Worksheet5
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Unity College *
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Course
201
Subject
Mathematics
Date
Feb 20, 2024
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docx
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5
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MATH 201 Statistics for Environmental Professionals ● Worksheet 5
Name
Suppose you work for the conservation of natural areas at the Bureau of Land Management. Your section concerns the effect of wildfires on natural areas. Your supervisor asked you to analyze the temporal trend in wildfires. In particular, she is interested in the following associations:
1.
Has the number of wildfires per year increased?
2.
Has the total burned area (in acres) per year increased?
3.
Has the burned area (in acres) per fire increased?
The accompanied data file contains the number of wildfires, total burned area, and burned area per fire in the U.S. from 2000 to 2019. Date Number of Fires
Acres Burned
Acres Burned per Fire
2000 9,135 606,869 66.4
2001 6,961 367,544 52.8
2002 13,942 1,702,508 122.1
2003 5,744 361,081 62.9
2004 6,554 1,142,287 174.3
2005 4,684 1,331,249 284.2
2006 15,403 1,196,351 77.7
2007 9,654 502,835 52.1
2008 9,536 672,117 70.5
2009 6,614 493,268 74.6
2010 4,027 812,459 201.8
2011 6,567 1,345,060 204.8
2012 5,415 1,363,293 251.8
2013 4,046 1,252,719 309.6
2014 4,463 172,860 38.7
2015 6,430 1,868,614 290.6
2016 5,230 526,926 100.8
2017 5,336 600,373 112.5
2018 5,112 812,501 158.9
2019 5,657 1,331,968 235.5
2020 5,939 1,035,963 174.4
Question 1.
Using Excel, create three scatter plots that show each association (year and number of wildfires, year and total burned area, and year and burned area per fire). Clearly label the graphs. Note that the year should be on the x-axis. Attach the scatterplot to this report. (15 pts.)
1995
2000
2005
2010
2015
2020
2025
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
Number of Wild Fires
1995
2000
2005
2010
2015
2020
2025
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
1,400,000
1,600,000
1,800,000
2,000,000
Acres Burned
1995
2000
2005
2010
2015
2020
2025
0
50
100
150
200
250
300
350
Acres Burned per Fire
Question 2.
Using the scatter plots created in Question 1, perform a visual assessment. Describe the trend, strength, and shape of each association. (15 pts.)
Association between year and number of wildfires:
The trend appears to fluctuate. There is no clear increasing or decreasing trend over the years. The shape is scattered, with no real pattern. The strength of the association is moderate, as there is some variation in the number of wildfires across different years,
Association between year and total burned area:
The trend here also shows some fluctuation but with an overall increasing pattern. The strength of association is moderate to strong, as there is a general increase in the burned area over the years. The shape of the association is slightly positive, with the points generally moving upwards.
Association between year and burned area per fire:
Once again, the trend shows some fluctuations but for the most part, it is an increasing pattern. The strength of association is moderate to strong, as there is a general increase in the burned area per fire over the years. The shape of the association is slightly positive, with the points generally moving upwards.
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Question 3.
Using the provided data, calculate the correlation coefficient (r) and coefficient of determination (r
2
) for each association and determine the values in the below table. (15 pts.)
Variables
Correlation coefficient (r)
Coefficient of determination (r
2
)
Year and number of wildfires
0.123
0.015
Year and total burned area
0.204
0.042
Year and burned area per fire
0.582
0.339
Question 4.
Based on the visual assessments and correlation coefficient in questions 2 and 3, select which
one of the three associations strongest linear relationship. Mark one. (5 pts.)
A.
Association between year and number of wildfires B.
Association between year and burned area
C.
Association between year and burned area per fire
Question 5.
Using the provided data, determine the regression equation for the association you have selected in question 4. Note that the year is the independent variable. Write down the equation. (15 pts.)
Y= -1,858.67+0.931x
Question 6.
Interpret the slope of the regression equation you have reported in Question 5 in words. Note that reporting the value of the slope is not sufficient. You need to describe what the value implies. (10 pts.)
The slope implies there is a positive relationship between the year (x) and the burned area per fire (y). As x increases, y is expected to increase as well, with each unit increase in x corresponding to an increase of 0.931 in y.
Question 7.
Based on the coefficient of determination you calculated, what percentage of the variability in the dependent variable is explained by year? (10 pts.)
33.9 %
for the burned acres per fire
Question 8.
Based on your analysis from Questions 1 to 7, what would you report to your supervisor? Is there any trend in the number of wildfires, area burned, and/or area burned per wildfire between 2000 and
2019? Describe your conclusion in 50-100 words. (15 pts.) The trends for both the area burned and the area burned per fire shows some fluctuations but with an overall increasing pattern. The strength of association is moderate to strong, as there is a general increase in the burned area over the years. The shape of the association is slightly positive, with the points generally moving upwards.