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4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 12, Problem 12.3P

Textbook Problem

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Case |
Level of Activity |
Number of Visitors |

A | 10 | 14 |

B | 11 | 12 |

C | 12 | 10 |

D | 10 | 9 |

E | 15 | 8 |

F | 9 | 7 |

G | 7 | 10 |

H | 3 | 15 |

I | 10 | 12 |

J | 9 | 2 |

To determine

**To find:**

The coefficients

**Given:**

The given statement is,

The residents of a housing development for senior citizens have completed a survey that indicated their level of inactivity and the number of visitors they receive each week.

The given table of information is,

Case | Level of inactivity | Number of visitors |

A | 10 | 14 |

B | 11 | 12 |

C | 12 | 10 |

D | 10 | 9 |

E | 15 | 8 |

F | 9 | 7 |

G | 7 | 10 |

H | 3 | 15 |

I | 10 | 12 |

J | 9 | 2 |

**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 number of visitors is the dependent variable. Thus, it is represented as *Y*.

The level of inactivity is the independent variables. Thus, it is as

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

Case | Level of inactivity |
visitors |
|||||

A | 10 | 0.4 | 0.16 | 14 | 4.1 | 16.81 | 1.64 |

B | 11 | 1.4 | 1.96 | 12 | 2.1 | 4.41 | 2.94 |

C | 12 | 2.4 | 5.76 | 10 | 0.1 | 0.01 | 0.24 |

D | 10 | 0.4 | 0.16 | 9 | 0.81 | ||

E | 15 | 5.4 | 29.16 | 8 | 3.61 | ||

F | 9 | 0.36 | 7 | 8.41 | 1.74 | ||

G | 7 | 6.76 | 10 | 0.1 | 0.01 | ||

H | 3 | 43.56 | 15 | 5.1 | 26.01 | ||

I | 10 | 0.4 | 0.16 | 12 | 2.1 | 4.41 | 0.84 |

J | 9 | 0.36 | 2 | -7.9 | 62.41 | 4.74 | |

Totals | 96 |

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