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 53 inches. Is the result dose to the actual weight of 475 pounds? Use a significance level of 0.05. 57 Chest size (inches) Weight (pounds) 44 59 55 59 44 O 403 645 563 587 548 406 Click the icon to view the critical values of the Pearson correlation coefficient r. What is the regression equation? < X Critical values of the pearson cerrelation coefficient r y=+x (Round to one decimal place as needed) What is the best predicted weight of a bear with a chest size of 53 inches? Critical Values of the Pearson Correlation Coefficient r NOTE To test H, p=0 a-0.01 0.990 0 959 0917 0.875 0.834 a-0.05 The best predicted weight for a bear with a chest size of 53 inches is pounds (Round to one decimal place as needed.) 0.950 0878 0.811 0.754 0.707 0 666 0 632 against H, p+0, reject H, jf the absolute value of ris greater than the critical value in the table 4. Is the result close to the actual weight of 475 pounds? 6. 8. O A. This result is exactly the same as the actual weight of the bear 0.798 0.765 0.735 0.708 0.684 0.661 0641 0623 0 606 0.590 O B. This result is not very close to the actual weight of the bear. 10 0.602 0.576 0 553 0532 11 OC. This result is close to the actual weight of the bear. 12 O D. This result is very close to the actual weight of the bear. 13 14 15 0.514 0.497 16 0.482 0.468 0456 0444 0.396 17 18 19 0575 0561 0 505 0 463 0430 20 25 30 0.361 0.335 0312 0 294 0279 0.254 0236 0.220 0 207 0 196 a-0.05 35 0.402 0378 0361 0330 0 305 0.286 40 45 50 60 70 80 0 269 0256 a-0.01 90 100

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### Educational Exercise: Regression Analysis of Bear Data

#### Problem Statement
The data below shows the chest size and weight of several bears. 

- **Objective:** 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 53 inches. Determine if the result is close to the actual weight of 475 pounds. Use a significance level of 0.05.

#### Data
- **Chest Size (inches):** 44, 59, 55, 59, 57, 44
- **Weight (pounds):** 403, 645, 563, 587, 548, 406

#### Tasks
1. **What is the regression equation?**
   \[
   \hat{y} = b_0 + b_1x \quad (\text{Round to one decimal place as needed.})
   \]

2. **What is the best predicted weight of a bear with a chest size of 53 inches?**
   \[
   \text{The best predicted weight is } \underline{\hspace{2cm}} \text{ pounds. (Round to one decimal place as needed.)}
   \]

3. **Is the result close to the actual weight of 475 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 close to the actual weight of the bear.
   - **D.** This result is very close to the actual weight of the bear.

#### Critical Values of the Pearson Correlation Coefficient \( r \)

The table provides critical values for different sample sizes \( n \) at significance levels \( \alpha = 0.05 \) and \( \alpha = 0.01 \). This is used to test the null hypothesis \( H_0: \rho = 0 \) against \( H_1: \rho \neq 0 \). You reject \( H_0 \) if the absolute value of \( r \) is greater than the critical value from the table.

**Table Columns:**
- **n:** Sample size
- **Critical Values (\( \alpha = 0.05 \)):** 0.950, 0.878
Transcribed Image Text:### Educational Exercise: Regression Analysis of Bear Data #### Problem Statement The data below shows the chest size and weight of several bears. - **Objective:** 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 53 inches. Determine if the result is close to the actual weight of 475 pounds. Use a significance level of 0.05. #### Data - **Chest Size (inches):** 44, 59, 55, 59, 57, 44 - **Weight (pounds):** 403, 645, 563, 587, 548, 406 #### Tasks 1. **What is the regression equation?** \[ \hat{y} = b_0 + b_1x \quad (\text{Round to one decimal place as needed.}) \] 2. **What is the best predicted weight of a bear with a chest size of 53 inches?** \[ \text{The best predicted weight is } \underline{\hspace{2cm}} \text{ pounds. (Round to one decimal place as needed.)} \] 3. **Is the result close to the actual weight of 475 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 close to the actual weight of the bear. - **D.** This result is very close to the actual weight of the bear. #### Critical Values of the Pearson Correlation Coefficient \( r \) The table provides critical values for different sample sizes \( n \) at significance levels \( \alpha = 0.05 \) and \( \alpha = 0.01 \). This is used to test the null hypothesis \( H_0: \rho = 0 \) against \( H_1: \rho \neq 0 \). You reject \( H_0 \) if the absolute value of \( r \) is greater than the critical value from the table. **Table Columns:** - **n:** Sample size - **Critical Values (\( \alpha = 0.05 \)):** 0.950, 0.878
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