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The question asks about the relationship between the linear correlation coefficient \( r \) and the slope \( b_1 \) of a regression line.

The correct answer is **C. The value of \( r \) will always have the same sign as the value of \( b_1 \).**

### Explanation:
- The linear correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables.
- The slope \( b_1 \) of a regression line describes how much the dependent variable changes with a one-unit change in the independent variable.
- If \( r \) is positive, the slope \( b_1 \) is also positive, meaning there is a positive linear relationship. If \( r \) is negative, \( b_1 \) is negative, indicating a negative linear relationship.
- Therefore, \( r \) and \( b_1 \) always have the same sign.

Would you like further details on this topic or any specific part of the explanation?

### Related Questions:
1. How is the correlation coefficient \( r \) calculated?
2. What does a value of \( r = 0 \) indicate in terms of slope \( b_1 \)?
3. Can the correlation coefficient \( r \) be greater than 1 or less than -1?
4. What happens to the slope \( b_1 \) if the data points show no correlation?
5. How do outliers affect the correlation coefficient \( r \) and the slope \( b_1 \)?

### Tip:
Always remember that the correlation coefficient \( r \) not only tells you about the direction (positive or negative) of the relationship but also its strength (how closely the points fit the line).

What is the relationship between the linear correlation coefficient r and the slope b1 of a regression line?

Understand the relationship between the linear correlation coefficient r and the slope b1 of a regression line. This problem covers key concepts in statistics, including the correlation coefficient and regression analysis. Suitable for students in Grades 10-12.

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