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` x^{2} = Addition of square 1st achieve

`sum` y^{2} = 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, X^{2}, Y^{2}

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` x^{2}, `sum` y^{2}.

`sum` x = 445

`sum` y = 23.6

`sum` xy = 2102.6

` sum` x^{2} = 39615

`sum` y^{2} = 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, X^{2}, Y^{2}

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` x^{2}, `sum` y^{2}.

`sum` x = 240

`sum` y = 17

`sum` xy = 819

`sum` x^{2} = 11530

`sum` y^{2} = 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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