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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)

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)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Do not solve 3. e part ii)
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 3.4 1.8 4.8 2.4 8.6 1.2 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. of 66
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 3.4 1.8 4.8 2.4 8.6 1.2 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. of 66
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