Chapter 14, Problem 25P

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8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

Problem 9 examined the relationship between weight and income for a sample of *n* = 10 women. Weights were classified in five categories and had a mean of *M* = 3 with *SS =* 20. Income, measured in thousands, had a mean score of *M* = 66 with *SS =* 7430, and *SP* = −359.

**a.**Find the regression equation for predicting income from weight. (Identify the income scores as*X*values and the weight scores as*Y*values.)**b.**What percentage of the variance in the income is accounted for by the regression equation? (Compute the correlation, r. then find r^{2}.)**c.**Does the regression equation account for a significant portion of the variance in income? Use α= .05 to evaluate the*F*-ratio.

Weight (X) |
Income (Y) |

1 | 125 |

2 | 78 |

4 | 49 |

3 | 63 |

5 | 35 |

2 | 84 |

5 | 38 |

3 | 51 |

1 | 93 |

4 | 44 |

**a**.

To determine

The regression equation for predicting income from weight.

Explanation

**Given info: For 10 women weights are classified in five categories with mean of **

Weight(X) |
Income(Y) |

1 | 125 |

2 | 78 |

4 | 49 |

3 | 63 |

5 | 35 |

2 | 84 |

5 | 38 |

3 | 51 |

1 | 93 |

4 | 44 |

**Calculation:**

Generally the linear regression equation is defined as

Formula to calculate

Formula to calculate the

Mean of the variable

Thus, the mean of the variable

Mean of the variable

Thus the mean of the variable y is 66.

For calculating

Sr |

**b**.

To determine

The Percentage of variance in the income accounted for the regression equation.

**c**.

To determine

The significance of the regression equation.

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Sect-14.4 P-2LCSect-14.4 P-1LCASect-14.5 P-1LCSect-14.5 P-2LCSect-14.5 P-3LCSect-14.5 P-1LCASect-14.5 P-2LCASect-14.6 P-1LCSect-14.6 P-2LCSect-14.6 P-3LCSect-14.6 P-4LCSect-14.6 P-1LCASect-14.6 P-1LCBSect-14.6 P-2LCBSect-14.6 P-3LCBSect-14.6 P-1LCCCh-14 P-1PCh-14 P-2PCh-14 P-3PCh-14 P-4PCh-14 P-5PCh-14 P-6PCh-14 P-7PCh-14 P-8PCh-14 P-9PCh-14 P-10PCh-14 P-11PCh-14 P-12PCh-14 P-13PCh-14 P-17PCh-14 P-18PCh-14 P-19PCh-14 P-20PCh-14 P-21PCh-14 P-22PCh-14 P-23PCh-14 P-24PCh-14 P-25PCh-14 P-26PCh-14 P-27PCh-14 P-28PCh-14 P-29P

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