Strong Correlation Coefficient

In this article we will discuss strong correlation coefficient.Strong correlation, however, does often warrant advance examination to conclude causation. The correlation of an idea from statistics is  the calculation of how well trends in the expected values follow trends in past real values. The correlation is a value between 0 and 1. If there is no relationship between the calculate d values and the definite values the correlation coefficient is 0 or very low. Now we will discuss  formula of strong correlation coefficient.

Formula for strong correlation coefficient:

Where
N = Sum number of values
X = 1st get
Y = 2nd get
`sum` XY = Addition of the 1st and 2nd achieve
`sum` X = Addition of 1st achieve
`sum` y = Addition of 2nd achieve
`sum` x2 = Addition of square 1st achieve
`sum` y2 = Addition of square 2nd get achieve

 

Example problems for strong correlation coefficient:

 

Strong correlation coefficient – Example 1:

Calculate the Correlation coefficient of following table

X 87 88 89 90 91
Y 4.1 4.6 4.8 5 5.1

 

Solution 1 for solves strong correlation coefficient:

 Step 1:  Count the number of values.
N = 5

  Step 2:  Calculate XY, X2, Y2

See the below table

 

X Y x*y x*x = x^2 y*y = y^2
87 4.1  87*4.1 = 356.7 87*87= 7569 4.1* 4.1=16.81
88 4.6 88*4.6 = 404.6 88*88= 7744 4.6* 4.6 =21.16
89 4.8 89*4.8 = 427.2 89*89= 7921 4.8* 4.8 =23.04
90 5  90*5   =  450 90*90= 8100    5*5 = 25
91 5.1  91*5.1= 464.1  91*91 = 8281 5.1* 5.1= 26.01

 

       Step 3: Find `sum` X, `sum` y, `sum` xy, `sum` x2, `sum` y2.

`sum` x = 445

`sum` y = 23.6

`sum` xy = 2102.6

` sum` x2 = 39615

`sum` y2 = 112.02

Step 4: Now, Substitute in the above formula specified.

= `[(5(2102.6) - (445)(23.6)) / ((sqrt([5(39615)-(445)^2][5(112.02)-(23.6)^2]))]]`

= `(10513 – 10501) / sqrt([198075 - 198025] [560.1 - 556.96])`

= `12 / sqrt(50 xx 3.14 )`

= `12/ sqrt(157)`

= `12/12.52`

= 0.958

          Answer is 0.958

Strong correlation coefficient – Example 2:

Find the Correlation coefficient of follow table

X Y
46 3
47 3
48 3
49 4
50 4

 

Solution for strong correlation coefficient:

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
46 3 46*3 = 138 46*46 = 2116 3*3= 9
47 3 47*3 = 141 47*47 = 2209 3*3= 9
48 3 48*3 = 144 48*48 = 2304 3*3= 9
49 4 49*4 = 196 49*49 = 2401 4*4= 16
50 4 50*4 = 200 50*50 = 2500 4*4= 16

 

Step 3: Find `sum` X, `sum` y, `sum` xy, `sum` x2, `sum` y2.

`sum` x = 240

`sum` y = 17

`sum` xy = 819

`sum` x2 = 11530

`sum` y2 = 59

Step 4: Now, Substitute in the above formula specified.

` “Correlation(r)”=[(N sum XY-(sum X)(sum Y))/((sqrt([(N sum X^2)-(sum X)^2][N sum Y^2-(sum Y^2)])) ]]`

= `[(5(819) - (240)(17)) / ((sqrt([5(11530)-(240)^2][5(59)-(17)^2]))]] `

= `(4095 – 4080)/sqrt([57650 - 57600] [295-289])`

= `15/sqrt(50 xx6)`

= `15/sqrt(300)`

= `15/17.32`

= 0.8660

            Answer is: 0.8660



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