is a measure of the
degree of relatedness of variables. It can help a business researcher
determine, for example, whether the stocks of two airlines rise and fall in any
related manner. For a sample of pairs of data, correlation analysis can yield a
numerical value that represents the degree of relatedness of the two stock
prices over time.
Correlation is determined using sample coefficient of correlation, r, where
r is a measure of the linear correlation of two variables.
The Correlation between 2 variables
can be computed using the Product
Pearson – Moment Correlation Coefficient which can be given by
Inferences of the value ‘r’ – The ‘r’ value ranges between -1 to 0
to +1. An r value of +1 denotes a Positive
relationship between the two set of variables. An r value of -1 denotes a Negative relationship between the two set
of variables and if 0, it means that there is no relationship between the two
set of variables.
Let us consider an example of Cement Production in India whose
production is expected to vary with the change in the Construction GDP of the country over a period of years.
|
YEAR
|
CONST
(x)
|
CEMENT
(y)
|
|
2012-13
|
4302.76
|
251947
|
|
2011-12
|
4124.12
|
230490
|
|
2010-11
|
3906.93
|
196960
|
|
2009-10
|
3557.18
|
206630
|
|
2008-09
|
2425.75
|
186940
|
|
2007-08
|
2263.25
|
174310
|
|
2006-07
|
2055.44
|
161310
|
|
2005-06
|
1838.68
|
147808
|
|
2004-05
|
1582.12
|
131559
|
|
2003-04
|
1362.24
|
123440
|
|
2002-03
|
1216.5
|
116348
|
|
2001-02
|
1126.92
|
106900
|
|
2000-01
|
1083.62
|
99520
|
|
1999-00
|
1020.07
|
100450
|
The Correlation of the above Problem could be determined
by either Manual or by using a Tool/Software.
MANUAL METHOD:
Determine the values that are needed to
determine/compute the value of ‘r’. This would lead to the computation of ∑xy, ∑x2 ,∑y2 as
follows.
|
year
|
CONST (x)
|
CEMENT (y)
|
xy
|
x^2
|
y^2
|
|
2012-13
|
4302.76
|
251947
|
1084067474
|
18513744
|
63477290809
|
|
2011-12
|
4124.12
|
230490
|
950568419
|
17008366
|
53125640100
|
|
2010-11
|
3906.93
|
196960
|
769508933
|
15264102
|
38793241600
|
|
2009-10
|
3557.18
|
206630
|
735020103
|
12653530
|
42695956900
|
|
2008-09
|
2425.75
|
186940
|
453469705
|
5884263
|
34946563600
|
|
2007-08
|
2263.25
|
174310
|
394507108
|
5122301
|
30383976100
|
|
2006-07
|
2055.44
|
161310
|
331563026
|
4224834
|
26020916100
|
|
2005-06
|
1838.68
|
147808
|
271771613
|
3380744
|
21847204864
|
|
2004-05
|
1582.12
|
131559
|
208142125
|
2503104
|
17307770481
|
|
2003-04
|
1362.24
|
123440
|
168154906
|
1855698
|
15237433600
|
|
2002-03
|
1216.5
|
116348
|
141537342
|
1479872
|
13536857104
|
|
2001-02
|
1126.92
|
106900
|
120467748
|
1269949
|
11427610000
|
|
2000-01
|
1083.62
|
99520
|
107841862
|
1174232
|
9904230400
|
|
1999-00
|
1020.07
|
100450
|
102466032
|
1040543
|
10090202500
|
|
SUM
|
31865.58
|
2234612
|
5839086396
|
91375280
|
388794894158.00
|
Now using the Correlation formula to determine the
coefficient by substituting the above values.
r = 14(5839086396) – (31865.58) (2234612)
√ [(14) (91375280)-(31865.58) ^2] [(14) (388794894158)-(2234612) ^2]
R = 0.967698462
CORRELATION
USING EXCEL
1.
Enter the Data Set containing two or
more set of variables in the Worksheet.
2.
Click on Data Tab and select the Data
Analysis option.
3.
Select Correlation as a choice and enter the Input Range of values in the Data
Analysis dialog box.
4.
The Correlation between the two
variables is computed and the ‘r’ values are presented in the table as follows.
Inferences
from the Example:
·
Correlation between the Production of the
cement and the GDP of the Construction sector is positive and the coefficient
is determined to be 0.967698462.
·
This signifies that if there is a
change in the GDP of the Construction by 100%, it would affect the production
of the Cement by approximately 96.7%
Blogged By : Piyush (2013197)
Group No. 1 Members:
Neeraj Garg (2013166)
Pallavi Gupta (2013187)
Prerna Bansal (2013209)
Priya Jain (2013210)
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