The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (X) Vall predicted weight of a bear with a chest size of 39 inches. Is the result close to the actual weight of 136 pounds? Use a significance level of 0.05.
The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (X) Vall predicted weight of a bear with a chest size of 39 inches. Is the result close to the actual weight of 136 pounds? Use a significance level of 0.05.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![### Analyzing Bear Weight Using Chest Size
The following data presents the chest size and weight of several bears. The goal is to find the regression equation, with chest size as the independent variable (x), and use this to predict the weight of a bear with a chest size of 39 inches. We will then determine if this predicted weight is close to the actual weight of 136 pounds, using a significance level of 0.05.
#### Data:
- **Chest Size (inches):** 44, 41, 41, 55, 51, 42
- **Weight (pounds):** 213, 206, 176, 309, 300, 178
[Click the icon to view the critical values of the Pearson correlation coefficient \( r \).]
---
#### Question:
Is the predicted weight close to the actual weight of 136 pounds? (Round to one decimal place as needed.)
##### Options:
A. This result is close to the actual weight of the bear.
B. This result is not very close to the actual weight of the bear.
C. This result is exactly the same as the actual weight of the bear.
D. This result is very close to the actual weight of the bear.
---
### Understanding Regression Analysis:
To answer this question, you will need to:
1. Calculate the regression equation using the provided data.
2. Use the regression equation to predict the weight for a chest size of 39 inches.
3. Compare the predicted weight to the actual weight of 136 pounds to determine which option (A, B, C, or D) is correct.
### Additional Notes:
The accuracy of the prediction can be evaluated based on the significance level and the critical values of the Pearson correlation coefficient \( r \), which tests the strength of the linear relationship between the chest size and the weight.
This exercise helps in understanding the application of regression analysis in predicting outcomes based on correlated variables.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F381c88fc-86c8-43b0-81f2-55a4fcd1abcd%2F91b53e25-fc3b-43ae-b972-43b94c43e116%2F13b6ysf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analyzing Bear Weight Using Chest Size
The following data presents the chest size and weight of several bears. The goal is to find the regression equation, with chest size as the independent variable (x), and use this to predict the weight of a bear with a chest size of 39 inches. We will then determine if this predicted weight is close to the actual weight of 136 pounds, using a significance level of 0.05.
#### Data:
- **Chest Size (inches):** 44, 41, 41, 55, 51, 42
- **Weight (pounds):** 213, 206, 176, 309, 300, 178
[Click the icon to view the critical values of the Pearson correlation coefficient \( r \).]
---
#### Question:
Is the predicted weight close to the actual weight of 136 pounds? (Round to one decimal place as needed.)
##### Options:
A. This result is close to the actual weight of the bear.
B. This result is not very close to the actual weight of the bear.
C. This result is exactly the same as the actual weight of the bear.
D. This result is very close to the actual weight of the bear.
---
### Understanding Regression Analysis:
To answer this question, you will need to:
1. Calculate the regression equation using the provided data.
2. Use the regression equation to predict the weight for a chest size of 39 inches.
3. Compare the predicted weight to the actual weight of 136 pounds to determine which option (A, B, C, or D) is correct.
### Additional Notes:
The accuracy of the prediction can be evaluated based on the significance level and the critical values of the Pearson correlation coefficient \( r \), which tests the strength of the linear relationship between the chest size and the weight.
This exercise helps in understanding the application of regression analysis in predicting outcomes based on correlated variables.
![The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best-predicted weight of a bear with a chest size of 39 inches. Is the result close to the actual weight of 136 pounds? Use a significance level of 0.05.
| Chest size (inches) | 44 | 41 | 41 | 55 | 51 | 42 |
|---------------------|----|----|----|----|----|----|
| Weight (pounds) | 213 | 206 | 176 | 309 | 300 | 178 |
Click the icon to view the critical values of the Pearson correlation coefficient \( r \).
---
What is the regression equation?
\[
\hat{y} = [ \, ] + [ \, ]x \quad (\text{Round to one decimal place as needed.})
\]
What is the best-predicted weight of a bear with a chest size of 39 inches?
The best-predicted weight for a bear with a chest size of 39 inches is \([ \, ]\) pounds. (Round to one decimal place as needed.)
Is the result close to the actual weight of 136 pounds?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F381c88fc-86c8-43b0-81f2-55a4fcd1abcd%2F91b53e25-fc3b-43ae-b972-43b94c43e116%2Fh3gczu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best-predicted weight of a bear with a chest size of 39 inches. Is the result close to the actual weight of 136 pounds? Use a significance level of 0.05.
| Chest size (inches) | 44 | 41 | 41 | 55 | 51 | 42 |
|---------------------|----|----|----|----|----|----|
| Weight (pounds) | 213 | 206 | 176 | 309 | 300 | 178 |
Click the icon to view the critical values of the Pearson correlation coefficient \( r \).
---
What is the regression equation?
\[
\hat{y} = [ \, ] + [ \, ]x \quad (\text{Round to one decimal place as needed.})
\]
What is the best-predicted weight of a bear with a chest size of 39 inches?
The best-predicted weight for a bear with a chest size of 39 inches is \([ \, ]\) pounds. (Round to one decimal place as needed.)
Is the result close to the actual weight of 136 pounds?
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