The Pearson correlation coefficient ($r$) of $-0.776$ between miles per gallon (mpg) and horsepower (hp) indicates a strong negative linear relationship between the two variables. This means that, generally, as horsepower increases, the miles per gallon decreases, and vice versa.

Here's a breakdown of what this value implies:

1. Strength of Relationship: Since $|r| = 0.776$, which is close to 1, the correlation is strong. Typically, values between 0.7 and 1 indicate a strong linear relationship.

2. Direction of Relationship: The negative sign suggests an inverse relationship. Thus, higher horsepower is associated with lower fuel efficiency (mpg).

3. Interpretation in Context: In practical terms, cars with higher horsepower engines tend to be less fuel-efficient, while cars with lower horsepower are typically more fuel-efficient.

4. Linearity: This coefficient measures the linear association, so it tells us that as one variable changes, the other changes in a predictable way.

5. Limits of Interpretation: Correlation does not imply causation. This relationship doesn't mean horsepower causes mpg to decrease directly, but rather that they tend to vary together.

Would you like a deeper analysis or help with a related question?

Here are five related questions that build on this concept:

1. What is the significance of a correlation value close to 1 or -1?
2. How is the Pearson correlation coefficient calculated?
3. What are other methods to measure relationships if the data is non-linear?
4. Can correlation tell us the causation between two variables? Why or why not?
5. How would the correlation between mpg and weight compare to that of mpg and horsepower?

Tip: When analyzing correlations, always visualize your data (e.g., with a scatter plot) to better understand the relationship’s nature and check for any non-linear trends that might affect interpretation.