Chapter 10

2. Measuring the height of a California redwood tree is a very difficult undertaking because these trees grow to heights of more than 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 t the breast height of a person. The following data represent the height (in feet) and diameter at breast height of a person for a sample of 21 California redwood trees.

chapter 11

2. Measuring the height of a California redwood tree is a very difficult undertaking because these trees grow to heights of moe than 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 and the thickness of the bark of the tree. The following data represent the height (in feet), diameter at breast height of a person, and bark thickness of a sample of 21 California redwood trees:

Seryak 1 Elizabeth Seryak BUSM 303 Professor Blakely End of Chapter Problems Chapter 10 2. Measuring the height of a California redwood tree is a very difficult undertaking because these trees grow to heights of more than 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 t the breast height of a person. The following data represent the height (in feet) and diameter at breast height of a person for a sample of 21 California redwood trees. Height Diameter at breast height Height Diamater at breast height 122.0 20 164.0 40 193.5 36 203.3 52 166.5 18 174.0 30 82.0 10 159.0 22 133.5 21 205.0 42 156.0 29 223.5 45 172.5 51 195.0 54 81.0 11 232.5 39 148.0 26 190.5 36 113.0 12 100.0 8 84.0 13 a. b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1. State the regression equation that predicts the height of a tree based on the tree's diameter at breast height of a person. c. Interpret the meaning of the slop in the equation. d. Predict the height for a tree that has a breast diameter of 25 inches. e. Interpret the meaning of the coefficient of determination in this problem. f. Perform a residual analysis on the results and determine the adequacy of the model. Seryak 2 g. Determine whether a significant relationship exists between the height of redwood trees and the breast diameter at the 0.05 level of significance. h. Construct a 95% confidence interval estimate of the population slop between the height of the redwood trees and breast diameter. Chapter 11 2. Measuring the height of a California redwood tree is a very difficult undertaking because these trees grow to heights of moe than 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 and the thickness of the bark of the tree. The following data represent the height (in feet), diameter at breast height of a person, and bark thickness of a sample of 21 California redwood trees: Height Diameter at Breast Height Bark Thick ness Height Diameter at Breast Height Bark Thick ness 122.0 20 1.1 164.0 40 2.3 193.5 36 2.8 203.3 52 2.0 166.5 18 2.0 174.0 30 2.5 82.0 10 1.2 159.0 22 3.0 133.5 21 2.0 205.0 42 2.6 156.0 29 1.4 223.5 45 4.3 172.5 51 1.8 195.0 54 4.0 81.0 11 1.1 232.5 39 2.2 148.0 26 2.5 190.5 36 3.5 113.0 12 1.5 100.0 84.0 13 1.4 8 1,4 a. a. Start 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. i. Interpret the meaning of the slopes in this equation. j. Predict the height for a tree that has a breast diameter of 25 inches and a bark thickness of 2 inches. k. Interpret the meaning of the coefficient of multiple determination in this problem. l. Perform a residual analysis on the results and determine the adequacy of the model. Seryak 3 m. Determine whether a significant relationship exists between the height of redwood trees and the two independent variables (breast diameter and the bark thickness) at the 0.05 level of significance. n. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model: indicate the independent variables to include in this model. o. Construct a 95% confidence interval estimate of the population slope between the height of the redwood trees and breast diameter and between the height of redwood trees and bark thickness