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

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. \( r = 1 \) is a perfect positive linear relationship, \( r = - 1 \) is a perfect negative linear relationship, and \( r = 0 \) means no linear relationship. A value of \( r = 0.9 \) indicates a strong positive linear relationship.

Step2: Analyze each scatter plot

• Top - left plot: The points are scattered randomly, so the linear relationship is weak (close to \( r = 0 \)).
• Top - right plot: The points are somewhat spread out, not showing a strong linear trend.
• Bottom - left plot: The points form a clear upward - sloping pattern, very close to a straight line, indicating a strong positive linear relationship (consistent with \( r = 0.9 \)).
• Bottom - right plot: The points form a downward - sloping pattern, indicating a negative linear relationship (so \( r \) would be negative, not \( 0.9 \)).

Answer:

The data set represented by the bottom - left scatter plot (where points show a strong positive linear trend) could have a correlation coefficient of \( r = 0.9 \).