|
Examples:
Calculate and analyze the correlation coefficient between the number of study hours and the number of sleeping hours of different students.
|
Number of Study hours
|
2
|
4
|
6
|
8
|
10
|
|
Number of sleeping hours
|
10
|
9
|
8
|
7
|
6
|
Solution:
The necessary calculation is given below:
|
X |
Y
|
|
|
|
|
|
|
2
|
10
|
-4
|
+2
|
-8
|
16
|
4
|
|
4
|
9
|
-2
|
+1
|
-2
|
4
|
1
|
|
6
|
8
|
0
|
0
|
0
|
0
|
0
|
|
8
|
7
|
+2
|
-1
|
-2
|
4
|
1
|
|
10
|
6
|
+4
|
-2
|
-8
|
16
|
1
|
|
|
|
|
|
|
|
|
 and 
There is perfect negative correlation between the number of study hours and the number of sleeping hours.
Example:
From the following data, compute the coefficient of correlation between X and Y:
|
|
X Series
|
Y Series
|
|
Number if Items
|
15
|
15
|
|
Arithmetic Mean
|
25
|
18
|
|
Sum of Square Deviations
|
136
|
138
|
Summation of products of deviations of X and Y series from their arithmetic means = 122.
Solution:
Here 
 and hence
| 
