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 50 inches. Is the result close to the actual weight of 417 pounds? Use a significance level of 0.05. Chest size (inches) Weight (pounds) 49 368 53 57 45 O 457 287 51 61 382 420 481 Click the icon to view the critical values of the Pearson correlation coefficient r. What is the regression equation? y =+ x (Round to one decimal place as needed.)
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 50 inches. Is the result close to the actual weight of 417 pounds? Use a significance level of 0.05. Chest size (inches) Weight (pounds) 49 368 53 57 45 O 457 287 51 61 382 420 481 Click the icon to view the critical values of the Pearson correlation coefficient r. What is the regression equation? y =+ x (Round to one decimal place as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
7- Hi Wonderful Bartleby Team (Thanks for all the help I do really aprecciate all you guys do) I need help with this exercise from stats.
This exercise has 3 parts, please provide an answer for all the parts. Thanks in advance
![**Chest Size and Weight Analysis of Bears**
The dataset provided examines the correlation between the chest size and weight of several bears. The task is to derive the regression equation, using chest size as the independent variable (x) and predict the weight for a given chest size. Specifically, the best predicted weight for a bear with a chest size of 50 inches is sought. The significance level for the analysis is set at 0.05.
**Data Table:**
- **Chest size (inches):** 49, 51, 53, 61, 57, 45
- **Weight (pounds):** 368, 382, 420, 481, 457, 287
To assist in the calculation, there is an option to view the critical values of Pearson's correlation coefficient, which assesses the strength and direction of the linear relationship between the variables.
**Objective:**
To establish the regression equation in the form:
\[ \hat{y} = a + bx \]
where \(\hat{y}\) is the predicted weight, \(a\) is the y-intercept, \(b\) is the slope of the line, and \(x\) is the chest size.
*Note: The equation needs to be rounded to one decimal place as necessary.*
This analysis will help determine how closely the predicted weight aligns with an actual weight of 417 pounds when the chest size is 50 inches.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd738ea4e-7dd9-4a93-94a4-9a76a5585029%2F80be6698-30a3-43d2-8c15-eea0684a6fc6%2Fv1aw0n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Chest Size and Weight Analysis of Bears**
The dataset provided examines the correlation between the chest size and weight of several bears. The task is to derive the regression equation, using chest size as the independent variable (x) and predict the weight for a given chest size. Specifically, the best predicted weight for a bear with a chest size of 50 inches is sought. The significance level for the analysis is set at 0.05.
**Data Table:**
- **Chest size (inches):** 49, 51, 53, 61, 57, 45
- **Weight (pounds):** 368, 382, 420, 481, 457, 287
To assist in the calculation, there is an option to view the critical values of Pearson's correlation coefficient, which assesses the strength and direction of the linear relationship between the variables.
**Objective:**
To establish the regression equation in the form:
\[ \hat{y} = a + bx \]
where \(\hat{y}\) is the predicted weight, \(a\) is the y-intercept, \(b\) is the slope of the line, and \(x\) is the chest size.
*Note: The equation needs to be rounded to one decimal place as necessary.*
This analysis will help determine how closely the predicted weight aligns with an actual weight of 417 pounds when the chest size is 50 inches.
![### Regression Equation Analysis
**Question: What is the regression equation?**
\[
\hat{y} = \text{(blank)} + \text{(blank)} x \quad \text{(Round to one decimal place as needed.)}
\]
**Question: What is the best predicted weight of a bear with a chest size of 50 inches?**
The best predicted weight for a bear with a chest size of 50 inches is \(\text{(blank)}\) pounds.
(Round to one decimal place as needed.)
**Question: Is the result close to the actual weight of 417 pounds?**
- **A.** This result is exactly the same as the actual weight of the bear.
- **B.** This result is not very close to the actual weight of the bear.
- **C.** This result is very close to the actual weight of the bear.
- **D.** This result is close to the actual weight of the bear.
### Critical Values of the Pearson Correlation Coefficient \(r\)
**Table Explanation:**
This table provides critical values of the Pearson correlation coefficient \(r\) for different sample sizes (\(n\)) and significance levels (\(\alpha = 0.05\) and \(\alpha = 0.01\)).
**Table Details:**
\[
\begin{array}{|c|c|c|}
\hline
n & \alpha = 0.05 & \alpha = 0.01 \\
\hline
4 & 0.950 & 0.990 \\
5 & 0.878 & 0.959 \\
6 & 0.811 & 0.917 \\
7 & 0.754 & 0.875 \\
8 & 0.707 & 0.834 \\
9 & 0.666 & 0.798 \\
10 & 0.632 & 0.765 \\
11 & 0.602 & 0.735 \\
12 & 0.576 & 0.708 \\
13 & 0.553 & 0.684 \\
14 & 0.532 & 0.661 \\
15 & 0.514 & 0.641 \\
16 & 0.497 & 0.623 \\
17 & 0.482 & 0.606 \\
18 &](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd738ea4e-7dd9-4a93-94a4-9a76a5585029%2F80be6698-30a3-43d2-8c15-eea0684a6fc6%2Fu4k7m19_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Regression Equation Analysis
**Question: What is the regression equation?**
\[
\hat{y} = \text{(blank)} + \text{(blank)} x \quad \text{(Round to one decimal place as needed.)}
\]
**Question: What is the best predicted weight of a bear with a chest size of 50 inches?**
The best predicted weight for a bear with a chest size of 50 inches is \(\text{(blank)}\) pounds.
(Round to one decimal place as needed.)
**Question: Is the result close to the actual weight of 417 pounds?**
- **A.** This result is exactly the same as the actual weight of the bear.
- **B.** This result is not very close to the actual weight of the bear.
- **C.** This result is very close to the actual weight of the bear.
- **D.** This result is close to the actual weight of the bear.
### Critical Values of the Pearson Correlation Coefficient \(r\)
**Table Explanation:**
This table provides critical values of the Pearson correlation coefficient \(r\) for different sample sizes (\(n\)) and significance levels (\(\alpha = 0.05\) and \(\alpha = 0.01\)).
**Table Details:**
\[
\begin{array}{|c|c|c|}
\hline
n & \alpha = 0.05 & \alpha = 0.01 \\
\hline
4 & 0.950 & 0.990 \\
5 & 0.878 & 0.959 \\
6 & 0.811 & 0.917 \\
7 & 0.754 & 0.875 \\
8 & 0.707 & 0.834 \\
9 & 0.666 & 0.798 \\
10 & 0.632 & 0.765 \\
11 & 0.602 & 0.735 \\
12 & 0.576 & 0.708 \\
13 & 0.553 & 0.684 \\
14 & 0.532 & 0.661 \\
15 & 0.514 & 0.641 \\
16 & 0.497 & 0.623 \\
17 & 0.482 & 0.606 \\
18 &
Expert Solution
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 2 steps with 4 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman