## 06.06 Assignment

## Question 1

The table represents data collected on the time spent studying (in minutes) and the resulting test grade.

Time Spent Studying (min) | 52 | 37 | 31 | 9 | 26 | 40 | 22 | 10 | 45 | 34 | 19 | 60 |

Grade on Test | 95 | 84 | 72 | 58 | 77 | 86 | 72 | 43 | 90 | 81 | 62 | 98 |

- Part 1: Create a scatter plot with the predicted line of best fit drawn on it. Determine the type of correlation (if any), and predict the model that will be used.
- Part 2: Find the line of best fit for the data either by hand or using technology. Explain your method. Find the predicted score for each time listed in the table.
- Part 3: Find the residuals, and decide if your model is a good fit. Explain your method. (If your model is not a good fit, complete Part 2 again with a different set of points or choose a different model.)

## Question 2

Look back at the data from the New York Marathon.

Year | Competitors* | Year | Competitors* | Year | Competitors* |
---|---|---|---|---|---|

1976 | 2.1 | 1987 | 22.5 | 1997 | 31.4 |

1977 | 4.8 | 1988 | 23.5 | 1998 | 32.4 |

1978 | 9.8 | 1989 | 25 | 1999 | 32.5 |

1979 | 11.5 | 1990 | 25.8 | 2000 | 30 |

1980 | 14 | 1991 | 26.9 | 2001 | 24 |

1981 | 14.5 | 1992 | 28.6 | 2002 | 32.5 |

1982 | 14.3 | 1993 | 28.1 | 2003 | 35.3 |

1983 | 15.2 | 1994 | 31.1 | 2004 | 37.3 |

1984 | 14.6 | 1995 | 29 | 2005 | 37.6 |

1985 | 16.7 | 1996 | 29 | 2006 | 38.4 |

1986 | 20.5 | * in thousands |

Use this original data, but update it with the following information so that it is accurate through 2011. (The 2012 NY Marathon was cancelled due to the aftermath of Hurricane Sandy.) Use the entire data set (1976-2011) to answer all parts of Question 2.

Year | Competitors (in thousands) |
---|---|

2007 | 39.2 |

2008 | 37.9 |

2009 | 43.7 |

2010 | 44.8 |

2011 | 46.8 |

- Part 1: Find a regression model for this new, updated data set (1976-2011). Explain your method.
- Part 2: How well does it fit? Explain your answer and reasoning.
- Part 3: Use your model to predict the attendance in 2017.