Question

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

correlation coefficients: ( r = -0.4 ), ( r = -0.9 )

Explanation:

Step1: Recall Correlation Coefficient

The correlation coefficient \( r \) measures the strength and direction of a linear relationship. Values closer to -1 or 1 indicate a stronger linear relationship, while values closer to 0 indicate a weaker one. A negative \( r \) means a negative linear trend (as \( x \) increases, \( y \) decreases).

Step2: Analyze Top Scatter Plot

In the top scatter plot, the points are very close to the regression line, indicating a strong linear relationship. Since \( r = -0.9 \) is closer to -1 (stronger) than \( r = -0.4 \) (weaker), the top plot matches \( r = -0.9 \).

Step3: Analyze Bottom Scatter Plot

In the bottom scatter plot, the points are more spread out from the regression line, indicating a weaker linear relationship. Thus, the bottom plot matches \( r = -0.4 \).

Answer:

Top scatter plot: \( r = -0.9 \)
Bottom scatter plot: \( r = -0.4 \)