Question

three scatterplots are shown, along with their best-fit lines and correlation coefficients, ( r_1 ), ( r_2 ), and ( r_3 ). choose the correct statement.
a ( r_1 < r_2 < r_3 )
b ( r_2 < r_1 < r_3 )
c ( r_3 < r_2 < r_1 )

Explanation:

Step1: Recall correlation coefficient meaning

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. A value closer to \( 1 \) (or \( -1 \)) means a stronger linear relationship, and closer to \( 0 \) means a weaker one. For positive linear relationships (as seen here, since best - fit lines have positive slopes), \( r>0 \), and the closer the points are to the line, the larger \( r \) is.

Step2: Analyze the scatterplots

• For \( r_1 \): The points are very close to the best - fit line, so \( r_1 \) is close to \( 1 \).
• For \( r_2 \): The points are somewhat close to the line, but not as close as in the first plot, so \( r_2 \) is less than \( r_1 \) but still positive.
• For \( r_3 \): The points are more spread out from the best - fit line compared to the other two plots, so \( r_3 \) is the smallest among the three (closest to \( 0 \)) while still being positive.

So the order from smallest to largest is \( r_3 < r_2 < r_1 \).

Answer:

C. \( r_3 < r_2 < r_1 \)