Question

Two hundred and eighty boys completed a test that measures the distance that the boy can walk on a flat, hard surface in 6 minutes. For each age group shown in the table, the median distance walked by the boys in that age group is given.

Age Group | Representative Age (Midpoint of Age Group) |
Median
Six-Minute Walk Distance (meters) |
---|---|---|

3–5 | 4.0 | 543.3 |

6–8 | 7.0 | 585.0 |

9–11 | 10.0 | 666.3 |

12–15 | 13.5 | 702.1 |

16–18 | 17.0 | 728.6 |

A

Find the equation of the least-squares regression line (the equation of the best fit line). (Round your values to three decimal places.)

ŷ = (____,_____)

B

Calculate the five residuals, make sure to use at least 5 decimals for the slope and intercept when calculating the predicted values and residuals. (Round your answers to three decimal places.)

Representative Age ( x) |
Residual |
---|---|

4.0 | |

7.0 | |

10.0 | |

13.5 | |

17.0 |

Answer #1

Ans:

a)

x | y | |

1 | 4 | 543.3 |

2 | 7 | 585 |

3 | 10 | 666.3 |

4 | 13.5 | 702.1 |

5 | 17 | 728.6 |

mean | 10.3 | 645.06 |

std. dev | 5.142956 | 78.49511 |

r | 0.975459 | |

slope,b | 14.88809 | |

intercept,a | 491.71267 |

Regression equation:

**y'=14.888 x+491.713**

b)

x | y | y'=14.88809x+491.71267 | residual=y-y' |

4 | 543.3 | 551.26503 |
-7.965 |

7 | 585 | 595.9293 |
-10.929 |

10 | 666.3 | 640.59357 |
25.706 |

13.5 | 702.1 | 692.701885 |
9.398 |

17 | 728.6 | 744.8102 |
-16.210 |

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