Question

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

Explanation:

The \( r \)-value (correlation coefficient) 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 tends to increase, and the points lie close to a straight line with a positive slope.

• The first graph shows a negative trend (points decreasing as the x - value increases), so its \( r \)-value is negative, not close to 1.
• The second graph shows a positive trend, and the points are relatively close to a straight line with a positive slope, indicating a strong positive linear relationship, so its \( r \)-value is likely close to 1.
• The third graph shows a negative trend (points decreasing as the x - value increases) with more scatter, so its \( r \)-value is negative and not close to 1.

Answer:

The second graph (the one with the yellow points showing a positive, relatively linear trend)