Question

question 3 of 25

which graph has a correlation coefficient, \\(r\\), closest to 0.95?

a. graph a
b. graph b
c. graph c
d. graph d

Explanation:

Analyze the sign of the correlation coefficient

A correlation coefficient of \(r \approx 0.95\) indicates a strong, positive linear relationship. This means as the horizontal variable increases, the vertical variable also increases, showing an upward trend from left to right.

• Graphs A and C show positive trends.
• Graphs B and D show negative trends (\(r < 0\)).

Compare the strength of positive trends

We compare the positive-trending scatter plots, Graph A and Graph C, to see which is closer to a perfect straight line (\(r = 1\)).

• Graph A shows a weak or non-linear positive trend with significant scatter.
• Graph C shows a very tight, highly linear upward pattern.

Determine the closest graph

Because the points in Graph C lie very close to a straight line with a positive slope, its correlation coefficient \(r\) is closest to \(0.95\).

Answer:

• A. Graph A
• B. Graph B
• C. Graph C (Correct answer)
• D. Graph D