Measuring the height of a Yellow Meranti is very difficult because these trees grow to heights over 300 feet. In 2016, a group of Yellow Meranti in Sabah’s Danum Valley was announced as the tallest tropical trees in the world. People familiar with these trees understand that the height of a Yellow Meranti is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person (in inches) and the thickness of the bark of the tree (in inches). The file YellowMeranti contains the height, diameter at breast height of a person, and bark thickness for a sample of 40 Yellow Meranti trees. a. Based on the ordinary least square estimate, calculate the estimated slope (?1) and the intercept (?0) when: i. the diameter of the tree at the breast height of a person (in inches) is the sole explanatory or independent variable. ii. the thickness of the bark of the tree (in inches) is the sole explanatory or independent variable. b. State the multiple linear regression model where the height of Yellow Meranti is treated as the dependent variable while the diameter and bark thickness of the tree are the explanatory variables. c. By referring to the p-value, determine whether the diameter and bark thickness of Yellow Meranti are significant in explaining its heights. d. Predict the height of the Yellow Meranti when the diameter of the tree at breast height of a person is 20 inches while the bark thickness is 4.4 inches.
Measuring the height of a Yellow Meranti is very difficult because these trees grow to heights over 300 feet. In 2016, a group of Yellow Meranti in Sabah’s Danum Valley was announced as the tallest tropical trees in the world. People familiar with these trees understand that the height of a Yellow Meranti is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person (in inches) and the thickness of the bark of the tree (in inches). The file YellowMeranti contains the height, diameter at breast height of a person, and bark thickness for a sample of 40 Yellow Meranti trees.
a. Based on the ordinary least square estimate, calculate the estimated slope (?1) and the intercept (?0) when:
- i. the diameter of the tree at the breast height of a person (in inches) is the sole explanatory or independent variable.
ii. the thickness of the bark of the tree (in inches) is the sole explanatory or independent variable.
b. State the multiple linear regression model where the height of Yellow Meranti is treated as the dependent variable while the diameter and bark thickness of the tree are the explanatory variables.
c. By referring to the p-value, determine whether the diameter and bark thickness of Yellow Meranti are significant in explaining its heights.
d. Predict the height of the Yellow Meranti when the diameter of the tree at breast height of a person is 20 inches while the bark thickness is 4.4 inches.
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