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For each clean data set given below, find an __exact__ fit equation. (For rational functions fit the equation.) Show all of your work clearly and neatly. Assume the top row is the inputs and the bottom row is the outputs. Do not just do Trendline or CurveFit. (6pts each)

**1. **

-8 | -6 | -4 | -2 | 0 | 2 | 4 | 6 | 8 |

-297 | -175 | -85 | -27 | -1 | -7 | -45 | -115 | -217 |

**2.**

-0.9 | -0.8 | -0.7 | -0.6 | -0.5 | -0.4 | -0.3 | -0.2 | -0.1 | 0 |

50 | 25 | 16.66667 | 12.5 | 10 | 8.333333 | 7.142857 | 6.25 | 5.555556 | 5 |

**3.**

-1.5 | -1.25 | -1 | -0.75 | -0.5 | -0.25 | 0 | 0.25 | 0.5 | 0.75 |

-1.875 | -0.703 | 0 | 0.328 | 0.375 | 0.234 | 0 | -0.234 | -0.375 | -0.328 |

For each set of dirty data given below, find a regression function which fits it well. Use the method that uses matrix equations that we learned in class. Trendline or CurveFit alone is insufficient. Show all of your work neatly and clearly labeled. (6pt each)

**4.**

-4 | -4 | -2 | -1 | -1 | 0 | 1 | 1 | 2 | 3 |

2 | 1.5 | 0 | -.8 | -.9 | -1.95 | -3.1 | -2.96 | -3.2 | -4 |

**5.**

-5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |

35.415 | 25.692 | 19.205 | 14.088 | 10.99 | 10 | 10.995 | 14.048 | 18.805 | 26.35 |

Time (in minutes) | 0 | .5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 | 5 | 5.5 | 6 |

Cat’s Temp (in Celsius) | 34.32 | 33.61 | 32.98 | 32.41 | 31.91 | 31.44 | 31.018 | 30.63 | 30.28 | 29.96 | 29.65 | 29.372 | 29.113 |

**6.** Brother Cox’s neighbor’s prized Siamese cat was discovered dead on the road in front of Brother Cox’s house. The neighbor ran to Brother Cox’s door asking if he knew when the cat had been killed. Brother Cox immediately ran and got a thermometer. He then went and took the temperature of the cat every 30 seconds for the next 7 minutes, while his neighbor stood flabbergasted. After a few moments alone with his computer, Brother Cox emerged with the data shown below. Open the spreadsheet Project3Data.xls. You will find the following complete set of data under the “Problem6” tab of the spreadsheet.

A) Find a regression formula of the form for the temperature of the cat using a spreadsheet. Make sure to show and label each step you use to find the regression formula on a spreadsheet printout.

B) The normal body temperature of a cat is 38 degrees Celsius. Using your formula from part A, determine how long the cat has been dead. Clearly show and explain your work.

C) The temperature of the environment surrounding the cat’s body should be the horizontal asymptote for the temperature data.

- From the data values, what do you think the surrounding temperature is?
- From your regression equation, what do you think the surrounding temperature is? How did you determine this temperature?
- Do your two temperature predictions agree? Why or Why not?

**Title:**
Mathematics Paper

**Length:**
3 pages
(803 Words)

**Style:**
N/A

**Preview**

Project#3

From each of the data set find an exact fit equation. (For rational functions fit the equation, y=a/(x+b)), show the work in clear and neat manner.

- a. Data and the graph for the data is as shown below

Problem 1 Data | Column1 | Column2 | Column3 | Column4 |

x | y | first differences | second differences | Ratio of first differences |

-8 | -297 | 122 | -32 | 1.35555556 |

-6 | -175 | 90 | -32 | 1.55172414 |

-4 | -85 | 58 | -32 | 2.23076923 |

-2 | -27 | 26 | -32 | -4.3333333 |

0 | -1 | -6 | -32 | 0.15789474 |

2 | -7 | -38 | -32 | 0.54285714 |

4 | -45 | -70 | -32 | 0.68627451 |

6 | -115 | -102 | ||

8 | -217 |

The graph is a quadratic equation since the second differences are equal but the first difference are not equal and their ratios vary.

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