Question

which graph shows data whose r-value is most likely closest to 1?

Explanation:

Step1: Recall r - value meaning

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. An \( r \)-value close to 1 indicates a strong positive linear relationship, meaning as one variable increases, the other variable also increases, and the points lie close to a straight line with a positive slope.

Step2: Analyze each graph

• First graph: The points seem to have a negative trend (as \( x \) increases, \( y \) decreases), so \( r \) would be negative, not close to 1.
• Second graph: The points show a positive trend, and they are relatively close to a straight line with a positive slope. This indicates a strong positive linear relationship, so \( r \) is likely close to 1.
• Third graph: The points seem to have a negative trend (as \( x \) increases, \( y \) decreases), so \( r \) would be negative, not close to 1.

Answer:

The Middle Graph