Question

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

Explanation:

Step1: Recall the concept of correlation coefficient \( r \)

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 tends to increase, and the points lie close to a straight line with a positive slope. An \( r \)-value close to \( - 1 \) indicates a strong negative linear relationship, and an \( r \)-value close to \( 0 \) indicates little to no linear relationship.

Step2: Analyze each graph

• First graph: The points seem to be scattered randomly with no clear linear trend (positive or negative). So, the \( r \)-value is close to \( 0 \).
• Second graph: The points show a negative trend (as one variable increases, the other decreases), so the \( r \)-value is negative (close to \( - 1 \) if the trend is strong, but we are looking for \( r \) close to \( 1 \), so this is not the one).
• 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 the \( r \)-value is close to \( 1 \).
• Fourth graph: The points do not show a clear positive linear trend (the scatter is more and the trend is not as strong as the third graph).

Answer:

The third graph (the one with points showing a strong positive linear trend, increasing from left - bottom to right - top and lying close to a straight line)