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Write a detailed note on Carl's Correlation Coefficient Algorithm. Justify the necessary of Algorithm by giving suitable example.

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Write a detailed note on Carl's Correlation Coefficient Algorithm. Justify the necessary of Algorithm by giving suitable example.

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written 7.3 years ago by |

Carl Pearson Coefficient of correlation is a measure of linear relationship between two variables. It lies between -1 and 1.

The closer it is to 1(or -1), the stronger the positive(or negative) linear relationship between the two variables. If it is close to 0, there is no linear relation.

Example :

X(height - cm) | Y(weight - kg) |
---|---|

174 | 61 |

175 | 65 |

176 | 67 |

177 | 68 |

178 | 72 |

182 | 74 |

183 | 80 |

186 | 87 |

189 | 92 |

193 | 95 |

Number of cases: n = 10

Sr. No. | X | Y | $X^2$ | $Y^2$ | XY |
---|---|---|---|---|---|

1 | 174 | 61 | 30276 | 3721 | 10614 |

2 | 175 | 65 | 30625 | 4225 | 11375 |

3 | 176 | 67 | 30976 | 4489 | 11792 |

4 | 177 | 68 | 31329 | 4624 | 12036 |

5 | 178 | 72 | 31684 | 5184 | 12816 |

6 | 182 | 74 | 33124 | 5476 | 13468 |

7 | 183 | 80 | 33489 | 6400 | 14640 |

8 | 186 | 87 | 34596 | 7569 | 16182 |

9 | 189 | 92 | 35721 | 8464 | 17388 |

10 | 193 | 95 | 37249 | 9025 | 18335 |

∑ | 1813 | 761 | 329069 | 59177 | 138646 |

∑ X = 1813

∑ Y = 761

∑ $X^2$= 329069

∑ $Y^2$ = 59177

∑ XY = 138646

∑ X ∑ Y = 138646

$r=\dfrac{n(∑xy)-(∑x)(∑y)}{\sqrt{[n∑x^2 -(∑x)^2 ][n∑y^2 - (∑y)^2 ]} }$

$\therefore$ Correlation coefficient: r = 0.9864

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