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To find the correlation coefficient \( r \) for this data, we can calculate it using the given pairs of values for distance (in miles) and time (in minutes). Here's how the values are organized:

- **Distance (mi):** 1.5, 2, 2.5, 3, 3.5, 4
- **Time (min):** 18, 23, 28, 34, 34, 40

Using these values, we can apply the formula for the correlation coefficient \( r \), or alternatively use a calculator or software tool that can compute it directly.

Here's a step-by-step outline:

1. **Calculate the means** of both the distance and time values.
2. **Determine the deviations** of each value from the mean.
3. **Compute the products** of the deviations for each pair.
4. **Calculate the sum** of these products.
5. **Use the formula for \( r \)** to finalize the calculation.

I’ll proceed with these calculations to give you the exact correlation coefficient.

Let me handle that for you.The correlation coefficient \( r \) for this data is approximately \( 0.984 \). This high positive value suggests a strong positive correlation between distance and time, indicating that as the distance increases, the time tends to increase as well.

Would you like further details on the calculation steps or more clarification?

Here are five related questions to expand your understanding:

1. What does a correlation coefficient close to 1 imply about the relationship between two variables?
2. How would the correlation coefficient change if the data showed an inverse relationship?
3. What is the significance of using a regression line in addition to the correlation coefficient?
4. How can we use this correlation to predict time for distances not included in the data?
5. How does correlation differ from causation?

**Tip:** A correlation coefficient close to 1 indicates a strong linear relationship, but it doesn't imply that one variable causes the other to change.

Use technology to find the regression line and correlation coefficient for the given data. What is the value of the correlation coefficient?

Learn how to calculate the correlation coefficient and regression line for a dataset involving distance and time. This guide provides a step-by-step solution using statistics and linear regression analysis, ideal for high school students studying data analysis and interpretation.

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