#### Predicting Pumpkin Weights

A typical contest in the fall is to guess the weight of a pumpkin without a scale. Using just a few measurements, can you predict the weight of a pumpkin? Your assignment is to write a paper that uses the modeling process to answer this question.

First, you will want to discuss variables and assumptions such as geometric similarity. You will also have to use one or more (length) measurements to estimate weight. If you have access to some pumpkins, you may wish to decide which variables are important and take your own measurements. If not, you may use the data found below.

After you have your data, solve/verify the model. You may want to use more than one technique, using one or more measurements. Which model did you feel was the "best"? How accurate is your model? Discuss the balance between accuracy and simplicity. How will measurement error affect your predictions? Overall, what model do you choose to predict a pumpkin's weight and why?

What about implementation? If you're just trying to predict one pumpkin's weight, then a complicated formula might be okay. However, suppose an organization is selling pumpkins to the general public and wants to base its prices on weight. If a scale is unavailable, then how would you suggest they implement your model?

If available, test your model on some new pumpkins. Discuss your conclusions.

circumferences | ||||

height | horiz. | vertical 1 | vertical 2 | weight |

4 | 22.8 | 19.3 | 19.2 | 0.25 |

6 | 30.4 | 26.4 | 26.5 | 0.6 |

7.5 | 31.1 | 28.7 | 29 | 0.75 |

9.7 | 50 | 42.5 | 42.3 | 2.4 |

14.7 | 46 | 48.8 | 48.8 | 2.8 |

19.7 | 66 | 66.5 | 66 | 7 |

31.2 | 66 | 85 | 88 | 10.1 |

24.7 | 85 | 86 | 81 | 12.5 |

32.7 | 83.7 | 97.5 | 99.5 | 16.9 |

23.2 | 101.2 | 93.3 | 89.8 | 17.2 |

all in cm, accurate to +/-0.1lbs |

circumferences | ||||

height | horiz. | vertical 1 | vertical 2 | weight |

7.4 | 27.8 | 27 | 27.5 | 0.625 |

8.1 | 41 | 35.5 | 35.8 | 1.125 |

8.4 | 50.5 | 41.7 | 42 | 2.125 |

12.5 | 47.5 | 46 | 46 | 2.75 |

18 | 67.5 | 64.5 | 66 | 7.625 |

21 | 74.6 | 73.5 | 72.5 | 8.875 |

19 | 85.8 | 81 | 79 | 11.25 |

26.5 | 78.3 | 90 | 89 | 12.75 |

25.4 | 90.1 | 89.5 | 89 | 16 |

23.5 | 101.5 | 93 | 94.5 | 19.375 |

all in cm, accurate to +/-0.1lbs |

Note: The 2004 data includes a “white” pumpkin. The rest are the typical orange variety. Can you determine which is the “white” one?