MATH 201 Statistics for Environmental Professionals ● Worksheet 5 Name Avada Suppose that 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: Has the number of wildfires per year increased? Has the total burned area (in acre) per year increased? Has the burned area (in acre) 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. Question 1. Using Excel, create three scatter plots which 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 year should be on the x-axis. Attach the scatterplot to this report. Refer to the textbook 12.2. (15 pts.) Question 2. Using the scatter plots created in Question 1, perform a visual assessments. Describe the trend, strength, and shape of each association. Refer to the textbook 12.2. (15 pts.) Association between year and number of wildfires: We see that there exists a low degree negative association between year and number of wildfires. Year increases, number of wildfire decreases. Association between year and total burned area: Trend: There is no relation between total burned area and the year. Strength: The coefficient of determination R2=0.0139, which shows that it is very weak. Shape: Judging by the shape there is not a relationship between the year and the total burned area. Association between year and burned area per fire: There exists low degree positive association between year and burned area per fire. Trend: The area of the acres burned per fire is increasing as the years pass. Strength: The coefficient of determination R2=0.1379, which shows that it is weak. Shape: There is an almost straight line with a positive slope showing a very weak positive linear relation. Question 3. Using the provided Excel sheet, calculate the correlation coefficient (r) and coefficient of determination (r2) for each association and determine the values in the below table. Refer to the textbook 12.3. (15 pts.) Variables Correlation coefficient (r) Coefficient of determination (r2) Year and number of wildfires -0.4929 0.2429 Year and total burned area 0.1181 0.0139 Year and burned area per fire 0/3714 0.1379 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. Clearly mark one. (5 pts.) Association between year and number of wildfires Association between year and burned area Association between year and burned area per fire Question 5. Using the provided Excel sheet, determine the regression equation for the association you have selected in question 4. Note that year is the independent variable. Write down the equation. Refer to the textbook 12.3. (15 pts.) Regression equation is y=5.2808*x-10466 Burned area per fire = 5.2808*year-10466 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. Refer to the textbook 12.3. (10 pts.) Based on the given equation, my interpretation is that the burned area per fire changes by 5.2808 per year. Question 7. Based on the coefficient of determination you calculated in Question 3, what percentage in the variability in the dependent variable is explained by year?
MATH 201 Statistics for Environmental Professionals ● Worksheet 5
Name Avada
Suppose that 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:
- Has the number of wildfires per year increased?
- Has the total burned area (in acre) per year increased?
- Has the burned area (in acre) 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.
Question 1. Using Excel, create three
Question 2. Using the scatter plots created in Question 1, perform a visual assessments. Describe the trend, strength, and shape of each association. Refer to the textbook 12.2. (15 pts.)
Association between year and number of wildfires:
We see that there exists a low degree negative association between year and number of wildfires. Year increases, number of wildfire decreases.
Association between year and total burned area:
Trend: There is no relation between total burned area and the year.
Strength: The coefficient of determination R2=0.0139, which shows that it is very weak.
Shape: Judging by the shape there is not a relationship between the year and the total burned area.
Association between year and burned area per fire:
There exists low degree positive association between year and burned area per fire.
Trend: The area of the acres burned per fire is increasing as the years pass.
Strength: The coefficient of determination R2=0.1379, which shows that it is weak.
Shape: There is an almost straight line with a positive slope showing a very weak positive linear relation.
Question 3. Using the provided Excel sheet, calculate the
|
Variables |
Correlation coefficient (r) |
Coefficient of determination (r2) |
|
Year and number of wildfires |
-0.4929 |
0.2429 |
|
Year and total burned area |
0.1181 |
0.0139 |
|
Year and burned area per fire |
0/3714 |
0.1379 |
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. Clearly mark one. (5 pts.)
- Association between year and number of wildfires
- Association between year and burned area
- Association between year and burned area per fire
Question 5. Using the provided Excel sheet, determine the regression equation for the association you have selected in question 4. Note that year is the independent variable. Write down the equation. Refer to the textbook 12.3. (15 pts.)
Regression equation is y=5.2808*x-10466
Burned area per fire = 5.2808*year-10466
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. Refer to the textbook 12.3. (10 pts.)
Based on the given equation, my interpretation is that the burned area per fire changes by 5.2808 per year.
Question 7. Based on the coefficient of determination you calculated in Question 3, what percentage in the variability in the dependent variable is explained by year?
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