Question

andy is trying to determine the correlation between the number of math homework assignments he completes and his test score. which is the best estimate for the correlation coefficient of the data? a ( r = 1.5 ) b ( r = 0.5 ) c ( r = 0.96 ) d ( r = -0.90 )

Explanation:

Step1: Recall correlation coefficient range

The correlation coefficient \( r \) ranges between \(-1\) and \( 1 \), so option A (\( r = 1.5 \)) is invalid as it's outside this range.

Step2: Analyze trend from scatter plot

The scatter plot shows that as the number of assignments (x - variable) increases, the test score (y - variable) also increases, indicating a positive correlation. So \( r \) should be positive, eliminating option D (\( r=-0.90 \)) which is negative.

Step3: Assess strength of correlation

The points in the scatter plot lie close to a straight line, suggesting a strong positive correlation. A correlation coefficient of \( 0.96 \) (option C) indicates a strong positive correlation, while \( 0.5 \) (option B) indicates a moderate positive correlation. The points' close alignment with a line supports a strong positive correlation, so \( r = 0.96 \) is the best estimate.

Answer:

C. \( r = 0.96 \)