https://file.aiquickdraw.com/mathbot/file/17264411748487rrremav.jpg

Here are the results based on the data provided:

1. **Correlation coefficient**: \(-0.8968\)
2. **Regression equation**: \( y = -0.116x + 57.085 \) (rounded to three decimal places)
3. **Predicted mpg for a car with 236 horsepower**: \( 29.80 \) (rounded to two decimal places)

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Here are 5 related questions to deepen understanding:
1. How does a negative correlation coefficient affect the relationship between horsepower and mpg?
2. What does the slope of the regression line represent in the context of this data?
3. How can you use the regression equation to predict mpg for other horsepower values?
4. What is the significance of rounding values in statistical analysis?
5. Why is it important to check the p-value when interpreting linear regression results?

**Tip**: The closer the correlation coefficient is to \(-1\) or \(1\), the stronger the linear relationship between the two variables.

The data below was collected from manufacturer advertisements of their vehicles horsepower (x) and highway gas mileage (mpg=y). Use this data to answer the following questions:
1. What is the correlation coefficient? Round to four decimal places.
2. Write the regression equation y = ax + b below. Round values to 3 decimals.
3. Using the data shown above, predict the highway gas mileage (mpg) for a car that has a horsepower of 236. (Round to 2 decimals).

Solve a linear regression problem to find the correlation coefficient, regression equation, and predict gas mileage for a car with 236 horsepower. The problem explores the relationship between vehicle horsepower and highway gas mileage using data analysis techniques. Suitable for Grades 10-12.

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