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Study Online Correlation Matrices

Introduction to study correlation matrices:

Correlation for all M variables are explained by the matrices are called correlation matrices. This correlation matrices are a m `xx` m symmetrical matrix with (i,j) element which are equivalent to the correlation coefficients r_ij of the variable (i) and (j). The diagonal element of the correlation matrix is always 1. The example for the correlation matrix

`[[1,,],[2,1,],[3,4,1]]`

Formula for finding number of correlation is

`(N xx (N-1))/2`

Where N is number of columns.


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Correlation Coefficient:


Two variable’s linear relationship of degree is indicated by the correlation coefficient. The correlation coefficient is between -1 and 1. -1 is the perfect linear negative relationship of two variables. 1 isthe perfect linear negative relationship of two variables. 0 is lackingof any one of the linear relation ship.


Examples to study correlation matrices:


Example 1:

Find the number of correlation of the following correlation matrix.

`[[1,,,],[2,1,,],[3,4,1,],[5,6,7,1]]`

Solution:

The given matrix is

`[[1,,,],[2,1,,],[3,4,1,],[5,6,7,1]]`

Formula for finding number of correlation is

`(N xx (N-1))/2`

Where number of columns is 4. So N = 4 Now we have to substitute N value in the formula.

= `(4 xx(4-1))/2`

= `(4 xx 3)/2`

= `12/2`

= 6

Therefore for total number of this matrix is 6

Example 2:

Find the number of correlation of the following correlation matrix.

`[[1,,,,],[2,1,,,],[3,4,1,,],[5,6,7,1,],[8,9,10,11,1]]`

Solution:

The given matrix is

`[[1,,,,],[2,1,,,],[3,4,1,,],[5,6,7,1,],[8,9,10,11,1]]`

Formula for finding number of correlation is

`(N xx (N-1))/2`

Where number of columns is 4. So N = 5 Now we have to substitute N value in the formula.

= `(5 xx(5-1))/2`

= `(5 xx 4)/2`

= `20/2`

= 10

Therefore for total number of this matrix is 10


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Example 3:

Find the number of correlation of the following correlation matrix.

`[[1,,,,,],[2,1,,,,],[3,4,1,,,],[5,6,7,1,,],[8,9,10,11,1,],[12,13,14,15,16,1]]`

Solution:

The given matrix is

`[[1,,,,,],[2,1,,,,],[3,4,1,,,],[5,6,7,1,,],[8,9,10,11,1,],[12,13,14,15,16,1]]`

Formula for finding number of correlation is

`(N xx (N-1))/2`

Where number of columns is 4. So N = 6 Now we have to substitute N value in the formula.

= `(6 xx(6-1))/2`

= `(6 xx 5)/2`

= `30/2`

= 15

Therefore for total number of this matrix is 15

Example 4:

Find the number of correlation of the following correlation matrix.

`[[1,,,,,,],[2,1,,,,,],[3,4,1,,,,],[5,6,7,1,,,],[8,9,10,11,1,,],[12,13,14,15,16,1,],[17,18,19,20,21,22,1]]`

Solution:

The given matrix is

`[[1,,,,,,],[2,1,,,,,],[3,4,1,,,,],[5,6,7,1,,,],[8,9,10,11,1,,],[12,13,14,15,16,1,],[17,18,19,20,21,22,1]]`

Formula for finding number of correlation is

`(N xx (N-1))/2`

Where number of columns is 4. So N = 7 Now we have to substitute N value in the formula.

= `(7 xx(6-1))/2`

= `(7 xx 6)/2`

= `42/2`

= 21

Therefore for total number of this matrix is 21