Question

If you were to develop a regression line to predict y by x, what value would the coefficient of determination have?

x 213 196 184 202 221 247

y 76 65 62 68 71 75

(Do not round the intermediate values. Round your answer to 3 decimal places.)

Coefficient of determination =

Answer #1

Solution:

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

213 | 76 | 16188 | 45369 | 5776 |

196 | 65 | 12740 | 38416 | 4225 |

184 | 62 | 11408 | 33856 | 3844 |

202 | 68 | 13736 | 40804 | 4624 |

221 | 71 | 15691 | 48841 | 5041 |

247 | 75 | 18525 | 61009 | 5625 |

n | 6 |

sum(XY) | 88288.00 |

sum(X) | 1263.00 |

sum(Y) | 417.00 |

sum(X^2) | 268295.00 |

sum(Y^2) | 29135.00 |

Numerator | 3057.00 |

Denominator | 3667.09 |

r | 0.8336 |

r square | 0.6949 |

Xbar(mean) | 210.5000 |

Ybar(mean) | 69.5000 |

SD(X) | 20.1391 |

SD(Y) | 5.0580 |

b | 0.2094 |

a | 25.4278 |

Coefficient of determination = r ^{2} =
**0.695**

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