# Solve A Correlation

Introduction to Correlation Co-efficient Definition:

Analyze of the power of linear connection between two variables. Solve Correlation is forever between -1.0 and +1.0. If the
solve correlation is +ve, we have a +ve relationship if it is -ve, the relationship is -ve.

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Solve Correlation Co-efficient Formula:
` "Correlation(r)" =[ NsumXY - ((sumX)(sumY)) / ((sqrt([NsumX^2) - (sumX)^2][NsumY^2 - (sumY)^2]))]`

Where
N = Number of values or elements
X = first Score
Y = second Score
` sum ` XY = Sum of the result of first and second Scores
` sum` X = Sum of first Scores
` sum` y = Sum of second Scores
`sum ` x2 = Sum of square first Scores
`sum ` y2 = Sum of square second Scores

## Solve Correlation Co-efficient - Examples:

Solve Correlation Co-efficient - Example 1:

Find the Correlation co-efficient of

 X Values Y Values 6 3 1 3 2 3 6 4 5 4

Step 1:

Count the number of values.
N = 5
Step 2:

Find XY, X2, Y2
See the below table

 X Value Y Value X*Y X*X Y*Y 6 3 6 * 3 = 18 6 * 6 = 36 3 * 3 = 9 1 3 1 * 3 = 3 1 * 1 = 1 3 * 3 = 9 2 3 2 * 3 = 6 2 * 2 = 4 3 * 3 = 9 6 4 6 * 4 = 24 6 * 6 = 36 4 * 4 = 16 5 4 5 * 4 = 20 5 * 5 = 25 4 * 4 = 1

Step 3:

Find `sum ` X, `sum` y, `sum` xy, `sum` x2, `sum ` y2.
` sum ` x = 20
` sum ` y = 17

` sum` xy = 71

` sum` x2 = 102

` sum ` y2 = 59
Step 4: Now, Substitute in the above formula given.

`"Correlation(r)" =[ NsumXY - ((sumX)(sumY)) / (sqrt([NsumX^2 - (sumX)^2][NsumY^2 - (sumY)^2])]]`

=`[5(71)-(20)(17)/sqrt(5(102)-(102)^2][5(59)-(17)^2]`

=`[15/sqrt(10404-510)][295-289].`

=[15]/[`sqrt(9894)(6)` ]

=15/ 243.647286

= 0.0615

Solve Correlation Co-efficient - Example 2:

Find the Correlation co-efficient of

 X Values Y Values 7 8 9 4 7 4 3 3 3 5

Step 1:

Count the number of values.
N = 5

Step 2:

Find XY, X2, Y2
See the below table

 X Value Y Value X*Y X*X Y*Y 7 8 7 * 8 = 56 7 * 7 = 49 8 * 8 = 64 9 4 9 * 4 = 36 9 * 9 = 81 4 * 4 = 16 7 4 7 * 4 = 28 7 * 7 = 49 4 * 4 = 16 3 3 3 * 3 = 9 3 * 3 = 9 3 * 3 = 9 3 5 3 * 5 = 15 3 * 3 = 9 5 * 5 = 25

Step 3:

Find `sum` X, `sum` y, `sum` xy, `sum` x2, `sum` y2.
`sum` x = 29
` sum` y = 24

`sum` xy = 144

`sum` x2 = 197

`sum` y2 = 130
Step 4: Now, Substitute in the above formula given.

`"Correlation(r)" =[ NsumXY - ((sumX)(sumY)) / (sqrt([NsumX^2 - (sumX)^2][NsumY^2 - (sumY)^2])]]`

=[5(144)-(29)(24)/sqrt(5(197)-(29)^2][5(130)-(24)^2]

=`[24/sqrt(985-841)][650-576].`

=`[24]/[sqrt(144)(74)]`

=24/ 103.227

= 0.2325

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## Practice Problems for Solve Corelation Co-efficient:

 X Values Y Values 2 5 4 6 8 0 3 4 7 6