Question

Here is a bivariate data set.

x | y |
---|---|

38 | 12 |

36 | 19 |

26 | -17 |

36 | 35 |

40 | 35 |

44 | 48 |

43 | 23 |

25 | 26 |

47 | 62 |

48 | 53 |

Find the correlation coefficient and report it accurate to four
decimal places.

*r* =

Answer #1

Solution:

X | Y | XY | X^2 | Y^2 |

38 | 12 | 456 | 1444 | 144 |

36 | 19 | 684 | 1296 | 361 |

26 | 17 | 442 | 676 | 289 |

36 | 35 | 1260 | 1296 | 1225 |

40 | 35 | 1400 | 1600 | 1225 |

44 | 48 | 2112 | 1936 | 2304 |

43 | 23 | 989 | 1849 | 529 |

25 | 26 | 650 | 625 | 676 |

47 | 62 | 2914 | 2209 | 3844 |

48 | 53 | 2544 | 2304 | 2809 |

n | 10 |

sum(XY) | 13451.00 |

sum(X) | 383.00 |

sum(Y) | 330.00 |

sum(X^2) | 15235.00 |

sum(Y^2) | 13406.00 |

Numerator | 8120.00 |

Denominator | 11934.44 |

r | 0.6804 |

r square | 0.4629 |

Xbar(mean) | 38.3000 |

Ybar(mean) | 33.0000 |

SD(X) | 5.4975 |

SD(Y) | 12.6183 |

b | 1.4344 |

a | -21.9366 |

r = **0.6804**

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x
y
49.7
34.8
43.9
30.9
48
30
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x
y
69.7
98.7
61
105.6
61.5
114.2
64.9
115.3
50.9
48.5
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58.1
55.3
43.3
33.7
74.5
36.9
56.2
27.7
54.4
1
58.2
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Dataset:
Husband Wife
53 50
38 34
46 44
30 36
31 23
26 31
29 25
48 51
65 46
29 26
28 23
29 32
25 22
22 21
21 24
43 50
24 27
38 33
33 26
35 29
40 29
27 25
27 24
49 38
48 39
27 27
26 24
40 34
35 37
21 26
32 39
30 28
60 52
36 40
25 23
66 55
52 34
41 40
43 ...

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