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).