Question

josh collected several sets of data and plotted the points as shown below. which of the following data sets could have a correlation coefficient of r = 0.9? choose the best answer.

Explanation:

Step1: Recall correlation coefficient meaning

A correlation coefficient $r=0.9$ represents a strong positive linear relationship between two variables, meaning data points cluster closely along an upward-sloping line.

Step2: Analyze each scatter plot

• Top-left: Points show no clear upward/downward trend (weak/no correlation).
• Top-right: Points follow a clear upward trend with tight clustering (strong positive correlation).
• Bottom-left: Points show an upward trend but with fewer points; while positive, the tightness matches a strong $r$, but the top-right has more consistent clustering.
• Bottom-right: Points show a downward trend (negative correlation, so $r$ would be negative).

Step3: Match to $r=0.9$

Only the top-right plot has the strong positive linear pattern consistent with $r=0.9$.

Answer:

The top-right scatter plot (the one with points forming a clear, tight upward-sloping pattern)