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
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
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 26PFA
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.
- 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 |
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
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…](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
![Big Ideas Math A Bridge To Success Algebra 1: Stu…](https://www.bartleby.com/isbn_cover_images/9781680331141/9781680331141_smallCoverImage.jpg)
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![Glencoe Algebra 1, Student Edition, 9780079039897…](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
![Big Ideas Math A Bridge To Success Algebra 1: Stu…](https://www.bartleby.com/isbn_cover_images/9781680331141/9781680331141_smallCoverImage.jpg)
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![Algebra: Structure And Method, Book 1](https://www.bartleby.com/isbn_cover_images/9780395977224/9780395977224_smallCoverImage.gif)
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
![Elementary Geometry for College Students](https://www.bartleby.com/isbn_cover_images/9781285195698/9781285195698_smallCoverImage.gif)
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
![College Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652231/9781305652231_smallCoverImage.gif)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning