https://file.aiquickdraw.com/mathbot/file/17267142811241fdpdmpe.jpg

The regression model provided in the image is:

\[
\hat{b} = 0.007 + 0.026a
\]

Where:
- \(\hat{b}\) is the predicted number of stoachlings.
- \(a\) is the territorial area in square meters (in this case, \(a = 63 \, \text{m}^2\)).

Substitute \(a = 63\) into the equation:

\[
\hat{b} = 0.007 + 0.026 \times 63
\]

Let me calculate that for you.The predicted number of stoachlings for a female stoach with 63 m² of territory is approximately 1.645.

Would you like more details or have any questions?

Here are some related questions to deepen your understanding:
1. How would the prediction change if the territorial area doubled?
2. What does the coefficient 0.026 in the model represent in terms of the territorial area?
3. How can you assess if this linear model is a good fit for the data?
4. If the area were 0, what would the model predict for the number of stoachlings?
5. What other factors might influence the number of stoachlings besides territory?

**Tip**: Understanding the units of each variable in a regression model helps clarify how the independent variable influences the dependent one.

A regression model has been fit to predict the number b of baby stoaches that a female stoach will give birth to each spring, on the basis of territorial area a. The regression model is b̂ = 0.007 + 0.026a. Assume a female stoach has 63 m² of territory, and that it is valid to make a prediction. Predict the expected number of stoachlings.

Learn how to predict the number of stoachlings a female stoach will give birth to, using the linear regression model b̂ = 0.007 + 0.026a. In this example, with 63 m² of territory, the expected number of stoachlings is approximately 1.645. Ideal for students in grades 9-12 interested in applying algebra and regression models.

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