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4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 12, Problem 12.2P

Textbook Problem

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Family |
Father’s Prestige |
Son’s Prestige |
Daughter’s Prestige |

A | 80 | 85 | 82 |

B | 78 | 80 | 77 |

C | 75 | 70 | 68 |

D | 70 | 75 | 77 |

E | 69 | 72 | 60 |

F | 66 | 60 | 52 |

G | 64 | 48 | 48 |

H | 52 | 55 | 57 |

Analyze the relationship between father’s and son’s prestige and the relationship between father’s and daughter’s prestige. For each relationship,

**a.** Compute the slope (*b*) and find the *Y* intercept (*a*).

**b.** State the least-square regression line. What prestige score would you predict for a son whose father had a prestige score of 72? What prestige score would you predict for a daughter whose father has a prestige score of 72?

**c.** Compute

**d.** Describe the strength and direction of each relationship in a sentence or two. Does the occupational prestige of the father have an impact on his children? Does it have the same impact for daughters as it does for sons?

To determine

(a)

**To find:**

The slope and

**Given:**

The Occupational prestige scores for a sample of fathers and their oldest son and oldest daughter are presented in the following table.

Family | Father’s prestige | Son’s prestige | Daughter’s prestige |

A | 80 | 85 | 82 |

B | 78 | 80 | 77 |

C | 75 | 70 | 68 |

D | 70 | 75 | 77 |

E | 69 | 72 | 60 |

F | 66 | 60 | 52 |

G | 64 | 48 | 48 |

H | 52 | 55 | 57 |

**Approach:**

The *Y* intercept (*a*) is the point of intersection of the regression line and the *y* axis.

The slope (*b*) of the regression line is the amount of change in the dependent variable (*Y*) by a unit change in the independent variable (*X*).

If the two variables are unrelated, the regression line would be parallel to the *x* axis.

**Formula used:**

The model for the least square regression line is defined as,

Where *Y* is the dependent variable,

Where *Y* is the dependent variable and *X* is the independent variable,

*b* is the slope of the regression line.

And

The *a*) is given by,

Where,

**Calculation:**

From the given information,

The father’s prestige is the dependent variable. Thus, it is represented as *Y*.

The daughter’s prestige is the independent variables. Thus, it is as

Consider the following table of sum of squares of son’s prestige and father’s prestige.

Family | Son’s prestige | Father’s prestige |
||||

A | 85 | 16.875 | 284.766 | 80 | 10.75 | 181.406 |

B | 80 | 11.875 | 141.016 | 78 | 8.75 | 103.906 |

C | 70 | 1.875 | 3.51563 | 75 | 5.75 | 10.7813 |

D | 75 | 6.875 | 47.2656 | 70 | 0.75 | 5.15625 |

E | 72 | 3.875 | 15.0156 | 69 | -0.9688 | |

F | 60 | 66.0156 | 66 | 26.4063 | ||

G | 48 | 405.016 | 64 | 105.656 | ||

H | 55 | 172.266 | 52 | 226.406 | ||

Totals | 545 | 554 |

The value of

From above table, substitute

Square the both sides of the equation.

Proceed in the same manner to calculate

Substitute

To determine

(b)

**To find:**

The least regression line and prestige score.

To determine

(c)

**To find:**

The coefficients

To determine

(d)

**To explain:**

The strength, direction and impact of father’s occupational prestige on his children.

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