what is the best-predicted weight for a bear with 43 inches, and What is the regression equation? ### Regression Analysis of Bear Chest Size and WeightFor the given data, we aim to determine the relationship between the chest size and weight of bears by finding the regression equation. Here, the chest size (in inches) is treated as the independent variable (x), and the weight (in pounds) is the dependent variable (y).#### Given DataA table is provided showing the chest size and weight of several bears as follows:| Chest Size (inches) | 50 | 54 | 44 | 54 | 40 | 36 ||---------------------|----|----|----|----|----|----|| Weight (pounds) | 279 | 339 | 219 | 292 | 201 | 116 |We seek the regression equation in the form:\[ \hat{y} = b_0 + b_1 x \]where:- $\hat{y}$ is the predicted weight,- $b_0$ is the y-intercept,- $b_1$ is the slope of the regression line,- $x$ is the chest size.#### Questions to Address1. **Find the Regression Equation:** Determine the values of $b_0$ and $b_1$ to complete the regression equation and round to one decimal place.2. **Predict Weight for a Given Chest Size:** Using the regression equation, predict the weight for a bear with a chest size of 43 inches.3. **Comparison with Actual Weight:** Assess how close the predicted weight is to the actual weight of 177 pounds.4. **Significance Level:** Use a significance level of 0.05 to determine if the prediction is statistically significant.The results and further interpretations will guide understanding the correlation between the chest size and the weight of bears, aiding in wildlife management and research efforts.For instructional purposes, we emphasize on rounding off the regression equation coefficients to one decimal place and explaining the regression line's fitting process.### Final NotesDetailed calculations are necessary to derive the precise coefficients of the regression equation and the subsequent prediction steps. This foundation can be expanded for deeper statistical analysis and hypothesis testing based on the specified significance level.

The variable x represents the chest size and y represents the weight.

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what is the best-predicted weight for a bear with 43 inches, and What is the regression equation?

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what is the best-predicted weight for a bear with 43 inches, and What is the regression equation?

### Regression Analysis of Bear Chest Size and Weight

For the given data, we aim to determine the relationship between the chest size and weight of bears by finding the regression equation. Here, the chest size (in inches) is treated as the independent variable (x), and the weight (in pounds) is the dependent variable (y).

#### Given Data
A table is provided showing the chest size and weight of several bears as follows:

| Chest Size (inches) | 50 | 54 | 44 | 54 | 40 | 36 |
|---------------------|----|----|----|----|----|----|
| Weight (pounds) | 279 | 339 | 219 | 292 | 201 | 116 |

We seek the regression equation in the form:
\[ \hat{y} = b_0 + b_1 x \]
where:
- $\hat{y}$ is the predicted weight,
- $b_0$ is the y-intercept,
- $b_1$ is the slope of the regression line,
- $x$ is the chest size.

#### Questions to Address
1. **Find the Regression Equation:** Determine the values of $b_0$ and $b_1$ to complete the regression equation and round to one decimal place.
2. **Predict Weight for a Given Chest Size:** Using the regression equation, predict the weight for a bear with a chest size of 43 inches.
3. **Comparison with Actual Weight:** Assess how close the predicted weight is to the actual weight of 177 pounds.
4. **Significance Level:** Use a significance level of 0.05 to determine if the prediction is statistically significant.

The results and further interpretations will guide understanding the correlation between the chest size and the weight of bears, aiding in wildlife management and research efforts.

For instructional purposes, we emphasize on rounding off the regression equation coefficients to one decimal place and explaining the regression line's fitting process.

### Final Notes
Detailed calculations are necessary to derive the precise coefficients of the regression equation and the subsequent prediction steps. This foundation can be expanded for deeper statistical analysis and hypothesis testing based on the specified significance level.

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