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4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 13, Problem 13.2P

Textbook Problem

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Precinct |
Percentage Democrat |
Percentage Minority |
Percentage Voter Turnout |

A | 33 | 9 | 36 |

B | 78 | 15 | 60 |

C | 62 | 18 | 64 |

D | 50 | 10 | 56 |

E | 45 | 12 | 55 |

F | 56 | 8 | 52 |

G | 85 | 20 | 25 |

H | 25 | 0 | 42 |

I | 13 | 5 | 89 |

J | 33 | 9 | 88 |

Take voter turnout as the dependent variable and do the following:

**a.** Find the multiple regression equations (unstandardized).

**b.** What turnout would you expect for a precinct in which 0% of the voters were Democrats and 5% were minorities?

**c.** Compute beta-weights for each independent variable and compare their relative effect on turnout. Which was the more important factor?

**d.** Compute

**e.** Write a paragraph summarizing your findings.

**12.4**

Precinct |
Percentage Democrat |
Percentage Minority |
Percentage Voter Turnout |

A | 33 | 9 | 36 |

B | 78 | 15 | 60 |

C | 62 | 18 | 64 |

D | 50 | 10 | 56 |

E | 45 | 12 | 55 |

F | 56 | 8 | 52 |

G | 85 | 20 | 25 |

H | 25 | 0 | 42 |

I | 13 | 5 | 89 |

J | 33 | 9 | 88 |

To determine

**(a)**

**To find:**

The unstandardized multiple regression equation with voter turnout as the dependent variable.

**Given:**

The table for a sample of ten precincts during the last national election is given below:

Precinct | Percentage Democrat | Percentage Minority | Percentage Voter Turnout |

A | 33 | 9 | 36 |

B | 78 | 15 | 60 |

C | 62 | 18 | 64 |

D | 50 | 10 | 56 |

E | 45 | 12 | 55 |

F | 56 | 8 | 52 |

G | 85 | 20 | 25 |

H | 25 | 0 | 42 |

I | 13 | 5 | 89 |

J | 33 | 9 | 88 |

**Formula used:**

Let the data values be

The formula to calculate mean is given by,

The formula to calculate standard deviation is given by,

Where,

The formula for calculating the correlation coefficient *r* is given as,

Where, *X* and *Y* are the two variables.

The formula to calculate the partial slopes for the independent variables is given by,

And,

Where,

The least square multiple regression line is given by,

The formula to calculate the

**Calculation:**

From the given information,

The voter turnout is the dependent variable. Thus, it is represented as *Y*.

The rest of the variables, i.e. democrat and minority are the independent variables and are represented as

The mean is given by,

For democrat, substitute 10 for

The mean of democrats is 48.

For turnout, substitute 10 for

The mean of turnout is 56.7.

Consider the following table of sum of squares of democrat and voter turnout.

Precinct | Democrat |
Voters Turnout |
|||||

A | 33 | 225 | 36 | 428.49 | 310.5 | ||

B | 78 | 30 | 900 | 60 | 3.3 | 10.89 | 99 |

C | 62 | 14 | 196 | 64 | 7.3 | 53.29 | 102.2 |

D | 50 | 2 | 4 | 56 | 0.49 | ||

E | 45 | 9 | 55 | 2.89 | 5.1 | ||

F | 56 | 8 | 64 | 52 | 22.09 | ||

G | 85 | 37 | 1369 | 25 | 1004.89 | ||

H | 25 | 529 | 42 | 216.09 | 338.1 | ||

I | 13 | 1225 | 89 | 32.3 | 1043.29 | ||

J | 33 | 225 | 88 | 31.3 | 979.69 | ||

Totals | 480 | 567 |

Substitute

Square the both sides of the equation.

Proceed in the same manner to calculate

The formula for calculating the correlation coefficient *r* is given as,

Substitute

The correlation coefficient between democrats and turnouts is

Square the above calculated value of

The formula to calculate standard deviation is given by,

For democrats, substitute 4746 for

The standard deviation of democrats is 21.8.

For turnouts, substitute

The standard deviation of turnouts is 19.4.

For minority, substitute 10 for

The mean of minority is 10.6.

Consider the following table of sum of squares of minority and voter turnout.

Precinct | Minority |
Voters Turnout |
|||||

A | 9 | 2.56 | 36 | 428.49 | 33.12 | ||

B | 15 | 4 |

To determine

**(b)**

**To find:**

The expected turnout for a precinct with 0% of democrats voters and 5% of minorities.

To determine

**(c)**

**To find:**

The beta weights for each given independent variable and the effect of the variable on turnout.

To determine

**(d)**

**To find:**

The coefficient of multiple determination.

To determine

**(e)**

**To explain:**

The relationship among the given three variables.

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