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4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 12, Problem 12.4P

Textbook Problem

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The following variables were collected for a sample of ten precincts during the last national election. Compute

Precinct |
PercentageDemocrat |
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

**To find:**

The coefficients

**Given:**

The given statement is,

The following variables were collected for a sample of ten precincts during the last national election. The voter turnout is the dependent variable.

The given table of information is,

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 |

**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,

*X* is the independent variable,

*a* is the *Y* intercept of the regression line

and, *b* is the slope of the regression line.

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

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

And

**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

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 |

From above table, substitute

Square the both sides of the equation.

Proceed in the same manner to calculate

Substitute

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