APPLICATIONS IN MATH A



APPL IN SEQ MATH NAME__________________________

LINEAR REGRESSION

US Wildfire Data

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Activity Overview:

Wildfires devastate millions of acres a year and cost millions of dollars in lost lumber, housing and suppression costs. However, the most alarming figure is the number of fatalities associated with wildfires. The USA TODAY snapshot “Wildfire deaths” displays the number of fatalities for the five years spanning 1998 through 2002. You will use related data on the number of wildfires deaths in the United States in the past decade to determine the linear model. You will examine the affect an outlier has on the model and compare methods to determine the best model.

Focus Questions:

1. How many wildfires deaths occur in the U.S. each year?

2. Will a linear model predict the number of wildfires deaths in a year?

3. How can the affect of an outlier(s) on an equation be minimized?

PROCEDURE:

Step 1

Using data collected from the National Interagency Fire Center on the number of U.S. firefighter fatalities due to wildland fires, from the table below, make two LISTS. L1 is year (type the last digits of the year) and L2 is number of wildfires deaths. STAT. EDIT.

|YEAR (x) LIST 1 |# of US Firefighter Wildland Fatalities LIST 2 |

|(2001 ) 1 |18 |

|(2002) 2 |23 |

|(2003) 3 |30 |

|(2004) 4 |20 |

|(2005) 5 |12 |

|(2006) 6 |24 |

|(2007) 7 |9 |

|(2008) 8 |25 |

|(2009) 9 |15 |

|(2010) 10 |8 |

|(2011) 11 |11 |

|(2012) 12 |15 |

|(2013) 13 |34 |

(Source:US Forest Service; National Interagency Fire Center, November 2013)

Step 2

Create a scatterplot. STAT PLOT ON. WINDOW. GRAPH.

Describe the trend you see in the graph of your data. (Use attached graph paper)

Step 3

Create a linear regression model for the data. DIAGONOSTIC ON. STAT. CALC. #4 Lin Reg, L1,L2. Enter. Type equation into Y1=.

Y1= -0.269x+20.65.______________. Record the r= -0.129 and r²=_0.0166__________ which is the correlation coefficient. The closer the values are to 1 or -1, the closer the relationship of the two data lists.

Step 4

Do you see any OUTLIERS in the data (data that does not fit with the others)? Circle the outliers in the table above.

Retype the values in L3 and L4 leaving out the outliers. Run a linear regression on the adjusted data and store the equation on Y2. STAT. CALC. #4 Lin Reg, L3,L4. Enter. Type equation intoY2=. Y2=_-0.584x+17.807____. Record the r= -0.525___________ and r²=__0.275__________.

Step 5

What are some of the factors that influence wildfires?

Are we able to utilize the best fit equation(s) to predict the number of wildfires (or fatalities or property damage) in any given year? Why or why not?

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