Question

a teacher tracked how long a student practiced their multiplication facts and how well they did on a timed quiz of 25 questions. the scatter plot shows the line of fit and the residuals for the data.

determine the strength and direction of the correlation of the data.

there is a strong, positive correlation between the variables
there is a weak, positive correlation between the variables

Explanation:

To determine the correlation:

1. Direction: The line of fit has a negative slope (as practice minutes increase, number of errors decreases), so direction is negative.
2. Strength: Residuals (vertical distances from points to line) are relatively small, and the points cluster closely around the line, indicating a strong correlation. Wait, but initial options had positive, which was wrong. Correct analysis: As x (practice) increases, y (errors) decreases → negative correlation. Residuals are small, so strong negative correlation. But the given options were wrong in direction. However, re - evaluating the graph: The line of fit is decreasing, so direction is negative. The points are close to the line, so strong. But the original options provided were about positive, which is incorrect. But if we go by the graph's trend (x up, y down) and tight clustering, the correct description is a strong negative correlation. But since the user's options were wrong, but to answer based on the graph:

• Direction: Negative (as practice time increases, number of errors decreases).
• Strength: Strong (points are close to the line of fit, residuals are small in magnitude).

Answer:

The correct description (not among the given wrong positive options) is: There is a strong, negative correlation between the variables.

(Note: The provided options in the original problem had incorrect direction (positive instead of negative). The correct analysis shows a strong negative correlation because as practice time (x) increases, number of errors (y) decreases, and the data points cluster closely around the line of fit (small residuals), indicating a strong relationship.)