Page 177 - DMGT404 RESEARCH_METHODOLOGY

Unit 9: Correlation and Regression

The values of different terms, given in the formula, are calculated from the following table: Notes
Xi Yi XiYi Xi Yi 2
2
12 14 168 144 196
9 8 72 81 64
8 6 48 64 36
10 9 90 100 81
11 11 121 121 121
13 12 156 169 144
7 3 21 49 9
70 63 676 728 651

Here n = 7 (no. of pairs of observations)
-
´
´
7 676 70 63
r =  0.949
XY
7 728 - ( ) 2 7 651 - ( ) 2
´
´
63
70
Example: Calculate the Karl Pearson’s coefficient of correlation between X and Y from the
following data:
2
2
Y -

No. of pairs of observations n = 8, (X i - X )  184, ( i Y )  148,
 (X - X Y - Y ) 164, X  11 and Y  10
i
)( i
Solution:
å (X - X )( i Y )
Y -
Using the formula, r = i , we get
å (X - X ) å ( i Y )
XY 2 2
Y -
i
164
r =  0.99
XY 184 148
Example: Calculate the correlation between Reading (X) and Spelling (Y) for the 10 students
whose scores are given below:
Student Reading Spelling
1 13 11
2 7 1
3 2 19
4 9 5
5 8 17
6 4 3
7 1 15
8 10 9
9 6 15
10 5 8

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