Measuring the height of a California redwood tree is very difficult because these trees grow to heights of 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. The data in the table represent the height (in feet) and diameter (in inches) at the breast height of a person for a sample of 21 California redwood trees. Interpret the meaning of the coefficient of determination in this problem. Perform a residual analysis on the results and determine the adequacy of the model. Determine whether there is a significant relationship between the height of redwood trees and the breast height diameter at the 0.05 level of significance. Height Diameter at breast height Bark thickness 122.0 20 1.1 193.5 36 2.8 166.5 18 2.0 82.0 10 1.2 133.5 21 2.0 156.0 29 1.4 172.5 51 1.8 81.0 11 1.1 148.0 26 2.5 113.0 12 1.5 84.0 13 1.4 164.0 40 2.3 203.3 52 2.0 174.0 30 2.5 159.0 22 3.0 205.0 42 2.6 223.5 45 4.3 195.0 54 4.0 232.5 39 2.2 190.5 36 3.5 100.0 8 1.4

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
Problem 2CYU
icon
Related questions
Topic Video
Question

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

  1. Interpret the meaning of the coefficient of determination in this problem.
  2. Perform a residual analysis on the results and determine the adequacy of the model.
  3. Determine whether there is a significant relationship between the height of redwood trees and the breast height diameter at the 0.05 level of significance.
Height Diameter at breast height Bark thickness
122.0 20 1.1
193.5 36 2.8
166.5 18 2.0
82.0 10 1.2
133.5 21 2.0
156.0 29 1.4
172.5 51 1.8
81.0 11 1.1
148.0 26 2.5
113.0 12 1.5
84.0 13 1.4
164.0 40 2.3
203.3 52 2.0
174.0 30 2.5
159.0 22 3.0
205.0 42 2.6
223.5 45 4.3
195.0 54 4.0
232.5 39 2.2
190.5 36 3.5
100.0 8 1.4
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Knowledge Booster
Research Design Formulation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL