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Correlation Co-efficient Tutorial

  


Correlation Co-efficient Definition:
     A measure of the strength of linear association between two variables. Correlation will always between -1.0 and +1.0. If the correlation is positive, we have a positive relationship. If it is negative, the relationship is negative.

  Formula:

Correlation Co-efficient :
Correlation(r) =[ NΣXY - (ΣX)(ΣY) / Sqrt([NΣX2 - (ΣX)2][NΣY2 - (ΣY)2])]
where
              N = Number of values or elements
              X = First Score
              Y = Second Score
              ΣXY = Sum of the product of first and Second Scores
              ΣX = Sum of First Scores
              ΣY = Sum of Second Scores
              ΣX2 = Sum of square First Scores
              ΣY2 = Sum of square Second Scores



Correlation Co-efficient Example: To find the Correlation of


X ValuesY Values
603.1
613.6
623.8
634
654.1


  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
603.160 * 3.1 = 18660 * 60 = 36003.1 * 3.1 = 9.61
613.661 * 3.6 = 219.661 * 61 = 37213.6 * 3.6 = 12.96
623.862 * 3.8 = 235.662 * 62 = 38443.8 * 3.8 = 14.44
63463 * 4 = 25263 * 63 = 39694 * 4 = 16
654.165 * 4.1 = 266.565 * 65 = 42254.1 * 4.1 = 16.81


  Step 3: Find ΣX, ΣY, ΣXY, ΣX2, ΣY2.
            ΣX = 311
            ΣY = 18.6
            ΣXY = 1159.7
            ΣX2 = 19359
            ΣY2 = 69.82

  Step 4: Now, Substitute in the above formula given.
            Correlation(r) =[ NΣXY - (ΣX)(ΣY) / Sqrt([NΣX2 - (ΣX)2][NΣY2 - (ΣY)2])]
            = ((5)*(1159.7)-(311)*(18.6))/sqrt([(5)*(19359)-(311)2]*[(5)*(69.82)-(18.6)2])
            = (5798.5 - 5784.6)/sqrt([96795 - 96721]*[349.1 - 345.96])
            = 13.9/sqrt(74*3.14)
            = 13.9/sqrt(232.36)
            = 13.9/15.24336
            = 0.9119

This example will guide you to find the relationship between two variables by calculating the Correlation Co-efficient from the above steps.



Related Calculator:
>> Correlation Co-efficient Calculator.

This tutorial will help you dynamically to find the Correlation Co-efficient problems.