Question

The table below shows the number of interceptions thrown during the season by seven randomly selected National Football League teams and the number of games those teams won during the season.

Wins | Interceptions |

2 | 20 |

5 | 18 |

10 | 15 |

13 | 6 |

10 | 8 |

8 | 24 |

8 | 10 |

**Find the correlation coefficient for this
data:**

Group of answer choices

0.53

-67.82

67.82

-0.53

Answer #1

n = 7

The last row represent the total of each coloumn

Wins (x) | Interceptions (y) | x*x | y*y | xy |

2 | 20 | 4 | 400 | 40 |

5 | 18 | 25 | 324 | 90 |

10 | 15 | 100 | 225 | 150 |

13 | 6 | 169 | 36 | 78 |

10 | 8 | 100 | 64 | 80 |

8 | 24 | 64 | 576 | 192 |

8 | 10 | 64 | 100 | 80 |

56 | 101 | 526 | 1725 | 710 |

r = [n* total of xy - (total of x) * ( total of y)]/ underroot [(n* total of x*x) -( total of x)2] * [(n* total of y*y) -( total of y)2

solving the numerator = 7*710 - (56*101) = 4970 - 5656 = - 686

Solving the denominator = underrrot(7*526)-(56)2 * (7*1725)-(101)2 = [3682 - 3136 ] * [12075-10201]

= 546 * 1874 = underroot 1023204 = 1011.535

r = -686/1011.535 = -0.67817

so coefficient of correlation = -0.67817 * 100 =
**-67.82**

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