The following table gives data relating a car's fuel efficiency in miles per gallon to its weight in pounds.

Weight w (pounds)	2100	2200	2400	2500	2800	3000	3200
Fuel Efficiency E (mpg)	37	34	29	27	26	25	23
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Using the black thread method, a model E(w) = –0.014(w – 2250) + 34 was obtained. Find the average error for this model. Only enter the number, in mpg, rounded to two decimal places.

To find the average error for the model \( E(w) = -0.014(w - 2250) + 34 \), we need to compute the estimated fuel efficiency \( E(w) \) for each given weight using the model, compare it to the actual fuel efficiency values, and then calculate the average of the absolute errors.

### Given dataTo find the average error for the model \( E(w) = -0.014(w - 2250) + 34 \), we need to compute the estimated fuel efficiency \( E(w) \) for each given weight using the model, compare it to the actual fuel efficiency values, and then calculate the average of the absolute errors.

### Given 
Weights (\( w \)): 2100, 2200, 2400, 2500, 2800, 3000, 3200  
Actual fuel efficiency values (\( E_{\text{actual}} \)): 37, 34, 29, 27, 26, 25, 23  

The model is:
\[
E(w) = -0.014(w - 2250) + 34
\]

### Steps to solve:
1. Compute the predicted fuel efficiency \( E(w) \) using the model for each weight.
2. Find the absolute error for each pair (actual and predicted).
3. Compute the average of these absolute errors.

Let me calculate that.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, you can also input the data manually into a calculator to find the average error, or I can guide you through it.

Would you like to proceed manually or ask about something else?

Here are some related questions you might find useful:

1. How do you interpret a fuel efficiency model in terms of real-life applications?
2. What are other methods to measure the average error of a model?
3. Can you explain the importance of residuals in model prediction?
4. How would you adjust this model if the weight range was different?
5. How does fuel efficiency typically vary with vehicle weight?

**Tip**: Always check residuals to understand how well your model fits the actual data points.

Using the black thread method, a model E(w) = –0.014(w – 2250) + 34 was obtained. Find the average error for this model. Only enter the number, in mpg, rounded to two decimal places.

Learn how to calculate the average error for a linear model predicting fuel efficiency based on vehicle weight. The problem involves analyzing the model E(w) = –0.014(w – 2250) + 34, comparing it with actual data points, and calculating the average error. Suitable for high school students in Grades 10-12.

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