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3. The heights of a stand of pine trees were measured along with the area under the cone formed by their branches. Height (m) Area (m²) 2.0 5.9 1.5 3.4 1.8 4.8 2.4 8.6 2.2 7.3 1.2 2.1 1.8 4.9 3.1 14.4 a) Create a scatter plot of these data. b) Determine the correlation coefficient and the equation of the line of best fit. c) Use a power regression to calculate a coefficient of determination and an equation for a curve of best fit. d) Which model do you think is more accurate? Explain why. e) Use the more accurate model to predict i) the area under a tree whose height is 2.7 m ii) the height of a tree whose area is 30 m² f) Suggest a reason why the height and circumference of a tree might be related in the way that the model in part d) suggests. 5

3. The heights of a stand of pine trees were measured along with the area under the cone formed by their branches. Height (m) Area (m²) 2.0 5.9 1.5 3.4 1.8 4.8 2.4 8.6 2.2 7.3 1.2 2.1 1.8 4.9 3.1 14.4 a) Create a scatter plot of these data. b) Determine the correlation coefficient and the equation of the line of best fit. c) Use a power regression to calculate a coefficient of determination and an equation for a curve of best fit. d) Which model do you think is more accurate? Explain why. e) Use the more accurate model to predict i) the area under a tree whose height is 2.7 m ii) the height of a tree whose area is 30 m² f) Suggest a reason why the height and circumference of a tree might be related in the way that the model in part d) suggests. 5

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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Solve d, e, and f
3. The heights of a stand of pine trees were measured along with the area under the cone formed by their branches. Height (m) Area (m²) 2.0 5.9 1.5 3.4 1.8 4.8 2.4 8.6 2.2 7.3 1.2 2.1 1.8 4.9 3.1 14.4 a) Create a scatter plot of these data. b) Determine the correlation coefficient and the equation of the line of best fit. c) Use a power regression to calculate a coefficient of determination and an equation for a curve of best fit. d) Which model do you think is more accurate? Explain why. e) Use the more accurate model to predict i) the area under a tree whose height is 2.7 m ii) the height of a tree whose area is 30 m² f). Suggest a reason why the height and circumference of a tree might be related in the way that the model in part d) suggests. 5.
Transcribed Image Text:3. The heights of a stand of pine trees were measured along with the area under the cone formed by their branches. Height (m) Area (m²) 2.0 5.9 1.5 3.4 1.8 4.8 2.4 8.6 2.2 7.3 1.2 2.1 1.8 4.9 3.1 14.4 a) Create a scatter plot of these data. b) Determine the correlation coefficient and the equation of the line of best fit. c) Use a power regression to calculate a coefficient of determination and an equation for a curve of best fit. d) Which model do you think is more accurate? Explain why. e) Use the more accurate model to predict i) the area under a tree whose height is 2.7 m ii) the height of a tree whose area is 30 m² f). Suggest a reason why the height and circumference of a tree might be related in the way that the model in part d) suggests. 5.
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