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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 ValueY ValueX*YX*XY*Y
787 * 8 = 567 * 7 = 49   
8 * 8 = 64
949 * 4 = 369 * 9 = 81
4 * 4 = 16
747 * 4 = 287 * 7 = 494 * 4 = 16
333 * 3 = 93 * 3 = 9
3 * 3 = 9
353 * 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


Answer:

Correlation : -0.4965