Questions: 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 close to the actual weight of 565 pounds? Use a significance level of 0.05. Chest size (inches): 44, 59, 55, 59, 57, 44 Weight (pounds): 403, 645, 563, 587, 548, 406 What is the regression equation? ŷ = □ □ x (Round to one decimal place as needed.)

Solution Steps

To find the regression equation, we need to perform a linear regression analysis with chest size as the independent variable and weight as the dependent variable. This involves calculating the slope and intercept of the best-fit line using the least squares method. Once we have the regression equation, we can use it to predict the weight of a bear with a chest size of 53 inches. Finally, we compare the predicted weight to the actual weight of 565 pounds to see if they are close.

To find the regression equation, we perform a linear regression analysis using the given data. The chest sizes are the independent variable \( x \), and the weights are the dependent variable \( y \). The regression equation is of the form:

\[ \hat{y} = b_0 + b_1 x \]

where \( b_0 \) is the intercept and \( b_1 \) is the slope. From the calculations, we have:

• Intercept (\( b_0 \)): 133.0
• Slope (\( b_1 \)): 7.4

Thus, the regression equation is:

\[ \hat{y} = 133.0 + 7.4x \]

Using the regression equation, we predict the weight of a bear with a chest size of 53 inches:

\[ \hat{y} = 133.0 + 7.4 \times 53 \]

Calculating this gives:

\[ \hat{y} = 133.0 + 392.2 = 525.2 \]

The predicted weight is 525.2 pounds. We compare this to the actual weight of 565 pounds to determine how close the prediction is.

Final Answer