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4th Edition

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Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 12, Problem 12.5P

Textbook Problem

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The basket ball coach at a small local college believes that his team plays better and scores more points in front of larger crowds. The number of points scored and attendance for all home games last season are reported here. Do these data support the coach’s argument?

Game |
Point scored |
Attendance |

1 | 54 | 378 |

2 | 57 | 350 |

3 | 59 | 320 |

4 | 80 | 478 |

5 | 82 | 451 |

6 | 75 | 250 |

7 | 73 | 489 |

8 | 53 | 451 |

9 | 67 | 410 |

10 | 78 | 215 |

11 | 67 | 113 |

12 | 56 | 250 |

13 | 85 | 450 |

14 | 101 | 489 |

15 | 99 | 472 |

To determine

**To show:**

The given data supports coach’s argument.

**Given:**

The given statement is,

The number of points scored and attendance for all home games last season are reported.

The given table of information is,

Game | Point scored | Attendance |

1 | 54 | 378 |

2 | 57 | 350 |

3 | 59 | 320 |

4 | 80 | 478 |

5 | 82 | 451 |

6 | 75 | 250 |

7 | 73 | 489 |

8 | 53 | 451 |

9 | 67 | 410 |

10 | 78 | 215 |

11 | 67 | 113 |

12 | 56 | 250 |

13 | 85 | 450 |

14 | 101 | 489 |

15 | 99 | 472 |

**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 Point scored is the dependent variable. Thus, it is represented as *Y*.

The Attendance is the independent variables. Thus, it is as

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

Case | Attendance |
Point scored |
|||||

1 | 378 | 6.933 | 48.0665 | 54 | 338.56 | ||

2 | 350 | 443.818 | 57 | 237.16 | 324.432 | ||

3 | 320 | 2607.84 | 59 | 179.56 | 684.298 | ||

4 | 478 | 106.933 | 11434.7 | 80 | 7.6 | 57.76 | 812.691 |

5 | 451 | 79.933 | 6389.28 | 82 | 9.6 | 92.16 | 767.357 |

6 | 250 | 14657.2 | 75 | 2.6 | 6.76 | ||

7 | 489 | 117.933 | 13908.2 | 73 | 0.6 | 0.36 | 70.7598 |

8 | 451 | 79.933 | 6389.28 | 53 | 376.36 | ||

9 | 410 | 38.933 | 1515.78 | 67 | 29.16 | ||

10 | 215 | 24356.9 | 78 | 5.6 | 31.36 | ||

11 | 113 | 66598.6 | 67 | 29.16 | 1393.56 | ||

12 | 250 | 14657 |

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