Page 185 - DMGT404 RESEARCH_METHODOLOGY

Unit 9: Correlation and Regression

Notes
Example: Given the following data, compute the coefficient of correlation r, between X
and Y.
Age (yrs.)  30 -50 50 -70 70 -90 Total
Marks 

0 - 5 10 6 2 18
5 - 10 3 5 4 12
10 - 15 4 7 9 20
Total 17 18 15 50
Solution:
Note: Instead of doing the computation work in a single table, it can be split into the following
steps:
Taking mid-values of the class intervals, we have
Mid-values (X) 2.5 7.5 12.5

Mid-values (Y) 40 60 80
X - 7.5 Y - 60
Let u = i and v = i
i
i
5 20
 various u values are : – 1 0 1
and various v values are : – 1 0 1
1. Calculation of f u v
ij i j

 f u v = 13
ij i j
2. Calculation of f u and f u 2 3. Calculation of f ¢v and f ¢v 2
i i i i j j j j
2
2 v ¢ f ¢ f v ¢ f v
u i f i f i u i f i u i j j j j j j
- 1 18 - 18 18 –1 17 – 17 17
0 12 0 0 0 18 0 0
1 20 20 20 1 15 15 15
T otal 50 2 38 T otal 50 – 2 32
Substituting these values in the formula of r, we have

-
50 13 2 ´ ( ) 2- 654
´
r = = = 0.376
-
´
-
´
50 38 4 50 32 4 1896 1596
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