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 no clear linear trend (maybe scattered or a weak/non - linear trend).
• Second graph: The points show a negative trend (as \( x \) increases, \( y \) decreases), so \( r \) would be close to - 1, not 1.
• Third graph: The points show a positive trend, and they lie relatively close to a straight line with a positive slope. This indicates a strong positive linear relationship, so its \( r \)-value is closest to 1.

Answer:

The third graph (the one on the right) shows data whose \( r \)-value is most likely closest to 1.