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Measuring the height of a California redwood tree is very difficult because these trees grow to heights over 300 feet. People familiar with these trees understand that the height of a California redwood tree 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 contains the height, diameter at breast height of a person, and bark thickness for a sample of 21 California redwood trees. a. State the multiple regression equation that predicts the height of a tree, based on the tree’s diameter at breast height and the thickness of the bark. b. Interpret the meaning of the slopes in this equation. c. Predict the height for a tree that has a breast height diameter of 25 inches and a bark thickness of 2 inches. d. Interpret the meaning of the coefficient of multiple determination in this problem. e. Perform a residual analysis on the results and determine whether the regression assumptions are valid. f. Determine whether there is a significant relationship between the height of redwood trees and the two independent variables (breast-height diameter and bark thickness) at the 0.05 level of significance.
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