Question

match each correlation coefficient to the appropriate scatter plot. the line in each scatter plot is the least squares regression line.
r = -0.1
r = -0.8

Explanation:

Step1: Recall Correlation Coefficient

The correlation coefficient \( r \) measures the strength and direction of a linear relationship. Values close to 0 mean weak correlation, values close to \(\pm1\) mean strong correlation. Negative \( r \) means negative (downward) linear trend.

Step2: Analyze \( r = -0.1 \)

\( r = -0.1 \) is close to 0, so the linear relationship is very weak. The scatter plot with points more spread out (less clustered around the regression line) corresponds to \( r = -0.1 \).

Step3: Analyze \( r = -0.8 \)

\( r = -0.8 \) is close to -1, so the linear relationship is strong. The scatter plot with points more tightly clustered around the downward - sloping regression line corresponds to \( r = -0.8 \).

Assuming the left scatter plot has more spread - out points (weaker linear relationship) and the right scatter plot has points more tightly clustered around the regression line (stronger linear relationship):

• The left scatter plot (with more spread - out points) matches \( r=-0.1 \).
• The right scatter plot (with points more tightly clustered around the regression line) matches \( r = - 0.8 \).

Answer:

If we assume the two scatter plots are the left - hand and right - hand ones:

• \( r=-0.1 \) matches the left scatter plot (with more spread - out points around the regression line).
• \( r = - 0.8 \) matches the right scatter plot (with points more tightly clustered around the regression line).