Question

match each correlation coefficient to the appropriate scatter plot. the line in each scatter plot is the least squares regression line.
r = 0.3
r = 0.9

Explanation:

Step1: Recall Correlation Coefficient

The correlation coefficient \( r \) ranges from -1 to 1. A value close to 1 (or -1) means a strong linear relationship, and close to 0 means a weak linear relationship. The closer the points are to the regression line, the higher the absolute value of \( r \).

Step2: Analyze Top Scatter Plot

In the top scatter plot, the points are more spread out from the regression line. So the correlation coefficient should be weaker, i.e., \( r = 0.3 \) (since it's positive, and 0.3 is closer to 0 than 0.9).

Step3: Analyze Bottom Scatter Plot

In the bottom scatter plot, the points are closer to the regression line, indicating a stronger linear relationship. So the correlation coefficient should be \( r = 0.9 \) (closer to 1).

Answer:

Top scatter plot: \( r = 0.3 \)
Bottom scatter plot: \( r = 0.9 \)